Relativistic Plasma Physics in Supercritical Fieldsa
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Relativistic Plasma Physics in Supercritical Fieldsa)
P. Zhang,1, b) S. S. Bulanov,2, c) D. Seipt,3, d) A. V. Arefiev,4, e) and A. G. R. Thomas3, f)
1)
Department of Electrical and Computer Engineering, Michigan State University, East Lansing,
Michigan 48824-1226, USA
2)
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
3)
Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, Michigan 481099-2099,
USA
4)
Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla,
California 92093, USA
(Dated: 15 May 2020)
arXiv:2001.00957v2 [physics.plasm-ph] 14 May 2020
Since the invention of chirped pulse amplification, which was recognized by a Nobel prize in
physics in 2018, there has been a continuing increase in available laser intensity. Combined
with advances in our understanding of the kinetics of relativistic plasma, studies of laser-
plasma interactions are entering a new regime where the physics of relativistic plasmas is
strongly affected by strong-field quantum electrodynamics (QED) processes, including hard
photon emission and electron-positron (e+ -e− ) pair production. This coupling of quantum
emission processes and relativistic collective particle dynamics can result in dramatically
new plasma physics phenomena, such as the generation of dense e+ -e− pair plasma from
near vacuum, complete laser energy absorption by QED processes or the stopping of an
ultrarelativistic electron beam, which could penetrate a cm of lead, by a hair’s breadth
of laser light. In addition to being of fundamental interest, it is crucial to study this new
regime to understand the next generation of ultra-high intensity laser-matter experiments and
their resulting applications, such as high energy ion, electron, positron, and photon sources
for fundamental physics studies, medical radiotherapy, and next generation radiography for
homeland security and industry.
I. INTRODUCTION tivistic plasma physics.
Strong field (SF) QED processes have for a long time
One of the predictions of quantum electrodynamics been believed to be the domain of elementary particle
(QED) is that in the presence of an electric field stronger physics17,18 , which has made tremendous progress in the
than a critical field strength, ‘break-down’ of the vac- last hundred years, from the formulation of basic laws
uum occurs, which results in the spontaneous creation and the construction of the first particle accelerators to
of matter and antimatter in the form of electrons and the creation of the elaborate Standard Model and its ex-
positrons1–3 . Extremely strong fields can also polarize perimental verification at grand-scale experimental facil-
the quantum vacuum; predicted exotic effects include ities, such as LEP, LEP II, SLAC, Tevatron, and LHC.
light-by-light scattering, vacuum birefringence, 4-wave One of the directions of research that follows this success
mixing, or high order harmonics generation from the is the study of the cooperative behavior of relativistic
vacuum4–11 . While QED is probably one of the best quantum systems and the basic properties of the quan-
verified theories so far on a single particle level12,13 , tum vacuum. High power laser-plasma interactions in
the new collective phenomena that arise when electrons, regimes that were not available previously can provide
positrons, and photons are exposed to strong electromag- the framework for the study of these effects (Fig. 1).
netic fields are not yet well understood. Strong elec- The highest laser intensities demonstrated to date are
tric fields are those that approach or exceed the QED seven orders of magnitude lower than necessary to reach
critical field strength, Ecr , in which interactions become the critical field Ecr . However, since the electric field
highly nonlinear. In particular, the prolific production of is not a Lorentz invariant, in the rest frame of an ul-
electrons and positrons can cause complex plasma inter- trarelativistic particle a subcritical field strength may
actions with these fields, which are conditions that are be boosted to the critical field strength and beyond.
only starting to be theoretically explored. The physics of Therefore, SF QED processes such as multiphoton Comp-
such plasmas in strong fields is relevant to early universe ton emission of photons and multiphoton Breit-Wheeler
conditions14 , extreme astrophysical objects such as neu- electron-positron pair production occur at significantly
tron star atmospheres15 and black hole environments16 , lower field strengths than Ecr . This allows studies of the
and is critical to future high-intensity laser driven rela- physics of plasmas in supercritical fields with present day
and near future technology. Particle accelerators or ex-
tremely powerful lasers are able to generate high-energy
a) Invited
particles that can experience these boosted field strengths
Perspective Article
b) Electronic mail: pz@egr.msu.edu
(e.g. return forces from ions in plasmas, or fields in stand-
c) Electronic mail: sbulanov@lbl.gov ing waves).
d) Electronic mail: dseipt@umich.edu
Laser fields may provide both the strong electromag-
e) Electronic mail: aarefiev@eng.ucsd.edu
netic field and generate the high-energy particles19 and
f) Electronic mail: agrt@umich.edu
therefore represent a particularly interesting environment
2
for studying plasma physics in supercritically strong large amplitude waves in underdense plasmas which in
fields5,7,8 . Despite tremendous progress achieved in re- turn can accelerate electrons to multi-GeV energies, so-
cent years, there are a lot of unanswered questions and called laser-wakefield acceleration (LWFA)22 . Laser ion
unsolved problems that need to be addressed both theo- acceleration from overcritical plasmas requires higher in-
retically and in experiments. tensities of 1019 − 1022 W/cm2 (a0 ∼ 10 − 100 for a
In this perspective article, we will give an introduction 800 nm laser)5,23,24 , and the highest intensity demon-
to the physics of relativistic plasma in supercritical fields, strated up to now is 5.5 × 1022 W/cm2 (see Refs. Yoon
discuss the current state of the field and give an overview et al. 25 , Yanovsky et al. 26 , Kiriyama et al. 27 ). Next
of recent developments, and highlight open questions and generation laser facilities28 , such as Extreme Light In-
topics that, in our opinion, will dominate the attention frastructure (ELI)29 , APOLLON30 , Center for relativis-
of people working in the field over the next decade or tic Laser Science (CORELS)31 , EP OPAL32 , Zetawatt
so. This is not a comprehensive review, comes from a US Equivalent Ultrashort pulse laser System (ZEUS) and
perspective, and the reader is referred to other papers Station of Extreme Light (SEL) are planned to be able
on the broader topic of the physics of extremely high to achieve 1023 − 1024 W/cm2 .
intensity lasers, such as ref.8 . In addition, a0 also controls multi-photon interactions
The structure of this perspective article is as follows. in QED scattering processes33 ; the number of laser pho-
In section II we describe the parameter space of plasma tons in a cylindrical volume of length λ/2π and transverse
in strong fields. Then in section III, we give an overview dimension of the (reduced) Compton length λC = ~/mc
of recent developments in strong field electrodynamics is a20 /(4πα), with fine structure constant α. Thus, a0 >1
and discuss some examples where QED strongly affects as the effective interaction strength signals that the in-
plasma dynamics. Finally, in section IV we outline teraction might have entered the multi-photon regime.
strategies for progress in this field. Strong field QED describes the physics of particles in
These stategies lead us to envision three facility con- such strong EM fields and is broadly characterized by
figurations to study this physics. The first one will environments where the strength of electric fields is of
feature a laser pulse colliding with an ultrarelativistic the order of the QED critical field
electron beamp with energy Ebeam such that the product
(Ebeam [GeV]) Plaser [PW] (λlaser [µm])
−1
1, where m2e c3
Ecr = = 1.3 × 1018 V/m , (1)
Plaser is the laser pulse peak power of wavelength λlaser . e~
The second one will employ multiple colliding laser pulses which is the field that classically would accelerate an
−1
that satisfy the condition (Plaser [PW]) (λlaser [µm]) electron to its rest mass energy in a Compton length3 .
