# Toward Native Artificial Intelligence in 6G Networks: System Design,
Architectures, and Paradigms

Jianjun Wu, Rongpeng Li, Xueli An, Chenghui Peng, Zhe Liu, Jon Crowcroft, and
Honggang Zhang

###### Abstract

The mobile communication system has transformed to be the fundamental
infrastructure to support digital demands from all industry sectors, and 6G is
envisioned to go far beyond the communication-only purpose. There is coming to
a consensus that 6G will treat Artificial Intelligence (AI) as the cornerstone
and has a potential capability to provide “intelligence inclusion”, which
implies to enable the access of AI services at anytime and anywhere by anyone.
Apparently, the intelligent inclusion vision produces far-reaching influence
on the corresponding network architecture design in 6G and deserves a clean-
slate rethink. In this article, we propose an end-to-end system architecture
design scope for 6G, and talk about the necessity to incorporate an
independent data plane and a novel intelligent plane with particular emphasis
on end-to-end AI workflow orchestration, management and operation. We also
highlight the advantages to provision converged connectivity and computing
services at the network function plane. Benefiting from these approaches, we
believe that 6G will turn to an “everything as a service” (XaaS) platform with
significantly enhanced business merits.

##  I Introduction

Mobile communication has stepped into a new and exciting era, where personal
devices such as smartphones and tablets are becoming the primary computing
platform for many applications. As these devices are used to facilitate our
daily lives (from professional to leisure and education to entertainment),
they simultaneously generate an unparalleled amount of personal and private
data. Meanwhile, the 3rd Generation Partnership Project (3GPP) Release 15, the
first full set of 5G specifications, was frozen in the middle of 2018, and the
first commercial 5G launch happened in 2019 in Korea, signaling that 5G has
been transformed from standardization to commercialization. Even though 5G
itself still needs several releases for gradual enhancement, it is the time to
begin to think, what will happen for beyond 5G.

From the perspective of mobile network evolution history as shown in Figure 1,
the provided services intrinsically determinate the native architecture, such
as a voice-centric network architecture in 2G, the incrementally functional
add-on methods to offer data services upon voice services in 3G, and a data-
native network architecture based on all-IP solutions emerged in 4G. 5G begins
a strong focus to support the digital transformation of vertical industries
and significantly improve the efficiency of the entire social-economic
activities. Therefore, 5G adds killer capabilities like enhanced mobile
broadband (eMBB), ultra reliable low latency (URLLC) and massive machine-type
communication (mMTC) and establishes a native service based architecture (SBA)
especially for the core networks (CN). Benefiting from the cloudification and
virtualization technologies, the SBA in 5G is capable to dramatically reduce
the standardization complexity especially on relevant network function,
interface and procedure definitions for newly introduced services. Such
features will be definitely carried on towards to the next generation.
Therefore, at this point in time, it would be natural and essential to think
and reflect, which new services will be provided by 6G and how to invoke the
required network architecture design innovation.

Figure 1: Mobile communication system evolution trend.

On the other hand, artificial intelligence (AI) has experienced promising
development in the past decades. The advanced progress in algorithms, platform
as well as chipset technology lets AI receive the sustainable momentum and
bring its impacts to many different industry sectors, which includes
telecommunication sector as well. 5G has initiated to provide a network design
suitable for AI services by introducing the Network Data Analytics Function
(NWDAF) [1] to the 5G CN to implement AI-based network automation and optimize
the related network functions (such as AI-based mobility management). Its base
is to collect and analyze data from other 5G network elements to train AI
models that can be used by network services. Meanwhile, similar mechanism like
collecting and analyzing data based on the existing SON/MDT (Self-Organizing
Networks and Minimization of Drive Tests) is adopted for 5G radio access
networks (RAN). Nevertheless, 5G retains the architecture scope of previous
generations, and only focuses on how to use AI to optimize the network itself.
What really matters is that the intelligent features can be utilized by the
end users, which however is out of the scope of 5G architecture design. In
this regard, the emergence of NWDAF is only the starting point to support AI.

Other than 3GPP, International Telecommunication Union (ITU) also initializes
work on how to integrate AI framework within the mobile communication system.
Their focus group has drafted several technical specifications for machine
learning for future networks, including interfaces, network architectures,
protocols, algorithms and data formats [2]. Academic research also provides
meaningful results to understand the relationship between mobile communication
technology and AI. For instance, AI technology could be used to optimize and
enhance network resource usage in order to achieve better performance. At the
radio link layer, radio resource scheduling or link adaptation can be better
implemented through radio channel prediction. Or at the network layer, AI is
used to solve the problem of self-driving network operation and management or
the twinning of future networks [3, 4]. On the other hand, it is also
envisioned that enhanced network capability that could provide better support
for AI services. AI would benefit from better connections with pre-processing
computing power [5].

6G has been on its journey since 2020. Many leading companies and industry
platforms have announced their vision on 6G. There is coming to a consensus
that 6G will treat AI as the cornerstone. Finnish 6G initiatives has published
a series of white papers [6] to lay out their vision on 6G technologies, in
which the authors also place their prediction on future trend, “the evolution
of telecom infrastructures towards 6G will consider highly distributed AI,
moving the intelligence from the central cloud to edge computing resources”.
In [7], the authors introduced a set of principles for the intelligent edge
for wireless communication with embedded machine learning capabilities.
However, if we simply take the edge computing as it is, being designed
orthogonal of the network architecture, it cannot provide native AI support
for the whole mobile communication system, which is devastatingly essential in
the near future.

This article aims to use a clean slate approach to define 6G end-to-end (E2E)
system architecture providing native support for intelligence inclusion, so as
to better leverage infrastructure resources, facilitate data governance,
system orchestration and management, as well as mobilize the enthusiasm of all
stakeholders. Upon such design, 6G networks will support secured and high
performance converged computing and communication, data governance framework,
and collaborative ecosystem. Finally, we also provide some initial case
studies for proof of concept.

Figure 2: 6G system with high level architectures for intelligence inclusion.

##  II 6G System Architecture Design Scope

“Intelligence inclusion”, which is completely different from the “connectivity
inclusion” in 5G and its precursors, is a high-level abstraction of our early
vision of 6G to provide native support for AI services. Intelligence inclusion
implies that 6G system should bring AI from the central cloud down to the
mobile communication system and everyone can have the same capability to be
able to access intelligent services anytime and anywhere. The merits of
intelligence inclusion are two-folded. Firstly, running AI at any possible
location in a distributed manner could further boost the learning efficiency
and resolve critical security concerns. Secondly, AI could also help 6G system
to realize enhanced network autonomous driving, which will further improve
system performance (e.g., throughput, latency, spectrum efficiency as well
energy efficiency) and user experience via online optimization. Hence, a true
Pervasive Intelligent mobile system, where communications and computing
resources are deeply converged and corresponding instruments (e.g.,
algorithms, neuronal networks, solvers, databases, and APIs) are effectively
integrated, will become an essential trait. However, such a vision does not
come at no cost. For example, real-time learning and inference on ubiquitous
connectivity and computing resources imposes stringent requirements (e.g.,
ultra-low latency and ultra-high data rates) on the mobile system and
necessitate a fundamental rethink on the system architecture, so as to fully
unleash the potential of the three major pillars (i.e., data, resource, and
algorithms). Accordingly, we foresee that the architecture changes should
incorporate at least the following methodologies:

  * •

Infrastructure: Shift from conventional connectivity-oriented service
provisioning to handling computing-intensive tasks like AI.

