contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
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# Snowmass21 Accelerator Modeling Community White Paper
by the Beam and Accelerator Modeling Interest Group (BAMIG)††thanks:
<EMAIL_ADDRESS>
Authors (alphabetical): S. Biedron  University of New Mexico, Albuquerque, NM
87106, USA  L. Brouwer  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  D.L. Bruhwiler  RadiaSoft LLC, Boulder, CO 80301, USA  N. M. Cook
RadiaSoft LLC, Boulder, CO 80301, USA  A. L. Edelen  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  D. Filippetto  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  C.-K. Huang  Los Alamos National
Laboratory, Los Alamos, NM 87545, USA  A. Huebl  Lawrence Berkeley National
Laboratory, Berkeley, CA 94720, USA  T. Katsouleas  University of Connecticut,
Storrs, CT 06269, USA  N. Kuklev  Argonne National Laboratory, Lemont, IL
60439, USA  R. Lehe  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  S. Lund  Michigan State University, East Lansing, MI 48824, USA
C. Messe  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  W.
Mori  University of California at Los Angeles, Los Angeles, CA 90095, USA
C.-K. Ng  SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA  D.
Perez  Los Alamos National Laboratory, Los Alamos, NM 87545, USA  P. Piot
Argonne National Laboratory, Lemont, IL 60439, USA  Northern Illinois
University, DeKalb, IL 60115, USA  J. Qiang  Lawrence Berkeley National
Laboratory, Berkeley, CA 94720, USA  R. Roussel  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  D. Sagan  Cornell University, Ithaca,
NY 14853, USA  A. Sahai  University of Colorado Denver, Denver, CO 80204, USA
A. Scheinker  Los Alamos National Laboratory, Los Alamos, NM 87545, USA  E.
Stern  Fermi National Accelerator Laboratory, Batavia, IL 60563, USA  M.
Thévenet  Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany  F.
Tsung  University of California at Los Angeles, Los Angeles, CA 90095, USA
J.-L. Vay  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  D.
Winklehner  Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
H. Zhang  Thomas Jefferson National Accelerator Facility, Newport News, VA
23606, USA

###### Contents

  1. Executive summary
  2. 1 Introduction
  3. 2 Previous Reports and Recommendations
  4. 3 Modeling needs
    1. 3.1 RF-based acceleration
    2. 3.2 Plasma-based wakefield acceleration
    3. 3.3 Structure-based wakefield acceleration
    4. 3.4 PetaVolts per meter plasmonics and Plasmonic acceleration
    5. 3.5 Materials modeling for accelerator design
    6. 3.6 Structured plasmas
    7. 3.7 Superconducting magnets
  5. 4 To the next frontier: ultraprecise, ultrafast virtual twins of particle accelerators
    1. 4.1 Interdisciplinary simulations
    2. 4.2 End-to-end Virtual Accelerators (EVA)
    3. 4.3 Virtual twins of particle accelerators
  6. 5 Cutting-edge and emerging computing opportunities
    1. 5.1 Advanced algorithms
    2. 5.2 Artificial intelligence, machine learning, and differentiable simulations
    3. 5.3 Quantum computing
    4. 5.4 Storage ring quantum computers
  7. 6 Computational needs
    1. 6.1 Hardware: CPU/GPU time, memory, archive
    2. 6.2 Software performance, portability and scalability
      1. 6.2.1 Performance
      2. 6.2.2 Portability
      3. 6.2.3 Parallel scalability
    3. 6.3 Scalable I/O and in-situ analysis
  8. 7 Sustainability, reliability, user support, training
    1. 7.1 Code robustness, validation & verification, benchmarking, reproducibility
    2. 7.2 Usability, user support and maintenance
      1. 7.2.1 Usability
      2. 7.2.2 User support
      3. 7.2.3 Maintenance
    3. 7.3 Training and education
  9. 8 Toward community ecosystems & data repositories
    1. 8.1 Loose integration: Integrated workflows
      1. 8.1.1 I/O standardization
    2. 8.2 Tighter integration: Integrated frameworks
      1. 8.2.1 Community development
    3. 8.3 Data repositories
    4. 8.4 Centers & consortia, collaborations with industry
      1. 8.4.1 Centers & consortia
      2. 8.4.2 Collaborations with industry
  10. 9 Outlook

## Executive summary

Computer modeling is essential to beam and accelerator physics research, as
well as to the design, commissioning and operation of particle accelerators.
Somewhat surprisingly, despite accelerator physics being a field with extreme
levels of coordination and long-range planning for the research, design,
construction, and operation of its largest accelerator complexes, e.g., at
CERN or at Fermilab, the development of beam and accelerator physics codes has
often been largely uncoordinated. This comes at a great cost, is not desirable
and may not be tenable.

Accelerator simulation is a large, complex topic, and much time and effort has
been spent in developing a large collection of simulation software that cover
an expanding range of intertwined physics topics. The complexity of the
overall endeavor has risen sharply in the last decade with the impetus to
adapt the algoritms and codes to rapidly changing computing hardware and
software environments, and the additional task of having to reimagine the
algorithms and recast them for quantum computing. This is compounded by the
need to infuse a rapidly evolving set of AI/ML technologies, which represent
tremendous opportunities but can also be very disruptive.

After a summary of relevant comments and recommendations from various reports
over the last ten years, this _community_ paper examines the modeling needs in
accelerator physics, from the modeling of single beams and individual
accelerator elements, to the realization of virtual twins that replicate all
the complexity to model a particle accelerator complex as accurately as
possible. A discussion follows on cutting-edge and emerging computing
opportunities, such as advanced algorithms, AI/ML and quantum computing,
computational needs in hardware, software performance, portability and
scalability, and needs for scalable I/O and in-situ analysis. Considerations
of reliability, long-term sustainability, user support and training are
covered next, followed by an overview of the benefits of ecosystems with
integrated workflows based on standardized input and output, and with
integrated frameworks and data repositories developed as a community. The last
section highlights how the community can work more collaboratively and
efficiently through the development of consortia and centers, and via
collaboration with industry.

The following high-level recommendations are provided to synthesize the
summary of recommendations for the topics discussed in the paper and listed
afterward:

  1. 1.

Develop a comprehensive portfolio of particle accelerator and beam physics
modeling tools in support of achieving Accelerator and Beam Physics Thrust
Grand Challenges on intensity, quality, control, and prediction.

  2. 2.

Develop software infrastructure to enable end-to-end virtual accelerator
modeling and corresponding virtual twins of particle accelerators.

  3. 3.

Develop advanced algorithms and methods including AI/ML modalities and quantum
computing technologies.

  4. 4.

Develop efficient and scalable software frameworks and associated tools to
effectively leverage next generation high-performance and high-throughput
computing hardware.

  5. 5.

Develop sustainable and reliable code maintenance practices, community
benchmarking capabilities, and training opportunities to foster the
cooperative application of accelerator software.

  6. 6.

Foster an open community that spans academia, national labs and industry to
(a) develop software ecosystems, libraries, frameworks and standards, (b)
curate data repositories, and (c) establish dedicated centers and distributed
consortia with open governance models.

## Summary of recommendations (extended version)

The Beam and Accelerator Modeling Interest Group (BAMIG) proposes the
following recommendations to the Snowmass21 conveners:

  1. 1.

Recommendation on Modeling needs: Support the development of a comprehensive
portfolio of particle accelerator and beam physics modeling tools for all
types of particle accelerators (e.g., RF-based, plasma-based, structured-based
wakefield, plasmonic), accelerator components (e.g., materials,
superconducting magnets, structured plasmas), and which target the Accelerator
and Beam Physics Thrust Grand Challenges on intensity, quality, control, and
prediction.

    1. (a)

Subrecommendation on RF-based acceleration: Support the development of
modeling tools and methods that target the Accelerator and Beam Physics Thrust
Grand Challenges (intensity, quality, control, and prediction), which will
require modeling of collective effects with improved fidelity on long time
scales, improving computational speed to allow for statistical ensembles and
design optimization, and improved integration with realistic magnet and RF
modeling.

    2. (b)

Subrecommendation on plasma-based wakefield acceleration: Support the
development of modeling tools and methods that will enable start-to-end
simulations that predict the full 6-D (+ spin) evolution of beams in a PBA-
based linear collider, from their creation to their final focusing at the
interaction point, and include all the intermediate phases of acceleration,
transport, manipulations, collisions, etc.

    3. (c)

Subrecommendation on structure-based wakefield acceleration: Support the
development of efficient and accurate algorithms capable of modeling the beam
interaction with its wakefield over long interaction lengths in structures
with arbitrary geometries and constitutive parameters.

    4. (d)

Subrecommendation on PetaVolts per meter plasmonics: Support the development
of a new quantum-kinetic approach to model large-amplitude plasmons sustained
by oscillations of ultra-dense conduction-band free electron Fermi gas.
Modeling the dynamics of ionic lattice and the energy band structure under the
influence of PetaVolts per meter plasmonic fields of relativistic, nonlinear
plasmons is critical to understand the effect on materials.

    5. (e)

Subrecommendation on materials modeling for accelerator design: Support the
development of automated scale-bridging methods that can autonomously
parameterize higher-scale models from large numbers of lower-scale
calculations, so as to enable predictive materials studies over a broad space
of materials and conditions.

    6. (f)

Subrecommendation on structured plasmas: Support the development and
integration of fluid and kinetic codes to meet the modeling demands for a new
class of structured plasma devices coupling macroscopic plasma properties with
strict requirements on kinetic interactions.

    7. (g)

Subrecommendation on superconducting magnets: Support the development of novel
mixed finite element formulations and algorithms, and their implementation in
open source software tailored for superconducting magnet design.

  2. 2.

Recommendation on the next frontier: ultraprecise, ultrafast virtual twins of
particle accelerators: Support the development of accelerator modeling
software that orchestrate interdisciplinary set of tools with standardized
data representations to enable end-to-end virtual accelerator modeling and
virtual twins of particle accelerators, which combine first-principle models
together with machine learning-based surrogate models, for tunability from
maximum precision for accurate and realistic accelerator design to maximum
speed for online particle accelerator tuning.

    1. (a)

Subrecommendation on interdisciplinary simulations: Support interdisciplinary
simulations especially efforts to establish standards that would ease the
sharing of information and data across codes as well as standards for
interfacing codes.

    2. (b)

Subrecommendation on end-to-end Virtual Accelerators (EVA): Support the
development of software that are capable of end-to-end virtual accelerator
(EVA) modeling (Grand Challenge of Accelerator and Beam Physics) that
incorporate all components (including both conventional and AAC sections) and
all pertinent physical effects.

    3. (c)

Subrecommendation on virtual twins of particle accelerators: Support the
development of virtual twins of particle accelerators, which combine high-
performance computing, first-principle models together with machine learning-
based surrogate models, with tunability from maximum precision for accurate
and realistic accelerator design to maximum speed for online particle
accelerator tuning.

  3. 3.

Recommendation on cutting-edge and emerging computing opportunities: Support
the research and development on cutting-edge and emerging computing
opportunities, including advanced algorithms, AI/ML methods, quantum computing
algorithms for beam and accelerator physics, as well as on the development of
storage ring quantum computers.

    1. (a)

Subrecommendation on Advanced algorithms: Support research on algorithms, from
refining the understanding of the properties and bottlenecks of existing
algorithms to the elaboration of novel algorithms that exhibit better
properties, remove the bottlenecks, and improve the speed and accuracy of
accelerator modeling.

    2. (b)

Subrecommendation on Artificial intelligence, machine learning, and
differentiable simulations: Support the development of ML modeling techniques
and their integration into accelerator simulation and control systems, with an
emphasis on fast-executing (up to real-time) and differentiable models,
continual learning and adaptive ML for time-varying systems and distribution
shifts, uncertainty quantification to assess confidence of model predictions,
and physics-informed methods to enable broader model generalization to new
conditions and reduced reliance on large training data sets.

    3. (c)

Subrecommendation on Quantum computing: Support quantum computing algorithm
and code development for accelerator modeling, feasibility study on quantum
computing implementation in accelerator modeling, and quantum computing
education in accelerator community.

  4. 4.

Recommendation on computational needs: Support the development of increasingly
powerful and specialized High-Performance Computing (HPC) and High-Throughput
Computing (HTC) capabilities for accelerator modeling, and maintenance of
software to run efficiently on these hardware (e.g., port of codes to GPUs)
with efficient and scalable I/O, post-processing and in situ data analysis
solutions, which will be needed to support ab initio modeling at increasing
fidelity, training of surrogate models and AI/ML guided designs.

