# Spinodal decomposition stabilizes plastic flow in a nanocrystalline Cu-Ti
alloy

J. M. Rosalie  University of Leoben, Leoben, Austria.  O.Renk  Erich Schmid
Institute, Austrian Academy of Sciences, Leoben, Austria.  R. Pippan
University of Leoben, Leoben, Austria.  Erich Schmid Institute, Austrian
Academy of Sciences, Leoben, Austria.

###### Abstract

A combination of high strength and reasonable ductility has been achieved in a
copper-1.7 at.%titanium alloy deformed by high-pressure torsion. Grain
refinement and a spinodal microstructure provided a hardness of $254\pm 2$
$H_{V}$, yield strength of 800 MPa and elongation of 10%. The spinodal
structure persisted during isothermal ageing, further increasing the yield
strength to 890 MPa while retaining an elongation of 7%. This work
demonstrates the potential for spinodal microstructures to overcome the
difficulties in retaining ductility in ultra-fine grained or nanocrystalline
alloys, especially upon post-deformation heating where strain softening
normally results in brittle behavior.

##### Keywords

Titanium-bronze, Severe plastic deformation, Precipitation strengthening,
High-pressure torsion.

##  1 Introduction

Ultra-fine grained (UFG) and nanocrystalline (NC) alloys can develop extremely
high strength due to the confined slip length for dislocations [1, 2, 3, 4].
However, the reduction of the grain volume also prevents storage of, and
interaction between dislocations, resulting in poor work hardening. As a
consequence plastic deformation becomes unstable even at small strains [5, 6,
7] resulting in poor ductility [8, 9, 5, 6]. This can be exacerbated if UFG
and NC materials are relaxed either thermally [10, 11, 12] or mechanically
[13, 14, 15]. While the reduction of defect densities within the grains and at
grain boundaries cause further strengthening, subsequent deformation and the
generation of defects cause strain softening and early localization within
shear bands and the behavior at the sample scale is brittle.

Huge efforts have been made to retain ductility in nanomaterials by
stabilizing plastic flow. Aside from the well-known example of nanotwinned
metals [16], other attempts to retain work-hardening focused on the
introduction of intragranular precipitates. Studies on materials with grain
sizes in the hundreds of nanometers have demonstrated intragranular
precipitation can improve ductility [17, 18, 19, 20].

However, for grain sizes smaller than 100 nm, intragranular precipitation is
barely achievable due to grain boundary segregation of solute, either
dynamically during severe plastic deformation or by diffusion during
subsequent heat treatment [21, 22, 23]. The escape of solute can be
accompanied by the formation of intergranular precipitates (i.e. heterogenous
nucleation of the phases). While stable grain boundary precipitates could
limit grain coarsening, their effect on the work-hardening rate and ductility
is limited. In addition, they may even deteriorate the performance as
intergranular cracks can form or grow more readily. Consequently, a different
strategy is required for the finest grain sizes.

Recent studies on systems forming Guinier-Preston zones (GPZ) [24] and
spinodal microstructures [25, 26, 27, 28] offer promise of a solution to this
problem. As these decomposition processes occur homogenously and are weakly
affected by the presence of defects such as grain boundaries, such features
might be retained for the finest grain sizes and so permit better control of
the work hardening behavior and ductility of NC metals. Unfortunately detailed
studies focusing in this direction are rare, especially when considering the
sub-100 nm grain size regime.

A Cu-Ti alloy was used herein to assess the effect of heat treatments on the
microstructure and mechanical properties of a spinodal NC alloy. Cu-Ti alloys
have been extensively studied [29, 30, datta1976structure, 31, 32] due to
their strong age-hardening response. Peak strengths of up to 1400 MPa for
extensively cold-worked and aged 5.4 wt.,% Ti (7.1ȧt.%) and 760 MPa for
similarly treated 1.5 wt.% Ti (2.9 at.%) alloy can be reached due to a fine
dispersion of Cu4Ti plates, which gradually develops via spinodal
decomposition [33, 34, 35]. However, although the limited solubility of Ti in
Cu should permit the generation of an extremely fine grained microstructure
upon high pressure torsion (HPT), there are to date few detailed studies of
microstructure and mechanical properties in aged NC Cu-Ti. Hence, the Cu-Ti
system offers a model system to study decomposition processes at the NC grain
scale and their impact on mechanical properties.

##  2 Experimental details

Chemically homogeneous button ingots of composition Cu-1.7 at.%Ti (1.3 wt.%)
were produced by repeatedly arc-melting Cu (Goodfellow, 99.95%) and commercial
purity Ti. These ingots were cold rolled to a thickness of $\sim$1.2 mm,
corresponding to a strain of about $\epsilon\sim 1.7$. Disks of 8 mm diameter
were cut from the rolled sheet using electric discharge machining (EDM). The
discs were encapsulated in Ar-filled tubes, solution treated (973 K, 24 h) and
water quenched. The solution-treated (ST) discs were stored in a freezer at
approximately $-10^{\circ}$C to prevent any natural ageing process and served
as the basis for all subsequent investigations.

The disks were deformed at ambient temperature in a quasi-constrained HPT
device [36] at 0.2 rotations per minute under a nominal pressure of 7.8 GPa.
Radial hardness profiles (Vickers microindentation, 0.3 or 0.5 Kg loads)
showed that 10 rotations were sufficient to reach homogeneity throughout the
disk, except for the very center part. The deformed disks were subjected to a
series of isothermal (up to five days) and isochronal (30 min) annealing
treatments up to 823 K. Undeformed and conventionally deformed (compressed to
$\sim 50\%$ thickness reduction) disks were heat-treated in a similar manner
to provide a comparison.

Changes of mechanical properties were tracked using microhardness measurements
and microtensile test on selected samples. Microtensile specimens were cut by
EDM from the HPT disks, with the gauge section being located at a radius of
$\sim 2$ mm, having a gauge length of 2.5 mm and a cross section of $\sim
0.5\times 0.5$ mm2. The tensile specimens were tested using a miniaturized
testing device (Kammrath & Weiß, Germany) at a cross head speed of 2.5 $\mu$m
s-1, corresponding to a nominal strain rate of $10^{-3}\,s^{-1}$. Strain was
measured locally on the sample surface using optical images taken at a
frequency of 2.5 Hz. Virtual strain gauges were then applied to the images
using digital image correlation software (GOM Correlate). A connection between
the testing rig and the camera allowed for accurate synchronization of the
force signal with the elongation data from the images. Reduction in area of
the respective samples and the fracture surfaces were analyzed using a Zeiss
Leo 1525 field emission gun SEM.

The microstructural evolution of the NC Cu-Ti samples was examined in the
axial direction using a JEOL 2100 F Cs corrected transmission electron
microscope (TEM), operating at 200 kV. Foils were produced by dimple grinding
and polished to perforation using a Gatan 691 precision ion polisher, equipped
with liquid nitrogen cooling. Grain sizes were determined by applying the line
intercept method to multiple bright-field STEM images. A minimum of 100
intercepts was used in all cases and the uncertainty estimated from the
standard error for the number of intercepts.

##  3 Results

###  3.1 Ageing response

The effect of high-pressure torsion on the ageing response was examined by
comparing these samples to conventional materials with micron-scale grain
sizes. The solution-treated alloy had a hardness of 95 $H_{V}$ (see Table 1),
which increased to 152$\pm$6 $H_{V}$ after compressive deformation. In
contrast, HPT deformed samples reached a saturated hardness111(i.e. the
hardness effectively became independent of the radial position) of 254$\pm$2
$H_{V}$, after 10 revolutions.

Isochronal ageing curves, presented in Figure 1(a), show a strong ageing
response in the STQ condition, which reached 1.68$\pm$20 $H_{V}$ ($\Delta
H_{V}$=73) for annealing at 773 K. Compressive deformation increased the peak
hardness to 233$\pm$17 $H_{V}$ at a reduced temperature of 723 K, but the
ageing response was similar ($\Delta H_{V}$=81) meaning the deformation caused
little net increase in extent of precipitation hardening. A similar ageing-
induced increase in hardness was seen in the HPT-deformed samples, but the
higher as-deformed hardness resulted in a peak hardness of 303$\pm$0.01
$H_{V}$ at 648K̇. Temperatures higher than the optimum condition resulted in a
dramatic softening, with the hardness of the HPT material approached the level
of the ST and compressed specimens at 800 K.