10. Finally, the third one will combine the capabilities of Vacuum pair production, known as the Sauter-Schwinger
the first two with that of the laser plasma based collider20 process, can be understood as virtual dipole pairs in
for the studies of plasma physics in supercritically strong the vacuum being torn apart by the field, becoming
fields at the highest intensities. To date, experiments real asymptotic pairs, the probability of which scales as
in this research area have all been performed using the ∝ exp{−πEcr /E} in a constant E field3 . Such a field
first configuration of a laser colliding with an electron strength corresponds to a light intensity of 4.65 × 1029
beam, but have not yet reached the critical field strength W/cm2 and a dimensionless amplitude, aS = mc2 /~ω, of
(although several notable experiments have come close). 4.1 × 105 for a 1 µm laser field. At fields of this strength,
With new facilities capable of achieving greater than 10 QED processes are highly nonlinear and cannot be de-
PW power, it will become possible to experimentally scribed by straightforward perturbation theories.
reach a new radiation dominated regime 21 where phe- The relevant parameter that characterizes the interac-
nomena, including prolific creation of matter from light, tion of electrons, positrons, and photons with strong EM
can be explored. fields is
|F µν pν |
χ= , (2)
II. PLASMA IN SUPERCRITICAL FIELDS mEcr
where F µν is the EM field tensor, and pν is the cor-
A. What is a supercritical field? responding particle 4-momentum. For electrons and
positrons the parameter χ has a simple physical mean-
In classical electrodynamics the interaction strength of ing, i.e., the EM field strength in the rest frame of the
electromagnetic (EM) fields with charged particles is usu- particle. Hence, for relativistic plasma where the bulk of
ally described in terms of the dimensionless amplitude the particles experience χ & 1, we define the fields to be
of the electromagnetic vector potential, a0 = eE/mωc, supercritical.
which represents the work done by the fields over a dis- There are two primary ways to achieve high χ for
tance λ/2π in units of the electron rest mass energy mc2 . electron-EM field interaction. By assuming a plane
Here ω and λ are the (oscillating) electromagnetic field EM wave (|E| = c|B| and E ⊥ B), we have χ =
frequency and wavelength, E is the amplitude, −e and (γ|E|/Ecr )(1 − β cos θk ), where γ is the Lorentz factor, β
m are the electron charge and mass, c is the speed of is the electron velocity, and θk is the angle between the
light. Hence, when a0 & 1 the interaction is always rel- electron momentum direction and the wave vector. Thus,
ativistic and nonlinear. Short laser pulses of that inten- χ can be maximized for electrons counter-propagating
sity (I & 2 × 1018 W/cm2 for a 800 nm laser) will drive with respect to wave vector (θk = π), i.e. an electron
3
1 10 34
χ = 1 (static field)
105
100000 32
10 32
10
High intensity QED plasma
104
10000 particle physics physics 30
10 30
10
I 2 [Wm -2 m 2]
spontaneous creation of plasma
by e +e − pair generation
a 01000
10 3
a0
28
10 28
10
χ = 1 (rotating electric field)
2
10
100 26
10 26
10
F
E
Single particle
=
Relativistic plasma
c2
relativistic
m te
physics
γm
as era
1 electrodynamics
10
10 24
1024
a
en
eg
pl
D
0
110
10
1e+10
10 1015
1e+15 1020
1e+20 1025
1e+25 1030
1e+30
Electron number density [cm -3 ]
FIG. 1. Different regimes of strong field physics as a function of plasma density and either field strength a0 (left scale) or laser
intensity (right scales). The line χ = 1 in the electron rest frame assumes a rotating configuration with the electron Lorentz
factor being γ = a0 .
beam colliding with a laser field. On thep other hand, as- usual. In a plane wave, the expectation of the momen-
suming |B| = 0 gives χ = (γ~|E|/Ecr ) 1 − β 2 cos2 θe , tum of a dressed lepton will be its canonical momentum
where θe is the angle between the electron momentum in classical mechanics. These two processes are known as
and the electric field. In this case, χ is maximized when multiphoton Compton emission (in a plane wave, or syn-
electron momentum is perpendicular to the electric field chrotron emission/magnetic bremsstrahlung in a constant
(θe = π/2), which can be achieved with colliding laser field) and multiphoton Breit-Wheeler pair-production,
pulses (at the magnetic nodes, where only rotating elec- respectively. As the lowest order processes, these dom-
tric field is present). In such a circular polarization, the inate high order processes by a factor ∼ α = 1/137 in
electric field and electron momentum in equilibrium mo- probability and thus are the most important to consider
tion (i.e. circulating) are (close to) perpendicular. In a for their effect on plasma dynamics. Other processes of
linearly polarized case, however, they are parallel, so a the same order in α, such as annihilation processes, are
boost from the laser electric field cannot be obtained di- negligible because of phase space suppression.
rectly. It is possible to have an electron with momentum When the classical field strength parameter a0 is large,
perpendicular to the linearly polarized field, but this has the coherence length (or “formation length”) of any quan-
to be externally supplied (with an accelerator). Apart tum process is short and therefore it is typical to as-
from maximizing χ these two configurations represent sume that the emission processes can be approximated
two fundamental schemes for the study of strong field by those in constant fields, the so called Local Constant
(SF) QED phenomena. The interaction of a high energy Field Approximation (LCFA). This is usually the case
electron with a plane EM wave can be considered as a if37,38 1 a0 and χ a30 . The formation length being
one-dimensional problem, when the energy of an elec- short is one of the basis assumptions for standard sim-
tron is high enough to neglect the transverse effect of the ulation codes, as described later. Typically, for a plane
EM field. In this case the dynamics of an electron is fully wave the formation length is estimated as Lf = 1/a0 ω 17 .
determined by its energy dissipation due to the radiation However, the formation length depends on the emitted
reaction effects, and permits an analytical solution34,35 .