    1. (a)

Subrecommendation on hardware: CPU/GPU time, memory, archive: Support the
development of increasingly powerful and specialized High-Performance
Computing (HPC) and High-Throughput Computing (HTC) capabilities for
accelerator modeling, which will be needed to support ab initio modeling at
increasing fidelity, interactive and parallel data analysis, training of
surrogate models and AI/ML guided designs.

    2. (b)

Subrecommendation on software performance, portability and scalability: Foster
the development and maintenance of codes that run efficiently on the latest
hardware (e.g., add support for GPUs/FPGAs) by using maintainable single-
source, portable solutions, and that are scalable on leadership-scale
supercomputers with multiple levels of parallelization and support for
effective dynamic load balancing.

    3. (c)

Subrecommendation on scalable I/O and in-situ analysis: Support the
development and maintenance of efficient and scalable I/O, post-processing, in
situ data analysis, and data sharing solutions in particle accelerator codes.
Coordinate on scientific data documentation, standardization, development of
interactive and reproducible analysis workflows and foster data reuse.

  5. 5.

Recommendation on sustainability, reliability, user support, training: Provide
sufficient resources for code maintenance, automated testing, benchmarking,
documentation and code reviews. Convene a community effort to identify topics
and teaching teams to deliver academic classes designed to foster sharing and
cooperation, to be taught at the U.S. Particle accelerator school.

    1. (a)

Subrecommendation on code robustness, validation & verification, benchmarking,
reproducibility: Establish and maintain open review, automated testing,
validation and benchmark procedures for modeling tools and ensure
reproducibility by tracking all changes in a documented and openly accessible
manner.

    2. (b)

Subrecommendation on usability, user support and maintenance: Consider
maintenance of code reviews for improvements, documentation, installation and
testing to be central to the mission of usable scientific software: establish
open feedback and support channels, perform regular releases with change logs,
use permissive open source licensing whenever possible and cover all
scientific functionality with automated tests.

    3. (c)

Subrecommendation on training and education: Convene a community effort to
identify topics and teaching teams to deliver academic classes designed to
foster sharing and cooperation. The classes should be taught in the US
Particle Accelerator School with course materials and linked
tutorials/extensions regularly maintained and publicly posted.

  6. 6.

Recommendation on community ecosystems & data repositories: Organize the beam
and accelerator modeling tools and community through the development of (a)
ecosystems of codes, libraries and frameworks that are interoperable via open
community data standards, (b) open access data repositories for reuse and
community surrogate model training, (c) dedicated Centers and distributed
consortia with open community governance models and dedicated personnel to
engage in cross-organization and -industry development, standardization,
application and evaluation of accelerator and beam modeling software and data.

    1. (a)

Subrecommendation on loose integration: Integrated workflows: Foster the
adoption and continued development of open community (meta-)data standards and
their implementation in modeling tools and data acquisition for seamless
integration of the community accelerator modeling tools into multiphysics
workflows.

    2. (b)

Subrecommendation on tighter integration: Integrated frameworks: Establish
open, contributable, modular libraries and integrated frameworks for central
computing, modeling and analysis tasks that foster the sharing of common
functionalities between applications, using open licenses and best
practices/policies.

    3. (c)

Subrecommendation on data repositories: Establish open access data
repositories and foster publishing of modeled and measured accelerator & beam
data to allow re-use (e.g. beam transport to applications), model training
(e.g. AI/ML), preservation, recasting and reinterpretation.

    4. (d)

Subrecommendation on centers & consortia, collaborations with industry:
Organize the beam and accelerator modeling community through the development
of dedicated Centers and distributed consortia. Dedicate resources to adopt
open community governance models and dedicate personnel to engage in cross-
organization and -industry cooperation.

##  1 Introduction

For particle accelerators—among the most complex and largest high-tech devices
ever built—computational tools are indispensable. Computer simulations are
critical to the design, commissioning, operation, and upgrading of accelerator
facilities which cost many millions to billions of dollars. It is thus widely
recognized that the importance of accelerators to society and the high cost of
new accelerator facilities demand that the most advanced and sophisticated
high-performance computing (HPC) tools be brought to bear on modeling
activities in accelerator science and technology [1, 2, 3, 4, 5, 6].

Accelerator simulation is a large, complex topic, and much time and effort has
been spent in developing a large collection of simulation software, many
developed by a single accelerator physicist and some by interdisciplinary
collaborations of computational accelerator physicists, computer scientists,
applied mathematicians and software engineers. Some address a single physics
topic while others involve multiphysics, interdisciplinary frameworks, or
workflows. Some software has grown very large. Some include very sophisticated
algorithms that are pushing the state-of-the-art in accelerator modeling, and
sometimes in applications outside of accelerator physics (e.g., astrophysics).
While some accelerator modeling research or design can be done on a laptop or
workstation, others need the full power of the largest supercomputers. For a
significant fraction of these activities, approximations, idealizations or
others means to reduce the computational needs are necessary to fit the
simulations within the available computer memory and runtime, eventually
compromising accuracy and fidelity. In addition to pursue its longstanding
tradition in research and development of novel algorithms, the accelerator
modeling community is investigating emerging opportunities based on machine
learning and quantum computing.

Despite accelerator physics being a field with extreme levels of coordination
and long-range planning for the research, design, construction, and operation
of its largest accelerator complexes, e.g., at CERN or at Fermilab, the
development of beam and accelerator physics codes has often been largely
uncoordinated. This comes at a great cost, is not desirable and may not be
tenable. Due to developers retiring or moving on to other projects, numerous
simulation programs have been completely abandoned or are seldom used. This
has resulted in a collection of codes that are not interoperable, use
different I/O formats and quite often duplicate some physics functionalities
using the exact same underlying algorithms. Frequently there is a huge
impediment to maintaining these programs due to poorly-written code and lack
of documentation. Additionally, many of the programs that are available tend
to be “rigid”. That is, it is generally difficult to modify a program to
simulate something it is not designed to simulate _a priori_. Adding a new
type of lattice element that a particle can be tracked through is one such
example [5]. Abandoned simulation programs represent a huge cost [7], not only
in terms of time and money spent in developing a program, but also in terms of
researchers leveraging existing technology. Indeed, a researcher who wants to
simulate something that existing programs are unable to, will, due to time and
monetary constraints, generally not be able to fully develop a comprehensive
simulation program from scratch as compared to what could have been done if
existing software could be leveraged. As simulation programs become more
complex due to the ever-increasing demands placed upon machine performance,
the situation will become worse if not addressed.

After a summary of relevant comments and recommendations from various reports
over the last ten years, this paper examines the modeling needs in accelerator
physics, from the modeling of single beams and individual accelerator
elements, to the realization of virtual twins that replicate all the
complexity to model a particle accelerator complex as accurately as possible.
We then discuss cutting-edge and emerging computing opportunities, such as
advanced algorithms, AI/ML and quantum computing, computational needs in
hardware, software performance, portability and scalability, and needs for
scalable I/O and in-situ analysis. Considerations of reliability, long-term
sustainability, user support and training are considered next, before
discussing the benefits of ecosystems with integrated workflows based on
standardized input and output, and with integrated frameworks and data
repositories developed as a community. Last, we highlight how the community
can work more collaboratively and efficiently through the development of
consortia and centers, and via collaboration with industry. A recommendation
is proposed at the beginning of each section and subsection.

##  2 Previous Reports and Recommendations

This section summarizes relevant comments and recommendations from various
reports over the last ten years.

##### 2012 Office of HEP Accelerator R&D Task Force report

> Software should help researchers optimize operating regimes and reduce the
> overall risk that underlies all modern accelerator design. Much of the
> current software has not taken advantage of the many computer improvements
> that have been developed in the last few decades. Such progress includes
> vastly increased processor speed, exploding memory capabilities, disk
> storage growth and cloud computing. There is not enough overall commercial
> demand for such high performance accelerator design software to have
> confidence this problem will be solved without US government intervention.
> …
> Accelerators across the board also need advanced simulation studies, and
> long-term support for code development and maintenance is therefore needed.
>
> — Office of HEP Accelerator R&D Task Force report, 2012

##### 2014 Particle Physics Project Prioritization Panel (P5) report

> The present practice is to handle much of the computing within individual
> projects. Rapidly evolving computer architectures and increasing data
> volumes require effective crosscutting solutions that are being developed in
> other science disciplines and in industry. Mechanisms are needed for the
> continued maintenance and development of major software frameworks and tools
> for particle physics and long-term data and software preservation, as well
> as investments to exploit next-generation hardware and computing models.
> Close collaboration of national laboratories and universities across the
> research areas will be needed to take advantage of industrial developments
> and to avoid duplication.
> Recommendation 29: Strengthen the global cooperation among laboratories and
> universities to address computing and scientific software needs, and provide
> efficient training in next-generation hardware and data-science software
> relevant to particle physics. Investigate models for the development and
> maintenance of major software within and across research areas, including
> long-term data and software preservation.
> …
> Computing in particle physics continues to evolve based on needs and
> opportunities. For example, the use of high-performance computing, combined
> with new algorithms, is advancing full 3-D simulations at realistic beam
> intensities of nearly all types of accelerators. This will enable “virtual
> prototyping” of accelerator components on a larger scale than is currently
> possible.
>
> — Report of the Particle Physics Project Prioritization Panel (P5), 2014

##### 2015 HEPAP report

> Recommendation 3. Support a collaborative framework among laboratories and
> universities that assures sufficient support in beam simulations and in beam
> instrumentation to address beam and particle stability including strong
> space charge forces.
> …
> With Scenario B funding, an ambitious computational accelerator science
> program could be initiated to develop new algorithms, techniques, and
> generic simulation code with the goal of end-to-end simulations of complex
> accelerators that will guide the design, and improve the operations, of
> future accelerators of all types. Advancing the capabilities of accelerator
> simulation codes to capitalize on the drive toward exascale computing would
> have large benefits in improving accelerator design and performance. New
> computational algorithms coupled with the latest computer architectures are
> likely to reduce execution times for many classes of simulation code by
> several orders of magnitude, thereby making practical end-to-end simulations
> of complex accelerator systems. Such capabilities will enable cost-effective
> optimization of wakefield accelerators, as well as near-real-time
> simulations of large operational machines such as megawatt proton
> accelerators or a very high-energy proton-proton collider. In the near term,
> advanced simulation tools will maximize the productivity of R&D for all
> future accelerators.
> …
> One area in which there has been some recent movement towards a nationally
> unified effort is in accelerator-related computation. Effort in the area has
> been boosted by funding from the SciDAC (Scientific Discovery through
> Advanced Computing) program jointly funded by ASCR (DOE Office of Advanced
> Scientific Computational Research) and HEP. One of the outgrowths of this
> effort is the CAMPA (Consortium for Advanced Modeling of Particle
> Accelerators) initiative from LBNL, SLAC, and Fermilab to establish a
> national program in advanced modeling of accelerators. There are, however,
> still many isolated simulation efforts within the program.
> …
> It is likely that there will be significant developments in accelerating
> technologies, both conventional (NCRF, SRF) and advanced (DWFA, PWFA, LWFA)
> technologies, in the coming decades. … Accelerator physics and simulation
> support in these areas are crucial for making progress.
> …
> Computer simulations play an indispensable role in all accelerator areas.
> Currently, there are many simulation programs used for accelerator physics.
> There is, however, very little coordination and cooperation among the
> developers of these codes. Moreover there is very little effort currently
> being made to make these codes generally available to the accelerator
> community and to support the users of these codes. The CAMPA framework is an
> exception, and such activities should be encouraged.
>  The direction of development in computer technologies makes it mandatory
> that the accelerator simulation codes (as well as all other HEP-related
> codes) adapt to modern computer architectures. High performance computers
> are another resource that HEP has not yet sufficiently exploited. The effort
> to coordinate such advanced computational activities for HEP is taking place
> within the Forum for Computing Excellence (FCE). Accelerator simulation
> effort in the direction of advanced computing should also be an integral
> part of the FCE, as are the other areas of HEP computation. An overall goal
> of this coordinated effort is to maintain and update mainline accelerator
> computer codes to take ad-vantage of the most modern computer architectures.
>  Advances in simulations, as well as in computational capabilities, raise
> the exciting possibility of making a coherent set of comprehensive numerical
> tools available to enable virtual prototyping of accelerator components as
> well as virtual end-to-end accelerator modeling of beam dynamics. It should
> be possible to construct real-time simulations to support accelerator
> operations and experiments, allowing more rapid and detailed progress to be
> made in under-standing accelerator performance.
>  Simulation efforts are vital for new accelerator development and supporting
> experimental accelerator R&D studies. Such coherent efforts could be
> tailored after the successful LARP model that identified mutual study goals
> for assuring success of a given project (HL-LHC in the case of LARP) and
> supported collaboration among various university and laboratory partners.
>
> — HEPAP report, 2015

##  3 Modeling needs

Recommendation: Support the development of a comprehensive portfolio of
particle accelerator and beam physics modeling tools for all types of particle
accelerators (e.g., RF-based, plasma-based, structured-based wakefield,
plasmonic), accelerator components (e.g., materials, superconducting magnets,
structured plasmas), and which target the Accelerator and Beam Physics Thrust
Grand Challenges on intensity, quality, control, and prediction.