Isothermal ageing tests showed significant differences between ageing at 473 K
and 648 K. (see Figure 1(b)) Typical age-hardnening behaviour was observed at
648 K with the hardness gradually declining to 2.3 GPa after 8000 s. In
contrast, ageing at 473 K resulted in a steady hardness plateau at 2.75 GPa
extending to at least 4$\times 10^{5}$ s.

(a)

(b)

Figure 1: Hardness evolution of differently processed Cu-1.7 at.%Ti samples during a) isochronal ageing for 30 minutes b) isothermal ageing of the HPT deformed samples at temperatures of 473 K and 648 K. Lines are include solely as a guide for the eye. Table 1: Comparison of hardness changes in each deformation condition. STQ: solution treated and quenched, STQC: STQ + compression, HPT: High-pressure torsion.  | Hardness ($H_{V}$) | Peak Temp.
---|---|---
State | Base | Peak | $\Delta H_{V}$ | K
STQ | 90 | 168 | 78 | 723
STQ-C | 153 | 233 | 80 | 673
HPT | 254 | 334 | 80 | 648

###  3.2 Microstructure

TEM characterization was performed to relate changes of hardness to the
microstructural evolution, focusing especially on the response of the HPT
deformed samples.

####  3.2.1 Solution treated and quenched

The ST material consisted of coarse ($\sim$50 $\mu$m) grains (Fig. 2(a)). This
bright-field image shows two adjacent grains and the boundary separating them.
The right-hand grain is in a two-beam condition, and dislocations and strain
contrast can be noted. High-resolution transmission electron micrographs
(HRTEM) (Fig. 2(b)) revealed the typical “tweed” contrast characteristic of
spinodal decomposition, resulting from local fluctuations in composition and
lattice parameter [37, 35, 30]. This is also evident in satellite spots in
Fast Fourier transforms (FFTs) (inset)222A Hann filter was used prior to
applying the FFT, to remove high-frequency artefacts..

####  3.2.2 HPT-deformed and aged

The spinodal structure is also present after HPT deformation (Fig. 2(d)) and
even after subsequent ageing (Fig 2(f)). However it appears to be broken up
into several differently-oriented 5–10 nm domains, which became more regular
and well-defined after ageing. The modulated structure extends to the grain
boundary, and grain boundary precipitation was seldom observed, compare Fig.
3.

There was no indication of grain coarsening in the peak-aged condition, with
the average grain size of $83\pm 4$ nm effectively unchanged from the $82\pm
5$ nm measured for the as-deformed material. The grain boundaries in the peak-
aged sample appear much sharper, indicative of defect relaxation. It should be
noted, that the grain sizes measured in axial direction, can be considered
only as an upper bound, while the minimum grain spacings (i.e. as seen in
radial direction) will be significantly smaller.

ST

(a)

(b)

HPT

(c)

(d)

HPT+PA

(e) HPT+PA

(f) HPT+PA

Figure 2: TEM images of the (a,b) ST, (c,d) HPT deformed and (e,f) peak-aged
microstructures.

(a)

(b)

Figure 3: Modulated structure in Cu-Ti alloy HPT deformed and aged 30 minutes
at 573 K. (a) Diffraction contrast and (b) high-resolution TEM images show the
modulated structure extending to the grain boundaries, as indicated by the
arrows.

###  3.3 Tensile tests

Microtensile tests on the as-HPT deformed and peak aged samples showed the
high strength typical of severely deformed metals and alloys. Representative
engineering and true stress-strain curves of the tensile tests are shown in
Fig. 4(a) and 4(b), respectively. A tensile strength of $\sim$800 MPa was
obtained for the deformed material, increasing to 890 MPa at peak age. Despite
this, both materials remained ductile, with an elongations to failure of 9 %
and 6 %, respectively. Work hardening rate curves (inset in Fig 4(b)) also
indicate appreciable hardening to true strains $>$0.02, being slightly
increased in case of the peak aged samples. The higher work hardening rate in
case of the peak aged samples is further evident when considering the true
fracture stress of the samples, compare Table 2. In case of the PA samples the
average true fracture stress is about 1300 MPa, significantly higher than the
one calculated for the as-HPT deformed specimens. But apart from the higher
absolute values, also the relative hardening capacity (i.e. the stress
increment form the yield stress to the true fracture stress) is clearly
enhanced for the PA samples.

(a) Engineering

(b) True

Figure 4: (a) Engineering and (b) true stress-strain curves for the as-deformed (AD) and peak-aged (PA) conditions (see Table 2). The inset in (b) shows the work hardening rate.  Table 2: Mechanical properties of the HPT deformed and additionally aged Cu-1.7 at.%Ti samples in tension. State | YS | UTS | Elong. | Area. redn. | true frac. stress
---|---|---|---|---|---
| (MPa.) | (%) | (MPa)
HPT | 700 | 810$\pm$40 | 9$\pm$1 | 43.1 $\pm$7.5 | 1035 $\pm$53
HPT-PA | 800 | 890$\pm$60 | 6$\pm$1 | 48.5$\pm$4.7 | 1309 $\pm$157

####  3.3.1 Post-fracture examination

SEM examination of the fracture surfaces of the tensile sample provided
additional evidence of substantial ductility at a micrometer scale (Figure 5).
The low magnifcation images (above) show a notable area reduction (see Table
2), with extensive microdimpling visible at higher magnification. These
microductile features are commonly observed in UFG or NC metals. However, the
dimple size observed here is significantly larger than the grain size, while
for UFG or NC materials the dimple size is typically only a few times the
grain size [38, 39]. The significantly larger dimple size observed here, is
further indicative of a pronounced intragranular dislocation activity. Roughly
spheroidal pores may indicate pull out of undissolved Ti particles.

Despite the fracture surface of the peak-aged sample being flatter and more
uniform than that of the as-deformed material, the images show no evidence of
intragranular fracture.

Figure 5: SEM images of the fracture surfaces of the (a) as-deformed and (b)
peak-aged Cu-Ti tensile samples.

##  4 Discussion

This work has demonstrated that NC Cu-Ti alloys have retain moderate
ductility, even when subjected to isothermal ageing. Moreover, the NC alloy
displayed exceptionally high strength for a low Ti content. The hardness of
334 $H_{V}$ for the PA condition compares favourably with literature reports
of Cu with a grain size of 30–40 nm [9], with a much higher elcongation of 7%.
Although grain sizes being by a factor of two larger were measured in axial
direction, the minimum grain spacing in radial direction may reasonably
compare to these values. The Cu-Ti alloy also show good thermal stability, as
shown in Fig 1(b). The factors underlying this promising combination of
properties are discussed in the following section, by comparing the
microstructure and mechanical properties with the coarse-grained material.

###  4.1 Coarse-grained Cu-Ti

The solution treated material was comprised of a modulated structure formed by
spinodal decomposition of the alloy during quenching (Fig. 2(d)), as
consistent with previous report on this system [30], albeit at lower solute
contents. This microstructure already offered significant strengthening, as
shown by a hardness of 0.90 GPa, compared to approximately 0.50–0.55 GPa for
well-annealed Cu of similar grain size [3].

The ageing response of the ST and ST-and-compressed samples can be attributed
to decomposition and precipitation processes, as expected for this alloy [37,
40, 41, 42]. During the early stages of ageing this is expected to take place
via an increase in the amplitude of the composition fluctuations, followed by
the precipitation of Cu4Ti precipitates.

In conventional, coarse-grained CuTi alloys the loss of mechanical properties
on overageing is attributed to the discontinuous precipitation of
intermetallic phases on the grain boundaries. The redistribution of solute to
these phases results in the loss of the intragrannular strengthening
structures (spinodal modulations and/or fine Cu4Ti precipitates).

###  4.2 Nanocrystalline Cu-Ti

HPT deformation resulted in extensive grain refinement, and a hardness of 2.54
GPa. This was almost twice the value of HPT deformed pure copper [43] and a
five-fold increase on well-annealed pure Cu [3]. HPT deformation further
accelerated the ageing kinetics, reducing the isochronal peak-ageing
temperature to 648 K, compared to 723 K for ST and 673 K for compressed
material. This is consistent with detailed studies on the age hardening
characteristics of Cu-Ti alloys, indicating a shift of the peak ageing
temperature to lower values with increasing pre-deformation [32, 35].

