# Generation of meter-scale hydrogen plasmas and efficient, pump-depletion-
limited wakefield excitation using 10 GeV electron bunches

C. Zhang1, D. Storey2, P. San Miguel Claveria3, Z. Nie1, K. A. Marsh1, M.
Hogan2, W. B. Mori1,4, E. Adli5, W. An6, R. Ariniello2, G. J. Cao5, C.
Clarke2, S. Corde3, T. Dalichaouch4, C. E. Doss7, C. Emma2, H. Ekerfelt2, E.
Gerstmayr2,8, S. Gessner2, C. Hansel7, A. Knetsch2,3, V. Lee7, F. Li4, M.
Litos7, B. O’Shea2, G. White2, G. Yocky2, V. Zakharova3, and Chan Joshi1
1Department of Electrical and Computer Engineering, University of California
Los Angeles, Los Angeles, CA 90095, USA  2SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  3LOA, ENSTA Paris, CNRS, Ecole
Polytechnique, Institut Polytechnique de Paris, 91762 Palaiseau, France
4Department of Physics and Astronomy, University of California Los Angeles,
Los Angeles, CA 90095, USA  5University of Oslo, 0316 Oslo, Norway
6Department of Astronomy, Beijing Normal University, Beijing 100875, China
7Department of Physics, Center for Integrated Plasma Studies, University of
Colorado Boulder, Boulder, CO 80309, USA  8Stanford Pulse Institute, Menlo
Park, CA 94305, USA<EMAIL_ADDRESS>
###### Abstract

High repetition rates and efficient energy transfer to the accelerating beam
are important for a future linear collider based on the beam-driven plasma
wakefield acceleration scheme (PWFA-LC). This paper reports the first results
from the Plasma Wakefield Acceleration Collaboration (E300) that are beginning
to address both of these issues using the recently commissioned FACET-II
facility at SLAC National Accelerator Laboratory. We have generated meter-
scale hydrogen plasmas using time-structured 10 GeV electron bunches from
FACET-II, which hold the promise of dramatically increasing the repetition
rate of PWFA by rapidly replenishing the gas between each shot compared to the
hitherto used lithium plasmas that operate at 1-10 Hz. Furthermore, we have
excited wakes in such plasmas that are suitable for high gradient particle
acceleration with high drive-bunch to wake energy transfer efficiency- a first
step in achieving a high overall energy transfer efficiency. We have done this
by using time-structured electron drive bunches that typically have one or
more ultra-high current ($>$30 kA) femtosecond spike(s) superimposed on a
longer ($\sim$0.4 ps) lower current ($<$10 kA) bunch structure. The first
spike effectively field-ionizes the gas and produces a meter-scale (30-160 cm)
plasma, whereas the subsequent beam charge creates a wake. The length and
amplitude of the wake depends on the longitudinal current profile of the bunch
and plasma density. We find that the onset of pump depletion, when some of the
drive beam electrons are nearly fully depleted of their energy, occurs for
hydrogen pressure $\geq$1.5 Torr. We also show that some electrons in the rear
of the bunch can gain several GeV energies from the wake. These results are
reproduced by particle-in-cell simulations using the QPAD code. At a pressure
of $\sim$2 Torr, simulations results and experimental data show that the beam
transfers about 60% of its energy to the wake.

##  1 Introduction

Plasma wakefield acceleration has emerged as a promising frontier in advanced
acceleration research [1], offering potential for significantly reducing the
size and cost of a future accelerator operating at the energy frontier of
high-energy particle physics. In recent years, significant progress has been
made in experimental and theoretical investigations of PWFAs. For instance,
high-gradient [2, 3], high-efficiency and narrow energy spread acceleration of
a distinct trailing electron bunch [4, 5], and narrow energy spread
acceleration of positrons [6, 7] have been demonstrated using the FACET
advanced acceleration test facility at the SLAC National Accelerator
Laboratory (SLAC). A similar program is underway at the FLASHForward facility
at DESY using a high brightness 1-GeV electron bunch, making progress in high-
resolution wakefield measurement [8] and energy spread preservation in PWFA
[9].

Most past PWFA experiments at SLAC have used either a laser ionized or a beam
ionized lithium plasma source [10, 11, 12, 13, 14]. Beam-ionized argon plasmas
have also been used in the earlier FACET experiments [15]. The wakes are
produced by either 4 ps (1.2 mm) long $e^{-}$ or $e^{+}$ bunches (laser
produced plasma) or highly compressed 15-50 $\rm\mu m$ $e^{-}$ or $e^{+}$
drive bunches (beam-ionized plasmas). The low ionization potential of Li (5.4
eV) allows for the formation of a partially ionized low density ($<2\times
10^{14}~{}\rm{cm^{-3}}$) plasma using laser ionization or a high density
($<2\times 10^{17}~{}\rm{cm^{-3}}$) fully beam-ionized meter-scale plasma
columns for peak drive-bunch (henceforth referred to as the drive beam, driver
or beam) current of $>8$ kA (for $\sigma_{r}=30~{}\rm\mu m$). In the laser
ionization case, the beam creating a wake has to be aligned to propagate on
the axis of the plasma column whereas in the beam-field ionization case the
plasma axis and the beam axis are self-aligned. While this source has proved
to be remarkably reproducible and robust in a number of groundbreaking PWFA
experiments (in addition to those mentioned above, see references [16, 17, 18,
14, 19, 15, 20, 7]), it is found to be a limiting factor in high repetition
rate experiments beyond 1 Hz in continuous wave (CW) mode or 10 Hz in a burst
mode operation due to accumulative heating of the plasma. Furthermore, since
the lithium vapor column is confined in a high temperature heat pipe oven [11]
enclosure by buffer helium gas, there is no access to the plasma in the
transverse direction for diagnostic purposes. These difficulties could
potentially be overcome if a hydrogen plasma could be used instead of lithium
plasma. The main difficulty is that the higher ionization potential (IP) of
the hydrogen molecule (15.4 eV) requires either a high intensity ($>5\times
10^{14}~{}\rm{W/cm^{2}}$), multi-TW laser beam [21] or an electron beam with a
peak current $>30$ kA for beam-induced ionization. We note that at the present
time we have not considered even lower IP noble gases such as Ar, Kr, Xe
because of possible beam-induced multiple ionization that is known to inject a
substantial dark current into the wake [22, 23] thereby increasing the
complexity of a future multi-stage collider.