###  3.1 RF-based acceleration

contributed by J. Qiang, C. Mitchell, C-K. Ng

Recommendation: Support the development of modeling tools and methods that
target the Accelerator and Beam Physics Thrust Grand Challenges (intensity,
quality, control, and prediction), which will require modeling of collective
effects with improved fidelity on long time scales, improving computational
speed to allow for statistical ensembles and design optimization, and improved
integration with realistic magnet and RF modeling.

In an RF accelerator, a train of charged particles is accelerated to very high
energy (TeVs) by RF cavities, and confined by magnetic elements for high
energy physics applications. For such a high intensity charged particle beam,
the collective effects from charged particle interactions among themselves and
from the other beams play an important role in limiting the beam quality and
accelerator performance. These collective effects include space-charge,
intrabeam scattering, coherent synchrotron radiation, short-range and long-
range wakefields, beam-beam, electron cloud and electron cooling effects.

A number of computational methods have been developed to model these
collective effects in an RF accelerator. The particle-in-cell method has been
used to simulate space-charge, beam-beam, and electron cloud effects on
massive parallel computers [8, 9, 10, 11, 12, 13]. The modeling of coherent
synchrotron radiation effects was reviewed in a recent publication [14], where
the recent advance has led to multi-dimensional and self-consistent simulation
capability for the first time. A Monte-Carlo method has been used to simulate
the intrabeam scattering effect [15]. A Langevin method was developed to self-
consistently simulate the intrabeam scattering effect by solving the Fokker-
Planck equations with the Landau/Rosenbluth potential [16]. The fast multipole
method was developed to simulate both the space-charge and the electron
cooling effects [17, 18].

Even though significant progress has been made in modeling RF accelerators,
self-consistent modeling of the above collective effects remains challenging,
especially for understanding dynamics on a long time scale. This includes
long-term simulation of space-charge and beam-beam effects, self-consistent
first-principles modeling of intrabeam scattering and electron cooling,
electron cloud and coherent synchrotron radiation effects. For example, one
key goal involves the accurate prediction of halo formation and low-level beam
loss at high intensity [19]. Fast advanced computational methods are needed to
improve both the speed and the accuracy of modeling these effects. The
computing time required must be sufficiently short to enable the large
ensembles of runs needed for design optimization. Parallel programming
paradigms that can make use of the latest computer hardware such as multi-node
GPUs are needed to further improve the speed of the simulation. Studies are
needed to understand numerical artifacts such as numerical noise associated
with long-term simulations. A final area lies in improved magnet modeling and
improved integration of RF and magnet models with existing tracking tools.
Methods such as surface methods that can include realistic external field
effects are needed for improving the fidelity of RF accelerator designs.

The manufacture of accelerator structures and components is a major cost of an
RF accelerator. Virtual prototyping of accelerator components has been a key
process in the design and optimization of accelerators. Therefore, the ability
to virtually prototype with HPC tools to create designs that work ”out of the
box” will substantially reduce the R&D and operational costs of these
accelerator components by eliminating the delicate, labor-intensive
modifications employed in previous practices. Virtual prototyping requires
multi-physics modeling capabilities for determining RF parameters such as
shunt impedance, wakefield effects and higher-order-mode (HOM) damping,
temperature distribution and thermal heat load, as well as mechanical stress
and shape deformation [20].

To provide the required luminosity for a linear collider, it is critical to
reduce emittance dilution in the main linac from machine tolerances such as
cavity misalignments and imperfections [21]. For example, in a superconducting
linac, misalignments can arise from individual cavity misalignments and
changes in the properties of coupled HOMs in a cryomodule with misaligned and
deformed cavities. The RF parameters and fields of the HOMs can be evaluated
for random distributions of cavity offsets (in a cryomodule) and cavity
deformations along the full linac. The fields are then used for beam emittance
dilution evaluation. A statistical analysis [22] using the constraints form
realistic fabrication and component placement tolerances will be facilitated
by the HPC capabilities of advanced simulation codes.

###  3.2 Plasma-based wakefield acceleration

contributed by J.-L. Vay, W. Mori, F. Tsung

Recommendation: Support the development of modeling tools and methods that
will enable start-to-end simulations that predict the full 6-D (+ spin)
evolution of beams in a PBA-based linear collider, from their creation to
their final focusing at the interaction point, and include all the
intermediate phases of acceleration, transport, manipulations, collisions,
etc.

This section summarizes the modeling needs for plasma-based accelerators
(PBAs). A more detailed description is given in [6], Section 2.1.

Several aspects of plasma-based accelerators (PBA) are particularly
challenging to model. These include detailed kinetic modeling of the wake
excitation; trapping of background plasma electrons in the wakefields; ion
motion for a nonlinear beam loading scenario; the need to model the processes
in three dimensions; the propagation of ultra-low emittance and energy spread
beams in the plasma over meter distances (many time steps), the long (ps to
ns) evolution of the perturbed plasma; the disparity in time and space scales
of wake and driver evolution; and the large number of 3D simulations required
to study the tolerances to nonideal effects.

The most widely used numerical tool to study plasma accelerators is the
particle-in-cell (PIC) algorithm [23]. However, ab initio simulations of
particle accelerators with PIC codes are limited by the number of time steps
that are needed to resolve the beam propagation through the accelerator and by
the number of grid cells that are sometimes needed to cover the wide disparity
of spatial scales. Several methods to reduce the computational cost, while
maintaining physical fidelity, have been developed. Reduced dimensionality:
When the beam and structure are nearly azimuthally symmetric, a two-
dimensional ($r$-$z$) representation with a truncated series of azimuthal
modes may be used [24, 25, 26, 27]. Quasistatic approximation: For PBA, one of
the most successful methods to speed up simulations is the quasistatic
approximation [28, 29, 30, 31, 32, 33], which relies on the separation of time
scales to make approximations and decouple the (long time scale) driver
evolution and the (short time scale) plasma wave excitation, providing orders
of magnitude speedup over standard PIC. Boosted frame: An alternative to
performing a quasi-static approximation to handle the disparity of scales is
to shrink the range of scales by using the Lorentz-boosted frame method [34].
With this method, the ultrahigh relativistic velocity of the driver is taken
advantage of by using a frame of reference that is moving close to the speed
of light, and in which the range of space and time scales of the key physics
parameters is reduced by orders of magnitude, lowering the number of time
steps—thus speeding up the simulations—by the same factor.

While enormous progress has been made in the algorithms and codes to model
PBAs, the modeling of a chain of tens to thousands of PBA stages for a multi-
TeV collider is extremely challenging, needing further developments [3, 6]. It
is also essential to integrate physics models beyond single-stage plasma
physics in the current numerical tools, including ionization and
recombination, coupling with conventional beamlines, production of secondary
particles, spin polarization, QED physics at the interaction point,
collisions, and in some cases plasma hydrodynamics for long-term plasma/gas
evolution and accurate plasma/gas profiles. Modeling PBA is currently
challenging because many beam-loading scenarios are still being considered.
These choices may differ between accelerating electrons and positrons, and the
best numerical choices for each scenario are not the same.

###  3.3 Structure-based wakefield acceleration

contributed by P. Piot

Recommendation: Support the development of efficient and accurate algorithms
capable of modeling the beam interaction with its wakefield over long
interaction lengths in structures with arbitrary geometries and constitutive
parameters.

Structure-based wakefield acceleration (SWFA) relies on high-charge “drive”
bunches [O(10–100 nC)] passing through slow-wave structures (SWSs) to excite
electromagnetic wakefields. SWFAs can be configured in either two-beam
acceleration (TBA) or collinear wakefield acceleration (CWA). The produced
wakefields can be directly used to accelerate a delayed “main” bunch (CWA) or
be out-coupled and guided to an optimized accelerating structure that
accelerates the main bunch (TBA) in a parallel beamline. CWA offers a simpler
configuration where both the drive and main bunches are transported along the
same beamline; the TBA scheme decouples the drive and bunch beam dynamics at
the expense of increased complexity (e.g., two parallel beamlines are
required). The beam dynamics associated with the simultaneous transport of the
accelerating main bunch and decelerating drive bunch is one of the major
challenges in CWA.

Significant achievements in TBA research include accelerating gradients in
excess of $\sim 300$ MV/m, wakefield-based power generation of $\sim 0.5$ GW,
[35] and demonstration of staged acceleration [36]. Similarly, recent progress
along the CWA includes the beam-based demonstration of 300-MV/m gradient in a
THz structure [37], the generation of record transformer ratio of $>5$ via
improved longitudinal beam shaping [38, 39], and significant advances in the
theoretical understanding of beam stability [40].

These developments have been possible due to consistent progress in software
capable of modelling the beam-wave interactions in complex accelerating and
power-extracting and transmission structures (PETSs). Modeling of the SWFA
includes radiofrequency (RF) design of complex structures where the RF
properties (e.g., $R/Q$, operating frequency, scattering parameters) are
optimized using a frequency-domain solver for eigenmode or scattering
parameters (e.g., such as omega3p and s3p [41]). Likewise, time-domain
simulations are performed to understand the coupling (wakefield generation and
acceleration) of an electron bunch with the mode supported by the structures.
These investigations are generally performed with computer programs such as
t3p [41] and warpx [42].

In unison with the roadmap elaborated in Ref. [43] the demonstration of SWFA
as a mature technology for a linear collider will require development to ($i$)
perform integrated experiments in dedicated test facilities, ($ii$) explore
high-efficiency schemes, and $(iii)$ push accelerating gradient. Such
developments can only be guided with high-fidelity simulations. Developing
integrated experiments demands software capable of simulating the long-term
beam dynamics within meter-scale structures. The target for high-efficiency
acceleration relies on a fine control of the phase-space distribution of the
drive and possibly main beams [44]. Understanding the precise evolution of
these phase-space distributions over long interaction distances is critical to
understanding the onset of the beam break-up (BBU) instability. Simulations
over long integration time are also needed for TBA where the generation of GW-
level power involves the deceleration of a train of bunches (with 100’s ps
separation) in a structure. Finally, pushing the accelerating gradient
requires optimization of complex electromagnetic structures operated in a
transient mode. Implementing boundaries with complex geometries frequency-
dependent electromagnetic and material properties is critical to the
development of exotic structures and understanding of their dynamical response
to intense fields [37]; see also Section 3.5.

###  3.4 PetaVolts per meter plasmonics and Plasmonic acceleration

contributed by Aakash Sahai along with T. Katsouleas, D. Filippetto and other
contributors of the PV/m plasmonics Snowmass paper

Recommendation: Support the development of a new quantum-kinetic approach to
model large-amplitude plasmons sustained by oscillations of ultra-dense
conduction-band free electron Fermi gas. Modeling the dynamics of ionic
lattice and the energy band structure under the influence of PetaVolts per
meter plasmonic fields of relativistic, nonlinear plasmons is critical to
understand the effect on materials.

PetaVolts per meter (PV/m) plasmonics effort [45, 46, 47, 48] focuses on
access to extreme electromagnetic fields using plasmonics. Plasmonics is based
upon the unique properties of condensed matter that stem from the structure of
the ionic lattice which inevitably gives rise to electronic energy bands. The
electrons that inherently occupy the conduction band in conductive materials
are free to move across the entire lattice in response to external excitation.
Plasmonic modes are collective oscillations of the Fermi gas that is
constituted by the conduction band electrons [49].

Below we briefly summarize the PV/m initiative and its modeling needs. Further
details are available in the above referred work as well as the independent
PV/m Plasmonic Snowmass paper [50].

The scope of PV/m plasmonics is limited to mechanisms where there exists a
strongly correlated ionic lattice and corresponding electronic energy bands
over relevant timescales. Under these conditions, quantum mechanical effects
dominate. Specifically, our effort focuses on acceleration and focusing
gradients as high as PetaVolts per meter [45, 46, 47, 48].