  * •

Data governance: Handle complex data collections from different technical and
business domains and provide data service which complies with security and
privacy regulation.

  * •

Operation Administration and Maintenance: Provide E2E orchestration and
management for AI workflows, which is seamlessly integrated with network
resource orchestration and management.

  * •

Third-party AI services: Easy and flexible deployment deep in the mobile
communication system.

Under this design methodology, we introduce the overall logical architecture
for 6G especially as illustrated in Figure 2. In essence, there are several
key features: (1) An independent data plane, (2) A novel intelligent plane,
(3) Converged communication and computing service provisioning at network
function plane, (4) XaaS (everything as a service) platform for a healthy and
robust mobile ecosystem. Generally speaking, these features from different
planes, which will be elaborated later, shall all consider the following two
aspects.

(1) Security: Since 6G becomes the digital foundation of the entire society,
it faces more serious security issues than before, especially when facing
threats from advanced technologies like quantum computing. Therefore,
traditional cryptography security based on computing complexity will become
less qualified. In addition, the introduction of new technologies like AI
inevitably bring more security risks and heavily require new mechanism to
combat increasingly intelligent attacks.

(2) Multi-party collaboration: The openness of the 6G ecosystem will attract
different business entities (e.g., communication operators and vendors, end
users, AI service providers) from both information and communication industry
(ICT) and other vertical industries. Therefore, the system design with
seamless multi-party support is a crucial feature.

##  III Network Function Plane

The network function plane of 6G system lays the very foundation to provide
converged communication and computing services across different technical
domains, including RAN, CN, and transport networks (TN). In particular, it is
expected to support a large-scale distributed system with intelligence and
sensing capability, so as to better reap gains from massive amounts of data
generated from mobile communication system itself. Therefore, the network
function plane should inherit the fundamental design principle like SBA and
cloudification. Meanwhile, it needs to add new features on top.

###  III-A Deep Converged Communication and Computing in RAN

6G RAN is envisioned to embrace heterogeneous resources organized in ad hoc
manner, which may cover terrestrial and non-terrestrial communication at the
same time. Base stations (BSs) could be fixed, or mobile (e.g. cars, drones,
or even satellites). Moreover, 6G RAN should be capable to support dynamic AI
service deployment with critical performance requirements.

Intelligence inclusive RAN is more than installing racks of servers at the
edge location and local break out of the traffic for edge processing. Instead,
it should provide deeply converged communication and computing capability.
Therefore, a 6G BS (denoted as xNB for consistency with 5G) can be further
divided into two parts: control base station (cNB) and service base station
(sNB). The cNB provides control function (e.g., including connectivity and
computing control) in a large area, while the sNB provides high-speed data
transmission and computing services in a smaller area, e.g., cell level. The
separation of the cNB and the sNB has the following advantages: (1) cNB can
provide more efficient resource coordination and heterogeneous resource
convergence control among sNBs and user equipment (UEs); (2) It can facilitate
the deployment, since cNB can provide good coverage with lower frequency,
while sNB can provide good throughput and energy-efficiency with higher
frequency; (3) it can reduce overhead for common control purpose.

Both cNB and sNB share some similarities with the 5G RAN like the control
plane (CP) and user plane (UP) functions. For example, the control functions
provided by the cNB include common and UE-specific computing resource control
and radio resource control (such as Master/System Information Block (MIB/SIB),
paging, and UE-specific radio resource control (RRC) signaling). Meanwhile, we
argue that it is worthwhile to introduce an independent computing plane (CmP),
which could be utilized to host certain services (e.g., AI or other third
party applications) and other extended CN functions. As shown in Figure 2, the
sNB is responsible to logically separate the CP, UP and CmP services.

When AI services are deployed at RAN level, they need to establish the
connection between terminals and these functions directly in order to provide
high-performance communication. This is essential especially for real-time AI
services. Therefore, new interfaces between CmP and CP, and between CmP and UP
shall be defined to support the dynamic service deployment, which will be
further explored in our future work.

###  III-B Task-oriented Connectivity

Conventional communications systems are connection-oriented, for which a
typical service could be establishing connection between two specific
terminals. Therefore, the communication source and destination are clearly
defined by end users and the services that they intend to use or the other
users that they plan to communicate with. In 6G, other than connectivity-
oriented services, it should provide AI-based services, for instance
predictive QoS for a car to perform full autonomous driving. In order to cater
such services, connections are explicitly or implicitly established between
many terminals and network equipment in a proactive or reactive manner and
computation resource shall be scheduled as well. Hence it requires to perform
coordination and communication among multi-terminals, multi-xNBs and multi-
computing resources in the form of Tasks. Typical scenarios of tasks could be
the provisioning of AI services to enhance the reliability for field level
communication in smart manufacturing scenario, or the adoption of AI services
at the xNBs in a specific region for better resource utilization. In order to
perform these tasks, task-oriented communication happens by executing the very
same actions (e.g., establishing connectivity, and computing resource
allocation) across numerous distributed nodes with proper coordination. It
poses new challenges to design the network function plane in 6G, and new
functionalities may emerge in order to perform task management and control.
For instance, as illustrated in Figure 2, task control plane (T-CP) and user
plane (T-UP) could be specifically designed in cNB and sNB, respectively.
Meanwhile, novel task protocol stack could be carried on 6G radio control
signaling (e.g., RRC), or radio data protocol (e.g., PDCP or SDAP) to transmit
task messages and implement task decomposition, distribution, activation, etc.
Task management entity might be designed outside of RAN, e.g., as a CN
function.

###  III-C User-centric Network Service Provisioning

In order to create a highly customized and secured network environment for
users, user-centric concept shall be introduced to design the system
architecture, so as to support users’ participation in network service
definition and operation, and provide users full control of data ownership. In
order to fulfill this design, the network architecture shall be divided as
user service node (USN) and network service node (NSN). For example, USN
contains customized services and network policies at end user level to meet
diversified service requirements in the 6G era. As a byproduct, it could
further support to establish the user profiling as the reflection of physical
entity.

##  IV Data Governance Framework with Independent Data Plane

Data is the key asset of the entire communication system in 6G. Since the
involved data types and magnitude in 6G change dramatically from AI operation
to management, from business to consumers, and from environment awareness to
terminals, it becomes incentive to provide a unified and efficient data
governance framework to efficiently collect, organize, desensitize, store and
access the data, thus providing better support for other third-party data
applications and satisfying data privacy protection requirements. Given the
complications to resolve three critical concerns addressed below, such a
framework can be more effectively implemented via an independent data plane as
shown in Figure 2.

###  IV-A Data Collection and Ownership

The 6G system will inherently generate a huge amount of diverse data from both
technical and business domains. An independent data plane in 6G could
contribute to organizing and managing data efficiently while also considering
privacy protection. (1) Infrastructure: all types of physical and virtual
resources in the mobile communication system evolve to potential data sources.
The data plane could help to accumulate the diverse data from the
heterogeneous infrastructure. (2) Operation and Business Supporting: This data
plane could conveniently store and analyze useful information for network
operation and management, including physical equipment status, system
operation information, service provisioning information, etc. On the other
hand, benefiting from all data related to the business logic (e.g., customer
relationship, partner relationship management) and more importantly customer
subscription related information (e.g., user personal data or enterprise level
data), the data plane could grant customers (no matter subscriber type or
enterprise type) the capabilities to have full control of their own data. (3)
Vertical Industries: Similarly, vertical industries could find room to store
their interested data related to use-case operation, admiration and
maintenance. Also, the data could be safely stored and securely accessed via
their own repositories. (4) Terminal: The data plane could add special space
for terminals to store computing and communication resource related data,
service usage profile, and sensing knowledge. Notably, data collection shall
comply with the regional or national data protection policies and regulations
of the data source in terms of usage rights and obligations, e.g., GDPR
(General Data Protection Regulations).