Even if one could trigger hydrogen ionization locally, the next challenge is
how to produce a long enough plasma to support a meter-scale wake such that
most of the drive bunch energy can be coupled to the wake for achieving a high
overall efficiency. Currently, work is in progress to produce meter-scale
columns of hydrogen plasma using laser ionization [24] and discharge in a
sapphire capillary [25]. One key experiment undertaken at the earlier FFTB
facility at SLAC showed that an ultra-high (50 GeV/m) gradient wake can be
sustained by a self-guided beam in a meter-scale lithium plasma [3]. In this
experiment the wake excited by a 42 GeV bunch was ultimately terminated by a
process called “head erosion” long before the drive bunch was substantially
depleted of its energy. Head erosion refers to the phenomenon where the
position of the ionization front in a beam ionized plasma recedes backwards
until the beam can no longer produce a wake [26]. Here we get around the head-
erosion limited beam propagation distance by reducing the drive bunch energy
to 10 GeV and using a relatively gentle beam focusing optics ($\beta^{*}\geq
50~{}\rm cm$) such that the head of the bunch ahead of the ionization front
diverges slowly, causing the ionization front to erode backwards slowly,
thereby increasing the pump depletion length [15]. Such beams and focusing
optics are now available at FACET-II, a state-of-the-art 10 GeV electron beam
facility for advanced accelerator research [27] that came online in 2022 at
the SLAC National Accelerator Laboratory.

The FACET-II facility is designed to deliver high-brightness electron bunches
with extreme parameters (e.g., $I_{\rm peak}>50$ kA) for advanced beam physics
research. It has been experimentally demonstrated that at the present stage of
commissioning of the FACET-II accelerator, the production of highly
compressed, low emittance beams can result in large shot-to-shot variation in
the current profile after the final stage of bunch compression due to radio-
frequency (RF) jitters and microbunching instability [28]. This leads to a
varying time-structured (not the usual single-Gaussian) pulse that features
one or multiple ultra-short ($<10$ fs) high peak current spikes. When focused
by the final focusing quadrupoles prior interaction point, the very first
spike can generate intense transverse electric fields capable of ionizing
higher IP molecular gases such as hydrogen over meter-scale lengths, whereas a
second much longer ($\sim$0.4 ps) but lower current bunch structure that
follows the ionization front excites a wake in the plasma. In a recent paper
[29] we have described the various diagnostics that we employ to characterize
the longitudinal phase space of the compressed electron bunch. These
diagnostics have shown that the 10 GeV electrons delivered by the linac,
operating in the single-bunch mode, have one or more current spikes but
neither their amplitude nor frequency can be presently resolved. Nevertheless,
in the past we have found that plasma formation in gases with different IPs
and the formation of non-evolving wakes as inferred from the energy loss of
the drive beam as a function of plasma density and length is ultimately the
best indicator of the beam brightness.

Another major innovation since the earlier experimental campaigns on the FFTB
and FACET is the development of the quasi-static PIC code QPAD [30]. QPAD is
particularly suitable for rapidly carrying out a large number of simulations
of the experimental outcomes as it effectively combines the quasi-static
approximation and azimuthal decomposition of the electromagnetic fields,
considerably accelerating the simulation process and making it feasible to
model meter-scale PWFA. This code in practice is typically an order of
magnitude more efficient than the previously used QuickPIC [31] and 2-3 orders
of magnitude more efficient than the fully self-consistent OSIRIS [32]. At
present the SLAC linear accelerator infrastructure allows experiments to be
carried out at a relatively high repetition rate (up to 30 Hz), while rapid
turnaround of the QPAD simulations makes it possible to simulate a large
number of experimental outcomes using the measured beam parameters for a
particular group of shots. In this experiment we have used QPAD extensively
for the first time to generate possible outcomes of the experiment using the
beamline simulations. This has allowed us to identify the conditions that are
needed to, i) generate meter-scale plasmas in hydrogen, ii) pump deplete the
10 GeV drive bunch, and iii) determine the energy transfer efficiency of the
portion of the drive bunch charge that is available to form the wake.

In this paper, we show that it is possible to generate a high-gradient wake in
meter-scale beam-ionized hydrogen plasma until some of the 10 GeV drive bunch
electrons are nearly fully depleted of their energy while transferring their
energy to plasma wake. Demonstration of pump depletion is one of the major
goals of the E300 experiment [33]. This onset of pump depletion occurs at a
hydrogen gas pressure of 1.5 Torr. At a higher pressure of 2.2 Torr more
electrons approach full pump depletion and nearly every shot shows pump
depletion. Despite the large shot-to-shot differences due to the variation in
the peak current and the current profile of the drive bunch, our analysis and
PIC simulations reveal that the energy transfer efficiency of the portion of
the drive bunch that follows the high current ionizing spike to the wake
reaches about 60%. This efficiency is observed for a plasma density of $\sim
7\times 10^{16}~{}\rm{cm^{-3}}$ (pressure of $\sim 2.2$ Torr) and a plasma
length of 50 cm. Furthermore, at this pressure we also observe the energy gain
of the tail electrons of several GeV.

##  2 Beamline and PIC simulations

###  2.1 Generation of time structured electron drive bunch and plasma
formation

Apart from the standard beam diagnostics found on an accelerator beamline,
such as wire scanners, beam position monitors and toroidal charge monitors
that give information about the beam size, position, and charge, the FACET-II
facility has advanced beam diagnostics such as electro-optic sampling (EOS)
[34], and an X-band transverse deflecting cavity (X-TCAV) [35] that measure
beam parameters like the length of a single bunch and separation between drive
and trailing bunches. When the beamline is set up for the high compression
mode of beam delivery, these parameters are extremely sensitive to RF
amplitude and phase jitter in the linac and can fluctuate from shot to shot.
During the current ramp up phase of the FACET-II facility not all the
diagnostics were operational for the experimenters. We therefore use
comprehensive start-to-end beamline simulations to predict the crucial beam
parameters at the interaction point. Starting from the photocathode injector-
modeled using the commercial code General Particle Tracer [36]\- the
simulations cover the entire one kilometer long beamline modeled using the
code Lucretia [37], a Matlab-based particle tracking script encompassing all
magnets, RF elements and collimators. Lucretia simulations on the LCLS
beamline have shown an excellent agreement with the experimental measurements
of the longitudinal phase space of the beam made using the X-TCAV diagnostic
[38].

Figure 1: Simulated current profile of the drive electron bunches. (a) Beam
current profile of 100 beamline simulations showing shot-to-shot fluctuations
of the peak current and the position of the current peak when a rms 0.1%
amplitude and 0.25-degree phase jitters of the 2.8 GHz RF are introduced. (b)
The longitudinal current profile of the first 25 shots. The lines are
vertically shifted to improve clarity.