PV/m plasmonics initiative [45, 46, 47, 48] introduces a novel class of non-
perturbative plasmonic modes that are strongly electrostatic. These novel
modes are excited by intense ultra-short charged particle beams. Optical
photons cannot directly excite these strongly electrostatic modes as their
energy is significantly smaller than metallic density plasmons. Moreover, high
amplitude optical plasmons are technologically infeasible due to the large
pre-pulse or pedestal energy in high-intensity optical pulses which ablate and
disrupt the ionic lattice. This turns any sample into solid-state plasma which
are out of the scope of the PV/m plasmonic effort.

The electrostatic nature of plasmons makes it possible to access unprecedented
PetaVolts per meter electromagnetic fields. Strong excitation of the Fermi
electron gas drives the oscillations to the wavebreaking limit. Because metals
have an equilibrium free electron density $n_{0}$, as high as $\rm
10^{24}cm^{-3}$, the coherence or “wavebreaking” limit [51] of EM fields is,

$\rm E_{plasmon}=0.1\sqrt{n_{0}(10^{24}cm^{-3})}PVm^{-1}.$

A comprehensive approach to modeling of relativistic and highly nonlinear
plasmonic modes in conductive materials is required to appropriately
incorporate the multi-scale and multi-physics nature of the underlying
processes. Being strongly electrostatic, nonlinear plasmonic modes
significantly differ from the conventional optical plasmons and do not lend
themselves to being modeled using purely electromagnetic codes. Optical
plasmons are conventionally modeled using the Finite-Difference-Time-Domain
(FDTD) method where the perturbative electron oscillations are simply
approximated using constitutive parameters. The FDTD approach with
constitutive parameters cannot be used when the collective oscillations become
non-perturbative.

Our work [45, 46, 48] has adopted the kinetic approach along with Particle-In-
Cell (PIC) computational modeling of collective oscillations of the free
electrons Fermi gas to account for the nonlinear characteristics of strongly
electrostatic plasmons. It is noted that PIC methodology already utilizes the
FDTD solver for calculation of electromagnetic fields but utilizes charge and
current densities based upon particle tracking. This approach utilizes the
collisionless nature of relativistic oscillations of the Fermi gas and does
not assume any constitutive parameters as part of the initial conditions.
However, initialization and self-consistent evolution of the electron density
implicitly accounts for most of the constitutive parameters. Moreover, as
relativistic oscillations of the free electron Fermi gas have been
experimentally observed to go beyond the Ohm’s law, evolution of these
oscillations still remains unaccounted for by collisionless modeling approach.
Specifically, conductivity, which is a critical constitutive parameter based
upon electron-ion collisions, is not properly understood in the relativistic
plasmonic regime. Therefore, heating processes resulting from relativistic
plasmonic modes are not fully incorporated in the kinetic modeling approach.

In consideration of this immense promise of PV/m plasmonics using
nanomaterials, we call for the support of the modeling community to engage
with the our effort and help understand several new challenges that are not
part of existing modeling tools.

Below we outline a few of the key challenges identified through our ongoing
efforts and bring out the unique requirements our modeling effort:

  * •

Modeling the effect of relativistic energy gain of free electron Fermi gas in
the the ionic lattice potential.

  * •

Understanding the effects of the energy density of plasmonic modes on the
energy-band structure.

  * •

Accounting for self-fields within the ultra-dense electron beams where
particle-to-particle interaction may play a relevant role.

  * •

Incorporating effects from atomistic modeling within the kinetic approach.

  * •

Devising an approach to handle collisions to determine the longer term effects
of electrostatic plasmonic fields and account effects related to conductivity.

###  3.5 Materials modeling for accelerator design

contributed by Danny Perez

Recommendation: Support the development of automated scale-bridging methods
that can autonomously parameterize higher-scale models from large numbers of
lower-scale calculations, so as to enable predictive materials studies over a
broad space of materials and conditions.

The quest for ever-higher acceleration gradients leads to stringent demands on
the ability of materials to maintain high performance in the harsh
environments typical of high-gradient accelerator cavities. Of special
interest is the understanding of the origin and properties of RF breakdown
precursors, with the goal of eventually using this understanding to develop
breakdown-mitigation strategies. These simulations are typically conducted at
multiple scales, ranging from first-principle quantum calculations using
methods such as density functional theory (DFT). Such calculations allow one
to accurately estimate elastic, thermodynamic, and electronic properties of
different alloys. However, the steep scaling of these methods (cubic in the
number of electrons) strongly limits possible simulation sizes and times. In
order to obtain nanostructural information, such as defect nucleation,
propagation, and reactions, classical molecular dynamics (MD) simulations are
instead employed. These simulations are typically extremely scalable
($O(N_{\mathrm{atoms}}$ or $O(N_{\mathrm{atoms}}\log N_{\mathrm{atoms}}$ ). A
key challenge with moving from DFT to MD is that electrons are typically
integrated out, which implies that electronic physics (e.g., the coupling of
electrons with the electric and magnetic fields in the cavity) has to be re-
introduced ”by hand”, which often requires ad hoc assumptions and is typically
extremely time-consuming. While MD simulations are orders of magnitude cheaper
than their DFT counterparts, simulations times ($<\mu$s) and sizes ($\sim
10^{9}$ atoms) remain extremely limited compared to engineering scales. This
requires the introduction of yet larger-scale models that operate at the
continuum level, including for example crystal plasticity or continuum heat
and mass transport codes. While these continuum codes are often extremely
scalable, accurately parameterizing the models with materials-specific physics
is also extremely tedious and requires a significant level of understanding of
the relevant factors, which is often not unambiguously available. We note that
the systematic and automated parameterization of continuum models from lower-
scale simulations is often not possible, except for “simple” properties such
as elastic constants.

The Materials Genome Initiative has pioneered the use of large numbers of
quantum simulations (typically at the DFT level) to explore the space of
possible material in search of solutions with optimized performance
characteristics. These approaches have proved very successful at exploring the
space of functional materials (such as materials for batteries), and
extensions to structural materials are also possible when suitable figures of
merit (i.e., computable from computationally-affordable DFT calculations) can
be defined. First applications to accelerator materials have recently been
carried out for dilute binary Cu alloys, which identified new candidates for
breakdown-tolerant materials, as well as rationalized the observed performance
of certain alloys like Cu/Ag. Extending this exploration to more complex
multi-component materials will prevent exhaustive enumeration and is instead
likely to require more sophisticated machine-learning-guided active-learning
approaches. Similarly, including complex microstructural effects in the figure
of merit (e.g., to also take into account the microstructure of the materials)
is likely to require a combination of state-of-the-art computational methods
with data-driven ML algorithms.

Further, the development of robust and automated workflows, such as those
described in section 8.1 ,for the estimation and upscaling of materials
properties to inform higher-scale models from lower-scale simulations would be
extremely valuable, as it would enable the development of predictive materials
models in a practical amount of human effort, compensating with a more
aggressive use of high-performance computing resources.

###  3.6 Structured plasmas

contributed by Nathan Cook

Recommendation: Support the development and integration of fluid and kinetic
codes to meet the modeling demands for a new class of structured plasma
devices coupling macroscopic plasma properties with strict requirements on
kinetic interactions.

This section summarizes the modeling needs for structured plasmas. A more
detailed description is given in [3], Section 2.4.

Structured plasmas, systems for which plasma density, temperature,
composition, and ionization state are tailored to enhance an interaction
between a beam or laser with that plasma system, are increasingly important
for future accelerators. Controllable plasma channels are essential to
increasing peak energy and quality across all types of PBAs; they permit the
guiding of intense lasers over long distances for laser-driven schemes [52,
53, 54, 55], control of plasma density over meter-scale distances as required
for beam-driven schemes [56, 57, 58], and the realization of plasma columns
for novel positron acceleration schemes [59, 60].Structured plasmas have also
found application as flexible focusing elements. Discharge capillaries can
produce orders-of-magnitude larger magnetic field gradients than traditional
electromagnets [61], subsequently enabling the compact staging of plasma
accelerators [62]. Alternative approaches include passive plasma lenses,
consisting of a narrow plasma jet outflow generated by laser pre-ionization
[63, 64], which can provide comparable focusing at high densities. Discharge
plasmas have been employed as tunable dechirpers to remove correlated energy
spreads from GeV-scale electron beams [65]. Finally, a class of proposed non-
destructive diagnostics with high spatiotemporal resolution will rely on
controllable plasma densities in concert with electron and laser beams [66].

Although specific needs vary with device type, scale, and application,
structured plasmas impose unique modeling requirements as compared with
simulations of other accelerator systems. Capillary discharge dynamics require
the characterization of a discharge current and corresponding plasma transport
properties, including electrical resistivity and thermal conductivity.
Magnetohydrodynamic (MHD) codes are well suited to capturing the basic physics
of these systems, while maintaining larger timesteps and reduced resolution
requirements from kinetic approaches. Significant progress has been made in
demonstrating their agreement with 1D analytical models and experimental
results for waveguides and active plasma lenses [67, 68]. The coupling of such
MHD codes with laser envelope models [69] have contributed to record-breaking
LPA acceleration of electrons to 8 GeV in 20 cm capillary [70, 71]. Similarly,
active plasma lens studies have benefited from the application of MHD to
reproduce species-dependent nonlinearities in current flow and magnetic field
[72, 73, 74]. MHD codes have also been used to support a new class if
structured plasmas predicted on the use of an extended laser focus, known as
hydrodynamic optical-field-ionized channels (OFI or HOFI) [75, 76]; Initial
investigations into these systems have been supported by 1D hydrodynamic
simulations [75, 77]. Despite these advances, MHD simulations face challenges
in accurately capturing dynamics at early timescales, where low ionization
rates and large temperature gradients impose constraints on fundamental
assumptions of local thermal equilibrium (LTE), and may introduce numerical
aberrations resulting from poor convergence of equation of state methods and
inaccurate transport models [78]. Overcoming these limitations can require
prohibitive increases in simulation runtime. More work is needed to improve
the speed, reliability, and accessibility of MHD codes for modeling these
systems.

Pre-ionized plasma sources, such as those used for PWFA stages and passive
lenses, present additional modeling challenges. Neutral gas dynamics
necessitate hydrodynamic simulation on $\mu$s-timescales to generate proper
initial conditions, while the ionization laser requires propagation of an
intense electromagnetic fields on fs-timescales. The resulting plasma does not
constitute a local thermal equilibrium, therefore the LTE dynamics implemented
by most MHD codes is insufficient to capture the ionization and heating
dynamics. Moreover, vacuum-plasma interfaces are of interest for matching
incident drive beams [79], and multi-species plasmas have been employed for
high-brightness injection scheme [80]. In these cases, kinetic codes, for
example PIC techniques, may be coupled with hydrodynamic codes to obtain
reasonable approximations, or alternatively, first principles models may be
employed [81, 63, 82, 64, 83]. Similar challenges are faced in understanding
the longterm evolution of these systems following laser or beam interactions.
More work is needed to improve the interfacing between fluid and kinetic
modeling tools to address the multi-physics nature of these systems across
disparate spatiotemporal regimes.

###  3.7 Superconducting magnets

contributed by Lucas Brouwer and Christian Messe

Recommendation: Support the development of novel mixed finite element
formulations and algorithms, and their implementation in open source software
tailored for superconducting magnet design.

Advanced modeling tools are currently utilized across the full range of US
Magnet Development Program (US-MDP) research activities [84], enabling the
design of improved conductors, magnets, and diagnostics. A diverse and
challenging set of new modeling tools are required to continue this effort and
ultimately improve design time, cost, and performance of future
superconducting accelerator magnets. The new developments include: (1)
simulation of conductor and cable, (2) advanced modeling of interfaces and
other potential sources of training in stress-managed designs, (3) modeling of
LTS/HTS hybrid magnets, and (4) radiation environment thermal effects on
magnets [85].

The material laws for superconducting materials are highly non-linear, which
implies that a lot of iterations must be made per simulated timestep to
achieve a numerically sufficient convergence. To reduce the high computational
cost of these material laws cause, a novel finite element formulation called
h- is being discussed within the HTS modeling community [86, 87]. By using the
scalar magnetic potential rather than the vector potential a that is
traditionally used to model the magnetic field in air and vacuum domains.
Since the computational effort is roughly proportional to the number of
unknowns to the power of two, this means that reducing the magnetic potential
form a vector to a scalar can reduce the computational effort up to a factor
of nine.

One challenge in sufficiently implementing this novel formulation into a
finite element code lies in the hybrid use of node and edge-based elements,
the way boundary conditions are imposed and how efficient implementations must
be designed. Another challenge lies in efficiently solving the system matrices
which are non-symmetric, non-positive-definite and ill-conditioned.