###  IV-B Data Processing

Depending on the regulation and data usage policy, data processing functions
could be executed on the data plane or it could be plugged in the other planes
(e.g., if raw data cannot be exported to data plane, it shall be pre-processed
in the data source). Nowadays, collecting and storing sensitive data is often
accompanied with privacy risks and responsibilities of protecting the privacy
embedded in the data. Therefore, it is essential to have data desensitization
modules as the key data processing services in the data plane. Meanwhile, data
policy enforcement modules in the data plane, which handle data according to
the regulatory as well as non-regulatory rules (e.g., geographic restriction),
will be executed by default to ensure the integrity and legitimate of data
processing. Data plane contains data processing model libraries to support
different data services. Moreover, it also exposes its capabilities to other
planes and perform access control for entities to access and utilize its data
services.

###  IV-C Data Storage and Provisioning

On data plane, (raw or processed) data could be stored flexibly in a
structured or unstructured format through centralized or fully distributed
method. Uniformed interfaces should be further defined to facilitate internal
customers of the mobile communication system, e.g., network service plane, and
intelligent plane. Moreover, it could also be easily extended to provide data
to external customers, e.g., vertical industry players, and enterprises.

##  V Intelligent Plane

The objective of the intelligent plane is to build comprehensive AI platform
capabilities in the mobile communication system. Network AI Management and
Orchestration (NAMO), which is responsible for orchestrating, managing, and
scheduling E2E network AI-related services and resources, is the essential
design for intelligent plane. Basically, NAMO should answer the following
questions: (1) How to leverage the 6G system capability and provision real-
time and high reliable AI services? (2) How to orchestrate and manage
heterogeneous and distributed resources? (3) How to define a universal and
efficient mechanism to provide diversified AI services, such as perception,
data mining, prediction, reasoning? (4) How to orchestrate seamless together
with other network services? To answer the above raised questions, NAMO
defines the following key processes.

###  V-A AI Service Orchestration

AI service orchestration focuses on the parsing and orchestration of network
AI services. An AI service is mapped to a logical AI workflow, which refers to
a set of (independent) processing modules. Depending on specific AI services,
logical AI workflows could consist of several modules that utilize different
AI models, such as support-vector machine (SVM), recurrent neural network
(RNN), long short-term memory (LSTM), and convolutional neural network (CNN).

The logical AI workflow may obtain data from the data plane, and the entry
module may further perform data processing in sequence. This processing may be
serial processing or based on directed acyclic graph. In addition, logical AI
workflow shall take QoS requirements of the related services into
consideration. Logical AI workflows are mapped to physical resources during
service deployment. Each processing module defined in the logic AI workflow
needs to be assigned with specific parameters or hyperparameters, which are
stored as models in the AI hub. If basic data services are involved, e.g.,
data collection and pre-processing, relevant functional modules shall be used
from the data plane.

It is worthwhile to note here that many deep learning technologies are
extremely inefficient (e.g., in terms of energy use). There are many works
towards optimizing neural networks by a certain extent of compressing (e.g.,
audio and image processing in smart phones). It is interesting and essential
to understand the capability constraints and the feasibility of AI
technologies before performing AI service orchestration.

###  V-B Infrastructure Orchestration

AI workflows need to be mapped to specific resources for execution, including
relevant components (e.g., a graphical processing unit, and a network
connection). This is implemented by the infrastructure orchestrator upon
heterogeneous and distributed resources at large scale.

###  V-C AI Service and Infrastructure Management

As the names imply, the AI service manager focuses on the status maintenance
and management of AI services, by issuing administration policies to add,
modify, and delete logical and physical AI workflows. Similarly, the
infrastructure manager is responsible for managing distributed communication
and computing resources. The foregoing NAMO function belongs to a logical
function, and is specifically deployed and mapped to physical entities in
different infrastructure layers, including xNBs, UEs, etc.

###  V-D Standardization or Open Source

NAMO should be a native multi-domain solution, where domains could be
different regional networks of a mobile operator or networks from different
mobile operators. Moreover, in order to enable easy deployment and attract
external service providers, NAMO should be capable to coordinate resources
through standardized interfaces and protocol. Put differently, AI services
should be easily deployed in 6G (at the edge or centrally) and the intelligent
plane should allow convenient service operation (e.g., deployment, update,
migration, and termination). It is essential to understand which technical
components fall into the scope of standardization (e.g., 3GPP), and which
could rely on open source approach. For instance, typical AI workflow
orchestration framework like Kubeflow and modelarts could be leveraged to
accelerate the design of AI workflows. Continuous integration/continuous
development (CI/CD) approach shall be adopted, especially to bring seamless
service development and provisioning.

##  VI XaaS Platform

Comprehensive and collaborative ecosystem, where a significant amount of AI
applications will be easily deployed, surely emerges as the key feature for 6G
era. Apart from AI-enabled network functions such as AI-empowered channel
prediction and AI-empowered mobility management, 6G could benefit third-party
AI applications from commercial partners and consumers like autonomous driving
and smart manufacturing, which require significant space and time flexibility
in resource usage and share many similar capability components. Owing to the
introduced data plane and intelligent plane, the development, deployment, and
management efficiency of these AI applications are greatly optimized. As a
result, 6G turns to a XaaS platform providing communication and computing
infrastructure services at the infrastructure as a service (IaaS) layer, basic
component services at the platform as a service (PaaS) layer, and AI
application services as a service (SaaS) layer. Such a 6G XaaS platform also
lays a solid foundation for business model innovation and reflects the
benefits of intelligent inclusion.

##  VII Concept Illustration via Use Cases

In this part, we first provide an overview of recent research progress on
multi-agent intelligent systems, and highlight the potential contributions of
networks to AI. Afterwards, as a special case, we experiment in an internet of
vehicles scenario and demonstrate the positive impact of intelligence
inclusive communications on AI.

###  VII-A Role of Networks in Multi-Agent Intelligent Systems

TABLE I: A list of typical multi-agent learning algorithms. Algorithm |  Summary | Key Features
---|---|---
Type | Environment | Execution | Training
IRL |  Independent reinforcement learning. | Value-based | No | Decentralized | Decentralized
DGN (ICLR 2020) |  Graph convolutional reinforcement learning. | Policy gradient | Cooperative | Centralized | Centralized
RIAL (NeurIPS 2016) |  A recurrent network for parameter sharing to train independent learning agents and address partial observability. | Value-based | Cooperative | Decentralized | Centralized
DIAL (NeurIPS 2016) |  Centralized gradient sharing; Variant of RIAL. | Policy gradient | Cooperative | Centralized | Centralized
MADDPG (AAMAS 2018) |  Each agent is capable to access (or at least model) the exact parameters of other agents. | Policy gradient | Mixed | Decentralized | Decentralized
VDN (AAMAS 2018) |  Training individual agents with a value-decomposition network architecture. | Policy gradient | Mixed | Decentralized | Centralized
QMIX (ICML 2018) |  Decompose the joint-action value functions into per-agent monotonic ones. | Value-based | Mixed | Decentralized | Centralized
COMA (AAAI 2018) |  Use a centralized critic and a counter-factual advantage function based on solving the multiagent credit assignment. | Policy gradient | Mixed | Decentralized | Centralized
QTRAN (PMLR 2019) |  Transforming the joint action-value function into an easily factorizable one. | Value-based | Mixed | Decentralized | Centralized
SIRL (TNNLS 2021) |  Apply stigmergy and federated learning to enhance the communications among agents. | Policy Gradient | Cooperative | Hybrid | Hybrid