Among the most crucial beam parameters is the current profile, or the
longitudinal phase space profile that directly influences the ionization
dynamics of the static-fill hydrogen gas. The optimal compression of the
electron bunch after propagation through the final bunch compressor before the
final focusing optics is sensitive to the RF amplitude and phase jitter. To
investigate this, we introduced in the simulation code a rms 0.1% jitter of
the RF amplitude and 0.25-degree jitter of the RF phase of the main
accelerator, and conducted 100 beamline simulations. These numbers are equal
to or smaller than the level of RF jitter expected for the SLAC linac. The
resulting simulated current profiles at the interaction point are summarized
in Fig. 1(a), with each row representing one independent simulation. To
enhance clarity, the current profiles of the first 25 shots are presented in
Fig. 1(b). We can see that there is a great deal of shot-to-shot variation of
the current profile even with such a small amount of jitter of the RF
amplitude and phase.

Figure 2: Meter-scale plasma generation. (a) An example of a current profile
derived from a slightly under compressed bunch [shot 4 from Fig. 1]. The
ionization degree, depicted by the black line, is calculated using the ADK
model, showing ionization initiation at 30 kA that reaches full ionization
within approximately 4 fs ($<$2 $\rm\mu m$). The grey shaded region indicates
the nonparticipating charge (NPC), while the orange shaded region represents
the participating charge (PC) following the ionization front. The inset
displays the corresponding longitudinal phase space of the bunch. (b)-(c)
Additional examples of a fully compressed and somewhat over compressed bunches
arising from the RF jitter. (d)-(f) Spatial distribution of ionization degree
of hydrogen molecule attained using the PIC code QPAD at 2 Torr gas pressure
using the bunches in (a)-(c), respectively. The white lines indicate the
length of the plasma (see text). The dashed black curves depict the spot size
evolution in vacuum.

The effects of variations in the magnitude and location of the current spike
on the formation of beam-ionized hydrogen plasmas were investigated using
QPAD. The results are shown in Fig. 2. Figure 2(a) shows the current profile
of the drive bunch, with RF amplitude and phase settings similar to those used
in the experiment [shot 4 in Fig. 1]. The current profile often exhibits one
or more (not resolved) femtosecond (fs) spikes, with an average peak current
surpassing 60 kA and a mean length of $\leq$2 $\rm\mu m$ (FWHM). Below the
prominent current spike, there exists a relatively lower current yet
considerably broader charge distribution spanning over up to 100 $\rm\mu m$
with a peak magnitude of $<10$ kA.

The black solid line in Fig. 2(a) shows the ionization degree of the first
electron of hydrogen molecules (IP=15.4 eV), plotted as a function of
longitudinal position. This calculation was performed at the radial position
where the transverse electric field of the beam attains maximum strength,
utilizing a spot size of $\sigma_{r}=30~{}\rm\mu m$ and the ADK model [39].
This calculation underscores that the narrow current spike is sufficiently
intense to rapidly ionize hydrogen molecules, leading to plasma production at
the location of the spike. Ahead of the spike, the beam current falls below
the threshold (30 kA) required for hydrogen molecule ionization. Consequently,
the energy contained in this part of the bunch is wasted and appears at the
initial energy point (nominally 10 GeV) on the spectrometer. We call this
charge and any additional charge that happens to be at the location in the
beam where the longitudinal electric field of the beam-induced wake is zero
and therefore does not lose energy as the non-participating charge [NPC,
marked by the grey shaded region in Fig. 2(a)-(c)]. For this current profile,
the percentage of NPC amounts to approximately 30% of the total charge,
consistent with the observations from the experimental data as we shall later
see.

Also shown in Fig. 2(a-c) are the longitudinal phase space plots of the drive
bunch for the nominal bunch compressor magnet settings that results in pulses
that are under compressed as in Fig. 2(a) to optimally compressed, Fig. 2(b),
to over compressed- Fig. 2(c). This case of over-compression leads to a
current profile that has two spikes separated by about 15 $\rm\mu m$.

A set of 50 PIC simulations were conducted using the simulated current
profiles [the first 50 shots in Fig. 1(a)] to investigate plasma and wake
formation in 2.0 Torr (one of the pressures used in the experiment) static-
fill hydrogen gas. The PIC simulations self-consistently include the
ionization of the hydrogen gas using the ADK model [39] and track the
evolution of the drive bunch within the meter-scale self-ionized plasma.
Molecular hydrogen has an ionization potential of 15.4 eV, larger than the
13.6 eV of hydrogen atoms. Therefore in these simulations, we employed atomic
hydrogen but with an ionization potential of 15.4 eV to accurately mimic the
ionization pathway of molecular hydrogen by an ultrashort beam [21, 40]. In
the simulation, we utilized a moving window with dimensions of
$z=10~{}c\omega_{p}^{-1}$ (beam direction) and $r=7~{}c\omega_{p}^{-1}$
(transverse direction), divided into 1000 and 400 cells along each direction,
respectively, where $c\omega_{p}^{-1}$ represents the plasma skin depth for
the normalized density of $n_{e}=6.48\times 10^{16}~{}\rm{cm^{-3}}$. The
current profile of the drive bunch, acquired from the beamline simulation, was
imported into the QPAD simulation using a piecewise-linear approximation with
a discretization step of $\Delta z=0.2~{}\rm\mu m$, ensuring the resolution of
fine structures in the current profile. For simplicity and stability, the
drive bunch was approximated by a cylindrically symmetric Gaussian
distribution in the transverse plane, with a normalized emittance of 20
$\rm\mu m$ and focused to a transverse spot size of 30 $\rm\mu m$, matching
the experimentally measured size. This approximation removes the slice
misalignment presented in the beam distribution obtained from the beamline
simulation due to coherent synchrotron radiation (CSR) in the final bunch
compressor.

Figure 2(d) displays the spatial distribution of gas ionization degree for the
nominal current profile shown in Fig. 2(a). This result was obtained by
stitching the radial ion density profile at a given longitudinal location
(e.g., average of the slices between 30 to 50 $\rm\mu m$ after the current
spike) within the moving simulation window for every time step. The black
dashed line traces the evolution of the beam’s spot size in vacuum, revealing
a 30 $\rm\mu m$ focus at $z=2$ meters. In this instance, hydrogen molecules
were ionized over a span of 50 cm as indicated by the white solid line, which
covers the region of plasma that is fully ionized and the on-axis un-ionized
region is narrow ($<5~{}\rm\mu m$). Note that other criteria, for instance,
the region where the transverse size of the fully ionized region is broader
than the unionized channel, results in a longer length, as indicated by the
white dashed line. Figure 2(e)-(f) exhibit the outcomes corresponding to the
other two representative current profiles shown in Fig. 2(b)-(c). In all cases
there is a $\rm\mu m$-scale on-axis region where no ionization occurs because
the radial electric field is below the ionization threshold.