Regarding the h- formulation, some of the most pressuring questions discussed
in the HTS modeling community are:

  * •

imposing current boundary conditions in a user-friendly fashion[88, 89]

  * •

discretization of tape structures (thin shells) in 2D and 3D space [90]

  * •

quench prediction (maxwell-thermal coupling)

  * •

delamination (maxwell-thermal-mechanical coupling)

Most of the published formulations have been implemented on top of commercial
toolboxes such as COMSOL and are not yet available to the general public.
Moreover, it is in the very nature of closed source codes to limit the access
the developer has to the data structure and the knowledge of underlying
algorithms. The desire of having full control over the data structure
motivated us to develop a custom codebase that is tailored to the needs of HTS
modeling. Having defined the project goals below, we decided to develop a new
finite element framework from scratch to achieve them:

  * •

Support h-a and h- formulations for 2D and 3D, as well as thin shells, both
with first and higher order elements.

  * •

Support multiphysics, specifically thermal and mechanical coupling, as well as
current sharing.

  * •

Have a text-based user interface that is tailored to the needs of HTS magnet
and cable modeling.

  * •

Use popular open-source data formats, such as HDF5, GMSH, and Exodus II
(ParaView)

  * •

Link against modern sparse linear algebra solvers such as STRUMPACK, PETSc,
PARDISO and MUMPS.

  * •

Run in parallel using the MPI standard.

  * •

Be readable, extendable and maintainable.

##  4 To the next frontier: ultraprecise, ultrafast virtual twins of particle
accelerators

contributed by Jean-Luc Vay, Axel Huebl, Rémi Lehe, Chengkun Huang, Nikita
Kuklev, Ji Qiang, David Sagan

Recommendation: Support the development of accelerator modeling software that
orchestrate interdisciplinary set of tools with standardized data
representations to enable end-to-end virtual accelerator modeling and virtual
twins of particle accelerators, which combine first-principle models together
with machine learning-based surrogate models, for tunability from maximum
precision for accurate and realistic accelerator design to maximum speed for
online particle accelerator tuning.

The development of future particle accelerators requires predictive modeling
tools that will range from (i) very detailed, full physics and dimensionality,
first-principle kinetic simulation tools that are needed for detailed runs for
physics studies (typically based on Monte-Carlo and Particle-In-Cell methods)
[91], to (ii) ultrafast simulation tools that are needed for ensemble runs for
design studies (using a combination of, e.g., reduced physics, low
dimensionality, low resolution, artificial intelligence (AI)/machine learning
(ML) surrogates [92, 93]).

###  4.1 Interdisciplinary simulations

Recommendation: Support interdisciplinary simulations especially efforts to
establish standards that would ease the sharing of information and data across
codes as well as standards for interfacing codes.

Interdisciplinary simulations are important in a number of areas. In vacuo
particle tracking coupled with particle/matter interactions is an example of a
growing need. One application is in simulating the radiation induced by ”dark
current” electrons in accelerating cavities. This radiation may cause damage
to cavities which leads to shortened lifetimes of the devices and a radiation
safety hazard for the surrounding environment. Dark current induced problems
have been observed at many facilities such as the CEBAF[94], LCLS-II[95], ANL,
etc. Sufficient shielding is required to properly contain the radiation which
in turn requires a good understanding and prediction of radiation levels
through simulations. Another example is the modeling of positron production in
a target from the impact of high-energy electron beams accelerated through a
linac injector. These simulations require accurate calculations using
electromagnetic RF codes for accelerator structures and beam dynamics codes
for particle transport in a beamline to characterize the beam profile before
it hits the accelerator enclosure or the target.

Particle/matter simulation codes exist. Examples include Geant4[96],
FLUKA[97], and MARS[98] which have traditionally been used for detector
simulation in HEP experiments. However, since these codes and accelerator
simulation codes have all been developed without common standards, interfacing
them is a laborious task. A seamless simulation requires the proper transfer
of field and particle data from accelerator to radiation codes. Communication
in a standardized format such as openPMD[99], which has been adopted in some
accelerator codes, would help ensure efficient and error-free field and
particle data transfers[100]. Another issue with an integrated simulation is
in matching of the geometry of the vacuum chamber surface. The surface
geometry in accelerator simulations is generally poorly defined if at all. The
most comprehensive simulations define the surface using a finite element mesh
generated from a CAD model (e.g., both WARP [8] and OPAL [13, 101] have some
limited capacity for this). In contrast, radiation codes generally employ a
faceted representation of the CAD model boundary. A converter for mapping
finite element curved surfaces to faceted divisions on an interface boundary
is required to accurately determine the location of a particle crossing from
one computational domain to another. Much time and effort would be saved if
the surface geometry descriptions were standardized so that a single converter
module could be used in multiple codes.

Increasingly, accelerator simulation tools are also incorporating more micro-
physics models to better describe the complex interplay of the various physics
phenomena. One particular example being the emission modeling of a high-
brightness electron photocathode gun. A photocathode gun provides a high-
brightness electron source for the downstream accelerator beamline where the
beam brightness can only be degraded, not improved. Thus, it is essential to
understand the cathode emission characteristics and the method to control the
beam quality in the gun environment through validated simulations. While Monte
Carlo photo-electron emission simulations have been widely employed in
studying photocathode performance for dedicated experiments, its potential in
integrated simulations has only been explored recently [102]. For such
purposes, a tight integration of the micro-physics models into existing gun
simulations can be achieved via the best practices and standardization as
discussed below.

###  4.2 End-to-end Virtual Accelerators (EVA)

Recommendation: Support the development of software that are capable of end-
to-end virtual accelerator (EVA) modeling (Grand Challenge of Accelerator and
Beam Physics) that incorporate all components (including both conventional and
AAC sections) and all pertinent physical effects.

The realization of software that are capable of end-to-end virtual accelerator
(EVA) modeling has been identified as a Grand Challenge of Accelerator and
Beam Physics [103].

Thorough modeling of a full particle accelerator in individual parts
(injector, magnets, beam dynamics, etc.) is already an important aspect of
particle accelerator development; one, without which no project nowadays can
proceed to the building stage. For example, start-to-end simulations have been
used in x-ray light source accelerator designs [104, 105, 106]. However,
simulating the system in many small units poses two significant challenges:
(i) The various codes used for the individual parts are often from different
areas, lack the state-of-the-art high-fidelity models for extremely bright and
intense beams, written in different languages (C/C++, Fortran, Python, etc.),
and use different standards for data I/O (particles, fields, etc.), slowing
down the design and simulation process; (ii) Without multiphysics couplings,
subtle, but important effects (collective effects, halo, coherent synchrotron
radiation, etc.) might not be considered in the design or without sufficient
accuracy, ultimately leading to issues during commissioning, the need to
modify the machine (shimming, additional steering, shielding, etc.), and
longer downtimes due to added radiation. Furthermore, opportunities for more
efficient working points that can be achieved only from system optimization of
the entire accelerator may be missed entirely.

Thus, there is a clear need for full physics 6-D computer simulations of the
entire accelerator system that incorporate all components (including both
conventional and AAC sections), all pertinent physical effects, and that
execute fast and reliably. Such EVAs need to be validated with experiments at
both the component and system levels. Furthermore, these EVAs should be able
to leverage modern computing infrastructure like HPC clusters and GPU
computing, and fully integrate AI/ML tools to maximize efficiency for
practical applications. The development of such tools requires continuous
advances in fundamental beam theory and applied mathematics, improvements in
mathematical formulations and algorithms, and their optimized implementation
on the latest computer architectures.

###  4.3 Virtual twins of particle accelerators

Recommendation: Support the development of virtual twins of particle
accelerators, which combine high-performance computing, first-principle models
together with machine learning-based surrogate models, with tunability from
maximum precision for accurate and realistic accelerator design to maximum
speed for online particle accelerator tuning.

Ultimately, the availability of multiphysics, end-to-end simulation
capabilities will lead to the realization of virtual twins of particle
accelerators. These will enable the design and optimization of future
accelerators at scale on supercomputers, with unprecedented levels of accuracy
and speed. This capability will dramatically increase the breadth of parameter
space that can be explored, thereby enabling the design of particle
accelerators that have not been possible before. Ultrafast and ultraprecise
tunability will let users simulate as needed: from maximum precision for
accurate and realistic accelerator design to maximum speed for online particle
accelerator tuning. Modern ML optimization frameworks can be used to take
advantage of this tunability via multi-fidelity algorithms, allowing for
faster scalable design refinement. Automated uncertainty quantification can be
used to provide hints as to where the computational budget should be applied
for best overall simulation quality.

##  5 Cutting-edge and emerging computing opportunities

Recommendation: Support the research and development on cutting-edge and
emerging computing opportunities, including advanced algorithms, AI/ML
methods, quantum computing algorithms for beam and accelerator physics, as
well as on the development of storage ring quantum computers.

Just as it is essential to continually invest in fundamental studies of
accelerator technologies and beam science, it is also essential to do the same
for the software and algorithms that enable such studies using computers. This
includes the continuation of the study and development of novel algorithms and
optimization strategies, as well as leveraging AI/ML and exploring algorithm
that will take advantage of upcoming quantum computers. This also includes the
development of modeling tools to study and design quantum computers based on
storage rings.

###  5.1 Advanced algorithms

contributed by Jean-Luc Vay, Ji Qiang

Recommendation: Support research on algorithms, from refining the
understanding of the properties and bottlenecks of existing algorithms to the
elaboration of novel algorithms that exhibit better properties, remove the
bottlenecks, and improve the speed and accuracy of accelerator modeling.

Computational beam and accelerator physics has spurred the development of many
algorithmic advances [107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117,
118, 34, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147,
148, 33, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162,
163, 164] that have boosted the computational capabilities tremendously, in
some instances by orders of magnitude at a time. Yet, the modeling of
particles accelerators remains very demanding, and even extremely challenging
in the case of design of future plasma-based or structure-based particle
wakefield HEP colliders. It is thus essential to pursue the research on
algorithms, from refining the understanding of the properties and bottlenecks
of existing algorithms to the elaboration of novel algorithms that exhibit
better properties, remove the bottlenecks, and improve the speed and accuracy
of accelerator modeling. The discovery of new and better algorithms for beam
and accelerator modeling is a fundamental topic that is poised to provide big
boosts to the other fundamental topics that are the discovery of new and
better accelerator technologies and concepts, and the discoveries of new laws
of natures with colliders that they enable.

This also includes the adoption of algorithms that have proven to be very
effective into other fields, such as adaptive mesh refinement [120], which
enables to zoom in on regions that need higher resolution (e.g., sharp edge of
high-intensity beam) while zooming out to simulate larger regions (e.g., beam
with pipe to include image charges and halo effects). This is discussed in
more detail in [6].

###  5.2 Artificial intelligence, machine learning, and differentiable
simulations

contributed by Auralee Edelen, Remi Lehe, Nikita Kuklev, Alexander Scheinker,
Ryan Roussel

Recommendation: Support the development of ML modeling techniques and their
integration into accelerator simulation and control systems, with an emphasis
on fast-executing (up to real-time) and differentiable models, continual
learning and adaptive ML for time-varying systems and distribution shifts,
uncertainty quantification to assess confidence of model predictions, and
physics-informed methods to enable broader model generalization to new
conditions and reduced reliance on large training data sets.

Machine learning (ML) and artificial intelligence (AI) have revolutionized
many computational tasks in recent years, from protein folding prediction to
fusion energy control. Speeding up computationally-intensive accelerator
simulations and aiding optimization of particle accelerators are two key areas
where ML & AI have also been making substantial contributions. Many ML/AI
tools are now technically mature, production-ready, and can be used as part of
standard computational toolkits for particle accelerators. Notable examples so
far include fast-to-execute accelerator models that can be used online as
“digital twins”, as well as in design and online optimization using Bayesian
optimization and other methods, whereby a model that is learned on-the-fly is
used to guide sampling of the parameter space. These methods, and tools
supporting their use, are beginning to be integrated into dedicated simulation
workflows and into control systems for use online that share common standards
for interoperability. For example, the open source package LUME [165] has been
used to deploy online ML and simulation models for a variety of systems, and
xopt [166] has been used to generate datasets (both offline and online) for
training ML models.

So far, most studies in AI/ML for accelerators have focused on proof-of-
principle tests of new methods under narrow operating conditions, rather than
integration into dedicated use online where they would be tested under a wide
variety of conditions and face additional challenges in robustness. Looking
forward, there is great potential to now expand upon the fundamental methods
algorithmically, combine the strengths of different methods in novel ways (for
example, combining neural network models or differentiable simulations with
uncertainty quantification and Bayesian optimization), and address the
challenges of dedicated deployment that often do not arise in R&D testing of
each new algorithm (e.g. robust uncertainty quantification and adaptation to
account for changing conditions over time or exploration of new regions of
parameter space, extension to very high dimensional systems with hundreds of
freely-tunable accelerator settings, etc.). We highlight some current and
future directions below.