Basically, in large-scale multi-agent intelligent systems, the complex
relationship among agents usually causes great difficulty for policy learning.
In many multi-agent systems, the interactions between agents often take place
locally, which means that agents neither need to coordinate with all other
agents nor need to coordinate with others all the time. Traditional methods
attempt to use pre-defined rules to capture the interaction relationship
between agents. However, these methods cannot be directly used in a large-
scale environment due to the difficulty of transforming the complex
interactions between agents into operation rules. Table I provides a list of
some typical multi-agent machine learning algorithms. It can be observed that
these state-of-the-art multi-agent learning algorithms share some
similarities, i.e., one of the most important part is that these algorithms
require a centralized or decentralized training or execution mechanism and
have to interact among agents by networks. In this regard, we argue the
following networking ingredients are essential and will lately show that the
networking ingredients could provide superior performance than totally
independent multi-agent learning.

  * •

We can model the relationship between agents by a complete graph and leverage
graph neural networks (GNNs) to further utilize the embedded relationship.
Given the wide existence of topology in cellular networks, GNNs could be
naturally enhanced in the intelligence plane with the explicit knowledge from
the data plane.

  * •

Federated Learning enables mobile terminals to collaboratively learn a shared
prediction model while keeping all the training data on device, decoupling the
gradient update and the original data. Such a federated learning framework,
which could significantly enhance the privacy, cannot neglect the effect of
networks.

  * •

Stigmergy aims to complete complex tasks by a small amount of indirect
information exchange like the pheromone left by ants in their walking paths.
Similarly, digital pheromone is often leveraged in the stigmergy to act as the
intermediate information. Accordingly, local information update among
partially networked agents becomes necessary, so as to update the digital
pheromone and reduce the behavioral localities [8].

###  VII-B Results of Network-Assisted Multi-Agent Learning

Figure 3: The mixed-autonomy traffic control simulation scenario.

Next, we manifest the importance of networking in multi-agent systems. Due to
the space limitation, we primarily consider the positive impact of network-
assisted multi-agent learning via a mixed-autonomy traffic control scenario
[9] as depicted in Figure 3. As a representative showcase, there are totally
14 vehicles running circularly along a one-way lane that resembles a shape
“eight (i.e., 8)” and an intersection is located at the lane. Besides, each
vehicle must adjust its acceleration to pass through this intersection in
order to increase the average speed, but slamming on the brakes will be forced
on vehicles that are about to crash, further terminating the current epoch,
which is $150$ second. Furthermore in this article, the scenario is slightly
modified by assigning the related local state of the entire environment to
each vehicle, including the position and speed of its own, and the vehicle
ahead and behind. Each vehicle collects its local state per $0.1$ second, and
optimizes its acceleration accordingly by periodically computing the gradient
from a $256$-minibatch.

In order to testify the performance of multi-agent learning, these 14 vehicles
can be categorized into two classes, namely, 7 cars underlying simulation of
urban mobility (SUMO) and 7 independent reinforcement learning (IRL) or
federated IRL (FIRL)-empowered cars, where FIRL implies the existence of
network assistance and IRL means not. Besides, considering that SUMO is an
open source, human being-level, highly portable and widely used traffic
simulation package [9], we treat 14 SUMO cars as the baseline. Figure 4
clearly verifies the advantage of FIRL over IRL and the gradual approaching of
FIRL towards the baseline, and demonstrates the importance of network
assistance.

Figure 4: The performance comparison of multi-agent learning with and without
network-assistance.

Figure 4 also depicts three typical cloud-based AI (instead of inclusive AI)
scenarios. Notably, the “FIRL-D” method simulates a direct latency increase by
synchronously delaying the gradient uploading and the local neural network
updating for all cars by 4 epochs and 2 epochs respectively. Furthermore, the
“FIRL-D-OR” method checks the performance when the out-of-order among the
neural network update packets occurs due to the multi-path and the fact that
the latest neural network updated packet is possibly overridden by a
previously delayed one. Meanwhile, “FIRL-D-LM” examines the case where the
network quality is rather low and the uploading periodicity has to enlarge
from $25.6$ second to $150$ second by locally merging 6 consecutive
minibatchs. It can be observed that, synchronously increasing the network
latency has trivial impact on the performance. However, the other cases leads
to apparent performance degradation, which could better manifest the
advantages to have the inclusive AI.

##  VIII Conclusion and Future Works

6G network architecture is envisioned to have inherent design that could
provision inclusive intelligence for all types of end users. In order to
realize this vision, this article provides an in-depth analysis from an E2E
design perspective. For instance, how to achieve converged communication and
computing capability at the deep edge via reconstructing the RAN, which is
done by introducing computing capability in RAN that could be controlled and
managed the same as connectivity services. Moreover, an independent data plane
has been introduced to provide comprehensive data governance scheme, meanwhile
an intelligent plane is established for E2E AI service orchestration and
management. All these novel technical features could support flexible business
models from XaaS platforms. To demonstrate the design scope described above,
some initial case studies have been done via simulations, which indicates
obvious advancement in some specific scenarios.

However, there are still a lot of research themes that need to be further
explored. For example, whether this kind of architecture can adapt to all
kinds of AI models, algorithms, etc. There could be new interfaces and
protocols that need to be defined due to new introduced functionalities. In
addition, it is also essential to consider how to build the right ecosystem
that include all key players. Therefore, the architecture that inherently
supports AI needs to be further improved in terms of technology and business
ecosystem to truly enable the 6G intelligent inclusion vision.

## References

  * [1] “3GPP TS 23.502. Technical specification group service and system aspects; system architecture for the 5G system (5GS),” v16.7.0.
  * [2] “ITU Focus group on machine learning for future networks including 5G,” https://www.itu.int/en/ITU-T/focusgroups/ml5g/.
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SNSN-323-63

Top-antitop charge asymmetry measurements in the lepton+jets channel with the
ATLAS detector

Matej Melo, on behalf of the ATLAS Collaboration †† © 2019 CERN for the
benefit of the ATLAS Collaboration.
Reproduction of this article or parts of it is allowed as specified in the CC-
BY-4.0 license.

Faculty of Mathematics, Physics and Informatics
Comenius University in Bratislava, Mlynská dolina 84248 Bratislava, Slovakia

> We report a measurement of the charge asymmetry in top quark pair production
> with the ATLAS experiment at the LHC using 20.3 fb-1 of $pp$ collision data
> at $\sqrt{s}=8$ TeV. The data are unfolded using a fully Bayesian unfolding
> method. Differential measurements of the charge asymmetry are performed.

> PRESENTED AT
>
>
>
>
> $11^{\mathrm{th}}$ International Workshop on Top Quark Physics
> Bad Neuenahr, Germany, September 16–21, 2018

##  1 Introduction

Charge asymmetry $A_{\mathrm{C}}$ in top-antitop quark pair ($t\overline{t}$)
production is defined as:

$A_{\mathrm{C}}^{t\overline{t}}=\frac{N(\Delta|y|>0)-N(\Delta|y|<0)}{N(\Delta|y|>0)+N(\Delta|y|<0)},$

where $\Delta|y|=|y_{t}|-|y_{\overline{t}}|$ and $y_{t}$ ($y_{\overline{t}}$)
is the rapidity of the top (antitop) quark.