Figure 2(d)-(f) show that the drive bunch with peak current exceeding 60 kA
can generate meter-scale plasmas. In experiments using tightly focused drive
bunches, the wake excitation may be limited by beam head erosion. If the beam
head erosion limited plasma length is less than the pump depletion length,
then the total energy transfer from the drive bunch to the wake can be
affected [3]. However, in simulations and experiments reported here, head
erosion is not a concern due to the relatively gentle beam focusing optics
($\beta^{*}\geq 50$ cm), much higher peak current and 10 GeV energy of the
beam. In this scheme, the product of the decelerating gradient and plasma
length (see Table 1) is sufficient to drive the beam electrons towards pump
depletion.

Table 1: Beam, plasma, and wake parameters derived from PIC simulations.

Shot number |  $Q_{\rm NPC}$ fraction | Peak plasma density | Plasma length | Max $E_{\rm DEC}$
---|---|---|---|---
|  | [$10^{16}~{}\rm cm^{-3}$] | [m] | [GeV/m]
4 | $30\%$ | 6.48 | 0.50a $\sim$ 0.75b | 14.0
6 | $21\%$ | 6.48 | 1.57 $\sim$ 2.77 | 16.4
8 | $9\%$ | 6.48 | 0.93 $\sim$ 2.03 | 28.1

aLength of the fully ionized region where the on-axis un-ionized channel is
narrow ($<5~{}\rm\mu m$), indicated by the white solid lines in Fig. 2(d)-(f).
bLength of the fully ionized region where the transverse size of the fully
ionized region is broader than the un-ionized channel, marked by the white
dashed lines in Fig. 2(d)-(f).

The key quantities relevant to the topic of this paper can be derived from
these simulations and are summarized in Table 1, highlighting substantial
variations arising from current profile fluctuations. For instance,
nonparticipating charge ranges from 9% to 30% for shots where ionization takes
place (NPC is 100% if peak current of the spike falls below the ionization
threshold). Notably, the minimum NPC fraction observed in the experiment was
about 25%. In beamline simulations, the initial current profile of the
electron bunch produced from the photocathode likely differs from the actual
profile in the experiment. With a peak current exceeding 60 kA, the electron
bunch is able to singly ionize hydrogen molecules, albeit over varying
distances from 0.5 to 1.6 meters. In contrast, electron bunches with peak
currents below 60 kA or gas pressures lower than 0.08 Torr (see Fig. 3)
partially ionize the gas over few tens centimeters, yielding a much shorter
plasma with nonuniform reduced densities. Consequently, the maximum
decelerating field experienced by the drive bunch fluctuates from 6 to 28
GV/m. Despite the substantial shot-to-shot fluctuations in plasma generation
and wake excitation observed in both simulations and experiments, we will
demonstrate that crucial information, including pump depletion and energy
transfer efficiency from beam to wake, can still be extracted from the
experimental data and PIC simulations.

###  2.2 Wake Excitation Modeled using QPAD Simulation

Following the ionization of hydrogen gas, these beams can excite a long thin
column of wake that is self-aligned to the plasma. Figure 3 illustrates
various representative simulation outcomes employing the nominal current
profile depicted in Fig. 2(a) at different gas pressures. Note that these
simulations begin one meter upstream of the drive bunch’s focal plane, as
opposed to the prior two meters. This is reasonable since plasma with a
density $>1\%$ of the fully ionized density is contained within this region.
In Fig. 3(a), we show the spatial distribution of the ionization fraction as a
function of hydrogen pressure. Once the plasma formation is triggered by the
large current spike, the plasma electrons begin to be expelled transversely
and the plasma ions exert a focusing force on the subsequent beam slices
following the ionization front. At the lowest pressure, the focusing force
remains relatively mild, and the transverse spot size of the beam diminishes
to roughly half its size in vacuum (illustrated by the dashed black line).
With increasing plasma density, however, the focusing force exerted by the
plasma ions intensifies, yielding a progressively narrower on-axis region that
remains un-ionized.

Figure 3: (a) Spatial distribution of ionization degree of hydrogen molecule
obtained from QPAD simulation using the nominal beam with three different gas
pressures. Experimental datasets were acquired at these and other pressures.
The dashed black line shows the evolution of the beam size in vacuum. (b)
Wakes excited by the drive bunch at the vacuum focus location. The blue lines
show the on-axis density profile of the drive bunch. The peaks are due to
betatron oscillations of these electrons. (c) The radial density profiles
(green for electron and grey for ion, both normalized to the corresponding
neutral gas density $n_{0}$) evaluated at $\xi=100~{}\rm\mu m$ [marked by the
dashed line in the top row of (b)]. (d) and (e) show the transverse focusing
field $F_{r}=E_{r}-B_{\theta}$ and the longitudinal field $E_{z}$ at the same
slice. The shaded regions (blue) indicate the micro channel where the hydrogen
gas is not ionized by the beam and contains a portion of the tail of the beam.

Figure 3(b) illustrates the density distribution of the drive bunch (orange)
and the plasma (green) at these various densities. The hydrogen gas is rapidly
ionized by the current spike, leaving the beam electrons in front of the spike
unaffected. At the lowest density, the drive bunch primarily occupies the
front of the wake, where the ionized electrons are blown out into the neutral
gas region. The beam electrons experience only the rising but small
decelerating field [0.5 GeV/m at the dotted line in Fig. 3 (b)], leading to a
small energy loss to the wake. With increasing plasma density, the wake’s
length shortens, while the field strength intensifies, causing the drive bunch
to lose energy at a higher rate. In the 0.5 Torr case, the back of the drive
bunch extends to the center of the bubble where the longitudinal electric
field changes sign. This represents a scenario where all the electrons among
the participating charge suffer a varying degree of energy loss. At higher
densities the wake wavelength becomes shorter relative to the drive bunch
length. In all of these cases, two longitudinal slices of the beam can suffer
the same energy loss because the decelerating field experienced by the beam is
double-valued. Consequently, there can be a charge peak around the minimum
energy (maximum energy loss) of the dispersed electron spectrum in the actual
experiment. At still higher plasma densities (e.g., $>1.5$ Torr case), the
charge comprising the back of the drive bunch crosses the point where the
electric field of the wake changes sign (where the the bubble radius is the
largest at roughly 100 $\mu m$) and extends into the accelerating phase,
extracting energy from the wake which corresponds to energy gain on the energy
spectrometer. These characteristic features of the wake are indeed reflected
in the measured electron spectra as we shall later see.