In the second case, the electron dynamics is determined
by the transverse motion in the rotating electric field and,
a k b
also, permits an analytical solution. The rotating field p′
configuration can be achieved in practice with colliding
laser fields or a laser reflecting from a dense surface19 . p k
B. Basic QED processes in strong fields p′ p
The two lowest order processes in strong field QED FIG. 2. The two lowest order processes in strong field QED.
theory are illustrated in Fig. 2. These are (a) emission (a) emission of a photon by a dressed lepton. (b) decay of
of a photon by a dressed lepton and (b) decay of a photon a photon into a dressed electron-positron pair. Double lines
into a dressed electron-positron pair. A dressed lepton denote Volkov electrons36 , i.e. electrons dressed through the
means it is a particle state in a background electromag- interaction with the laser photons.
netic field and not a free (vacuum) particle state as is4
acceleration5,23,24 may occur. Even higher particle densi-
Relativistic
Affects: ties result in particle kinetic energies becoming equivalent
plasma physics EM fields to their Fermi energy, which is characteristic of the “De-
Particle momenta generate Plasma” regime. The Fermi energy for relativis-
Affects: p
Plasma density tic plasma is EF = ~2 (3π 2 ne )2/3 c2 + m2e c4 − me c2 .
Particle momenta QED processes: At higher laser intensities but low particle densities,
Pair production, photon emission the interactions are in the domain of ”High intensity par-
ticle physics”. Here, the particle dynamics is dominated
by radiation emission and quantum processes including
FIG. 3. The coupling of QED processes and relativistic interactions with the quantum vacuum, but collective ef-
plasma dynamics. fects are negligible. For example, light-by-light scatter-
ing, thought to be responsible for the attenuation of X-
rays by background light in cosmology, is such a process.
Under certain conditions, the spontaneous generation of
photon energy, Lf = Lf (ω 0 ), and for sufficiently low ω 0
electron, positron, and photon plasma in strong fields
the formation length can become of the order of a laser
becomes possible, which is usually referred to as EM cas-
wavelength, making the LCFA invalid39,40 .
cades (shower or avalanche type, see discussion below in
These two quantum processes affect the dynamics of
Sec. III B). This prolific plasma creation in high-intensity
the plasma by modifying the
laser fields rapidly pushes the interaction into the “QED
• electron kinetics through momentum loss in ener- plasma physics” domain, where both collective and quan-
getic photon emission (“radiation reaction”). tum processes determine the particle dynamics. Produc-
tion of dense electron, positron, and photon plasma will
• plasma density through electron-positron pair pro- provide new opportunities for laboratory studies of the
duction. most extreme astrophysical environments.
There are two natural QED thresholds in this picture,
These quantum effects would therefore continuously the QED critical field in the laboratory frame (dotted
change the basic plasma parameters (e.g. plasma density, red line) and the QED critical field in the particle rest
plasma temperature, and plasma frequency etc) during frame (solid red line). Experimental results achieved up
the interaction of light and matter. As a result, the col- to date all lie below the dotted line in Fig. 1, including
lective behavior of QED plasmas would be very different demonstrations of matter creation from light18 and quan-
from those of the classical plasmas. tum radiation reaction41,42 . Theoretical research stud-
Moreover, since the quantum processes themselves de- ies have only recently started to explore physics beyond
pend on the momentum distribution of the particles and this boundary. Already at this threshold, the particle
the EM fields generated by the plasma dynamics, there dynamics is dominated by radiation emission and is not
is a strong coupling between the two which should lead completely understood because of the approximations re-
to rich new phenomena. The complex feedback between quired in the theory to obtain tractable solutions. Hence,
QED and collective plasma processes (Fig. 3) is what achieving super-critical fields in plasma is a frontier area
makes the QED-plasma regime unique . of research.
C. Collective effects in supercritical fields D. Connections to Astrophysics
The connection of these strong field QED processes to QED plasma is of interest in many fields of physics
plasma physics also requires consideration of collective in- and astrophysics. The new plasma state that is created
teractions between particles. To illustrate this we sketch in the presence of supercritical fields is similar to that
the landscape of laser-plasma interactions in the (plasma thought to exist in extreme astrophysical environments
density, laser intensity) plane in Fig. 1, with the under- including the magnetospheres of pulsars and active black
lying assumption of a rotating field configuration. At holes. Electron-positron plasmas are a prominent feature
lower laser intensities and particle densities, the particle of the winds from pulsars15 and black holes16 . In these
trajectories are determined by their classical dynamics environments where the fields are typically purely mag-
in the laser field alone without the influence of collective netic and particles are typically ultrarelativistic, one can
effects, i.e., it is “Single particle electrodynamics”. As use the crossed-field configuration in place of a magnetic
the density of particles increases, collective plasma ef- field. This is because E · B is a Lorentz invariant, and
fects start to dominate the single particle dynamics. The the angle between B0 and E0 in the boosted frame is set
boundary between collective and single particle motion is by B0 · E0 /|B0 ||E0 | = B · E/|B0 ||Eq
0
|. Further, E 2 − B 2
defined using the threshold where the Coulomb force due
to the fully perturbed (δn/n ∼ 1) plasma balances the is an invariant so |B0 ||E0 | = |E0 |2 1 + (B 2 − E 2 )/E 0 2 .
ponderomotive force due to the laser, a0 = 4πre ne /k02 , Hence, if the boosted electric field |E0 | |E|, |B|, then
where ne is the electron number density. This is when the angle between E0 and B0 in the boosted frame is
the interaction enters the domain of “Relativistic plasma cos θ ≈ (E · B)/|E0 |2 1. Hence, ultrarelativistic parti-
physics”, in which interesting physics phenomena such cles see in their rest frame an arbitrary field as approxi-
as plasma wakefield acceleration22 and laser driven ion mately crossed.5
The recent release of the first image of a black hole43 the understanding of physics and where the concentrated
is expected to inspire new interest in the study of rel- effort of the scientific community should be directed.
ativistic electron-positron plasma physics. The 1.3 mm
wavelength image reveals an asymmetry in brightness in
the ring, which is explained in terms of relativistic beam-
A. Quantum Radiation Reaction
ing of the emission from a plasma rotating close to the
speed of light around a black hole. Some of the models
suggest that the mm emission is dominated by electron- When an accelerated charged particle emits radiation,
positron pairs within the funnel, even close to the horizon it experiences an effective recoil force, which is usually re-
scale44,45 . Electron-positron pairs are produced from the ferred to as the radiation reaction (RR) or radiation fric-
background radiation field or from a pair cascade pro- tion. In classical electrodynamics it is a well known effect,
cess following particle acceleration by unscreened electric first described by Lorentz-Abraham-Dirac equation53,54 .