It was surprising that a similar modular structure was present after HPT
deformation to equivalent strain of $\sim 136$ (at a disk radius $r=3\,$mm)
(Fig. 2(f)), and it will be made clear in this section that this influences
the mechanical properties in a similar way as for the coarse-grained material.
In fact, the Cu-Ti system showed no evidence of a perfect single phase
supersaturated solid solution after HPT, in contrast with numerous other alloy
systems, including many which are immiscible under normal conditions [44, 45,
46, 47]. This could be either related to an enhanced diffusion during HPT or
fast relaxation at room temperature handling enabled by the large defect
densities present. While the first scenario seems plausible based on reports
claiming superfast diffusion (e.g. [48], where the self-diffusion of Cu
increased by $10^{19}$ [49, Refs 4,14 in]), a fast natural ageing (i.e.
decomposition) allowing the material to rapidly relax to the metastable
modulated structure seems more plausible. If decomposition would occur already
during processing, the modulated structure should appear kinked or deformed at
least in certain grains. Moreover, fast natural ageing was already reported
for this kind of alloys within reasonably short time frames, e.g. Refs. [27,
26]. Although difficult to prove unambiguously, a supersaturated solid
solution may thus be present directly after HPT deformation.

A fast relaxation might further explain why, in contrast to the starting
microstructure the typical “tweed” contrast of the decomposed structure is
composed of multiple nanoscale “domains” as can be seen in the HR-TEM
micrographs (Fig 2(f)). Spinodal decomposition in this system involves
composition fluctuations in the (soft) $\langle 100\rangle$ directions [30]
hence three variants are possible. Such nanodomain formation would be
consistent with the rapid relaxation of the structure at very short length
scales.

Relaxation of intra- and intergranular defects during annealing of UFG and NC
metals (“hardening by annealing”) can be a significant contributor to strength
[10, 12, 50, 14, 15]. For nanomaterials, relaxation of grain boundaries and
intragranular dislocation densities, potentially accompanied by solute
segregation, is known to enhance the flow stress of the material as
dislocation sources need to be activated to ensure plastic flow [51, 10]. This
phenomenon is reported even in modulated systems such as Al-Zn [52] and
manifests as a hardness plateau even after prolonged annealing times as long
as grain growth is absent [15, 50, 53]. However, although some relaxation of
the grain boundaries appears to have occurred (compare Figs. 2(d) and 2(f))
the isothermal ageing curves (Fig 1(b)) show a substantial decline in hardness
after extended ageing, suggesting that relaxation strengthening is not the
sole contribution to the age-hardening of the material. The domain-like
structure is retrained even upon heating, as shown in Figure 2(e), 2(f) and 3.
The amplitude of the composition fluctuations would be expected to increase
during spinodal composition. This effect, in addition to defect relaxation
and/or segregation results in increased strengthening during ageing [54, 55].

The overaging mechanism here is expected to be similar to that occur in the CG
case, and preliminary observations on overaged NC samples did detect grain
boundary phases. In this case the loss of strengthening is probably
exacerbated by grain coarsening; although grain boundary particles can act as
pining sites, rapid, preferential diffusion along the grain boundary could
rapid coarsen the larger particles, at the expense of the loss of the smaller
ones, and hence reduce the number of pining sites.

To quantify the contribution of modulation strengthening vs. hardening by
annealing to the 30% strength increase would require careful consideration of
the models describing the strength increase by spinodal decomposition
(e.g.[54, 55]), and other contributions such as grain-size strengthening. This
would be best suited to techniques in which in situ measurements can be made
during ageing, for example small angle x-ray scattering.

From the results it is evident that it is the decomposed structure, not the
minimum obstacle spacing which governs strength. The large fraction of grain
boundaries present in the NC sample still plays a dominant role. Although the
wavelength (i.e. the modulation period) of the decomposed structure is more or
less independent of the grain size or the treatment prior to annealing (see
Fig. 2), for the HPT deformed NC samples, the PA is about 1.2 GPa larger than
for the coarse-grained PA samples, Table 1. This suggests, that even for
nanoscaled coherent or semi-coherent decomposed or precipitated structures a
NC grain structure can add significant additional strength. Moreover, apart
for further strengthening the NC grain structure could help to retain
ductility for such systems, as discussed in the remainder.

However, from the tensile tests it is evident, that no matter if defect
relaxation occurs, the results differ significantly to systems without
decomposition or precipitation. Anneal-hardening is generally associated with
a massive reduction in ductility, as any defect (dislocation) introduced to
the crystal after the heat treatment can readily propagate, resulting in a
significant strain softening, shear band formation and early failure, compare
Refs. [56, 10]. The peak aged samples studied here behave differently, with
reasonable ductility and no evidence of macroscopic strain localization
despite the gain in strength. This indicates that the decomposed structure is
suitable to hinder dislocation motion and induce some work hardening. This is
well-known from coarse grained materials. Spinodally decomposed systems or
clusters act as obstacles for dislocation motion, but as they are penetrable
or shearable, the resistance against dislocation motion remains relatively
weak. Hence, their strengthening effect to coarse grained metals generally
comes along with sharp reduction of ductility [57], the opposite to what is
observed here. Therefore, the observed larger work hardening in case of the
peak aged samples and the almost unaffected ductility despite the higher
strength explained by the increased amplitude of the decomposed regions seems
surprising. As the decomposed structure hardly changes due to the grain size
reduction (compare Fig. 2), the different effect on ductility might be
rationalized based on the grain size.

In case of the HPT deformed samples, the overall tensile strain is only on the
order of up to 10 %. Hence, the number of number of dislocations per grain
involved is fairly limited and can be estimated by $0.1=N*b/d$. For NC
structures and fairly low strains, the number of dislocations required thus
not exceed several tens of dislocations. This may not be sufficient to shear
decomposed structures or precipitates, hence, soft pathways may not be
established, supported by the measured larger work hardening rates in case of
the peak aged samples.

This is perhaps best illustrated by an example: In a coarse grained material
(Fig 6) generating a plastic strain in the range of 1-2% requires the passage
of literally hundreds of dislocations. As a rough estimate, for a 10$\mu$m
grain, a 1% strain equates to 100 nm. With a Burgers vector for $a/2\langle
110\rangle$ or 0.26 nm, that would require approximately 400 dislocations per
grain. Given that the modulation wavelength is of the order of 1-2 nm, it is
easy to conceive that this amount of deformation will locally disrupt the
modulated structure, establishing soft pathways for further deformation,
especially if concentrated in a handful of slip planes.

In contrast, if the grain size is reduced to 100 nm (Fig 6(b)), the same 1%
strain would be accommodated by a mere 4 dislocations, giving rise to a total
shear displacement which is of a similar magnitude to the modulation
wavelength (1–2 nm, see Figs. 2(d), 2(f). Even if concentrated on a single
slip plane, this would not be sufficient to completely disrupt composition
modulations with a wavelength of roughly 2 nm. Furthermore even at slightly
higher strains of perhaps 5%, the mutual repulsion between dislocations would
restrict the number of dislocations on closely-aligned slip planes.

(a) Coarse-grained spinodal

(b) UFG spinodal

Figure 6: Schematic illustrating the effect of grain refinement on the
deformation of the spinodal structure.

The NC alloy also displays good thermal stability. The grain size of the HPT
sample showed no significant increase during brief ageing at 646 K (a
homologous temperature, $T/T_{m}$, of 0.48) and the hardness remained stable
indefinitely at 473 K ($T/T_{m}\sim$0.35) (Fig 1b). This is in sharp contrast
to pure copper which can coarsen even at room temperature ($T/T_{m}$=0.22
[58]). Grain boundary precipitates are scarce even in the peak-aged condition
and it seems improbable that the few particles observed would be sufficient to
prevent coarsening. However, ab-initio calculations indicates that titanium
has with -0.504 eV333The calculation was performed for a $\Sigma$5 $[100]$
$\\{012\\}$ grain boundary a moderately strong grain boundary segregation
energy [59], and this thermodynamic stabilisation could explain the observed
stability.

The successful use of a modulated structure to stabilise plastic flow in a NC
alloy despite a strength increase suggests several avenues worthy of further
investigation. Quantitative modelling of the different contributors to the
strength, particularly grain size and the spinodal structure would assist in
optimising the processing route to provide the best combination of strength
and ductility.

##  5 Conclusions

Plastic flow in a NC Cu-1.7 at.%Ti alloy has been stabilised by introducing a
modulated, spinodal structure.

  * •

The hardness ($254\pm 2$ $H_{V}$) and yield strength (800 MPa) of the UFG
alloy are comparable with micro-grained Cu-Ti alloys containing 3 at.%Ti.