The rest of Fig. 3 displays the radial density profiles of electrons ($n_{e}$)
and ions ($n_{i}$), Fig. 3(c), along with the radial variations of the
transverse focusing Fig. 3(d), and longitudinal decelerating field Fig. 3(e)
for the drive bunch evaluated at $\xi=100~{}\rm\mu m$. As plasma density
increases, the focusing field of the wake intensifies, causing the low-density
tail of the drive bunch to contract in the transverse direction. Consequently,
the un-ionized region (marked by the blue shaded area) becomes narrower. The
proportion of drive bunch charge within these channels diminishes from 22% for
the 0.08 Torr case to 2.5% for the 1.5 Torr case. Therefore, this small
fraction of the electrons enclosed in the un-ionized channel region has
negligible impact on the beam-to-wake energy transfer efficiency. Importantly,
as shown in Fig. 3(d) and (e), the focusing field is zero within the unionized
channel (see the regions marked in light blue) and the decelerating field is
uniform and has the same value inside as that outside the channel, making it
suitable for positron acceleration [14].

###  2.3 Experimental setup

The FACET-II experimental area is described in detail in [29]. Here in Fig. 4,
we present a sketch of the setup and focus on the relevant diagnostics for the
results presented in this paper.

Figure 4: Sketch of the FACET-II experimental area and relevant diagnostics
for the results presented in this paper. The 10 GeV electron beam propagates
from left to right and undergoes focusing by two (only one set is shown) sets
of focusing quadrupoles into the experimental chamber. The region between the
two beryllium windows with self-drilled holes is filled with hydrogen gas at
an adjustable pressure ($<5$ Torr). Following interaction with the beam
(field)-ionized plasma, the electron beam is dispersed and imaged by an energy
spectrometer, comprising finely tunable imaging quadrupoles, a coarsely
adjustable dispersive dipole, and a large field of view (LFOV) phosphor
detector. An x-ray detector measures the integrated betatron x-ray signals.
Three cameras, Topview, Sideview1 and 2 collect the time-integrated plasma
light in the visible portion of the electromagnetic spectrum.

The compressed 10 GeV electron beam was focused by two sets of quadrupoles
into a static fill of hydrogen gas with a tunable pressure between 0.07 Torr
to 2.2 Torr (maintained within 1% precision). The gas was confined by two 50
$\rm\mu m$ thick beryllium windows, with holes drilled in situ by the electron
beam itself, spaced approximately four meters apart. The slow rate of flow of
hydrogen gas out of these small holes in the Be windows is matched by a
continuous flow of gas into the system to maintain a constant gas pressure
between the Be windows. The rate of flow through this system is not expected
to product a significant density gradient from the upstream to downstream
beryllium window. The gas flowing out of the Be windows is pumped out by a
four-stage differential pumping system that is used to reduce the beamline
pressure back to ultra-high-vacuum ($10^{-9}$ Torr) in the accelerator from
the four-meter-long hydrogen gas region between the two beryllium windows
which formed the hydrogen gas chamber. The beam was focused at the location
monitored by the topview camera (downstream side of the experimental chamber)
to a round spot of $\sim$30 $\rm\mu m$ with $\beta^{*}\approx 50$ cm.

As the transverse electric field of the electron beam surpasses the hydrogen
molecule field ionization threshold, a plasma is rapidly formed. The resulting
self-emission from this plasma was observed by three cameras covering a total
distance of approximately 1.5 meters. Plasma light was evident on all three
cameras for hydrogen gas pressures exceeding 0.07 Torr, which indicates the
formation of meter-scale plasmas. However, this does not necessarily imply
that the plasma density, temperature or duration of the plasma emission was
the same at these three locations. After passing through the plasma, the beam
was directed to downstream diagnostics, enabling measurements of parameters
such as charge, energy spectrum, and emittance [41]. The charge entering the
hydrogen chamber was measured by a toroid positioned upstream of the chamber.
All these diagnostics operated on a single-shot basis [42].

##  3 Experimental Results

###  3.1 Energy Loss as a Function of Gas Density

In the experiment, the pressure of the static-fill hydrogen gas was varied
between 0.07 and 2.2 Torr- the upper range of pressure being limited by the
differential pumping system. As the electron beam interacted with the plasma,
its longitudinal slices underwent energy loss to or gain from the wake. The
energy spectrum of the electron beam after interaction was recorded by the
large field of view (LFOV) screen of the imaging spectrometer. For each
hydrogen pressure setting, we recorded approximately 200 consecutive shots to
ensure reliable data collection.

Figure 5: Linearized energy spectra of three representative datasets obtained
at varied pressures. Each column represents a single-shot measurement. Each
dataset was sorted by the total energy loss (in increasing order) of the
bunch. Insets in (a) show two illustrative spectra, highlighting the 10 GeV
peak (orange) and the decelerated segment of the beam (green). The shots
enclosed by the dashed red rectangles in (a)-(c) are used to calculate the
energy deposited in the plasma. For the 0.08 Torr shots the total charge with
and without beam propagation through plasma is conserved, whereas for (b) and
(c) a significant number of electrons with $<$5 GeV energy are not captured by
the spectrometer.

Figure 5 presents “waterfall plots” of 200 linearized energy spectra for the
drive bunch across three datasets obtained at varying gas pressures. The
camera that monitors the LFOV screen was covered by an ND2 filter so as to
avoid possible saturation of the detector by the large amount of charge in the
10-GeV peak to allow for full charge reconstruction. Each column within a
dataset represents a single shot measurement (integrated over the undispersed
direction). The 10 GeV peaks observed across all datasets suggest the presence
of electrons that did not interact with the plasma. The signal below the 10
GeV peak corresponds to drive bunch energy loss. Unsurprisingly, all three
datasets exhibit considerable fluctuations in energy loss, consistent with
substantial variability in drive bunch parameters- most likely the peak
current of the spike and its location within the bunch, as well as bunch
length of the low current bunch structure, crucial factors in hydrogen gas
ionization and energy loss to the wake. Despite these fluctuations, a clear
trend of larger energy loss (electrons with energy $<10$ GeV) with increasing
pressure is evident, indicating that a larger wake amplitude-length product
resulted as the hydrogen gas pressure was increased. It is worth noting that
the shot-to-shot charge variation in these datasets was about 2%, namely,
charge variation cannot account for the energy loss variation on a shot-to-
shot basis. Also note that at and beyond a pressure of 0.5 Torr, there is some
energy gain signal (electron signal with energies $>$10 GeV).