##### Fast-executing, adaptive accelerator models

Physics-based accelerator models can very accurately predict expected beam
phase space evolution. These models can be calibrated offline by hand or
online based on feedback from diagnostics, such as using energy spread spectra
to tune a model to predict the beam’s longitudinal phase space at FACET [167].
The major limitation of physics-based simulation models is that they are
computationally expensive and therefore cannot give real-time (e.g. at rates
of 120 Hz to MHz) predictions in the control room. For physics-based
simulations that include the major nonlinear collective beam effects,
prediction latencies can be on the order of tens-of-minutes to hours depending
on the simulation fidelity. In contrast, trained ML models do have the
potential to provide real-time predictions, in some cases providing orders of
magnitude improvements to execution speed [168]. Many studies in ML-based
modeling of accelerator systems have relied on supervised learning on bulk
inputs/outputs and fairly standard neural network architectures, such as
multi-layer perceptrons [169, 170, 171, 172, 168] and convolutional neural
network (CNN) based encoder-decoder architectures [173, 174, 175, 176], as
well as Gaussian process models [177, 178]. Common inputs and outputs include
accelerator settings such as magnet currents, cavity gradients, and initial
conditions such as laser parameters; common outputs include scalar beam
parameters such as the emittance and bunch length, and 2D projections of the
beam phase space. When trained on large simulation datasets of input-output
variables, these models have been demonstrated to have as much as a million
times speedup in execution speed with reasonable prediction accuracy [168].
Training on measured data (either from scratch or by adapting a model that is
pre-trained on simulations) also enables differences between the as-built
machine and the simulation to be represented.

Looking forward, there is a need to further develop methods for making ML-
based accelerator models reliable under shifting input-output data
distributions. For example, this can include both time-varying changes in
inputs from an operational accelerator and deliberate changes in operating
conditions or simulation inputs that go beyond the statistical distribution of
the training data. Methods to flag when model performance is degraded, as well
as methods to adapt models to new conditions are needed. Having accurate
uncertainty estimates in addition to model predictions is critical for
applications in accelerators, especially in cases where decisions about
control actions, analysis, or design are made based on model predictions.
Uncertainty quantification methods, such as the use of Bayesian neural
networks[179] and ensembling [180], have been used in accelerators to
highlight cases where model uncertainty is high. However, additional work is
needed to ensure robustness of uncertainty estimates under changing
conditions. In general, further work incorporating state-of-the-art methods
from continual online learning [181] and transfer learning [182] could be used
to maintain model accuracy over time and aid re-use of models in different
settings. This could also help reduce reliance on large training data sets
when transferring models between specific accelerators (for example, between
injectors with similar designs). Operation in tandem with local feedback
algorithms can also help retain model accuracy over time as conditions change.
Sample-efficiency is a key consideration for accelerator problems in which the
data collection is very time-consuming or detailed beam measurements would
interrupt operations. By incorporating physics constraints within ML
frameworks, such as developing beam dynamics models based on Taylor maps, it
is possible to greatly reduce the amount of data needed for re-training models
[183], as discussed in more detail below. Further work is also needed in
developing advanced methods for cases where online re-training is not feasible
or practical. Some avenues toward addressing this challenge without re-
training include the use of adaptive feedback / local optimization to make the
overall ML system more robust to unknown and time-varying system changes and
inputs. Some work towards the challenge of ML without re-training is utilizing
adaptive feedback within the ML framework by adjusting ML model inputs or
internal parameters with gradient-free adaptive feedback algorithms [184,
176]. In the context of accelerator tuning, it can also be accomplished by
combining ML system models for control with local adaptive feedback or
optimization algorithms [185].

##### Physics-informed and physics-guided ML modeling

Recently there has been interest in incorporating physics information more
directly into ML models. This is expected to improve sample efficiency and
accurate generalization to unseen regions of parameter space. Such “physics-
informed” modeling spans a wide variety of techniques that use physics
information more or less directly (see [186] for a review). In the most broad
sense of “physics informed”, training on very broad, high-fidelity simulation
data sets introduces observational biases that allowing ML models to learn
functions, vector fields and operators that reflect the physical structure of
the data [186]. Numerous examples exist in the literature where training on
broad accelerator simulation data sets enables enough of the underlying
physics to be represented in a sufficiently generalizable form that the
learned models can reliably interpolate to unseen configurations or provide
qualitative estimates of beam behavior even outside of the training
distribution [168, 172], for both scalar predictions and beam phase space
projections. A recent example highlights that this can also be extended to
unobserved components of the beam parameter space [176]. In that work, a
convolutional neural network (CNN)-based encoder-decoder trained and then
utilized in an unsupervised adaptive approach to predict the 15 unique 2D
projections of a beam’s 6D phase space for an unknown and time-varying input
beam distribution. The approach in [176] is to adaptively tune the low-
dimensional latent space of the encoder-decoder to match a measured 2D
(longitudinal phase space) projection of an unknown 6D phase space
distribution and in doing so accurately predict the other unmeasured 2D
projections of the 6D distribution.

More direct methods of making “physics-informed” models include adding
physics-based constraints into the learning process [187, 186], or structuring
the learning algorithm in a way that mathematically resembles the physics
problem (e.g., replacing one component of a Hamiltonian update with a neural
network [188]). In accelerator physics this avenue has been less explored but
holds significant potential. In one accelerator example, the Hessian from a
physics-based or learned model is used to inject expected correlations into a
Gaussian process kernel [189], which results in more sample-efficient learning
and optimization. Another accelerator example uses a differentiable
formulation of beam dynamics in a ring, implemented in the tensorflow machine
learning library, to enable learning of free parameters using traditional ML
workflows [183]. For more efficient predictions, Galerkin-based or symplectic
reduced order modeling (ROM) may present new opportunities for nonlinear beam
dynamics study beyond the theoretical formulation.

##### Differentiable simulators

While there is a long history of using automatic differentiation in
accelerator physics for higher-order calculations in rings [190], accelerator
physics simulation codes do not readily support arbitrary computation of
gradients. This necessitates the use of numerical estimation of gradients when
using gradient-based optimization methods. Having simulation codes that
inherently support automatic differentiation would enable gradient-based
optimization to be more readily used with accelerator physics simulations.
Tying together simulations with gradient-based learning algorithms also has
significant promise; for example, this could aid gradient-based learning of
free parameters, as was done for accelerators with a differentiable lie map
formulation in [183] and for a differential hysteresis model in [191]. This is
similar to examples using adaptive feedback that approximates gradient descent
to optimize free parameters in physics models [167]. Gradient-based learning
of external ML algorithms (such as learning a control policy in reinforcement
learning) can also be aided by a differentiable forward model, as was done for
example in [171] but with a differentiable learned ML model rather than a
differentiable simulator. Tying together standard simulation tools with ML
components (e.g., using a learned model for one machine section or one
computation component) would benefit substantially from having end-to-end
differentiability. Expanding this concept to detailed differentiable
simulations of non-linear collective effects (e.g., with particle-in-cell
codes) could enable new capabilities in optimizing particle accelerator
simulations and using them in conjunction with AI/ML. One example of
integrating optimization with a differentiable physics model is given in
[191], where an analytic model of hysteresis is made differentiable and used
in conjunction with measured data to efficiently learn an accurate model of a
magnet response that includes hysteresis; this is then used for hysteresis-
aware Bayesian optimization that can more precisely optimize the resultant
beam.

ML/AI frameworks have highly-optimized implementations of automatic-
differentiation and other low level computational tools for running
efficiently on CPU/GPU. Major libraries (PyTorch, TensorFlow, JAX, Julia)
provide low level hooks for these routines. Some frameworks can be used to
provide gradients for existing codes written in C or Fortran. This presents
two promising avenues toward making differentiable physics simulators: (1) re-
writing or translating existing low-level accelerator physics codes into
formats compatible with automatic differentiation and (2) wrapping sections of
existing code with external software to provide derivatives. This also opens a
path toward using efficient AI/ML learning algorithms and frameworks directly
with physics simulations.

##### Model-based optimization

The development and use of advanced algorithms for accelerator design and
optimization aims to efficiently solve challenging optimization problems in
high dimensional parametric spaces. The so called “curse of dimensionality”,
where optimization difficulty scales exponentially with the number of free
parameters, limits the number of optimization problems that can be done,
especially when running high-fidelity accelerator simulations is
computationally expensive. To make a problem solvable with a limited
computational budget, either assumptions are made to simplify the simulation
itself or the free parameter space must be heavily restricted. However, if
novel techniques that substantially improve the efficiency of simulated
optimization can be implemented, previously unsolvable optimization problems
in accelerator physics can be realistically tackled.

Traditional design optimization in accelerators has relied on computationally
intensive algorithms such as genetic algorithms (e.g. NSGA-II [192]) and
particle swarm optimization, which require many simulation samples to converge
and do not leverage any learned representations of the system. ML-based
optimization methods that attempt to learn a model on-the-fly during
optimization or use an existing model can improve sample efficiency and
convergence speed by enabling more judicious choices of input variables to
examine.

In cases where gradient information is not available, known as “Black Box”
problems, model based optimization (such as Bayesian optimization) techniques
can be used to maximize optimization efficiency. These algorithms have already
been shown to perform well in certain experimental [177, 189] and simulated
[193, 194] contexts. However, there remains substantial room for further
innovation and improvement in sample efficiency, scaling, and tailoring to
specific applications. For example, multi-fidelity Bayesian optimization
[195], where evaluations of the optimization objective at a lower fidelity are
used as a proxy for high fidelity simulations, is naturally well-suited to
simulated optimization of accelerator based problems where multiple fidelities
are straightforward to interpret. These algorithms could be used to help
balance computational resources and required fidelity automatically during
search refinement. Furthermore, if models used for these algorithms also
provide an associated confidence metric in their predictions, they can be used
in information-based optimization to either speed up optimization in high
dimensional parameter spaces based on model confidence regions [196] or
improve mutual information gain during nested optimization procedures [197].

Model based algorithms also enable the use of transfer learning based-
techniques, where previously created models of similar systems are used to
inform algorithms applied to novel optimization problems and aid sample-
efficiency. For example, using information about correlated input parameters
from a physics simulation to inform the internal model in Bayesian
optimization of an operating accelerator [189, 177] can also be considered a
form of kernel-based transfer learning. Physics-informed models or
differentiable simulators also have great potential for use in sample-
efficient, model-based optimization across different systems. They can be used
in conjunction with gradient-based optimization to learn system model
parameters on-the-fly with limited data and exploit this information in
control. For example, in [191], the parameters of a general differentiable
hysteresis model for magnets is learned from beam measurements and is used in
conjunction with Bayesian optimization for hysteresis-aware fine-tuning.

###  5.3 Quantum computing

contributed by He Zhang, Ji Qiang

Recommendation: Support quantum computing algorithm and code development for
accelerator modeling, feasibility study on quantum computing implementation in
accelerator modeling, and quantum computing education in accelerator
community.

The start-to-end simulation of an accelerator using real beams with billions
or more particles remains challenging and expensive even with state-of-the-art
exascale machines. The development of quantum computers, which can potentially
provide an exponential improvement in efficiency for some classes of
simulations, may bring new opportunities to enhance the particle accelerator
community’s simulation abilities.

The technique for building quantum computer has entered the Noisy Intermediate
Scale Quantum (NISQ) era [198]. Current state-of-the-art quantum computers
have above 50 qubits and quantum supremacy has been demonstrated on some
specific problems [199, 200]. Quantum computing is currently available to the
public through cloud services provided by some commercial companies such as
IBM [201], D-Wave [202], Amazon [203] and Microsoft [204]. Meanwhile, studies
on quantum algorithms have also been booming in the past few years. One hot
topic is quantum machine learning. Machine learning can be used to optimize
the performance of accelerators in design, commissioning and operation. Some
time-consuming simulations can also be replaced by well-trained learning
systems. Quantum computing can speed up many learning algorithms, including
SVM [205, 206], Bayesian networks [207], convolutional neural networks [208],
Bayesian deep learning [209], reinforcement learning [210, 211], etc.