Figure 1: Box (left) and Born (right) diagrams [1].

In the Standard Model (SM), non-zero asymmetry is predicted due to
interference of higher order quark-antiquark annihilation diagrams. Main
contribution to the $A_{\mathrm{C}}$ comes from the Box and Born diagram
interference [1], shown in Figure 1. Many theories beyond the Standard Model
(BSM) predict an enhancement of the asymmetry, especially in the region of
high $t\overline{t}$ invariant mass. Two measurements were performed by the
ATLAS experiment [2] at the LHC using 20.3 fb-1 of $pp$ collision data at
$\sqrt{s}=8$ TeV in the lepton+jets channel: in the so-called resolved
topology [3] and using events with highly boosted top or antitop quarks [4].

##  2 Event Selection and Reconstruction

Single lepton trigger requirements are applied in the lepton+jets decay
channel and exactly one good lepton (electron or muon) with
$p_{\mathrm{T}}>25$ GeV is required in both topologies. To suppress background
contribution various criteria on missing transverse energy
$E_{\mathrm{T}}^{\mathrm{miss}}$ are applied, depending on the multiplicity of
$b$-tagged jets. In resolved topology, at least four jets with
$p_{\mathrm{T}}>25$ GeV are required. Kinematic Likelihood Fitter [5] is then
used to reconstruct $t\overline{t}$ kinematics and events are separated into
six signal regions based on the lepton charge ($+1,-1$) and $b$-tag
multiplicity (0, 1, $\geq 2$), obtained by using a working point of the
$b$-tagging algorithm corresponding to an efficiency of 70% for identifying
$b$-jets. In the boosted topology, at least one jet with $p_{\mathrm{T}}>25$
GeV close to the charged lepton ($\Delta R<1.5$) is required. The boosted
topology requires also at least one large radius jet ($R=1.0$) with
$p_{\mathrm{T}}>300$ GeV, top-quark tagged by using jet substructure variables
and well separated from the lepton with
$\Delta\phi(\ell,\mathrm{jet}_{R=1.0})>2.3$. Either the jet close to the
lepton or the jet matched to the large jet within $\Delta R<1.5$ must be
$b$-tagged using the 70% efficient working point.

##  3 Unfolding

Fully Bayesian Unfolding (FBU) [6] is used in both measurements to unfold the
reconstructed distributions to the parton level. In the case of the boosted
topology, the measurement is performed in a fiducial phase space
($m_{t\overline{t}}>0.75$ TeV and $-2<\Delta|y|<2$) due to small acceptance
outside this region. For all systematic uncertainties, except those related to
Monte Carlo generator modelling and the unfolding procedure itself, nuisance
parameters are assigned. FBU enables to marginalize and to contrain systematic
uncertainties. In the resolved topology 0-$b$ tag region is used for in situ
calibration of the $W$+jets background, Figure 2.

Figure 2: Comparison between prediction and data for the 18 bins used in the
inclusive $A_{\mathrm{C}}$ measurement in the resolved topology after applying
the simultaneous unfolding procedure and $W$+jets in situ calibration [3].

##  4 Results

The inclusive asymmetry measured in the resolved topology is
$A_{\mathrm{C}}=0.009\pm 0.005$ (stat. + syst.), compatible with the Standard
Model prediction $A_{\mathrm{C}}^{\mathrm{SM}}=0.0111\pm 0.0004$ [7]. The
fiducial asymmetry ($m_{t\overline{t}}>0.75$ TeV and $-2<\Delta|y|<2$)
measured in the boosted topology is $A_{\mathrm{C}}=0.042\pm 0.032$,
compatible with $A_{\mathrm{C}}^{\mathrm{SM}}=0.0160\pm 0.0004$ [1]. Results
of the $A_{\mathrm{C}}$ measurements in the resolved topology as a function of
mass, $\beta_{z}$ and $p_{\mathrm{T}}$ of the $t\overline{t}$ system are shown
in Figure 3, as well as the mass-dependent measurement in the boosted
topology. Inclusive and differential measurements as a function of the
$t\overline{t}$ mass are mostly limited by statistical uncertainties;
measurements as a function of the top pair $\beta_{z}$ and $p_{\mathrm{T}}$
are mostly limited by modelling uncertainties. No significant deviations from
the SM predictions are observed.

Figure 3: Measured $A_{\mathrm{C}}$ values in the resolved topology as a
function of bin-averaged $t\overline{t}$ mass (top left), $\beta_{z}$ (top
right), $p_{\mathrm{T}}$ (bottom left) and fiducial and mass-dependent
measurement in the boosted topology (bottom right). Measured values are
compared with the SM predictions and in the case of the upper two plots also
with BSM predictions [3, 4].

###  4.1 Impact on BSM Scenarios

The ATLAS 8 TeV $A_{\mathrm{C}}$ measurements in the lepton+jets channel allow
for the exclusion of a large region in the parameter space of various BSM
models, as demonstrated in Figure 4. The cloud of points in Figure 4
corresponds to a number of models described in Refs. [8, 9]: a $W^{\prime}$
boson, a heavy axigluon $G_{\mu}$, a scalar isodoublet $\phi$, a colour-
triplet scalar $\omega^{4}$ and a colour-sextet scalar $\Omega^{4}$. Each
point corresponds to a choice of the new particle’s mass in the range between
100 GeV and 10 TeV, as well as a choice of the couplings to SM particles which
are required to be compatible with the Tevatron cross-section measurements.

Figure 4: Measured $A_{\mathrm{C}}$ inclusive (left) and in the high mass
region of $m_{t\overline{t}}>1.3$ TeV (right) versus the Tevatron forward-
backward asymmetry $A_{\mathrm{FB}}$ results, compared with the SM predictions
as well as predictions incorporating various potential BSM contributions [8,
9]. The uncertainty bands correspond to 68% confidence level interval [3, 4].

##  5 Summary

Measurements of the $t\overline{t}$ charge asymmetry $A_{\mathrm{C}}$ by the
ATLAS experiment at the LHC using 20.3 fb-1 of $pp$ collision data in the
lepton+jets topology are consistent with the SM predictions and disfavour a
large phase-space of parameters describing several BSM scenarios.

## References

  * [1] J. H. Kuhn and G. Rodrigo, JHEP 1201 (2012) 063.
  * [2] ATLAS Collaboration, JINST 3 (2008) S08003.
  * [3] ATLAS Collaboration, Eur. Phys. J. C 76 (2016) 87.
  * [4] ATLAS Collaboration, Phys. Lett. B 756 (2016) 52.
  * [5] J. Erdmann et al., Nucl. Instrum. Meth. A 748 (2014) 18-25.
  * [6] G. Choudalakis, arXiv:1201.4612 (2012).
  * [7] W. Bernreuther and Z. G. Si, Phys. Rev. D 86 (2012) 034026.
  * [8] J. A.-Saavedra and M. P.-Victoria, Phys. Rev. D 84 (2011) 296-363.
  * [9] J. A.-Saavedra and M. P.-Victoria, JHEP 09 (2011) 097.