fields. These processes would efficiently emit gamma- However, due to the fact that this equation has self-
rays via curvature and inverse-Compton processes45 . The accelerating non-physical solutions, the Landau-Lifshitz
suppression of emission from the disk and funnel wall, (LL) prescription34 is usually employed to describe the
and the simultaneous production of a sufficiently pow- RR, which uses certain assumptions for the charged par-
erful jet would be subjects of future research using pair ticle motion and the forces acting on it. We note that the
plasma models44 . The study of relativistic plasmas in exact form of the classical equation of motion with RR
supercritical fields in the laboratory may help us better included is still under discussion in the scientific commu-
understand this and other extreme astrophysical events, nity, as well as how to derive them as a low energy limit of
such as Gamma Ray Bursts46 . exact QED calculations (see Ref.55 and references cited
therein). However, as more energetic electron beams in-
teracting with more intense lasers are being considered,
III. STRONG FIELD QUANTUM ELECTRODYNAMICS: the classical LL description ceases to be valid. This
RECENT DEVELOPMENTS strong RR regime is characterized by a number of quan-
tum effects, such as stochastic photon emission56 , a hard
While the Sauter-Schwinger process (electron-positron cutoff in the emitted photon spectrum57 , straggling58 ,
pair production in vacuum) is inaccessible by present quantum quenching59 , and trapping in travelling60,61
day laser and accelerator technologies, the multiphoton and standing62–64 EM fields. The cut-off in the spec-
Compton and Breit-Wheeler processes have already been trum means that the radiated power is reduced com-
observed in experiments18,41,42 . In principle, the scope pared to the classically predicted radiated power, by a
of SF QED is much wider, and includes the study of factor g(χ) = Pquantum /Pclassical . Interestingly, even for
strong field effects on elementary particle decays and the χ = 0.1, g(χ) is already 0.66. This effect can be taken
searches of the physics beyond the Standard Model8,17 . into account phenomenologically by modifying the LL
However, in terms of their effects on plasma interactions, equation. Other quantum radiation reaction effects re-
these lowest order processes are dominant. quire full SF QED treatment of the underlying physics.
Most of the classical SF QED results were obtained Quantum radiation reaction has been the subject of
by assuming a plane monochromatic wave or a constant active theoretical and computational research in the
crossed field (|E| = c|B| and E ⊥ B), since these two past decade (see e.g.8,56,65–68 ) while the experimental ef-
configurations allow analytical formulae for the proba- fort was missing. However, this situation recently has
bilities of Compton and Breit-Wheeler processes8,17,47 to changed with two experiments carried out on the Gemini
be obtained quite easily. However, due to the pulsed laser41,42 , which were studying the interaction of GeV-
nature of strong lasers, it became clear that the plane class electron beams with intense laser pulses (a0 > 1).
wave approximation is not able to adequately describe Both experiments reported on a significant (30-40%)
the physics of these processes. Moreover, in such fields electron beam energy loss after the interaction with a
multi-staged processes dominate the interaction, i.e., the counter-propagating laser pulse. The analysis of the ex-
mean free path of an electron or positron with respect to perimental data showed that the results clearly rule out
the probability of radiating a photon is smaller than the a no-RR possibility (see Fig. 4). However, these exper-
characteristic size of the pulsed field. The same is true iments were not able to accurately distinguish between
for a photon decay into an electron-positron pair. These the LL description and the full SF QED one, although
considerations led to the study of Compton and Breit- both studies indicated that the quantum model gave bet-
Wheeler processes in short pulsed fields, as well as to the ter agreement. Nevertheless, they are an important mile-
first steps in the study of multi-staged processes, includ- stone in the study of SF QED effects, not only because
ing double Compton48,49 and trident50–52 . These studies the previous study was performed at SLAC18 more than
are intrinsically connected with the calculation of higher two decades ago using conventional accelerator technol-
order Feynman diagrams, which at certain field strength ogy and much lower laser intensities, such that a0 was
indicate the breakdown of the perturbation theory and small, but because at the Gemini facility laser plasma
the need for new paradigms in SF QED. accelerated electrons, which were of very small beam size
In what follows we briefly review the main recent de- allowing overlap between most of the electrons and the
velopments in SF QED and the related plasma physics, tightly focused laser beam, were used to collide with a sig-
which, from our point of view, illustrates both the direc- nificantly more intense laser pulse in a high a0 and high χ
tion the field is taking as well as the regions where we lack regime where the radiation emission plays an important6
icantly upshifted, reaching χ ∼ 0.27 at a0 ∼ 0.32, to be
able to generate high-energy photons from multiphoton
Compton scattering, some of which were subsequently
converted into e+ e− pairs in the multi-photon BW pro-
cess.
We note, the above mentioned setups do not offer the
possibility of pair plasma production, but this can be
achieved even in moderate intensity laser interactions
with high−Z solid targets. In this case, when relativistic
electrons generated in the pre-plasma propagate through
the solid target, MeV bremsstrahlung photons are gen-
erated, which lead to the production of pair plasma in
the field of the high-Z target nuclei through the Bethe-
Heitler (BH) process77–80 . Generation of neutral dense
pair plasma in the laboratory is also reported81 , with
FIG. 4. Comparison of experimental data (points with error observation for a Weibel like instability driven by the
bars) and different models (shaded areas) for the critical en- pair plasma82 . When the laser intensity is increased fur-
ergy crit as a function of the postcollision energy of the elec- ther, prolific pair plasma production is possible, mostly
tron beam f inal . crit is a characteristic energy of the photon due to SF QED effects. This has been extensively
spectrum, measuring the spectral shape41 . Reproduced with studied theoretically and using particle in cell (PIC)
permission from J. M. Cole et al., Phys. Rev. X 8, 011020 simulations68,83,84 .
(2018). Copyright 2018 American Physical Society. However, as the energies of particles and intensity
of EM fields are increased, a new possibility for pro-
ducing pair plasma arises, through a cascaded pro-
duction process of electrons, positrons, and high en-
role in determining the electron kinematics. Note that
ergy photons19,76,85–87 . These cascades come in two
quantum RR was also recently studied experimentally in
types85,88 . The first is the shower-type cascade, where
aligned crystals69 .
the initial particle energy is repeatedly divided between
the products of successive Compton and BW processes
and typically happens in the collision of a high energy
B. Pair-plasma production
particle beam with an intense laser pulse. In this case,
the EM field has almost no effect on the particle trajec-
Electron-positron pair production, as predicted by tories. The second is the avalanche-type cascade, where
QED theory70 , offers the possibility of a direct trans- the EM field both accelerates the charged particles and
formation of light into matter, for example by the Breit- causes QED processes. In this case, the number of par-
Wheeler (BW) process (γγ → e+ e− )71 . The observation ticles grows exponentially, fueled by the energy transfor-
of the BW process is challenging because one needs not mation from the EM field into electrons, positrons, and
only high photon energies to surmount the production high energy photons. It has been proposed that the maxi-
threshold at the rest mass energy of the pair, but also mum attainable laser intensity may be determined by the
high photon densities to overcome the smallness of the cascade development76,85 .