  * •

The resulting alloy possess much higher ductility than typical UFG alloys, as
evidenced by the good elongation to failure of $\sim$9 %, area reduction of
$\sim$40% and the presence of microdimples on the fracture surfaces, which are
huge compared to the grain size.

  * •

The spinodal structure can be retained during post-HPT annealing, leading to
increased strength (890 MPa) while retaining acceptable elongation to failure
(7%).

  * •

The improved ductility is attributed to work-hardening due to the presence of
the spinodal structure and their increased amplitude.

  * •

The deformation response after ageing is not indicative of hardening by
annealing.

  * •

The success of this approach suggests that spinodal decomposition offers a
means to overcome plastic instability in subsequent poor ductility in UFG and
NC alloys. This especially holds true in case of heat treatments, where stable
solid solutions undergoing anneal hardening would completely lose ductility, a
phenomenon not observed here.

## Acknowledgements

The authors would like to thank Peter Kutleša for assistance with the HPT
experiments, Dr. Sergey Ketov for the use of the arc-melting facility and
Silke Modritsch and Gerard for assistance with the SEM and TEM sample
preparation.

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<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Two-chamber gas target for laser-plasma accelerator electron source

P. Drobniak  E. Baynard  K. Cassou  D. Douillet  J. Demailly  A. Gonnin  G.
Iaquaniello  G. Kane  S. Kazamias  N. Lericheux  B. Lucas  B. Mercier  Y.
Peinaud  M. Pittman  Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
- IJCLab - UMR9012 - Bât. 100 - 15 rue Georges Clémenceau 91405 Orsay cedex -
France

###### Abstract

Exploring new target schemes for laser wakefield accelerators is essential to
meet the challenge of increasing repetition rates while ensuring stability and
quality of the produced electron beams. The prototyping of a two-chamber gas
cell integrated into the beam line and operating in continuous gas flow is
introduced and discussed in the frame of ionisation injection. We report the
numerical fluid modeling used to assist the density profile shaping. We
describe the test bench used for cell prototype assessment, in particular the
plasma electron density and longitudinal distribution of species relevant for
ionisation injection. The lifetime of the target key part is measured for
different materials. Perspectives to high power operation are outlined.

###### keywords:

Suggested keywords

##  1  Introduction

Laser wakefield acceleration (LWFA) is a promising high-gradient accelerator
technology, and the interest of the accelerator community is growing due to
its compactness 1, 2, 3. Significant progress has been made in the
optimisation of laser-plasma electron source (so-called ’target’) achieving
GeV-level4, but also controlled high charge beams, and optimisation of
spectral brightness 5, 6. Long operation runs at various repetition rates is
also a key issue 7, 8. All these improvements are possible only with advanced
control of both laser and plasma target. In the under-dense plasmas used in
plasma wakefield accelerators, the gas typically takes the form of supersonic
jets, gas cells, capillary discharge waveguides 9 or plasma ovens 10.
Depending on repetition rate and integration constraints, targets are operated
in pulsed or continuous gas flow mode. A deep understanding and control of the
target density profile, species distribution and gas flow is essential to
ensure high-quality and reproducible electron beam production.

A high compactness approach using a two-chamber target directly integrated
into the beamline is developed. Section 2 presents a review of existing laser-
driven accelerator targets. Section 3 introduces the prototype mechanical
design with fluid simulations, together with predicted density profiles.
Section 4 describes the test bench used for target prototype experimental
characterisation. Eventually section 5 concludes with the qualification of the
fluid simulation model, and prototype lifetime consideration.

##  2 Targets for laser-driven plasma accelerator

As reviewed by I. Prencipe et al.11 and J. Garland et al.12, several plasma
target designs have been investigated in the last two decades: mainly gas
jets, gas cells and capillary discharges. In all designs tried, the challenge
is to tune the plasma composition and longitudinal density profile. For the
particular case of laser-driven electron injectors, the target is composed by
a first stage where injection occurs, a second stage for acceleration and a
third with controlled density ramp to limit emittance growth13. The various
approaches are summarised in Tab.1.

Gas jets are the most commonly used and often based on a single jet technique
using either the principle of self-injection 14, optical injection (with
colliding pulses 15), ionisation injection 16, 17, or down-ramp injection 18,
19, 20, 21 triggered by a shock using a blade 18, 20 or a wire 21 or by
shaping the plasma with a transverse beam 19. Other schemes have been proposed
using two jets, the first jet being the injector, the second one the
accelerating stage. For the injection, the techniques tried were down-ramp 22
or ionisation 23 injection. The main advantage of gas jets is the easy
alignment with the laser and the wide solid angle for diagnostics. Pulsed
operation is advised to avoid too much gas leaks, leading to pumping system
overload and pollution. At high operation rate (typically kHz), gas jet high
density tends to induce high thermal and mechanical loads, resulting in
wearing of mechanical parts, vibrations and shot-to-shot instability 12, 24,
25. Typical electron densities offered by gas jets lie in the range of
$10^{18}-10^{20}$ cm-3.

target type | density range [cm-3] | distribution species | lifetime [shots] | repetition rate [Hz]
---|---|---|---|---
jet | $10^{18}-10^{20}$ | mixed | $>10^{5}$ | $0.1-1000$
cells | $10^{17}-10^{19}$ | mixed, localised | $>10^{5}$ | $0.1-10$
channels | $10^{17}-5\times 10^{18}$ | mixed, localised | $>10^{4}$ | $0.1-10$
capillary discharge | $10^{17}-5\times 10^{18}$ | mixed, localised | $>10^{4}$ | $0.1-10$
Table 1: Overview of state-of-the-art target properties for laser-plasma
accelerator electron source

Gas cells are divided into two categories. The first one is a tank 26, 27 or
several tanks 28, 29, filled with gas in steady state flow or pulsed mode.
Apertures allow the laser to pass through, and keeping them as small as
possible is critical to prevent leaks. The second category is gas channels 30,
5, 6, 31, where gas is injected by various transverse inlets into a main
longitudinal channel with reduced cross section. In most cases, the first
transverse inlet is for electron injection, the other ones for electron
acceleration. Gas exhaust occurs at the main channel entrance/exit and may
additionally go through a specific transverse aspiration outlet.

Whether using a tank or channel geometry, gas cells are particularly
interesting for an ionisation injection regime, where a fraction of high-Z gas
(called dopant) is added into a background gas. Various techniques have been
developed to avoid continuous ionisation injection using a downward focusing
in gas jet or gas cell or a sharp confinement of the dopant28 allowing to
reduce the accelerated beam energy spread and control beam-loading 6.

Whereas gas jets require quite high backing pressures (in the range of several
bars), gas cells are less demanding in terms of gas consumption and pressure
gradient in the gas circuit. Depending on the vacuum integration (differential
pumping), they can be operated in pulsed or continuous gas-injection mode,
which yields a better shot-to-shot stability 12. On balance, the main drawback
of gas cells are: (1) lifetime, since laser may enlarge cell apertures, (2)
reduced solid angle for diagnostics, since their material may diffuse light,
or potentially be coated by plasma pollution.

The design investigated here is a gas cell divided in two separate chambers,
delimited by transparent optical quality plane surfaces, specifically suited
for transverse optical diagnostics. It is inspired by the pioneer work done by
Kononenko 29, in a more compact approach and focusing on the dopant mitigation
in the first zone, with pure background gas in the second zone.

##  3 Target multi-cell design

The motivation of this work is: (1) a compact integration directly into the
accelerator beam line, (2) a large range online tunability of dopant
concentration and gas density profiles, (3) together with their online
transverse optical diagnostics, (4) an easy replacement of critical elements
which are strongly irradiated by the laser, especially at high repetition
rate.

###  3.1 Design and features

The prototype design is presented in Fig. 1 and Fig. 2. It consists in a main
body and two nozzles defining two separate chambers (called chamber 1 and 2
along laser propagation direction), each supplied with gas through an
injection hose: helium doped with nitrogen ($He$/$N_{2}$) for the chamber 1
and pure helium ($He$) chamber 2. They are separated by a wall, with a small
central aperture ranging from $0.25\,$ to $1\,$mm in diameter. The laser
enters chamber 1 through the inlet nozzle, passes through the central aperture
and exits chamber 2 by the outlet nozzle.