[1]The University of Texas at Austin, Department of Physics, Austin, Texas
78712-1081, USA. [2]The Helmholtz-Zentrum Dresden-Rossendorf, Institute for
Radiation Physics, 01328 Dresden, Germany<EMAIL_ADDRESS>
# Nonlinear Inverse Compton Scattering from a Laser Wakefield Accelerator and
Plasma Mirror

A. Hannasch  M. LaBerge  R. Zgadzaj  J. P. Couperus Cabadağ  A. Laso Garcia
T. Kurz  T. Cowan  U. Schramm  A. Irman  M.C. Downercor1

###### Abstract

We generate inverse Compton scattered X-rays in both linear and nonlinear
regimes with a 250 MeV laser wakefield electron accelerator and plasma mirror
by retro-reflecting the unused drive laser light to scatter from the
accelerated electrons. We characterize the X-rays using a CsI(Tl) voxelated
scintillator that measures their total energy and divergence as a function of
plasma mirror distance from the accelerator exit. At each plasma mirror
position, these X-ray properties are correlated with the measured fluence and
inferred intensity of the laser pulse after driving the accelerator to
determine the laser strength parameter $a_{0}$. The results show that ICS
X-rays are generated at $a_{0}$ ranging from $0.3\pm 0.1$ to $1.65\pm 0.25$,
and exceed the strength of co-propagating bremsstrahlung and betatron X-rays
at least ten-fold throughout this range of $a_{0}$.

##  1 INTRODUCTION

The discovery and development of X-ray sources has spurred progress over the
last 100 years in material science Jaeschke  _et al._ (2016), geology Ketcham
and Carlson (2001), industry Hanke, Fuchs, and Uhlmann (2008), diagnostic
medicine Lewis (1997); Suortti and Thomlinson (2003), high-Z radiography Chen,
Bennett, and Perticone (2007) and probing warm dense matter (WDM) Falk  _et
al._ (2014). Many such X-ray sources require meter- to kilometer-scale radio
frequency (RF) accelerators to generate synchrotron or bremsstrahlung
radiation. Laser plasma accelerators (LPAs) Tajima and Dawson (1979); Esarey,
Schroeder, and Leemans (2009) offer a compact alternative, capable of
accelerating electrons up to MeV energies over millimeters or GeV energies
over centimeters Wang  _et al._ (2013); Gonsalves  _et al._ (2019) with narrow
bandwidth (1-15%) and 100s of pC of charge Couperus  _et al._ (2017);
Götzfried  _et al._ (2020). When the accelerated electrons scatter from a
counter-propagating laser pulse, they transfer energy to the photons via
inverse Compton scattering (ICS) Corde  _et al._ (2013). The laser strength
parameter $a_{0}\approx
0.85\lambda[\mu\mbox{m}]\sqrt{I[10^{18}\,\mbox{W/cm}^{2}]}$ plays a
significant role in X-ray generation via ICS and defines the scattering
regime. For $a_{0}\ll 1$, the emitted radiation is narrowband and peaks at
$\approx 4\gamma_{e}^{2}\hbar\omega_{L}$ where $\gamma_{e}$ is the electron
Lorentz factor and $\hbar\omega_{L}$ is the energy of the scattering laser
photons. As $a_{0}$ approaches 1 the scattering becomes relativistic as the
laser imparts significant momentum to the electrons, resulting in high flux
and broadband X-rays Corde  _et al._ (2013); Krämer  _et al._ (2018);
Khrennikov  _et al._ (2015). Such tabletop LPA-based ICS sources, or “all-
optical undulators”, can generate hard X-ray pulses comparable in peak
brilliance to those from large-scale synchrotrons Corde  _et al._ (2013).

There are two methods for generating ICS X-ray beams from a compact LPA. The
first method uses two separate laser pulses; the first drives the accelerator
while the second, split from the drive pulse before acceleration, scatters
nearly head-on with the accelerated electron bunch. The secondary pulse can
reach $a_{0}>4$ when focused tightly with low f/# optics to the collision
point Yan  _et al._ (2017); Cole  _et al._ (2018); Sarri  _et al._ (2014), but
is difficult to align and borrows energy from the LPA drive pulse. The second
method for generating ICS uses a single laser pulse that first drives the LPA
and then reflects from a plasma mirror (PM) to scatter from the trailing
relativistic electrons Ta Phuoc  _et al._ (2012); Tsai  _et al._ (2015).
Because the LPA drive pulse leads the electrons by no more than tens of
microns the reflected pulse is automatically overlapped with the electrons.
This ”self-aligning” feature makes ICS highly reproducible, ideal for use as
an electron beam diagnostic Krämer  _et al._ (2018) or an experimental probe
without requiring an additional laser pulse or reducing the drive laser
energy. It is therefore the method of choice for smaller LPA laboratories with
limited available laser power and funds. However, the properties of ICS X-rays
generated in this way have not been systematically characterized. In
particular, the ability of this method to reach the important relativistic ICS
regime ($a_{0}>1$) has not previously been demonstrated.

Figure 1:  LPA X-ray characterization overview. (a) Schematic set up showing
(left to right) incident laser pulse, gas jet, tilted plasma mirror (PM)
positioned at $0<z<0.5$ cm from gas jet exit for generating ICS X-rays,
converter at $z\approx 30$ cm for generating bremsstrahlung, 1 T magnetic
electron spectrometer, and 3 cm thick CsI(Tl) profiling scintillator outside
of vacuum. (b) Representative single-shot electron spectrum. Left: raw data
from luminescent Lanex screen. Right: electron energy distribution averaged
over emission angle. (c) i.-iii. ICS profiles for a 25-$\mu$m-thick Kapton PM
at varying positions after the accelerator and iv.-v. bremsstrahlung profiles
generated with 25-µm-thick Kapton (iv) or 100-µm-thick Lanex (v) placed 30 cm
after the accelerator. Multiplicative factors indicate what each profile
signal is multiplied by in order to directly compare with the ICS profiles.

Here, we characterize an ICS X-ray source based on a 250 MeV laser wakefield
electron accelerator and a plasma mirror in both linear and nonlinear
scattering regimes. The laser fluence is measured after driving the LPA and
the radiative properties of the ICS source are characterized with a compact
scintillating detector. We demonstrate that the scattering regime can be
easily tuned by changing the placement of the PM relative to the gas jet.

###  1.1 PROCEDURE

Experiments were performed on the DRACO Ti:Sa chirped pulse amplification
laser system at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) Irman  _et al._
(2018) which can deliver up to $\sim$ 4 J, 30 fs pulses with a spot size of 20
$\mu$m (FWHM) to a 3 mm long He gas jet with 1 % Nitrogen doping [see Fig.
1(a)]. The accelerator operates in a self-truncated ionization injection
regime Couperus  _et al._ (2017); Mirzaie  _et al._ (2015) and the typical
parameters for the experiments presented here are 2 J on target and electron
density of $4\times 10^{18}$ $\mathrm{cm^{-3}}$. A magnetic spectrometer
placed 30 cm downstream from the gas jet sweeps accelerated electrons off-axis
vertically and measures their spectrum and horizontal divergence Schramm  _et
al._ (2017); Kurz  _et al._ (2018) [see Fig. 1(b)]. The profile and fluence of
the laser pulse were characterized by picking off the drive laser after the
magnet with no PM in place and imaging the profile to a camera outside the
target chamber under acceleration conditions with and without gas. The total
laser energy on target was calibrated with a power meter and the beam size was
calibrated by imaging a 20 $\mu$m tungsten wire placed at the exit of the gas
jet. The laser fluence is characterized at selected positions downstream of
the accelerator by integrating the camera signal within a calibrated radius of
4 $\mu$m at the maximum. This area is chosen to best match the interaction
area of the electrons with the reflected laser. The ICS profile and total
radiated energy are diagnosed at an electron density of $4\times
10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$ by a $7\times 7\times 3$ cm
CsI(Tl) profiling scintillator placed on-axis 2 m after the gas jet and
outside of vacuum. Scintillating crystal detectors are well-suited for
detecting X-rays between 0.1 and several MeV photon energy because of their
high Z, high photon output and relatively flat spectral response in this
range. They measure changes in total radiated energy accurately. To determine
the range of $a_{0}$ over which we can generate ICS photons with a PM, we
varied the position of the PM between $z=-0.2$ mm (inside the accelerator) and
$z=4$ mm downstream and imaged the total scintillator signal with a CCD
camera. Figure 1(c) shows the ICS profile from a 25 $\mu$m Kapton PM placed 0
(i.), 2 (ii.), and 4 (iii.) mm after the accelerator. The profiles generated
by a target placed at the entrance of the magnet (z = 30 cm) are dominated by
bremsstrahlung and are multiplied by the factor shown to compare to the ICS
shots on the same scale. Bremsstrahlung from a 25 $\mu$m Kapton film (iv.) is
$\sim 10\times$ less bright than the ICS signal, while bremsstrahlung from a
100 $\mu$m Lanex screen (GdS:Tb, v.) is $>5\times$ brighter. Betatron
radiation can also deposit energy in the scintillator, however no observed
signal is recorded by the scintillating camera when the LPA is on but no
material is placed in the accelerated electron beam path.