During these data runs, the imaging energy of the spectrometer was set to 5
GeV but the dipole magnet was set such that electrons with energy less than 5
GeV were not captured by the spectrometer, however, the measurement of lower
charge is possible with this diagnostic down to $<$2 GeV through the use of
reduced dipole strength as we shall see later. We segment the energy spectrum
recorded by the spectrometer into two distinct portions: the 10 GeV peak and
the decelerated part (5-10 GeV), as exemplified in the insets of Fig. 5(a). In
the case of shot no. 43, a single peak at 10 GeV is evident, indicating that
the drive bunch experienced no energy loss, likely due to the peak current of
the beam not reaching the required threshold for ionizing hydrogen molecule.
Conversely, for another example (shot no. 193), the energy spectrum exhibits a
large but reduced magnitude peak at 10 GeV (orange) alongside a broader peak
at lower energies (green) which represents the decelerated segment of the
drive bunch. In both cases, the 10 GeV peak corresponds to the non-
participating charge, which can be distinguished and separated from the
decelerated segment by applying a Lorentzian fit to the spectrum. The minimum
NPC fraction ($Q_{\rm NPC}/Q_{\rm total}$) observed in the experiment was
$\sim 25\%$.

###  3.2 Direct and Deduced Evidence for Energy Depletion of the Drive Bunch

To attain the highest energy transfer efficiency from the drive bunch to the
wake, a significant depletion of the drive bunch energy is necessary. The most
straightforward way to observe energy depletion is to demonstrate that the
minimum energy recorded by the spectrometer approaches zero. For instance, a
recent work shows that a fraction of a 500-MeV electron bunch loses almost all
its energy by driving wakes in discharge plasmas in a 20-cm-long
capillary[25]. However, the beamline after the interaction point can
effectively focus and transport electrons only within a certain energy range.
For instance, at FACET-II, electrons with energy $<$1 GeV in particular, are
prone to loss during the transport due to their substantial divergence.

Figure 6: Direct (a)-(c) and deduced (d) evidence of some electrons
approaching pump depletion. (a) A representative energy spectrum (raw data
before linearization of the energy axis) recorded at a pressure of 2.17 Torr
but with a lower dispersion setting of the spectrometer dipole shows that the
energy of some of the decelerated charge indeed extends to below 2 GeV. Note
that the 10 GeV peak is saturated on the LFOV screen. (b) A dataset of 100
consecutive shots at 2.17 Torr. (c) Linearized spectra of the dataset shown in
(b), sorted by increasing energy loss of the electrons. The NPC appears as a
broad peak after linearization due to saturation of the signal. Also note that
the quads were set to focus at 2 GeV, broadening the 10 GeV peak further. The
shots enclosed by the red dotted rectangle are used to calculate the energy
deposited in the plasma and for estimating the energy transfer efficiency.
Note that 73 out of 100 of the shots shown in (b) and (c) show decelerated
electrons with energy extending below 2 GeV. (d) Maximum energy loss observed
on the spectrometer plotted against betatron emission-x-ray yield obtained in
a narrow cone angle in the forward direction (Fig. 4) for a different dataset
taken at 2.0 Torr [Shown in Fig. 5(c)]. For this dataset the spectrometer only
captured electrons with an energy loss smaller than 5 GeV (indicated by the
dashed red line). The red line represents a linear fit to the correlated data
for x-ray yield less than $5\times 10^{8}$ counts and energy loss less than 5
GeV. If this correlation continued up to 10 GeV energy loss, the intersection
of the linear fit with the 10 GeV line would indicate the onset of pump
depletion. The dashed black lines indicate the 95% confidence interval of the
fit. A larger x-ray yield beyond the intersection of the blue dotted line and
the x-ray counts implies more energy-depleted electrons.

In Fig. 6(a) we show an example of the measured energy spectrum at a pressure
of 2.17 Torr but with a less dispersive spectrometer dipole setting which
allowed us to record on the LFOV sub-5 GeV electrons. The raw dataset of 100
shots before linearization of the energy axis is shown in Fig. 6(b). These
data show that the spectrum indeed extends to below 2 GeV, providing direct
evidence of approaching pump depletion at this pressure. The linearized
spectra for the whole dataset are shown in Fig. 6(c). Note that after
linearization, the low-energy signal becomes more prominent. In 73 out of the
100 shots, the charge of electrons with $E<3$ GeV exceeds 100 pC, indicating
that for a plasma density of $7\times 10^{16}~{}\rm cm^{-3}$ these 73 shots
approached drive bunch pump depletion.

Now we provide supporting evidence of energy depletion in our experiment from
the x-ray diagnostic [43]. In Fig. 6(d), we present the correlation between
the maximum energy loss recorded by the spectrometer and the total x-ray yield
in the forward direction mainly due to betatron motion of the electrons in the
wake’s ion cavity. This data is from energy loss shown in Fig. 5(c) where the
maximum energy loss limited by the setting of the dipole dispersion is 5 GeV.
Although the energy loss data is only available up to 5 GeV, the x-ray
emission data is available for all shots. A linear correlation between the
energy loss and x-ray emission is therefore only observed up to 5 GeV followed
by a constant energy loss for higher values of x-ray signal. The red line in
Fig. 6(c) shows the best fit to the data points with an energy loss up to 5
GeV. Here we only show the 2.0 Torr dataset for clarity but all three datasets
in Fig. 5 show a similar trend albeit with different slopes since the maximum
decelerating field and plasma length are pressure dependent. The maximum
energy loss corresponds to the maximum decelerating field experienced by one
slice of the beam throughout the plasma length at a given plasma density. In
contrast, apart from the wakefield strength (focusing force) and plasma
length, the betatron x-ray yield also depends on variables such as beam energy
and particle displacement from the beam propagation axis. Despite these
complex inter-dependencies of x-ray yield with beam, wake, and plasma
parameters, we hypothesize that the observed linear correlation of the
betatron x-ray yield and the maximum energy loss up to 5 GeV can be
extrapolated up to 10 GeV, as indicated by the red line representing the best
fit to the data.