cross-section and achieve an appreciable yield. Laser- In order to reach χ > 1 with minimal total laser en-
driven gamma-ray sources are the key to overcoming ergy, an optimal field configuration is needed. It was first
these challenges. Two different approaches have been identified in the study of e+ e− pair production that col-
proposed that rely on such sources. One approach is liding multiple laser pulses at one spot provides such a
to fire a laser generated gamma-ray beam into the high- configuration89 , which in a limiting case of many laser
temperature radiation field of a laser-heated hohlraum72 , pulses can be seen as the inverted emission of a dipole
whereas another proposed approach is to collide two antenna90,91 . This field configuration is also advanta-
gamma-ray beams73–75 . Similar approaches may be ex- geous for the generation of QED cascades, both shower-
tended to multiple colliding photon beams instead of and avalanche-types, producing copious amounts of high
two76 . Such multiple colliding photon beams may yield energy gammas92 , and serving as a radiation beam dump
different scalings in terms of pair production, in which for high energy particle beams93 . Many of these appli-
a specific n-photon process may be studied in isolation cations of the multiple colliding laser pulse configuration
from other events. rely on another interesting property; radiative particle
Although the (linear) BW process has not been directly trapping63,94 .
observed in experiment, the conversion of a photon into
electron-positron pair in the presence of a strong EM
field (multiphoton BW process, γ + nγ 0 → e+ e− ) was
detected at the E-144 experiment at SLAC18 , where the C. Radiative trapping
46.6 GeV electron beam from SLAC’s linear accelerator
collided with a counter-propagating ∼ 1018 W/cm2 laser A multiple colliding laser pulse configuration not only
pulse with photon energy of 2.35eV. In the rest frame of enhances pair production due to the BW process, it also
the electrons, the laser intensity and frequency are signif- has the interesting property of trapping charged particles7
near the maxima of its electric field63 , and occurs only in
sufficiently high field intensities. This trapping originates
from the general tendency of charged particles to align
their motion along the radiation-free direction when they
rapidly lose energy and enter the radiation-dominated
regime95 and can even be observed in simple mechanical
systems with strong friction forces and strong periodic
driving96 .
It has also been recently shown that charged particles
in the strong EM fields formed by colliding pulses tend
to move along trajectories that are defined by either at-
tractors or limit cycles64,94,97,98 . While such behavior
is mostly attributed to intense radiation losses that are
typically modeled based on the classical description of
radiation reaction, in terms of either a Landau-Lifshitz
(LL) equation of motion or a “modified” LL equation, the
mechanisms behind the observed phenomena are tolerant
to the quantized nature of emission and similar behaviour
has also been observed in computer simulations based on FIG. 5. (a) Electron trajectories for laser-driven (a0 ≈ 200)
probabilistic quantum treatment of radiation losses64 . electron acceleration in a strong magnetic field assisted by
radiation friction, in (px , py ) momentum-space without and
with radiation friction (instantaneous energy in red-yellow
and blue-green colorbar, respectively). The stars indicate
D. Collective Processes in the QED-Plasma Regime photon emission with energy εγ > 50 MeV. (b) Same elec-
tron trajectories as in (a) in (x, y) coordinate-space (energy
color-coded as in (a)) and the transverse laser electric field at
Collective plasma processes in the QED-Plasma regime the electrons position (red-blue colorbar). (c) Electron den-
are expected to be dramatically different from the well sity ne /nc (nc is the plasma critical density) as a function of
studied classical plasmas. There are several examples time t and position x from 1D QED-PIC simulation for two
of such processes in the literature already, starting from counter propagating lasers interacting with a foil, when QED
radiation reaction effects, to electron-positron pair pro- is off, and (d) when QED is on. Also plotted are the contours
duction in plasma by plane EM waves99 , which does not for ion density (black lines) and positron density (green con-
happen in vacuum, to the backreaction of pair produc- tour lines). (a) and (b) are reproduced with permission from
tion on the properties of the EM wave due to the created Z. Gong, et al., Sci. Rep. 9, 17181 (2019). Copyright 2019
electron-positron plasma100 , to the laser absorption by Nature Publishing. (c) and (d) are reproduced with permis-
sion from P. Zhang, C. P. Ridgers, and A. G. R. Thomas, New
created electron-positron plasma during the avalanche-
J. Phys.17, 043051 (2015). Copyright 2015 IOP Publishing.
type cascade101,102 , to the laser driven ion103,104 and
electron105 acceleration, to the reversal of relativistic
transparency in QED plasma68 . In the last case, elec-
trons in the plasma are accelerated to such high energy
in the ultra-relativistic regime that their effective mass is
much greater than their rest mass, leading to a reduced
plasma frequency by a factor 1/hγi, where hγi is the aspect here is that no energy gain takes place if the ra-
average Lorentz factor of the electrons. Consequently, diation friction is not included into the analysis. The
”relativistically induced” transparency may occur: an red stars in Fig. 5(a) show the emission of photons with
opaque (and nominally overdense) plasma may become energy above 50 MeV. It is evident that the emission pro-
transmissive, if hγi is sufficiently high106 . However, in cess is not classical at high electron energies: the photons
the QED-plasma regime, radiation reaction becomes sig- are not emitted continuously and each of the emissions
nificant, the electron motion is damped and hence hγi significantly reduces the electron energy.
is reduced. Furthermore, at even greater laser intensi-
ties, sufficiently dense pair plasma may be produced to QED PIC simulations show radiation reaction dramat-
shield the laser fields. Thus, a relativistically transpar- ically changes the dynamics of QED plasma in the config-
ent plasma would become opaque for laser pulses due to uration of a thin foil plasma illuminated from two sides by
QED effects68 . two counterpropagating laser pulses68 . When SF QED
Configurations with a strong collective plasma field107 is turned off, hot, back-injected electrons are acceler-
can serve as a novel test-bed for studies of radiation re- ated away from both sides of the plasma slab (Fig. 5(c)).