##  2 RESULTS

###  2.1 Laser fluence

Figure 2 shows the (a) vacuum focus laser profile with a FWHM beam size of 20
$\mu$m, the laser profile after propagating through 3 mm of He at a density
$n_{e}=4\times 10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$ at (b) $z=0$, (c)
$z=1$ mm ,and (d) $z=2$ mm downstream of the gas jet exit. Before
acceleration, the laser has a FWHM pulse duration of 30 fs, peak intensity of
$2\times 10^{19}\leavevmode\nobreak\ \mbox{W/cm}^{2}$ and $a_{0}\approx 3$.
During acceleration, the laser loses energy to the plasma and the spatial
profile modulates, however, the pulse duration is expected to decrease as the
front edge of the laser etches back Decker  _et al._ (1996); Zhu, Palastro,
and Antonsen (2012). Simulations predict that under the acceleration
conditions presented here the laser pulse can decrease to as low as $\sim
10-15$ fs. Figure 2(e) shows the calculated laser intensity based on the
measured fluence for a pulse duration of 20 fs and density of $n_{e}=2\times
10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$ (black circles) and $4\times
10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$ (red squares). The error bars
represent the statistical error from the standard deviation over $\sim 10$
shots and the shaded regions give the range from the lower bound intensity
which assumes a pulse duration of 30 fs, and an upper bound intensity that
assumes a pulse duration of 15 fs. The calculated intensity after acceleration
(data points) is fit to $(z^{2}+z_{r}^{2})^{-1}$ which assumes a local
Gaussian propagation of Rayleigh length $z_{r}$ once the laser leaves the gas
jet. These fits are shown by the dotted lines for both densities.

Figure 2:  The imaged laser focus in vacuum is presented in (a) and is 20
$\mu$m FWHM and $2\times 10^{19}\leavevmode\nobreak\ \mbox{W/cm}^{2}$. Panels
(b)-(d) show characteristic examples of the imaged laser profile after
acceleration for a density $n_{e}=4\times 10^{18}\leavevmode\nobreak\
\mathrm{cm^{-3}}$ at (b) $z=0$, (c) $z=1$ and (d) $z=2$ mm after the gas jet
exit. (e) The laser intensity is inferred from the measured fluence at
multiple locations after the accelerator exit for pulse duration of 20 fs and
a density of $n_{e}=2\times 10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$
(black circles) and $n_{e}=4\times 10^{18}\leavevmode\nobreak\
\mathrm{cm^{-3}}$ (black circles).

###  2.2 Total Radiated Energy

Figure 3 shows the background subtracted total integrated scintillator signal
averaged over $\sim 5$ shots (red circles) for each position of the PM
relative to the exit of the gas jet at $n_{e}=4\times
10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$. The data is scaled to the
maximum value and the black dashed line provides the normalized scintillator
signal when the PM was moved 30 cm downstream, indicating a baseline for the
bremsstrahlung signal generated through the 25 $\mu$m-thick Kapton film. The
weakest signal generated via ICS with the PM at z = 4 mm has $\sim 6\times$
more energy than this baseline, indicating that the measurements are dominated
by the ICS contribution. Furthermore we observe a $\sim 13\times$ increase in
the signal when the PM is placed within the jet exit versus 4 mm downstream
offering a simple but robust tunability of the scattering regime.

Figure 3: Total integrated scintillator signal for each position of the plasma
mirror averaged over $\sim$5 shots for a density $n_{e}=4\times
10^{18}\leavevmode\nobreak\ \mathrm{cm^{-3}}$. The bremsstrahlung baseline is
determined by the total integrated scintillator signal when the PM is placed
at z = 30 cm where the laser is not intense enough to generate ICS radiation.

###  2.3 Divergence

Figure 4(a) shows the HWHM divergence of the electrons for different plasma
mirror positions (green triangles) averaged over $\sim$5 shots. The dashed
line represents the average HWHM divergence of electrons without the PM in
place of $1.9\pm 0.3$ mrad. The shaded bar shows the standard deviation of the
unperturbed electrons to indicate the shot to shot fluctuations during the
experiment. We observe an increase of $\sim 2\times$ in the electron
divergence when the PM is close to the jet ($<$ 1 mm) resulting from strong
magnetic fields within the plasma mirror at relativistic laser intensities Raj
_et al._ (2020); Schumaker  _et al._ (2013).

Figure 4: Divergence of the (a) electrons in the horizontal plane of the
electron spectrometer as a function of plasma mirror position after the
accelerator exit at $n_{e}=4\times 10^{18}\leavevmode\nobreak\
\mathrm{cm^{-3}}$. The dotted black line represents the unperturbed average
electron divergence with no plasma mirror in place and the shaded region
corresponds to the standard deviation. (b) The divergence of the ICS profiles
for the corresponding shots in the vertical dimension (blue squares) and
horizontal dimension (red circles). The dotted line represents the average
divergence for PM placed $z>1.5$ mm which most closely corresponds to a linear
scattering regime.

The perturbation from the electrons passing through the PM bulk occurs _after_
the reflected laser scatters from the accelerated electrons, thus we can
assume that the electron divergence remains constant at $\sim 1.9\pm 0.3$ mrad
during the ICS interaction.

Figure 4(b) shows the HWHM divergence of the ICS X-rays as a function of
plasma mirror position where we observe divergence growth in the X-rays as the
PM is moved $\leq 1$ mm. The linear ICS divergence can be found by averaging
the divergence of the X-ray beam when the PM is placed at $z\geq 1.5$ mm
downstream. The result is $3.4\pm 0.6$ mrad HWHM, indicated by the dashed line
and shaded region in figure 4(b). The ICS divergence is up to $\sim 60\%$
larger than this baseline when the PM is place $<0.5$ mm after the gas jet
and, assuming the electron divergence remains constant, this X-ray divergence
growth is caused by nonlinear ICS scattering effects. Expectations of the ICS
divergence dependence on electron divergence will be discussed in more detail
in the Discussion.