Figure 1: View of the two-chamber target prototype with the input and exit
T-pipe for efficient gas evacuation with a zoom on the chambers. The present
prototype is equipped with MACOR ceramic nozzle. Figure 2: CAD section view of
target connected in the beamline with a laser propagating from left to right.
Gases are injected with two connections on the top (only one visible in this
’section’ view), flow towards the chambers (blue and orange areas), and exit
through the nozzles. They expand in the pumping tees and most of the flow is
sucked out by efficient primary pumping (upwards in this schematic view). Two
$8\,$mm-apertures (differential holes) provide a differential pumping at the
entrance and exit of the T-pipes.

Nozzles are necessary to reduce the leak in the vacuum chamber. Their inner
dimensions (radius, thickness) allow an additional tuning of the gas density
in- and out-ramp shape. The central separation serves as frontier between the
target chambers. Some gas flow between chambers may appear and is governed by
the pressure difference and conductance of the central aperture.

Dimensions of the cell close to the axis are described in Fig. 3 and given in
Tab. 2. Many combinations have been considered, and a typical configuration is
given in Tab. 2. Varying the nozzle total length gives an adjustment of
chamber 1 and 2 longitudinal dimensions called $L_{2}$ and $L_{4}$ (see Fig.
3). The tank volume of each chamber is $\sim 5\,$cm3.

Figure 3: Cell dimensions nomenclature with associated variables. $D_{1}$, $D_{3}$ and $D_{5}$ respectively are the diameters of: inlet nozzle, central aperture and outlet nozzle. $L_{1}$, $L_{2}$, $L_{3}$, $L_{4}$ and $L_{5}$ respectively correspond to the lengths of: inlet nozzle, chamber 1, central aperture, chamber 2 and outlet nozzle. Gas paths are indicated for $He/N_{2}$ (blue filled region) and $He$ (orange filled region). Laser path is schemed in red and propagates from left to right. Table 2: Typical cell dimensions close to the axis, with nomenclature defined in Fig. 3. All in mm. $L_{1}$ | $L_{2}$ | $L_{3}$ | $L_{4}$ | $L_{5}$ | $D_{1}$ | $D_{3}$ | $D_{5}$
---|---|---|---|---|---|---|---
$1$ | $0.6$ | $0.25$ | $1.2$ | $3$ | $0.6$ | $0.25$ | $1$

Primary vacuum (sub-mbar) is ensured close to the nozzle exit by a pumping
system connected with T-pipes (Fig. 2). Secondary vacuum is obtained further
from the cell after a differential hole, both downstream and upstream, which
produces a two-decade pressure drop.

The main body has been manufactured using wire electro-discharge machining in
aluminium block, while nozzles are either made of aluminium or MACOR ceramics.
The centering mechanical tolerance ($\pm 50\,\mu$m center to center) was
achieved for the nozzles using numerical milling machining.

In addition to its mechanical features, the design allows to perform
transverse optical diagnostics across chamber 1 and 2. The diagnostics can be
placed in air thanks to optical windows, that are the direct frontier between
chambers and experimental room. Such a feature is particularly interesting for
convenient experimental measurements of gas and plasma characteristics.
Compared to channel type gas cells the optical transverse diagnostics are
eased even if the central separation wall introduces shadowing in the imaging
of the two chambers for 2D spectroscopic light collection. The transverse
distance from the center (interaction region) and the optical windows is
$\approx 3\,$cm avoiding a rapid darkening due to pollution by the laser.

###  3.2  Fluid simulation set-up

The gas density distribution is modelled using the open-source fluid
simulation code OpenFOAM 32. Typical simulation cases from this article are
online and open to the scientific community 33. Depending on the desired
problematic, the solver used is either:

  * •

rhoPimpleFoam 34: for transient compressible single species simulation,

  * •

interMixingFoam 35: for transient incompressible miscible fluids,

No solver modeling miscibility for compressible flows were found in the
OpenFOAM library, therefore two simulation steps were necessary.

The geometry is designed with a CAD software and automatic meshing is
performed using the routine snappyHexMesh 36. A 3D geometry applied to a
reduced volume is used for simulations, as presented in Fig. 4, in order to
limit the total number of cells to an average of $10^{5}$ and thus limit the
computation time.

Figure 4: Longitudinal clip of the reduced mesh used in OpenFOAM simulations
for a target configuration with geometry
$(L_{1},L_{2},L_{3},L_{4},L_{5},D_{1},D_{3},D_{5})=(1,0.6,0.25,1.2,3,0.5,0.95,0.6)$.
The snappyHexMesh-generated mesh is presented in the original CAD design .stl
file (top image, the .stl is in grey) and zoomed-in with visible mesh
refinement areas (bottom image). $p$ is the pressure in Pa. Laser travels from
left to right.

Boundary conditions are: fixed pressure at the inlets, constant volumetric
flow at the outlets (estimated from the pump characteristics).

Simulations are run on a computer single-cpu and the average simulation time
is roughly $1\,$h for the reduced volume case.

###  3.3  Simulation of the density profiles for single species

First simulations are run for pure $He$ with rhoPimpleFoam. The resulting
steady-state is obtained from an initial empty cell a few hundreds of $\mu$s
after valve opening. The longitudinal density profiles obtained for cell
dimensions $(L_{1},L_{2},L_{3},L_{4},L_{5},D_{1},D_{3},D_{5})$ =
$(1,0.6,0.25,1.2,3,0.5,\\\ 0.95,0.6)$ at several operating pressures are
presented in Fig. 5.

Figure 5: Evolution of longitudinal on-axis density with pressure according to
rhoPimpleFoam simulations with pure $He$. Simulations are run with
$p_{Left}=p_{Right}$ on geometry $(1,0.6,0.25,1.2,3,0.5,0.95,0.6)$, with names
referring to the maximum pressure in the plateau. The associated electron
density is in parenthesis, assuming $He$ full ionisation. A polygonal fit is
added in red. Inlet and outlet nozzle extensions are respectively depicted in
red and grey areas. The cell center (central aperture) is depicted with a
vertical black dashed line. Laser goes from left to right.

Injection pressures for chamber 1 ($p_{Left}$) and chamber 2 ($p_{Right}$)
satisfy $p_{Left}=p_{Right}$, in order to have a flat plateau between both
chambers. This feature prevents convection and is further discussed below in
the gas mixture simulation. Note that $D_{3}$ is voluntarily taken as
$0.95\,$mm to model a $0.25\,$mm realistic damaged central aperture, but
simulation results are similar.

Within the $[10;120]$ mbar pressure range, the longitudinal profile shape is
conserved, with slight compression effects, mostly at the outlet nozzle
entrance. With cylindrical nozzles, the up- and down-ramp shape is pretty
linear. The overall pressure profile can thus easily be approximated with
scalable linear functions, that can be tabulated over a wide range of pressure
to serve as input for optimisation with laser-plasma PIC simulation (see
polygonal fit in Fig. 5). Also note that the pressure upstream the inlet
nozzle quickly decreases below the mbar range for all configurations, limiting
undesired laser-plasma interaction before the cell.

The transverse density profile is depicted in Fig. 6, where three planes along
the laser propagation axis are selected: inlet nozzle entrance ($x_{1}$),
chamber 2 center ($x_{2}$), outlet nozzle center ($x_{3}$). Both chamber
pressure is set to $30$ mbar and the geometry is the same as for Fig. 5.

Figure 6: Evolution of transverse density with propagation according to
rhoPimpleFoam simulations with pure $He$ at injection pressures
$p_{Left}=p_{Right}=30$ mbar, with geometry $(1,0.6,0.25,1.2,3,0.5,0.95,0.6)$.
Transverse plots (orange) are extracted at $x_{1}$, $x_{2}$ and $x_{3}$
respectively corresponding to inlet nozzle entrance, chamber 2 center and
outlet nozzle center. A longitudinal plot on axis is added (blue). Two typical
laser envelopes are added: $w_{0}=55$ $\mu$m in red and $w_{0}=19$ $\mu$m in
pink.

Fig. 6 shows a constant transverse density, whether for a $19$ $\mu$m (PALLAS
project37) or a $55$ $\mu$m (test bench) laser waist at the interface between
the two chambers.

The influence of inlet nozzle geometry is presented in Fig. 7, where the
reference profile $(1,0.6,0.25,1.2,3,0.5,\\\ 0.95,0.6)$ is kept and compared
with other diameter or length.