Another topic that is relevant for accelerator modeling is solving linear
systems [212, 213, 214, 215, 216] as well as ordinary differential equations
(ODEs) and partial differential equations (PDEs) [217, 218, 219, 220, 221].
Solving Poisson’s equation and the Vlasov equations — which are often used in
the simulation of collective effects such as space charge and beam-beam
interactions — with quantum computing is being explored [222, 223, 224]. From
the perspective of programming, quantum computer simulators, as code
developing-, debugging-, and testing platforms, are available for almost all
mainstream programming languages, e.g. C/C++, Python, Java, Matlab, etc. There
also exist some languages specifically designed for quantum computing [225].
All these provide the community with the fundamental blocks to build
simulation tools for beam and accelerator physics.

To make a problem suitable for quantum simulations, it has to be described by
unitary operators so that the system, which may be classical, is
mathematically equivalent to a quantum system. Additionally, in quantum
computing, all variables are stored in quantum states and reading out the
results accurately can be time intensive, which should be carefully managed.
Many problems in accelerator modeling and beam dynamic simulations meet the
above criteria. The motion of a charged particle, even under collective
effects, can often be described as Hamiltonians, the evolution of which can be
carried out by unitary operators. Recently, a quantum Schrodinger approach was
used to solve the Poisson-Vlasov equations to simulate space-charge effects in
high intensity beams [226]. Although particles are used to model beams, in
many cases we care more about the macroscopic property of the beam, e.g.,
emittance, momentum spread, bunch size, luminosity, etc., rather than the
individual particle and reading out the results of all the particles can be
avoided.

However, most previous work on quantum algorithms focused on the realization
of an algorithm with quantum circuits, but applying the algorithm to solve a
practical scientific problem is seldom discussed [227]. Clearly there is a gap
between the development of the algorithms and their implementation. To
implement the quantum computing technique in accelerator modeling, we need to
keep abreast with the latest developments and get involved in algorithm design
and program development. We expect, at least in the near future, a quantum
computer will not replace a classical computer but will probably work together
with one. It is thus probably better for now to focus on how to make new
quantum simulation tools that collaborate with the existing pool of
accelerator modeling programs. Ideally a protocol will be invented through
which the quantum packages could be called by the classical programs. Also
needed are innovative analyzing tools to process the simulation results before
the reading-out. To achieve these tasks, the accelerator physics problems that
will benefit from quantum computing need to be identified and for each of them
the proper mathematical model will need to be established, which may be
different from the conventional classical one. For this, contributions from
experts in both accelerator physics and quantum computing are required.

###  5.4 Storage ring quantum computers

contributed by Sandra Biedron, Jean-Luc Vay

Recommendation: Support research and development of storage ring quantum
computers.

In addition to benefit from quantum computing in the future, storage rings can
be used as quantum computing devices themselves [228], with the advantages,
over Paul [229, 230] or Penning traps [231], of longer coherence time, the
ability to store a significantly higher number of ions and the possibility of
storing multiple ion chains [228]. A storage ring quantum computer (SRQC)
could potentially store thousands of ions to form an Ion Coulomb Crystal in a
closed trajectory. For SRQC, we anticipate unique challenges associated with
the unprecedented large number of ions in the ICC. For example, on timing the
laser pulses to efficiently cool the ICC beam to its equilibrium energy
configuration, from which ion manipulations can be initiated. The solutions to
the equilibrium positions of the ICC can be solved numerically for an
arbitrary N, but they quickly become lengthy and impractical as N becomes
large, from hours to days. A solution that employs AI/ML techniques was
described recently that brings the prediction to a few seconds [232].

SRQC presents a particularly interesting case, where the design of the storage
ring can benefit from high-performance computing and AI/ML, to produce quantum
computing devices that will open unprecedented capabilities in computing with
application to many fields, including beam and accelerator physics and designs
themselves.

##  6 Computational needs

Recommendation: Support the development of increasingly powerful and
specialized High-Performance Computing (HPC) and High-Throughput Computing
(HTC) capabilities for accelerator modeling, and maintenance of software to
run efficiently on these hardware (e.g., port of codes to GPUs) with efficient
and scalable I/O, post-processing and in situ data analysis solutions, which
will be needed to support ab initio modeling at increasing fidelity, training
of surrogate models and AI/ML guided designs.

###  6.1 Hardware: CPU/GPU time, memory, archive

contributed by Jean-Luc Vay, Axel Huebl

Recommendation: Support the development of increasingly powerful and
specialized High-Performance Computing (HPC) and High-Throughput Computing
(HTC) capabilities for accelerator modeling, which will be needed to support
ab initio modeling at increasing fidelity, interactive and parallel data
analysis, training of surrogate models and AI/ML guided designs.

Many activities in accelerator modeling research and design both push the
envelope in High-Performance Computing (HPC) as well as High-Throughput
Computing (HTC). Typical HPC problems are spearheaded by plasma-based
accelerator modeling, where simulations are limited by the available
computational resources, whether in spatial grid resolutions, number of
macroparticles, number of time steps, even if using the most powerful
supercomputers available at the time of writing [233]. Emerging techniques
like machine-guided optimization of ensemble studies and AI/ML workflows are
often HTC workflows, where many parallel runs need to be coordinated.
Likewise, parallel data analysis tasks are often interactive HTC workflows
that furthermore can require interactivity and elasticity of the allocated
compute resources (e.g., Jupyter Notebooks). Over time as computational
resources available at leadership-scale computing facilities and individual
institutions grow, some prior HPC workflows become HTC workflows as
exploration phases evolve into design phases.

Some accelerator software have been or are being ported to GPUs and are being
ready to run efficiently on upcoming Exascale supercomputers [234, 235]. It is
expected that alongside GPUs, additional specialized compute hardware such as
Field Programmable Gate Arrays (FPGA), reduced instruction set (RISC)
multicore-CPUs, tensor-processing units (TPUs) and specialized neural engines
will be part of near-term computing architectures.

While the mentioned improvements on GPUs will increase the fidelity and
accuracy of the simulations, the bar of fidelity and accuracy to aim at is
being raised at the same time. The needs in computational hardware are
expected to increase in the foreseeable future, whether to simulate up to
every real particle, including in the halo, of beams that can be composite of
many bunches, to account with high fidelity of collective effects in complex
geometries or to simulate beams for very long times in conventional, plasma-
based or structure-based wakefield colliders. While there is an increasing
amount of efforts aimed at speeding up simulations with surrogate models, the
training of these models will rely on simulations, in addition to experimental
data. Producing the large volume of data from simulations will require
tremendous needs in computational power, memory and archiving capabilities.

###  6.2 Software performance, portability and scalability

contributed by Axel Huebl, David Sagan

Recommendation: Foster the development and maintenance of codes that run
efficiently on the latest hardware (e.g., add support for GPUs/FPGAs) by using
maintainable single-source, portable solutions, and that are scalable on
leadership-scale supercomputers with multiple levels of parallelization and
support for effective dynamic load balancing.

####  6.2.1 Performance

Performance increase for modeling software is generally desirable, even
outside of large-scale HPC runs, and improves overall scientific productivity
when studying particle accelerators at all scales. For instance, most
optimization and machine-learning workflows are GPU-accelerated as well to
increase computational throughput for studies, while ultraprecise numerical
schemes can often use GPU-accelerated linear algebra and FFT routines; thus
GPU acceleration also benefits small model sizes.

Developing software for multiple GPU-platforms in parallel to existing CPU
architectures is an undertaking that requires the redesign of many existing
algorithms and code-bases. Programming models and languages evolve rapidly and
the need to port algorithms to significantly more fine-grained parallelism is
a good incentive to rewrite and adopt modern software practices and popular
programming languages.

####  6.2.2 Portability

Portability of implementations is important as many scientists work with three
major platforms (Linux, macOS, Windows), although the former two (Unix-like)
variants are certainly dominating with HPC developers and machines. An
additional challenge arises with the diversity in GPU and other compute
hardware, which ideally should be addressed with performance-portable software
design. In such a design, an algorithm is ideally implemented only in a
single, abstract form and then specialized/optimized for the specific hardware
needs at compilation-time.

Performance portability relies on using and contributing to standard,
industry-supported programming languages to allow such a single-source
approach. Performance portability layers (e.g., Kokkos [236], Alpaka [237],
Raja [238]) are currently implemented predominantly as modern C++ libraries.
The Julia language natively supports coroutines, multi-threading, distributed
and GPU computing. Other languages lacking significantly in release time,
compiler variety and robustness. It is to be expected that performance
portability architecture will evolve into standardized programming language
components, such as ISO C++, in coming years. HEP modeling needs can provide
important input to their standardization by openly sharing critical community
use cases and codes and interacting directly with computer scientists for
development.

Common numerical and data management libraries (e.g., AMReX [239], CoPA [240])
build on such performance portability layers and only as the next steps,
domain-specific libraries and applications are implemented to benefit from all
aforementioned developments.

####  6.2.3 Parallel scalability

Parallel scalability on leadership-scale machines continues to be only
achievable with additional parallelization over multiple coupled compute nodes
(each powered with CPUs or GPUs). Methods that (a) split the computational
domain into local sub-problems, and (b) ideally overlap communications
(usually of data in guard cell regions) between collaborating nodes with
computation within each node, are essential for such capability simulation
runs. Furthermore, at large-scale, load balancing of particle-based methods as
well as refinement of fidelity needs (e.g., adaptive mesh-refinement) of the
simulation domain become important to make optimal use of available resources.

Looking at the rapidly evolving HPC landscape, many themes in advancing
accelerator and beam modeling software are common, e.g., Poisson solvers,
robust particle pushers, need to model hybrid particle accelerators combining
conventional and advanced accelerator elements, etc. It is thus evident that
collaborative efforts between conventional and advanced accelerator
development can benefit the community, relying for instance on similar or
compatible low-level parallelization layers, but also coordination when
implementing and sharing domain-specific numerics can ensure that scalable
solution can be readily extended for research needs.

###  6.3 Scalable I/O and in-situ analysis

contributed by Axel Huebl, Jean-Luc Vay

Recommendation: Support the development and maintenance of efficient and
scalable I/O, post-processing, in situ data analysis, and data sharing
solutions in particle accelerator codes. Coordinate on scientific data
documentation, standardization, development of interactive and reproducible
analysis workflows and foster data reuse.

While modern programming models, software design and advanced algorithms
ensure that simulations can execute efficiently, one further challenge emerges
to scientific productivity on HPC hardware: When comparing the computational
peak performance evolution to the parallel system storage bandwidth of HPC
machines as in Table 1, the gap between potential simulation fidelity that can
be computed and data that can be stored for analysis widens with every new
machine generation.

System Specs | Titan | Summit | Frontier
---|---|---|---
Peak Performance | 27 PFLOP | 200 PFLOP |  $>$1.5 EFLOP
Storage Bandwidth | 1 TB/s | 2.5 TB/s | 2-4x Summit
Ratio | 27:1 | 80:1 | 150-300:1
Table 1: Evolution of leadership-scale machines at the Oak Ridge Leadership
Computing Facility with respect to peak performance and storage bandwidth,
according to https://www.olcf.ornl.gov/frontier/.

Following this trend, modeling applications that run at a system’s capability
and follow the traditional workflow of simulation + post-processing will spend
more of their time in large-scale data input and output, which eventually can
dominate the time-to-solution. Driven by this trend, several steps can be
taken by simulation developers.

As a first step, adopting scalable, parallel I/O libraries with adequate data
layouts [241] can extent the applicability to truly make optimal use of
parallel filesystems [242]. Implementing these libraries in both data
producing as well as data consuming codes opens another possibility to
standardize on and share the community solutions, as demonstrated in the
openPMD project [99].

As a second step and long-term solution, data analysis and processing need to
be transitioned to in situ-processing, running online with the modeling
simulation and avoiding traditional, file-based long-term storage for raw
data. This approach essentially moves the design of data analysis to the setup
and design phase of a simulation that, similar to an experimental setup, needs
to plan the locations, acceptance and dynamic ranges of “virtual diagnostics”
before even starting a high-fidelity modeling run. Virtual diagnostics can
reduce data sizes and thus data throughput needs by orders of magnitudes,
e.g., by calculating beam momenta, phase space histograms, spectra and even 3D
videos as a simulation runs instead of storing realistically trillions of
particles in regular intervals to disk for later analysis. While in-situ data
processing and analysis are not new, and have even been mainstream in some
accelerator codes or frameworks (e.g., Warp [126], PIConGPU [243]), the
discrepancy between peak performance and storage bandwidth reported in Table 1
triggers the development of community libraries that enable a more systematic
description of new diagnostics in an in-situ approach, ensuring high
efficiency and scalability.