##  3 DISCUSSION

Understanding the strength of the laser during the scattering process is
important for predicting the scattering regime and diagnosing the emitted
radiation. For applications that require a narrowband source of X-rays, the
laser strength parameter $a_{0}$ must remain small ($a_{0}\ll 1$) so that the
interaction with the accelerated electrons is linear. If a higher flux source
is needed and a narrowband source is not, then a nonlinear interaction is
required ($a_{0}\geq 1$). Estimates can be made based on the measured laser
fluence prior to PM reflection and the resulting relative integrated signal
observed with the profiling scintillator. The expected energy radiated from a
single relativistic electron is proportional to $\gamma_{e}^{2}$, and when
integrated over the total electron spectrum
$E_{tot}\propto\int{\gamma^{2}\frac{dN_{e}}{d\gamma_{e}}d\gamma_{e}=N_{b}\left<\gamma_{e}^{2}\right>}$.
Inverse Compton scattered radiation is additionally proportional to
$a_{0}^{2}\propto I_{L}$ Esarey, Ride, and Sprangle (1993) such that
$E_{tot}\propto N_{b}\left<\gamma_{e}^{2}\right>a_{0}^{2}$. The integrated
scintillator signal, which is roughly proportional to the total radiated
energy of the ICS source, can be normalized to the electron bunch parameter
$N_{e}\left<\gamma_{e}^{2}\right>$ which reduces the shot-to-shot variation
observed in Fig. 3 and isolates the effect $a_{0}$ has on the resulting ICS
radiation.

Figure 5: (a) Combined plot of the calculated scattering laser intensity after
reflecting from the PM and the resulting total ICS signal as measured from the
CsI(Tl) scintillator. The corresponding laser intensity for the linear ICS
data (black squares, PM @ $z>0.5$ mm) was converted to $a_{0}$ and fit to a
quadratic model in (b) and to provide a method for interpolating the
scattering intensity for the nonlinear ICS data (blue triangles, PM @ $z<0.5$
mm).

Figure 5(a) shows the _normalized_ ICS integrated scintillator signal (data
points) on the left axis and the calculated laser intensity (red dashed curve)
on the right axis. The laser intensity is calculated from the measured
fluence, assuming a 20 fs pulse duration and an 85% reflectivity efficiency of
the PM Tsai  _et al._ (2017). The shaded region represents a $\pm 25\%$
combined uncertainty in the pulse duration and reflectivity of the PM and the
two sets of data are linearly fit to find the corresponding scattering
intensity at each PM position. However, this procedure only allows for an
estimate of the ICS scattering intensity for PM positions $z>0.5$ mm, referred
to as ”Linear ICS data” in Fig. 5(a) (black squares). For PM positions $z<0.5$
mm, the ICS intensity deviates from the laser intensity curve, suggesting that
the real scattering intensity and $a_{0}$ is larger than that estimated by the
laser intensity curve alone. This observation may indicate a nonlinear
response of the PM to the incident laser intensity. Simulations and
experiments have shown that a laser pulse with $a_{0}\approx 1$ induces a
curvature at the PM surface and focuses the laser pulse with a focal length as
small as 25 $\mu$m, resulting in a larger intensity of the reflected pulse
compared to the incident pulse Tsai  _et al._ (2017).

To estimate the value of $a_{0}$ at PM positions near the gas jet exit (Fig.
5(a) ”Nonlinear ICS data”, blue triangles), the linear ICS data can be plotted
as a function of $a_{0}$ and a quadratic fit can be performed, including the
normalized bremsstrahlung baseline as the y-intercept. The resulting quadratic
function that relates the normalized integrated scintillator signal and the
corresponding values of $a_{0}$ from Fig. 5(a) enables extrapolation of the
nonlinear ICS $a_{0}$ values. Figure 5(b) illustrates this procedure where the
”Nonlinear ICS data” for PM positions $z<0.5$ mm (Fig. 5(b) blue triangles) is
extrapolated based on the quadratic fit of the ”Linear ICS data” to $a_{0}$
(Fig. 5(b) red dashed curve). This extrapolation indicates that the intensity
of the scattering laser can reach up to $a_{0}=1.4\pm 0.2$. The possible PM
focusing effect suggests that the PM method for generating ICS radiation is
not wholly limited by the intensity of the laser after driving the
acceleration process, and is capable of generating radiation in both the
linear ($a_{0}\ll 1$) and nonlinear ($a_{0}\geq 1$) ICS regime.

The observed divergence growth when the PM is placed $z<0.5$ further supports
the conclusion that we observe both linear and nonlinear ICS from an LPA and
PM. ICS from a single electron has a HWHM divergence $\theta_{x}\approx
1/\gamma_{e}$ for $a_{0}\ll 1$ and increases to $\theta_{x}\approx
a_{0}/\gamma_{e}$ when $a_{0}>1$ Corde  _et al._ (2013). When scattering from
an electron bunch with HWHM divergence $\theta_{e}$, the resulting ICS
divergence can be approximated as
$\theta_{ICS}=\sqrt{\theta_{e}^{2}+\theta_{x}^{2}}$. Assuming the scattering
electron divergence remains constant for each PM position, the expected linear
ICS divergence based on this equation is $2.9\pm 0.8$ and agrees with the
measured linear ICS divergence to within uncertainty. The observed divergence
growth of the ICS when the PM is placed $z<0.5$ mm is a result of nonlinear
ICS when the value of $a_{0}$ approaches and exceeds 1. This nonlinear
divergence growth has been observed in ICS experiments using a separate
colliding pulse instead of a PM Yan  _et al._ (2017). Finally, the unperturbed
electron divergence and the linear ICS divergence can be used to estimate an
upper bound value of $a_{0}$ for the nonlinear ICS data of $1.9\pm 0.2$.

##  4 CONCLUSION

We have presented scintillator based measurements of the nonlinear
characteristics of ICS radiation from a 250 MeV LPA and plasma mirror. The
total radiated energy of the linear ICS beam is $\sim 6\times$ larger than the
bremsstrahlung generated from the 25 $\mu$m Kapton plasma mirror when placed 4
mm after the accelerator exit. Moreover, we observe $\sim 13\times$ more
energy radiated when the PM is placed 200 $\mu$m within the gas jet compared
to 4 mm downstream indicating a $\sim 3.6$ increase in the scattering
parameter $a_{0}$. Measurements of the laser fluence and inferred intensity
show that the laser remains relativistic with $a_{0}$ of $1.2\pm 0.2$ after
driving the LPA and reduces to $a_{0}\sim 0.3\pm 0.1$ after propagating 4 mm
from the gas jet. By assuming a PM reflectivity of 0.85 and pulse duration of
20 fs we are able to fit the integrated scintillator signal from the linear
ICS to the corresponding laser intensity, providing a method for extrapolating
the value of $a_{0}$ when the PM is placed $<0.5$ mm. We find that the
scattering laser intensity could reach as high as $a_{0}$ of $1.4-1.9$ when
the PM is placed within the exit of the gas jet. This increase is also more
than would be suggested by the measured fluence of the laser pulse and may be
caused by an induced curvature of the PM by the intense laser pulse resulting
in a focused and higher reflected intensity at the point of interaction with
the electrons. These measurements are supported by the increase in the ICS
divergence from the linear to nonlinear ICS scattering regime. To the best of
our knowledge this is the first observation of both linear and nonlinear ICS
from a laser plasma accelerator and plasma mirror.

##  5 ACKNOWLEDGMENTS

U. Texas authors acknowledge support from U. S. Department of Energy grant DE-
SC0011617, A.H. from the National Science Foundation Graduate Research
Fellowship grant No. DGE-1610403 and M. C. D. from the Alexander von Humboldt
Foundation. HZDR authors acknowledge support from the Helmholtz Association
under program Matter and Technology, topic Accelerator R & D.

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