Figure 7: Calculated normalised density for different inlet nozzle geometries
from rhoPimpleFoam simulations for pure $He$ at $p_{Left}=p_{Right}=30$ mbar.
The reference geometry (magenta) is
$(L_{1},L_{2},L_{3},L_{4},L_{5},D_{1},D_{3},D_{5})=(1,0.6,0.25,1.2,3,0.5,0.95,0.6)$
mm. The top graph presents results for the inlet nozzle length variation
$L_{1}$: $0.25$, $0.50$, $0.75$ and $1.00$ mm (reference geometry) with
constant $D_{1}=0.50$ mm. The bottom graph shows the influence of inlet nozzle
diameter $D_{1}$: $0.30$, $0.40$, $0.50$ (reference geometry), $0.70$ and
$1.00$ mm, with constant $L_{1}=1.00$ mm. Laser travels from left to right.

The longitudinal extent of the up-ramp scales linearly with $L_{1}$ but does
not depend on $D_{1}$. Increasing the diameter leads to higher upstream tee
pressure that reaches the mbar range for $D_{1}>0.5$ mm, but also degrades the
flatness of the plateau in chamber 1. Ideally, the shortest and thinnest
nozzle as possible is desired. We choose $L_{1}=1$ mm and $D_{1}=0.5$ mm for
machining and robustness reasons. $D_{1}$ must obviously also be larger than a
few laser waists.

The influence of outlet nozzle dimensions at $30\,$mbar is presented in Fig.
8, where the length $L_{5}$ is varied between $[0;5]\,$mm at fixed $D_{5}=0.6$
mm and the diameter $D_{5}$ between $[0.40;1.00]\,$mm at fixed length
$L_{5}=3$ mm. The same reference case as for the inlet nozzle study is
included for comparison.

Figure 8: Calculated normalised density on axis for different outlet nozzle
geometries from rhoPimpleFoam simulations for pure $He$ at
$p_{Left}=p_{Right}=30$ mbar. The reference geometry (magenta) is
$(L_{1},L_{2},L_{3},L_{4},L_{5},D_{1},D_{3},D_{5})=(1,0.6,0.25,1.2,3,0.5,0.95,0.6)$
mm. The top graph presents results for the outlet nozzle length variation
$L_{5}$: $1.00$, $2.00$, $3.00$ (reference geometry), $4.00$ and $5.00$ mm
with constant $D_{5}=0.60$ mm. The bottom graph shows the influence of outlet
nozzle diameter $D_{5}$: $0.40$, $0.50$, $0.60$ (reference geometry), $0.80$
and $1.00$ mm, with constant $L_{5}=3.00$ mm. Laser travels from left to
right.

Similarly to the inlet nozzle, the ramp length linearly scales with nozzle
length $L_{5}$, with a preserved shape. Indeed, for each length tried (top
graph in Fig. 8), the down-ramp follows the same pattern: a linear decrease
along roughly $L_{5}$ followed by an exponential decrease of $\approx 1$ mm
(gas expansion). The outlet diameter $D_{5}$ has the same influence as
previously observed with $D_{1}$.

Contrary to the inlet, the outlet profile has to be as smooth and long as
possible for emittance preservation 38, which corresponds to large $L_{5}$.
Together with a small $D_{5}$, this might be a problem due to laser divergence
and possibly ablation. A compromise is made with $L_{5}=3\,$mm and
$D_{5}=0.60$ mm.

###  3.4  Simulation of dopant confinement

As introduced earlier, dopant confinement is a key process to ensure high
quality beams with a small energy spread. Specific incompressible two-gas
simulations are run with interMixingFoam to account for diffusion issues. They
are performed in a reduced geometry with boundaries up to each nozzle center,
where the flow can still be approximated as incompressible ($Ma<0.3$). The new
outlet boundary conditions are simply the pressure values extracted from
previous compressible simulations at the new physical boarders.

Such an approximation is verified by simulating comparable cases, both in
compressible (rhoPimpleFoam) and incompressible (interMixingFoam) mode with
$He$ only 111Results are still valid when adding a few % $N_{2}$ in chamber 1,
since the gas characteristics remain comparable, especially in low kinematic
areas, such as the chambers interface.. Results for cell pressures within
$[10-120]$ mbar are presented in Fig. 9, where the difference for the pressure
between compressible and incompressible models
$\epsilon{}_{p}=(p_{comp}-p_{incomp})/p_{comp}$ [%] is added.

Figure 9: Pressure distribution comparison on axis between compressible
(rhoPimpleFoam) and incompressible (interMixingFoam) simulations, with pure
$He$ at plateau pressures: $10$, $30$, $50$, $80$ and $120$ mbar. Upper graph
displays compressible plots (dashed line) and incompressible plots (solid
line). Lower graph presents the difference between compressible (’comp’) and
incompressible (’incomp’) as: $\epsilon{}_{p}=(p_{comp}-p_{incomp})/p_{comp}$
[%]. Target geometry is $(1,0.6,0.25,1.2,3,0.5,0.25,0.6)$ and a reduced mesh
is used, limited to the presented x-axis extent. Positions of the inlet and
outlet nozzles respectively are indicated by light red and grey areas. Laser
goes from left to right.

From Fig. 9, a good agreement appears between compressible and incompressible
simulations, with a maximum $8\,$% deviation close to the nozzles, and almost
no difference in the chambers, which is the zone where dopant mitigation
should occur. The same kind of study was done for temperature and velocity
profiles with the same conclusion at the diffusion interface, and a
significant divergence close to the nozzles. Incompressible simulations thus
correctly match compressible ones 222The reader might note that all plateaus
actually have gradients. This particular shape is explained by the difficult
and time-consuming search for a perfect match on axis ($p_{Left}=p_{Right}$)
using approximate boundary conditions..

The dopant confinement study is then performed with two gases in
interMixingFoam to evaluate the effect of pressure difference between chamber
1 and 2 $\Delta{}p=p_{Right}-p_{Left}$ (convection) or statistical mixing of
the two gases at equal pressure (diffusion). The result is shown in Fig. 10
for a test at $30\,$mbar, with $He/N_{2}$ injected in chamber 1 at dopant
concentration $c_{N_{2}}=10\%$ and pure $He$ in chamber 2.

Figure 10: Influence of a pressure gradient between chambers
$\Delta{}p=p_{Right}-p_{Left}$ (upper graph, solid lines) on dopant
concentration $c_{N_{2}}$ (upper graph, dashed lines) and longitudinal flow
velocity $U_{x}$ (bottom graph, solid lines). Results are obtained with
incompressible miscible simulations (interMixingFoam) using $He/N_{2}$ (at
$c_{N_{2}}=10\,$%) and pure $He$ respectively in chamber 1 and 2. Cell
geometry used is $(1,0.6,0.25,1.2,3,0.5,0.25,0.6)$ with the same reduced mesh
as for Fig. 9. The cell center is indicated with a vertical dash-dotted line
(central aperture) and positions of the inlet/outlet nozzles are added.

For a negative/positive gradient $\Delta{}p=-1/+1$ mbar, the dopant is pushed
to the right/left through convection (visible on the flow velocity $U_{x}$ in
Fig. 10). $\Delta{}p=-1$ mbar causes $N_{2}$ leaks towards chamber 2 and
$c_{N_{2}}$ never reaches $0$ in chamber 2 (no dopant confinement).
$\Delta{}p=+1$ mbar triggers the opposite effect, with $He$ leaking into
chamber 1. This case however offers $c_{N_{2}}=0$ in chamber 2 (dopant
confinement). In both cases, the transition from $c_{N_{2}}=10\,$% to roughly
$0$ occurs on $\approx 1.0$ mm.

For equal pressures, the interface is centered on the central aperture ($x=0$)
and the $c_{N_{2}}$ transition is due to pure diffusion (no longitudinal flow
velocity $U_{x}$). It takes $\approx 0.5$ mm for $N_{2}$ to decrease from
$10\,$% (chamber 1) to strictly $0$ (dopant confinement).

Dopant confinement is thus ensured for equal pressures or a slight positive
gradient $\Delta{}p$. Setting $\Delta{p}=0$ mbar provides a clear separation
of gases in both chambers, with original mix and pure $He$ remaining
respectively in chamber 1 and 2, while positive gradients induce $He$ leaks
into chamber 1. The shortest $c_{N_{2}}$ transition from $10\,$% to $0$ occurs
for equal pressures. Working with $10\,$% dopant is a dimensioning case and
results are valid for lower concentrations.