action. For example, the radiation reaction or radiation When SF QED is included, these hot electrons are radia-
friction is able to enhance the electron energy gain from tively cooled such that they get trapped in the nulls of the
the laser field even though it is an energy loss mech- ponderomotive potential. These electrons form equally
anism108 . Figures 5(a) and (b) illustrate how an elec- spaced ultra-high-density thin electron and positron lay-
tron with a significant transverse momentum becomes ers, of approximately equal density, in the nodes of the
strongly accelerated after losing some of its transverse standing wave formed by the incident and reflected wave
momentum due to radiation friction. The remarkable (Fig. 5(d)).8
Monte-Carlo sampling of Generate macro-
the various QED processes (Fig. 6), which will intrinsi-
drj
=
kj multiphoton Breit-Wheeler particles (electron- cally introduce statistical noises in the calculation. These
dt !j pair production rate positron pair)
AAACIXicbZDLSsNAFIYnXmu9RV26GSyCq5JUwW6EohuXFewFmlAmk0k7diYJMxOhhLyKG1/FjQtFuhNfxkkaQVsPDPz83znMOb8XMyqVZX0aK6tr6xubla3q9s7u3r55cNiVUSIw6eCIRaLvIUkYDUlHUcVIPxYEcY+Rnje5yXnvkQhJo/BeTWPicjQKaUAxUtoamk0nEAinvsORGntBKrLhQ5b6KoNXcI5+yKQgTsTJCGk1NGtW3SoKLgu7FDVQVntozhw/wgknocIMSTmwrVi5KRKKYkayqpNIEiM8QSMy0DJEnEg3LS7M4Kl2fBhEQr9QwcL9PZEiLuWUe7ozX1custz8jw0SFTTdlIZxokiI5x8FCYMqgnlc0KeCYMWmWiAsqN4V4jHSuSgdalWHYC+evCy6jbp9Xm/cXdRa12UcFXAMTsAZsMElaIFb0AYdgMETeAFv4N14Nl6ND2M2b10xypkj8KeMr297OqWR
shortcomings are not shared by the Boltzmann/Vlasov
!e+ e
N! photon position R ( ) based approaches, which calculate only the particle en-
update AAACG3icbVDLSgMxFM3UV62vqks3wSIoYpmpgi5FNy6r2FrotOVOetsGk5khyShl6H+48VfcuFDEleDCvzF9LLR6IHA4515uzgliwbVx3S8nMzM7N7+QXcwtLa+sruXXN6o6ShTDCotEpGoBaBQ8xIrhRmAtVggyEHgT3J4P/Zs7VJpH4bXpx9iQ0A15hzMwVmrlS74E0wuC9GrQTP0uSAm+4t2eAaWie4rNfWweDHZ91uOtsb3XyhfcojsC/Uu8CSmQCcqt/IffjlgiMTRMgNZ1z41NIwVlOBM4yPmJxhjYLXSxbmkIEnUjHWUb0B2rtGknUvaFho7UnxspSK37MrCTwyR62huK/3n1xHROGikP48RgyMaHOomgJqLDomibK2RG9C0Bprj9K2U9UMCMrTNnS/CmI/8l1VLROyyWLo8Kp2eTOrJki2yTXeKRY3JKLkiZVAgjD+SJvJBX59F5dt6c9/FoxpnsbJJfcD6/AYhaoa4=
ergy distribution functions. The latter also has the ad-
Nq charged particle classical Standard PIC
Generate macro- equations of motion algorithm
vantage of handling particles in the high energy tail of
photons dpi
dt
= qi E(xi ) + qi vi ⇥ B(xi ) the distribution, which are challenging in typical QED
PIC.
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
Monte-Carlo sampling Fields interpolated Current density
of nonlinear Compton to particle position interpolated to mesh
emission rate E(x, t) ! E(xi (t))
AAACJ3icbVDLSsNAFJ34rPUVdekmWIQWpCRV0JUURXBZwT6gCWUynbRDJw9mbtQS8jdu/BU3goro0j9x2kbQtgcGDuecy9x73IgzCab5pS0sLi2vrObW8usbm1vb+s5uQ4axILROQh6Klosl5SygdWDAaSsSFPsup013cDnym3dUSBYGtzCMqOPjXsA8RjAoqaOf2z6GvuslV2nxlz6kR1CyBev1AQsR3s+NdFgRSqWOXjDL5hjGLLEyUkAZah391e6GJPZpAIRjKduWGYGTYAGMcJrm7VjSCJMB7tG2ogH2qXSS8Z2pcaiUruGFQr0AjLH6dyLBvpRD31XJ0Z5y2huJ87x2DN6Zk7AgioEGZPKRF3MDQmNUmtFlghLgQ0UwEUztapA+FpiAqjavSrCmT54ljUrZOi5Xbk4K1YusjhzaRweoiCx0iqroGtVQHRH0iJ7RG3rXnrQX7UP7nEQXtGxmD/2D9v0D3HGnIQ==
AAACKHicbVDLSgMxFM34rPU16tJNsAgtSJmpgu4sunFZwT6gHYZMmmljMw+SO2oZ+jlu/BU3Iop065eYPgRteyBwOOdccu/xYsEVWNbQWFpeWV1bz2xkN7e2d3bNvf2aihJJWZVGIpINjygmeMiqwEGwRiwZCTzB6l7veuTXH5hUPArvoB8zJyCdkPucEtCSa162AgJdz0/vB/lf+jRweR4KhZbknS4QKaNHvDB2AgXXzFlFaww8T+wpyaEpKq753mpHNAlYCFQQpZq2FYOTEgmcCjbIthLFYkJ7pMOamoYkYMpJx4cO8LFW2tiPpH4h4LH6dyIlgVL9wNPJ0ZJq1huJi7xmAv6Fk/IwToCFdPKRnwgMER61httcMgqirwmhkutdMe0SSSjobrO6BHv25HlSKxXt02Lp9ixXvprWkUGH6AjlkY3OURndoAqqIoqe0Sv6QJ/Gi/FmfBnDSXTJmM4coH8wvn8AtTSnlQ==
j(xi (t)) ! j(x, t)
e± !e± + Numerical Maxwell
R ( e) equations
AAACH3icbVBNSwMxFMz6bf2qevQSLEJFKLsq6lH04rGKtYVuLW/T1zaY7C5JVinL/hMv/hUvHhQRb/03pnUPah0IDDPv8TITxIJr47pDZ2p6ZnZufmGxsLS8srpWXN+40VGiGNZYJCLVCECj4CHWDDcCG7FCkIHAenB3PvLr96g0j8JrM4ixJaEX8i5nYKzULh75Ekw/CNKr7DbF29SPZeYr3usbUCp6oLm05/dASsjKPuvzNu62iyW34o5BJ4mXkxLJUW0XP/1OxBKJoWECtG56bmxaKSjDmcCs4CcaY2B30MOmpSFI1K10nC+jO1bp0G6k7AsNHas/N1KQWg9kYCdHafRfbyT+5zUT0z1ppTyME4Mh+z7UTQQ1ER2VRTtcITNiYAkwxe1fKeuDAmZspQVbgvc38iS52a94B5X9y8PS6VlexwLZItukTDxyTE7JBamSGmHkkTyTV/LmPDkvzrvz8T065eQ7m+QXnOEX4VGkEQ==
@E j IV. STRATEGIES FOR PROGRESS
= c2 r ⇥ B
QED-PIC algorithm 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
@t "0
A. Theory and Simulations
FIG. 6. Framework of QED PIC.