With this premise, the point where the extrapolated red line reaches the 10
GeV energy loss denotes the onset of pump depletion, i.e., signifies that some
of the beam electrons have lost all 10 GeV energy while experiencing the
largest decelerating field. Extending the same hypothesis, any further
increase of the x-ray yield is interpreted as more electrons reaching pump
depletion.

##  4 Comparison between PIC simulations and Experiments

Up until now we have discussed the observed pressure-dependent energy loss of
the drive bunch. However, as shown in Fig. 3, when the pressure becomes $>0.5$
Torr some of the tail electrons begin experiencing the accelerating phase of
the wake and therefore we expect to see the onset of energy gain in addition
to energy loss on the spectrometer. Qualitatively, this is indeed what is
observed in Fig. 5(b), (c) and Fig. 6. Since the beam current profile changes
dramatically and is unknown in real-time data and we have used one particular
current profile- that shown in Fig. 2(a)- to simulate the energy gain and loss
results as a function of gas pressure any quantitative agreement is somewhat
fortuitous. The results are presented in Fig. 7.

Figure 7: Energy loss and gain of the drive bunch: comparison with PIC
simulations. (a) Energy spectrum of an example shot from a 0.3 Torr dataset.
Left panel: raw image from the spectrometer. Right panel: x-integrated energy
spectrum. (b) Another example spectrum from a 1.5 Torr dataset with the
spectrometer set to highlight the accelerated charge. Simultaneous
measurements of energy loss portion of the spectrum were not taken. (c) Energy
spectrum of the nominal drive bunch [see Fig. 2(a)] after interaction with
hydrogen gas at varying pressures from PIC simulations (blue lines) and
experiments (thick orange lines). The dashed black lines show the spectrometer
limit (electrons with energy below this limit were not captured) for these
datasets (note that the dipole setting for the 1.5 Torr case in the bottom row
is different in order to measure electrons that have gained energy). The
imaging energy was set to 5 GeV for the top three rows and 18 GeV for the
bottom row in (c).

In Fig. 7(a), an example of raw energy spectrum of the decelerated bunch from
the 0.3 Torr dataset is displayed. The spectrum indicates a minimum energy of
6 GeV (equivalent to a maximum energy loss of 4 GeV). At this low density, the
nonlinear wake wavelength is relatively long such that the entire bunch
experiences only deceleration. In contrast, Fig. 7(b) shows a spectrum from
the 1.5 Torr dataset, where the spectrometer imaging energy is set at 18 GeV.
The smallest size appears to be at 16 GeV because there is very little charge
at 18 GeV [see the orange line in the bottom row of Fig. 7(c)]. Nevertheless,
this result shows that some charge has indeed gained 8 GeV energy from the
wake. Figure 7(c) shows the linearized energy spectra for four representative
shots obtained at different gas pressures. The experimental data is
illustrated by the orange lines. Across all cases, the prominent 10 GeV peak
stems from the NPC. For datasets with pressures below 0.3 Torr, the lower-
energy peak corresponds to the maximum decelerating field. As we have
explained, this peak results from the double-valued decelerating field
experienced by the drive bunch. The 5 GeV cut-off in the 0.5 Torr data arises
from the spectrometer limit. In the 1.5 Torr case, the accelerated segment of
the energy spectrum features a slight peak at 14 GeV and extends up to 18 GeV.
Such a peak at 14 GeV could result from the drive bunch having a similar but
smaller secondary charge peak at a particular longitudinal location. The
simulated energy spectra, depicted by the blue lines, exhibit a reasonable
agreement with the observed spectra. This comparison suggests that the
longitudinal phase space distribution or the current profile we used for our
QPAD modeling was likely the most frequent profile in the experiments.

##  5 Energy Deposited into the Wake and Beam-to-Wake Energy Transfer
Efficiency

###  5.1 Energy Deposited by the Beam into the Plasma Wake

In PWFA, energy transfer from the drive to the trailing or accelerating beam
occurs in two steps: First, the driver deposits its energy by exciting a
large-amplitude wake and second, the particles in the trailing bunch extracts
energy from this wake as it gains energy. In the blowout regime of PWFA
reached in previous experiments that used a Li plasma [4, 5, 6], the
(nonevolving) wake, once formed, does not change as the drive beam propagates
through the plasma and eventually approaches pump depletion. This makes it
rather straightforward to determine the energy deposited/extracted into/from
the wake per unit length over the length of the wake. During this data run on
FACET-II, we have used just one (drive) bunch to estimate the energy transfer
efficiency from the driver to the wake when at least a portion of the beam
charge was fully depleted of its energy.

Utilizing the raw data such as that presented in Fig. 5, we can calculate the
energy deposited into the plasma by the drive bunch directly for shots where
the maximum energy loss is $<$5 GeV (i.e., for hydrogen pressure $<$0.5 Torr).
For these data the drive bunch propagation is neither beam-head erosion nor
pump depletion limited. This is done by integrating the energy spectrum to
quantify the energy carried by the beam recorded by the spectrometer at the
end of the transport line. The charge of the original beam was measured by a
toroid upstream of the gas region, allowing us to calculate the total initial
energy contained in the incoming 10 GeV beam (16 J at 1.6 nC of total charge).
We find that for a maximum energy loss up to 5 GeV, all electrons (within a
measurement error of $<$2.5%) reach the spectrometer after they are dispersed
after interaction with the plasma. Assuming that these highly relativistic
electrons only couple their energy to the wake, we evaluated the energy
deposited in the plasma for ten shots enclosed in the dotted dashed rectangle
in Fig. 5(a), by subtracting the final energy measured on the spectrometer
from the initial beam energy. We then calculated the percentage efficiency of
energy transfer to the wake, from the fraction of the energy actually
deposited in the plasma divided the maximum energy available to be deposited
in the plasma times 100. Note that the efficiency calculation was done on a
shot-to-shot basis since the NPC thus the available energy fluctuates. This
procedure works well for energy loss data taken below hydrogen pressures of
0.5 Torr (see Fig. 5).

Figure 8: Deposited energy and effective beam-to-wake energy transfer
efficiency vs. gas pressure. (a) Deposited energy. The blue and orange lines
represent the lower and upper bound of deposited energy calculated using the
spectrometer data. Each data point represents the average of 10 shots with
largest deposited energy and the error bars indicate the standard deviation.
For datasets with pressure $\leq 0.3$ Torr, the two curves overlap since
charge loss during beam transport after interaction did not happen. For higher
pressures, the unknown energy of the missing charge introduces separation
between the two estimates (lower and upper bound) where the actual deposited
energy falls in the grey shaded region. The green line depicts the results
obtained from QPAD simulations using the nominal current profile [see Fig.
2(a)]. (b) Beam-to-wake energy transfer efficiency. The red diamonds in (a)
and (b) show the deposited energy and efficiency retrieved from the 2.17 Torr
dataset shown in Fig. 6(b).