A challenge arises in the rapid setup of in situ processing pipelines, since
typical approaches of implementing a virtual detector in the simulation code
itself can be more complicated compared to scripted (serial) analysis
workflows on files. Innovative software design can potentially alleviate this
challenge, with approaches such as streaming data with close-to-file-like
analysis syntax [244] or embedding of interpreters into running simulations to
execute scripts on in-memory data. Continued research in this area and close
collaboration with computer science and engineering teams will be essential to
ensure that flexible, science-case specific analysis can be designed by
accelerator and beam physicists.

##  7 Sustainability, reliability, user support, training

contributed by Axel Huebl, Rémi Lehe, David Sagan, Christopher Mayes, Jean-Luc
Vay, Kiersten Ruisard, Steven Lund

Recommendation: Provide sufficient resources for code maintenance, automated
testing, benchmarking, documentation and code reviews. Convene a community
effort to identify topics and teaching teams to deliver academic classes
designed to foster sharing and cooperation, to be taught at the U.S. Particle
accelerator school.

An important aspect of the development of scientific modeling tools is to
ensure that the corresponding software is robust, easy to use and can be
extended for new science cases. This is made more difficult by the fact that
these tools are oftentimes constantly evolving, with new capabilities being
continuously added to meet ever changing computational needs. Here we mention
a few important practices [245] that facilitate this process.

Accelerator simulation is a large, complex topic, and much time and effort has
been spent in developing simulation software. Nevertheless, in the field of
accelerator physics, simulation code development has often been a haphazard
affair. Due to developers retiring or moving on to other projects, numerous
simulation programs have been completely abandoned or are seldom used.

As simulation programs become more complex due to the ever-increasing demands
placed upon machine performance, the situation will become worse if not
addressed. Such demands include the accelerator and beam physics Grand
Challenges that have been identified recently by the community [103, 91]

  * •

Increasing beam intensities by orders of magnitude.

  * •

Increasing the beam phase-space density by orders of magnitude, towards the
quantum degeneracy limit.

  * •

Complete and highly accurate start-to-end “virtual particle accelerators”
simulations.

  * •

Fast and accurate multi-objective optimization methods to speed up the design
process.

Accelerator and beam modeling software development should allow for extensive
testing of new functionality while preserving demonstrated capabilities on
previously validated scenarios[245]. Performance and interoperability must be
constantly improved to increase understanding (multi-physics problems) and
optimization (machine learning). One must also ensure a transfer of knowledge
over generations of scientists in form of formal education and easy
accessibility to the tools.

Addressing these Grand Challenges will require a community effort to
coordinate and modernize the current set of modeling tools, with capabilities
that extend far beyond what the current software can do, including
interdisciplinary simulations and advanced models for virtual prototyping of
complete accelerator systems.

###  7.1 Code robustness, validation & verification, benchmarking,
reproducibility

Recommendation: Establish and maintain open review, automated testing,
validation and benchmark procedures for modeling tools and ensure
reproducibility by tracking all changes in a documented and openly accessible
manner.

Figure 1: There are a number of aspects that make software sustainable.
Broadly, they can be grouped into the “intrinsic” characteristics of the
software itself and the “extrinsic” environment in which the software is
developed and used.

There are several aspects that must be addressed to enable the development of
the quality software that will be needed for the machines of tomorrow. One
facet can be put under the rubric of “software sustainability” which can be
defined as [246]:

> “the capacity of the software to endure. In other words, sustainability
> means that the software will continue to be available in the future, on new
> platforms, meeting new needs.”

There are many aspects to software sustainability, as illustrated in Fig 1.
Broadly, these aspects can be grouped into the “intrinsic” characteristics of
the software itself and the “extrinsic” environment in which the software is
developed and used. Software sustainability has been studied academically and
there is even a Software Sustainability Institute [247], which promotes “the
advancement of software in research by cultivating better, more sustainable,
research software to enable world-class research”.

As mentioned above, many software packages developed for simulating
accelerators, while showing excellent results for their specific application
and their era, are not “sustainable” in the long run. However, software
sustainability is extremely important given the limited resources that the
accelerator community has for code development in conjunction with the even
more limited resources for maintaining codes. To meet future needs, it is
imperative that there is a community wide effort to promote sustainable
practices.

Because modeling tools are being continuously improved and extended by
developers, there is always a risk that a given change to the source code may
introduce bugs and produce erroneous results in some specific cases. It is
therefore paramount that the developers track the changes to the source code
(with a version control tool such as git), and that they simultaneously
maintain a comprehensive suite of tests that the code should always
successfully pass. In the case of scientific modeling codes, these tests can
consist of a number of physical setups for which there are well-known
theoretical predictions. It can thus be checked that the results of the code
conform to these predictions. In order for these tests to be most effective,
they need to be run _automatically_ whenever the source code is modified – a
process known as _continuous integration_.

In addition to validating against theoretical predictions, it is also critical
to benchmark against experimental observations. The relevance of code
predictions to accelerator performance and output may be limited by a number
of factors, such as:

  * •

results from experiments that are not fully characterized (e.g., magnet
misalignments)

  * •

initial beam distribution is unknown or incompletely known (e.g., beam phase-
space projections from experiments may not allow full reconstruction of beam
6-D phase-space accurately)

  * •

diagnostics or simulations with insufficient range or resolution to fully
characterize relevant parameters (e.g., phase space diagnostics that are
sensitive to halo / beam loss levels [19])

  * •

missing or incompletely described physics in simulations

Proper benchmarking of codes against theory and experiments is time-consuming
and requires dedicated resources. In general, there are few resources
dedicated to code benchmarking at experimental facilities and in simulation
teams. As the complexity of codes and the computers that they run on increase,
it is essential to ensure enough resources for proper benchmarkings, including
dedicated beam time and test stands for well-characterized experimental
results [19].

In addition, the development of large-scale scientific tools nowadays involve
a whole community of developers and users rather than a single, isolated
developer. Therefore, the robustness and quality of the software is generally
greatly improved by the adoption of collaborative development platforms. These
online platforms allow the developers to easily and efficiently review each
other’s changes to the source code, before these changes are incorporated in
the mainline version of the code. They also provide a central venue for users
to raise issues and questions, and generally communicate their needs with the
developers.

Finally, another aspect of a code’s robustness is its interface with the user.
As the code evolves, the interface with the user often needs to be modified so
as to enable functionalities or generalize existing ones. It is not uncommon
that these changes break some of the users’ scientific workflows. Thus, it is
important for the developers to regularly publish releases of the source code,
where these changes are clearly documented. The different releases of a given
software can be made citable and available through an online archival service,
so that users can roll back to a previous release if needed and scrutinize
changes in a reproducible manner.

###  7.2 Usability, user support and maintenance

Recommendation: Consider maintenance of code reviews for improvements,
documentation, installation and testing to be central to the mission of usable
scientific software: establish open feedback and support channels, perform
regular releases with change logs, use permissive open source licensing
whenever possible and cover all scientific functionality with automated tests.

####  7.2.1 Usability

In order to maximize the impact of a given software tool on its scientific
community, it is also key that this tool be user-friendly. For example, a
common obstacle to the adoption of some scientific tools is their complex
installation procedure, especially if many dependencies are involved. The
developers can drastically simplify the installation procedure of a given
software tool by making it available through modern package managers [248,
249, 250]. These package managers can automatically download and compile the
source code as well as its set of dependencies. They can also ensure that
compatible versions of the dependencies are being used. Importantly, some of
these package managers can allow users to have the exact same installation
workflow on large-scale HPC resources as on their desktop workstation.

Another key aspect of the user experience is the code documentation. For
scientific modeling tools, the documentation usually includes sections on how
to install and use the code, as well as a description of algorithm being used
along with relevant references. Since, again, scientific tools are often
continuously evolving, it can be beneficial that the documentation be
generated automatically, whenever the source code is modified or whenever a
new release is published. Just as the modeling tools themselves, documentation
should be easily accessible for the whole community and easy to improve from
developers and users alike.

####  7.2.2 User support

In order for scientific codes to continuously improve and meet the needs of
the community, it is important to have a communication channel for users to
provide feedback [245]. This feedback may include potential bug reports,
questions on installation issues, and inquiries on typical usage. Again, many
tools exist, including issue trackers (e.g., GitHub issues [251]), chat rooms
(e.g., Gitter [252] or Slack [253]), mailing list, forums, stack-overflow,
etc. These different tools have different purposes and target different
segments of the user pool. The aim is thus certainly not for a developer to
embrace all of them simultaneously, but rather to select one or two channels
that are best suited for their particular code. These communication channels
should also be clearly identified in the documentation.

It can also be helpful for these communications channels to be openly
accessible and easily searchable, so as to avoid that multiple users report
the same issues. In this regard, some of the conversations in chat rooms may
sometimes have to be transferred to an issue tracker, or summarized in the
documentation.

Open user support channels establish significant synergies not only across
related accelerator modeling projects, but with the computational physics
community as a whole. For instance, documented computational and numerical
issues, testing approaches, chosen conventions and implemented automation
frameworks add significantly to the effectivity of the community, in terms of
development speed, issue triage, installation, solution/work-around
propagation, communication with high-performance computing centers and
adoption of best-practices, to name a few.

####  7.2.3 Maintenance

##### Version control and software releases -

It is now widely accepted, in the scientific community, that any significant
software development project should be managed with a version control system
(e.g., git [254]). However, a less common practice is that of regularly
publishing new releases of the code.

Code releases are important because scientific codes are constantly evolving
and improving, and, as part of this process, the code interface with the user
may change, bugs may be fixed, and new bugs may occasionally be introduced. It
is therefore not uncommon for a new version of the code to suddenly break a
workflow that a user previously relied on. Well-documented releases (e.g.,
with a CHANGELOG document) help the user understand how the code has evolved
with each release, and how to update their workflow to adapt to these changes.
Archiving each release (e.g., with tools such as Zenodo [255]) may also allow
the user to roll back to a previous version of the code, if a new version is
altogether incompatible with a prior workflow. Also here, readily available
services can speed up the generation of CHANGELOG documents and publication
with package managers through so-called automated deployments.

##### Access and licensing -

over the last decade, it emerged that scrutinizable implementations and low-
barrier contributions to accelerator modeling software are highly desirable
for scientific productivity. Consequently, a significant part of the community
considers open source development [256, 257, 258] and permissive open source
licensing [259, 260] the preferred way for software access, contribution,
teaching, collaboration and reuse [256, 245, 261, 262]. For a few modules
where such a model is not possible, e.g., due to export control constrains,
other community sharing methods such as limited access through a memorandum of
understanding (MoU) exist.

##### Automated testing -

In order to minimize the risk of new bugs, it is important to verify that the
code still works as expected, whenever the source code is modified. In the
case of scientific codes, this can be done for instance by comparing the
results of the code against known solutions, for a number of analytically-
tractable problems. This process has long been done by hand, but experience
shows that it is time-consuming and may in practice be often omitted by the
developers.

Instead, these tests can be done automatically and systematically, whenever
the source code is modified. Automated tests usually also results in faster
code development, since the different contributors to the code can be rapidly
assured that their changes do not break previous functionalities. A number of
tools that are free to open source software allow to easily setup those
automated tests, including GitHub Actions [263], Azure Pipelines [264] and
Travis-CI [265]. Automated test on exotic hardware or HPC platforms is
intricate, but addressed for instance by the E4S [266] effort within the
Exascale Computing Project.

###  7.3 Training and education

Recommendation: Convene a community effort to identify topics and teaching
teams to deliver academic classes designed to foster sharing and cooperation.
The classes should be taught in the US Particle Accelerator School with course
materials and linked tutorials/extensions regularly maintained and publicly
posted.

Training and education are key to the long term viability of positions put
forth in this white paper. University classes cover the core of essential
programming skills, numerical algorithms, AI/ML, and some software development
and maintenance tools. Traditionally workers in the field rely heavily on
online documentation and training materials as well as help from colleagues.
Much benefit is derived from the larger plasma and EM modeling communities.
Accelerator science and engineering also relies on specialized training
provided by the US Particle Accelerator School (USPAS). The USPAS convenes
two, intensive-format sessions per year to provide graduate-level training in
topics that are not practical to teach regularly at universities.
Recommendations for enhancing the USPAS are covered in a separate Education,
Outreach, and Diversity white paper [267]. Specific to accelerator modeling,
USPAS offerings have been primarily centered on code demonstrations and
applications in various accelerator dynamics, design, and applications
classes. Recent classes have covered optimization and ML, python/matlab
applications, and levels of self-consistent modeling in beams and plasmas. It
would benefit the community if more offerings were regularly available in the
USPAS. The USPAS classes are also an excellent opportunity to foster community
cooperation via team teaching efforts and to help ingrain productive