There are a number of unanswered fundamental ques-
tions in SF QED physics, the better understanding of
E. Numerical models for QED plasma which would be essential to study the relativistic plasma
physics in supercritical fields:
The study of QED plasma (as exemplified in the 1. Beyond the plane wave approximation. Present-
previous subsections) relies extensively on particle-in- day laser systems achieve very high intensities localized
cell (PIC) methods with QED extensions. The QED in a small space-time volume with a characteristic size
PIC is typically implemented by coupling the QED pro- of a wavelength and the electromagnetic field has a com-
cesses, such as gamma-ray photon emission by electrons plicated, 3-dimensional structure. However, most stud-
and pair production by gamma-ray photons, through a ies of the fundamental strong-field QED processes are
Monte Carlo algorithm to the classical particle-in-cell performed for plane monochromatic waves or constant
code109–112 , as illustrated in Fig. 6. The electromag- crossed fields. In these cases, the Dirac equation for an
netic field is split into high (i.e. gamma ray) and low electron in the strong field has exact solutions, which
(i.e. optical/plasma) frequency components. The low enable one to quite easily obtain analytic formulae for
frequency components are coherent states that are as- the probabilities of quantum processes. This is possi-
sumed to be unchanged in QED interactions. The evo- ble since plane waves are null fields with high degree
lution of these macroscopic fields is determined by solv- of symmetry115 . Most field configurations, especially in
ing Maxwell’s equations on the grid. Note that in strong multi-laser beam collision scenarios do not possess such
fields Maxwell’s equations may be modified by non-linear a high degree of symmetry. There have been studies
field-dependent effects7 . Electron and positron basis of QED processes for focused fields116,117 , but the re-
states are influenced by these low-frequency fields, which sults apply only in the regime γ a0 . Finding new
are treated as a classical background that interacts with (approximate) analytic solutions to the Dirac equation
the charged particles and the high frequency component and corresponding probabilities for quantum processes
of the field, using the strong-field QED representation. in more realistic field configurations, and the influence
The motion of electrons and positrons is subject to the of a background plasma medium on them, is important
Lorentz force on classical trajectories between point-like not only for benchmarking results from QED-PIC simu-
QED interaction events. lations against them, but also to better understand the
Despite being the “backbone” of QED plasma stud- limitations of the QED-PIC approach and identify situa-
ies, the benchmark of the QED PIC results against ex- tions where a self-consistent treatment of these processes
periments is, however, generally missing. With the de- in the case of a non-plane wave is required118–121 .
velopment of new experimental facilities with extreme 2. Beyond the local constant field approximation. If
laser intensity, experimental validation of the QED PIC the formation length/time of a quantum process is much
calculations is urgently needed. It is also important to smaller than the respective spatial and temporal inho-
understand the limitations of various simplified assump- mogeneities of the laser pulse, the local probability of
tions made in the QED PIC calculations and when these the process can be calculated in the framework of local
assumptions break down. The validations against experi- constant field approximation (LCFA) model, which is al-
ments would help build a more robust and accurate QED most always used in present day calculations. However,
PIC. it is already understood that the formation length of low
Alternative approaches to PIC include Boltzmann-like energy photons is not small compared to the respective
kinetic quantum plasma equations113,114 , which have the spatial and temporal inhomogeneities of the laser pulse.
advantages of not having statistical noise and are able Moreover, as higher intensities are being used, plasma
to handle particle creation/destruction processes easily. response leads to the generation of strong and very local-
As a large number of new particles (such as gamma pho- ized EM fields. In this case the formation lengths of the
tons and pairs) are created over a short period of time, QED processes may become comparable to or even longer
QED PIC will become computationally costly and time than the scale of spatial and temporal inhomogeneities of
consuming. QED PIC relies on Monte Carlo sampling of these fields.9 For the photon emission process it been discussed dis- field. There is an initial effort in addressing the ana- cussed that the LCFA fails at low light-cone energy of the lytical calculations of the multi-staged processes. Up to emitted photon39 . An explicit benchmarking of the valid- now two stage processes were investigated, such as double ity of the LCFA was performed by Blackburn et al. 122 , Compton48,49,135–137 and Trident50–52,138–140 processes. by comparing calculations made using LCFA with one However, a full QED treatment of multi-staged cascade using full QED, especially for the regime a0 . 10 which processes is still to be achieved. is relevant for present day experiments. Corrections and 5. Beyond the external field approximation. One of improvements of the LCFA rates have been recently pro- the open questions is the back reaction of the processes posed, e.g. by including local field gradients123 or by ex- of either pair production or photon emission on the in- plicitly checking whether the radiation formation length tense electromagnetic field. Usually these processes are is not short38,40 . In either case one needs not only the considered using an external field approximation, which local field values, but also derivatives along particle tra- assumes that the external field has infinite energy. How- jectories. In addition, the usual assumption of collinear ever, in a number of papers it was pointed out that the emission has been scrutinized40 . It remains a significant creation of new particles can lead to the depletion of the future research program to improve QED-PIC codes by electromagnetic field energy, which invalidates the ap- implementing those enhanced rates. proximation of the external field89,101,141–144 . For exam- 3. Inclusion of lepton spin. With increasing inter- ple, it would require Ne ∼ 1012 of 10 GeV electrons local- est in high intensity laser-plasma interactions, it is es- ized in a λ3 volume to deplete the EM field with a0 ∼ 103 , sential to also understand the interplay between lepton according to the condition a1.080 γ −0.92 Ne ∼ 6.8 × 1011 spin effects and the overall plasma dynamics. Not only from Ref.142 . Moreover, in the context of QED-plasma will the electron spin vectors precess in strong fields, but studies, one needs to understand how SF QED processes also the fundamental QED process of photon emission both backreact on and are initiated by plasma fields. Up and pair production are all spin-dependent124–127 , as are to now such studies are performed either on the level radiation reaction effects128 . Consequences of the latter of analytical estimates, or by employing PIC QED ap- are, for instance, altered equilibrium orbits in the radi- proach. The ultimate goal for theory here would be a ation dominated dynamics in rotating electric fields128 , consistent ab-initio real-time description of all quantum- or spin-polarization dependent deflections of electrons in plasma phenomena. laser electron beam collisions129,130 . 