When the maximum energy loss exceeds 5 GeV we estimate the maximum and minimum
energy deposited into the plasma (for hydrogen pressure of 0.5, 1, 1.5 and 2
Torr datasets) as follows. We assume that the energy contained in the x-rays
and plasma emissions is small enough to be neglected. We then first estimate
the energy deposited by the electrons that have lost up to 5GeV energy as
before. The second part is the energy deposited by those electrons that lose
more than 5 GeV energy and therefore do not appear on the spectrometer screen
[“the missing charge” (MC)]. We can estimate the upper and lower bounds for
the energy these electrons deposit. To do this, we attribute two extreme
energies contained in the MC. For instance, if we assume that the energy of MC
is $E_{\rm MC}=5$ GeV, then the additional deposited energy would be $Q_{\rm
MC}\times 5$ GeV. Conversely, if we assume that MC has been fully depleted of
energy, i.e., $E_{\rm MC}=0$, then the additional energy deposited into the
plasma by the missing charge is $Q_{\rm MC}\times 10$ GeV. These two estimates
added together give lower (underestimate, shown by the blue curve) and the
upper (overestimate, shown by the orange curve) bounds for the energy
deposited into the plasma wake, respectively. The results are shown by the
blue and orange curves in Fig. 8(a), where each data point represents the
average of the 10 shots with maximum deposited energy for that dataset
(enclosed by dashed red rectangles in Fig. 5) and the error bar indicates the
standard deviation. For pressures higher than 0.3 Torr, these two curves
deviate due to the unknown energy of the missing charge. It is not a surprise
that the relatively large energy range not covered by the spectrometer (0-5
GeV) introduces a large uncertainty in the deposited energy (the grey shaded
region). The actual deposited energy should fall in the grey shaded region.

The green curve represents the QPAD simulation result. In these simulations,
we used the nominal current profile depicted in Fig. 2(a) and changed gas
pressure only. The simulation curve shows a similar trend with the
experimental data and suggests a deposited energy of $\sim 7$ J for datasets
with pressure above 1.0 Torr.

The red diamond in Fig. 8(a) represents the measured deposited energy
retrieved using the 2.17 Torr dataset shown in Fig. 6(b), where the energy
spectra extend to below 2 GeV. For this dataset a lower estimate of the
deposited energy was obtained by calculating the energy lost by the electrons
with $E<$8 GeV range on the LFOV spectrometer since the 10 GeV peak in the raw
images was saturated due to the removal of the ND2 filter so as to make the
low-energy part of the spectra more prominent. The data point is the average
of 5 shots with the largest energy loss and the error bar represents the
standard deviation.

###  5.2 Estimate of Beam-to-Wake Energy Transfer Efficiency at Pump Depletion

Once we have the deposited energy (on a shot-by-shot basis), we can calculate
the energy transfer efficiency from the beam to the wake by dividing the
deposited energy by the total available energy (i.e., the energy carried by
the NPC charge is omitted) for that shot and times 100. The results are
plotted in Fig. 8(b). Again, each data point with $\leq 2$ Torr pressure
corresponds to the average of 10 shots with maximum deposited energy for that
dataset. The red diamond represents the efficiency retrieved from the 2.17
Torr dataset, where only the electrons with $E<8$ GeV were used in calculating
deposited energy and efficiency. The green curve shows the QPAD simulation
results using the current profile shown in Fig. 2(a). Note that when
calculating the simulated efficiency, the energy carried by the 30% non-
participating charge has been omitted like we did in the experimental data
analysis. The simulation results suggest that for datasets with a pressure
above 1.0 Torr, the beam-to-wake energy transfer efficiency reaches about 65%,
which agrees reasonably with the 60% efficiency retrieved from the 2.17 Torr
dataset. These results therefore suggest that the beam-to-wake energy transfer
efficiency has reached 60% for pressures higher than 1.0 Torr (plasma density
$>3.2\times 10^{16}~{}\rm cm^{-3}$).

##  6 Conclusion

In conclusion, we have presented the analysis of the first experimental run by
the PWFA Collaboration carried out at FACET-II. All experiments were conducted
utilizing a single drive electron bunch. The linac setup produced time-
structured beams that frequently featured one or more ultrashort, high-current
spikes superimposed on a broader lower-current charge distribution. Our
experimental observations and beamline simulations have revealed noteworthy
fluctuations in plasma production and subsequent wake excitation, primarily
attributable to variations in beam compression induced by RF jitter.
Nevertheless, we have demonstrated the feasibility of utilizing such high
current spike beams to field-ionize molecular hydrogen, thereby generating
meter-scale plasmas. Furthermore, we showed the capability of generating
large-amplitude wakes that, beyond a certain pressure threshold ($>$1.5 Torr),
lead to energy depletion of a significant portion of the 10 GeV electrons
while transferring approximately 60% of the useful beam energy to the wake. We
also provided evidence that certain electrons in the rear of the bunch can
gain up to 8 GeV of energy from the wake. All experimental observations are
reasonably replicated by PIC simulations conducted using the QPAD code.

## Acknowlegement

This work was supported at UCLA by the U.S. Department of Energy through Grand
No. DE-SC0010064, and at SLAC by the U.S. Department of Energy under contract
number DE-AC02-76SF00515. This research used resources of the National Energy
Research Scientific Computing Center (NERSC), a U.S. Department of Energy
Office of Science User Facility located at Lawrence Berkeley National
Laboratory, operated under Contract No. DE-AC02-05CH11231 using NERSC award
HEP-ERCAP-MP113. The authors thank Qianqian Su, Lance Hildebrand and Yujian
Zhao for their help with the QPAD code development, as well as Lauren Alsberg,
Max Gilljohann, Carsten Hast, Ryan Loney, Aime Matheron, and Marcellus Parker
for their help with the experiment. A. Knetsch and P. San Miguel Claveria were
supported by the France-Stanford Center for Interdisciplinary Studies for
their travels to SLAC National Accelerator Laboratory. E. Gerstmayr was
supported by the U.S. Department of Energy, Office of Science, Fusion Energy
Sciences under Award DE-SC0020076.

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