We observe in simulations that increasing the working pressure from $10\,$mbar
to $120\,$mbar makes the tuning of the transition position more sensitive to
the pressure difference as the central aperture conductance depends on the sum
of the pressure in the two chambers. The transition length remains stable.

Simulations have also been performed for a larger aperture up to $0.95\,$mm.
As conductance is higher when increasing the central aperture diameter, it
shows a higher sensitivity with $\Delta p$. This sensitivity is confirmed by
the experimental results in Section 5.

##  4 Target test bench

###  4.1 Experimental setup

The vacuum and mechanical setup used at IJCLab target test facility is
presented in Fig. 11 with its characteristics summed-up in Tab. 3.

Figure 11: Schematic diagram of the vacuum setup used for cell characterisation. Pressures are monitored using gauges G1, G2, G3 and G4 respectively measuring pressures $p_{1}$, $p_{2}$, $p_{3}$ and $p_{4}$. Vacuum is ensured by secondary turbomolecular pumps (TMP1,TMP2) with forevacuum primary pump (PP). The target gas flow is directly pumped upward and downward the target with a roots pump (PRP). Gas injection pressures are measured with ceramic piezo type gauges GL and GR respectively measuring $p_{Left}$ and $p_{Right}$. element | parameter | value | unit
---|---|---|---
TMP1,2 | pumping speed | $300$ | l/s
TMP1,2 | gas through output | $160$ | mbar.l/s
PP | pumping speed | $40$ | l/s
PRP | pumping speed | $>400$ | l/s
G1,G4 | gauge type | cold cathode | -
G2,G3 | gauge type | pirani | -
GL,GR | gauge type | capacitance | -
Table 3: Characteristics of vacuum system elements given for helium at the
working pressure

Gases are injected using a specific gas injection system (Fig. 12), with one
injection line for each chamber. For chamber 1, the user specifies the
$He/N_{2}$ mixture injection mass flow and dopant concentration in $\%$
(partial pressure ratio) within $[0;100]\pm 0.2$. For chamber 2, a pure $He$
injection mass flow is set.

Figure 12: Schematic diagram of the gas injection system. The mass flow
controllers MFC1 and MFC2 set the concentration of $N_{2}$ in the gas mixture.
The MFC3 and MFC4 set the mass flow injected on the chamber 1 and chamber 2
respectively. The GAUGE-$A-D$ are the gauges for injection automation. SV0X
are solenoid valves and MVOX manual valves.

Several gauges monitor the pressure. Their names follow the laser propagation
direction: G1, G2, G3, G4 respectively measuring $p_{1}$ (secondary vacuum),
$p_{2}$ (primary vacuum), $p_{3}$ (primary vacuum) and $p_{4}$ (secondary
vacuum). Pressure at the injection is monitored with capacitance gauges GL and
GR, whose measurements are independent of gas type.

Monitoring the pressure is of particular importance to constantly check the
state of the cell and alert on associated pollution propagating upstream the
laser line. Additionally, gauges can serve as verification tool for fluid
simulations. They allow to cross-check aperture-induced pressure drop far from
axis (static pressure difference between chamber 2 and downstream pumping tee
for instance). This serves as flow modeling validation regarding gas
thermophysical properties and flow regime (laminar VS turbulent).

###  4.2 Laser line

The pump/probe optical setup is described in Fig. 13, where the laser beam
comes from LaseriX platform 39.

Figure 13:  Optical scheme used for target characterisation. The optical paths
for the pump and probe beams respectively are in red and orange. The pump beam
is focused into the target by MS (spherical mirror), the probe beam is
extracted by BS1 (5/95 beamsplitter). Other optical components are: P
(pinhole), DL (motorised delay line), DBS (dichroic beamspliter), LEN1-4
(lenses), D (adjustable diaphragm), OBJ (microscope objective). Optical
diagnostics are: WFS (wavefront sensor), VIS SPEC (visible spectrometer),
TRANS (camera).

The pump beam (characteristics in Tab. 4) is focused in the target and serves
for ionisation. $10\,$% of the total energy is dedicated to the probe beam.

Parameters | value | typical errors | unit
---|---|---|---
central wavelength; $\lambda_{0}$ | $810$ | $\pm 1$ | nm
minimum pulse duration (FWHM); $\tau$ | 50 | $\pm 5$ | fs
repetition rate | $10$ | - | Hz
Flattened Gaussian beam order; $N$ | $5$ | - | -
energy on target; $E_{0}$ | $1\rightarrow 60$ | $\pm 5$ | mJ
focal length; $f$ | $1100$ | - | mm
waist in the focal plane; $w_{0}$ | $55$ | $\pm 5$ |  $\mu$m
Strehl ratio | $0.55$ | $\pm 0.05$ | -
focal spot longitudinal position range; $\Delta x_{foc}$ | $30$ | - | mm
probe delay; $\Delta t$ | $180$ | $\pm 0.03$ | ps
Table 4: Parameters of the laser pulse from LaseriX platform 39 used for
target gas ionisation (pump beam) and transverse optical diagnostics (probe
beam) on IJCLab target characterisation test bench.

The optical diagnostics used on the test bench for the target characterisation
are: a wavefront sensor 40 for plasma channel density measurement 41, 42 and a
visible spectrometer 43 (or a camera 44) for ion species measurement.

##  5 Experimental qualification

###  5.1  Neutral gas pressure measurement

Simulation are cross-calibrated with experimental results: experimental
pressure measurements validate the flow hypothesis (laminar versus turbulent)
for the solver and its ability to reproduce pressure drops induced by the
apertures. Simulations were performed with rhoPimpleFoam in laminar mode.

Whether for $He$ or $N_{2}$, the pressure in chamber 1 is predicted with an
error below $10\,$%, which diminishes for higher injection pressures. The
primary vacuum pressure $p_{3}$ prediction slightly deviates from the
experiment, with a maximum error corresponding to $0.1$ mbar. Sources of
deviations are: a central aperture shape not perfectly modeled, a pumping
system overestimated in simulation at low pressures and the inability of the
solver to model quasi-discontinuous flows for very low pressures. Simulations
manage to correctly reproduce the flow down to $0.1$ mbar. The relevance of
gas property choice, such as viscosity is confirmed, together with the use of
laminar mode: turbulence does not have to be activated, which greatly reduces
the simulation time.

###  5.2  Electron plasma density profiles

Additionally to gauge pressure measurements far from axis, the density profile
on axis is assessed using a wavefront sensor. The latter is used to record the
phase difference introduced by the plasma channel in chamber 1, close to the
axis. A typical phase map is presented in Fig. 14.

Figure 14: Averaged phase difference measured with the wavefront sensor (on
$20$ consecutive shots) in chamber 1 for $He$ at $30$ mbar (pressure gauge
measurement) with two additional slices: longitudinal plot extracted at $y=0$
(bottom graph), transverse plot at $x=0.64$ mm (right graph). The ’std’ for
each 1D plot is added in the cloud around the mean curve (computed using the
shot-to-shot variation). Laser goes from left to right.

The plasma channel has a constant diameter of $100$ $\mu$m compatible with the
laser width $2\times w_{0}=110$ $\mu$m. 1D plots envelopes are standard
deviations computed from 20 shot series taken at $1\,$Hz 333Although the pump
and probe lasers are at $10\,$Hz, acquisitions are performed at $1$ Hz
(software constraints).. The important noise level can be explained by:
ambient air density variations integrated over the whole probe beam path (a
few meters), test bench vibrations or laser ablated particles projecting
impurities in the chambers. Since the phase remains quite stable above $0.2$
mm from axis (no plasma), cropping is performed on each phase map, to increase
the signal-to-noise ratio. In the worst case (low pressure), the signal-to-
noise ratio was always $>4$.

Typical phase maps acquired for $He$ at $10$, $30$, $50$ and $80$ mbar in
chamber 1 are presented in Fig. 15.

Figure 15: Averaged phases (on $20$ consecutive shots) acquired with the
wavefront sensor for $He$ in chamber 1 at $10$, $30$, $50$ and $80$ mbar.
Longitudinal plots (blue line) extracted at $y=0$ are added on each image,
with corresponding ’std’ (blue filled) based on their shot-to-shot variation.
Laser goes from left to right.

They display similar features than for Fig. 14. However, for a high pressure
($80$ mbar) a longitudinal gradient appears, probably due to ionisation
defocusing of the laser.

Abel inversion is used on phase maps to retrieve the corresponding electron
plasma density distribution. The resulting density maps are presented in Fig.
16 were inversion has been performed on phase maps from Fig. 15.