6. Breakdown of the quasi-classical approximation in Due to asymmetries in the spin-flip rates electrons can extremely strong fields and the Ritus-Narozhny conjec- spin-polarize as they interact with high intensity laser ture. The QED-PIC method is based upon a separa- pulses, a phenomenon known as Sokolov-Ternov effect tion of time-scales: That the formation time for quan- from lepton storage rings, where the electron’s spins align tum processes is very short with classical propagation anti-parallel to the magnetic field. In the magnetic nodes between incoherent quantum events. However, calcula- of two counterpropagating circular laser pulses the or- tions (for constant crossed fields) show that in extremely biting electrons can spin-polarize perpendicular to their strong fields, χ 1, the mean free paths for electrons plane of motion within a few femtoseconds128,131 . In and photons are on the order of the Compton wavelength collisions of electron beams with linearly polarized laser λC ∼ 1/m for αχ2/3 ∼ 1. Of course, the concept of a pulses one needs to break the symmetry of the oscilla- classical particle and thus classical motion has no mean- tions of the magnetic field in order to establish a dis- ing on the Compton scale, seriously challenging the ap- tinguished ”down” direction. This can be achieved, e.g., plicability of QED-PIC at extreme field strengths145 . by using ultra-short127,132 or bichromatic laser pulses, Calculations of the radiative corrections indicated that where both polarized electron and positron beams could those loop corrections in strong-field QED might increase be generated133,134 . with a power of the energy scale, instead of a logarithmic The studies of spin-polarization effects in the context of increase in the absence of strong fields145–147 . This is QED-plasma interactions have only started recently and sometimes referred to as ”Ritus-Narozhny conjecture”: more work is required. For future progress these spin- That for αχ2/3 ∼ 1 the semi-perturbative expansion interactions need to be included into QED-PIC codes. of SF QED (i.e. perturbative [tree-level] interactions of 4. Multi-staged processes. The most straightfor- quantized photons and non-perturbatively laser-dressed ward examples of multi-staged processes are avalanche- fermions) breaks down and an exact theory of the in- and shower-type cascades, which are fascinating phenom- teraction with the radiation field is required, taking into ena of fast transformation of laser and/or charged par- account all radiative corrections. ticle beam energy into high-energy photons and e+ e− However, recent studies148,149 showed that there seems pairs. These processes bring to life a plethora of other to be no universal behavior for χ → ∞, which is basi- effects, such as radiative trapping, attractors and chaos cally a product of field strength and particle energy, when in charged particle motion, and generation of high en- the calculations are performed for short laser pulses in- ergy photon and positron sources. A question whether stead of constant crossed fields. The power law scaling the maximum attainable laser intensity is determined by ∼ αχ2/3 from constant crossed fields was recovered only the cascade development76,85 also falls into this category. in a low-frequency-high-intensity limit, and the high- Theoretical and simulation studies of the cascades and energy limit yields a logarithmic scaling coinciding with related processes are usually relying on the fact that for- ordinary QED. This extreme-field regime is mostly un- mation length/time is much smaller than the respective charted territory. Further studies are required to resolve spatial and time inhomogeneities of the electromagnetic the connections and the possible transitions among dif-
10
ferent power law scalings under various input conditions.
7. Other theoretical problems Other important the- classical
oretical problems include the study of the properties radiation
of the quantum vacuum under the action of strong dominated
fields8 , radiation corrections, including Cherenkov radi-
quantum
ation in strong fields150,151 , beam-beam interaction in
QED plasmas152 , as well as the manifestations of the
physics beyond the Standard Model. Alternative simula-
Ritus-Narozhny
tion methods not relying on PIC may also be explored,
such as real-time lattice QED153,154 .
Schwinger field e-beam laser collision
B. Experiment and Facilities
Experiments in this area depend highly on the avail-
ability facilities capable of reaching large values of χ,
since it will not be feasible in the near term to achieve the
classical
critical field strength in the laboratory frame. We note radiation
that reaching large values of χ is an important problem dominated
by itself that needs to be addressed by future facility de-
signs. It is due to the fact that electrons and positrons
quite easily radiate their energy away when interacting
with strong EM fields, so several approaches were pro- quantum
posed to counter this energy loss93,155,156 to ensure that Ritus-Narozhny
high energy particles reach the region of highest field in-
tensity. Schwinger field multiple colliding lasers
As has been described in Section II, critical fields in
the zero momentum frame of a high energy particle (pair)
can be achieved with two basic configurations: either an
externally accelerated relativistic charged particle beam
interacting with a perpendicular field or a particle or- FIG. 7. The different regimes of SF QED plasma interactions
biting in a rotating field configuration. In addition to can be reached with various laser power and wavelength for
that, the choice of laser wavelength plays an important the e-beam laser collider (upper) and the multiple-laser beam
role in what areas of the interaction parameter space can interactions (lower). The blue diagonal band in the upper
plot marks the transition from the classical for the quantum
be accessed94,98 . In Figure 7 we show how the wave-
regime at χ = 1 for colliding beams of various electron beam
length of lasers used affects the ability to access strong energy. The green solid curve in the lower plot is the same
field QED regimes (defined by reaching χ = 1) and for the multiple laser interaction. Below the dash-dotted lines
strongly radiation dominated regimes [defined by reach- is the Ritus-Narozhny regime (Note that it is most easily ac-
ing αa0 χg(χ) = 1, where g(χ) ≤ 1 describes the re- cessed using short-wavelength radiation in the collider sce-
duced radiated power in the quantum regime17,62 ], in ei- nario). The shaded regions right of the dashed curves is the
ther a multiple colliding laser configuration (lower panel) radiation dominated regime. The intersection point of the
or laser colliding with a 5-50GeV lepton beam (upper quantum-classical transition and the transition to radiation
panel). It is clear from these charts that very short wave- dominated dynamics occurs around 30 PW and 1 µm for the
length lasers are able to reach the χ = 1 limit most multiple laser beam interaction case. We assume focusing to
easily and may therefore be the optimal experimental a 2λ spot size for both plots.
platforms to study nonlinear QED processes. The tech-
nology able to produce very short wavelength lasers with
required power is not yet developed. Moreover, to study (iii) laser plasma collider, featuring multiple PW-class
the physics of relativistic plasmas in supercritical fields, lasers, with 0.1-1EW of total power, capable of being re-
where the process rates are sufficient that the quantum configured into either an e-beam laser collider or multiple
processes affect the plasma dynamics, we also need to be beams setups. The following discussion is mostly aimed
in the radiation dominated regime. For the multiple laser at ∼1 µm lasers which are the most prevalent and tech-
pulse configuration, the crossing point where radiation nologically advanced ultra-high peak power laser tech-
dominated and quantum dominated regimes are simul- nology today. An alternative is beam-beam interactions,
taneously important is near 1 µm wavelength at 10’s of see Ref152 for further details.
PW laser power. Stage 1 (facility) : The study of basic quantum pro-
We therefore envision three basic stages of high-power cesses of strong field QED in the high-intensity particle-
laser facility development for experimental research into physics regime together with the relativistic plasma
QED-plasma regime, as illustrated in Fig. 8: (i) PW-class physics phenomena can be carried out at a PW-class
laser facility with an additional colliding beam, (ii) multi- laser facility featuring an additional colliding beam. This
beam laser facility with 10-100 PW of total power, and could mean either with two laser beamlines, with one ofYou can also read