Figure 16: Electron densities obtained with Abel inversion on Fig. 15 phases
maps. Additional symmetrisation is applied. A longitudinal plot (light blue
line) at $y=0$ is added. The straight horizontal line (dark blue) represents
the density corresponding to fully ionised $He$. Laser goes from left to
right.

Theoretical maximum densities expected for fully ionised $He$ at $10$, $30$,
$50$ and $80$ mbar are respectively $4.86\times 10^{17}$, $1.46\times
10^{18}$, $2.43\times 10^{18}$ and $3.89\times 10^{18}$ cm-3. They are
indicated with horizontal lines on Fig.16. For low pressure, electron density
on axis is quite constant, slightly below the theoretical value with some
peaks along propagation. For $50$ and $80~{}$ mbar, ionisation likely remains
at the $He^{+}$ level, with a progressive drop for $80$ mbar above $0.55$ mm.
This confirms that at high pressure, the pump beam is not intense enough to
ionise the two levels of $He$, due to stronger ionisation defocusing.

We conclude that theoretical measured pressures match simulations, with a
longitudinal density having a constant plateau-like shape in the first
chamber. A similar behaviour is expected for chamber 2, since its geometry is
quite similar to chamber 1.

###  5.3 Dopant longitudinal profile

The prototype ability to confine the dopant is experimentally assessed with an
imaging spectrometer. It relies on excited species emission, with a resolution
of $1\,$nm over the considered wavelength range ($400-600\,$nm).

To get a good resolution on the diffusion of $N_{2}$ along the two chambers,
pure $N_{2}$ is injected in chamber 1, while pure $He$ is injected in chamber
2. This case is not representative of a typical working point for the target,
but will provide conservative information on dopant confinement. The
spectrometer gives the possibility to select various emission lines to track
simultaneously the corresponding species. Experimental results for different
pressure gradients $\Delta p=p_{Right}-p_{Left}$ are presented in Fig. 17,
with the largest achievable central aperture diameter ($0.95$ mm).

Figure 17: Dopant localisation using spectrometer measurements for different
gradient values $\Delta p=p_{Right}-p_{Left}$ between chamber 1 and chamber 2,
with an average plateau-pressure on axis of $30$ mbar. Pure $N_{2}$ and pure
$He$ respectively are injected in chamber 1 and 2. Geometry is
$(1.5,1.15,0.25,0.95,1.5,0.5,0.95,0.5)$. The central aperture (central wall)
position is added (black dashed line). Laser goes from left to right.

For $p_{Left}=p_{Right}$, the dopant is confined in chamber 1 (orange curve in
Fig. 17). For a slight positive gradient, the dopant is strongly pushed to the
left (red curve in Fig. 17), reducing the size of the injection zone
(truncated ionisation injection). On the contrary, even for a rather small
negative $\Delta p$, the dopant leaks into chamber 2 (blue curve in Fig. 17).
Nevertheless, a clear stable confinement of the gas mixture is demonstrated in
agreement with the simulations.

###  5.4 Target lifetime

Previous characterisation and simulations of course remain valid as long as
the target retains its geometry under high intensity laser irradiation.

The target main body is composed of aluminium, while nozzles are either in
aluminium or in ceramics (MACOR). The most critical part of the design is the
inlet nozzle. As shown in numerical simulations and experimental measurements
the gas mixture confinement can be obtained with a central wall aperture
diameter up to $\approx 1\,$mm.

Typical aperture dimensions and shape variations before and after $300\,000$
shots at $60$ mJ for aluminium nozzles are presented in Fig. 18.

Figure 18: Aluminium nozzle evolution before (top row) and after (bottom row)
$300\,000$ shots at $60\,$mJ. Images are: inlet nozzle concave face (A,E),
inlet nozzle convex face (B,F), outlet nozzle convex face (C,G), outlet nozzle
concave face (D,H). Initial nozzles dimensions are $D_{1}=520\pm 10$ $\mu$m
(inlet nozzle, average of ’A’ and ’B’) and $D_{5}=600\pm 10$ $\mu$m (outlet
nozzle, average of ’C’ and ’D’). Damaged nozzles dimensions are $D_{1}=910\pm
10$ $\mu$m (inlet nozzle, average of ’E’ and ’F’) and $D_{5}=990\pm 10$ $\mu$m
(outlet nozzle, average of ’G’ and ’H’), with damaged apertures approximated
as circles. Nozzle aperture lengths are $L_{1}=1$ mm (A,B,E,F) and $L_{5}=3$
mm (C,D,G,H).

Our experimental observation is that even at $60$ mJ (well below the $1$ J
required for laser-plasma acceleration), the aluminium nozzles are strongly
damaged.

A solution is to use MACOR nozzles as shown in Fig. 19.

Figure 19: Comparison between aluminium (top row) and MACOR nozzles (bottom
row) after approximately $300\,000$ shots at $60\,$mJ. Images are: inlet
nozzle concave face (A,E), inlet nozzle convex face (B,F), outlet nozzle
convex face (C,G), outlet nozzle concave face (D,H). Initial diameters were
$D_{1}=D_{5}=500\pm 10$ $\mu$m for all four nozzles. Damaged apertures are
approximated as circles. Damaged aluminium nozzles dimensions are
$D_{1}=830\pm 10$ $\mu$m (inlet nozzle, average of ’A’ and ’B’) and
$D_{5}=740\pm 10$ $\mu$m (outlet nozzle, average of ’C’ and ’D’). Damaged
MACOR nozzles dimensions are $D_{1}=710\pm 10$ $\mu$m (inlet nozzle, average
of ’E’ and ’F’) and $D_{5}=740\pm 10$ $\mu$m (outlet nozzle, average of ’G’
and ’G’). Nozzle aperture lengths are $L_{1}=1.5$ mm (A,B,E,F) and $L_{5}=1.5$
mm (C,D,G,H).

Qualitatively, higher MACOR resistance is visible on the post-mortem pictures.

An online estimation of the nozzle state can be done through pressure control.
We experimentally observed an inlet pumping tee pressure rise up to the mbar
range for aluminium nozzles after $\sim 30$ min of operation, while remaining
in a $10^{-1}\,$mbar range for MACOR nozzles. Ceramics greatly improve the
cell lifetime. This conclusion from the characterisation test bench has to be
confirmed on real scale laser plasma experiments.

In the case of acceptable nozzle deterioration, we are able to take into
account the evolution of nozzle apertures with time, with continuous
adjustment of the gas injection flows to maintain a constant pressure in the
chambers. In the optimisation of electron beam parameters, the laser focusing
position may also be tuned during operation to counterbalance the elongation
of the in-ramp length. After a few thousand shots, a saturation of the
ablation is observed, leading to more stability.

Regarding optical diagnostic, the design is quite robust and for more than
$10^{6}$ shots at $60$ mJ, no optical window had to be replaced or even
cleaned, allowing continuous cell characterisation and monitoring through
transverse diagnostics. This is favoured by the distance between plasma and
window of roughly $30$ mm, preventing direct deposition of ablated material.

##  6 Discussion and conclusion

The density profile of a two-chamber gas cell prototype for ionisation
injection has been assessed using the open-source fluid simulation library
OpenFOAM. It has been cross-checked with experimental results comming from the
diagnostics installed on the LaseriX test bench. Simulation results are open
to the scientific community.

Our multi-cell target design offers density distribution control and precise
dopant confinement, which have been experimentally demonstrated with online
diagnostics that also allow to monitor the target state evolution during the
experiment.

For emittance conservation issues, the output nozzle can be shaped to optimise
passive plasma lensing with an adapted density out-ramp. The target
integration in the beamline also offers a compact laser-plasma injector
design. This allows for a compact beam transport line for further injection
into a second accelerating stage. For example, the first magnet for PALLAS
project can theoretically be put as close as $\approx 15\,$cm from the source.

The results of this target design characterisation have been used as input for
Particle-in-Cell simulations, with the aim to find optimal working points for
electron injection. Four parameters have been varied: chamber pressure
$p_{Left}$ (with $p_{Left}=p_{Right}$), dopant concentration $c_{N_{2}}$,
laser energy $E_{0}$ and laser focal position $x_{foc}$ 45. The numerical
results show that electron beams with a charge over $30$ pC, energy ranging
between $150-250$ MeV, energy spread below $5\,\%$ and transverse normalised
emittance below $2\,\mu{}$m can be obtained.

##  Appendix A Appendixes

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