Generating ultra-dense pair beams using 400 GeV/c protons
C. D. Arrowsmith, N. Shukla, N. Charitonidis, R. Boni, H. Chen, T. Davenne, D. H. Froula, B. T. Huffman, Y. Kadi, B. Reville, S. Richardson, S. Sarkar, J. L. Shaw, L. O. Silva, R. M. G. M. Trines, R. Bingham, G. Gregori
GGenerating ultra-dense pair beams using 400 GeV/c protons
C. D. Arrowsmith , N. Shukla , N. Charitonidis , R. Boni , H. Chen , T. Davenne ,D. H. Froula , B. T. Huffman , Y. Kadi , B. Reville , S. Richardson , S. Sarkar ,J. L. Shaw , L. O. Silva , R. M. G. M. Trines , R. Bingham , , G. Gregori Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK GoLP/Instituto de Plasmas e Fus˜ao Nuclear, Instituto Superior T´ecnico,Universidade de Lisboa, 1049-001 Lisboa, Portugal European Organization for Nuclear Research (CERN), CH-1211 Geneva 23, Switzerland University of Rochester Laboratory for Laser Energetics, Rochester NY 14623, USA Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, California 94550, USA Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK Max-Planck-Institut f¨ur Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany Atomic Weapons Establishment, Aldermaston, Reading, Berkshire RG7 4PR, UK Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK (Dated: November 10, 2020)A previously unexplored experimental scheme is presented for generating low-divergence, ultra-dense, relativistic, electron-positron beams using 400 GeV/c protons available at facilities such asHiRadMat and AWAKE at CERN. Preliminary Monte-Carlo and Particle-in-cell simulations demon-strate the possibility of generating beams containing 10 − electron-positron pairs at sufficientlyhigh densities to drive collisionless beam-plasma instabilities, which are expected to play an impor-tant role in magnetic field generation and the related radiation signatures of relativistic astrophysicalphenomena. The pair beams are quasi-neutral, with size exceeding several skin-depths in all dimen-sions, allowing for the first time the examination of the effect of competition between transverseand longitudinal instability modes on the growth of magnetic fields. Furthermore, the presentedscheme allows for the possibility of controlling the relative density of hadrons to electron-positronpairs in the beam, making it possible to explore the parameter spaces for different astrophysicalenvironments. I. INTRODUCTION
The environmental conditions in the magneto-spheresof pulsars, magnetars and black holes are known topresent sites of copious electron-positron pair production[1–6]. Outflows from these compact objects, in the formof winds or collimated jets, are inevitably pair-plasmaenriched. The energy dissipation mechanisms, that ul-timately determine the electromagnetic radiative signa-tures we measure from Earth, are expected to differ sub-stantially from equivalent electron-ion outflows.A particular case of pair-dominated outflows are thosethought to generate gamma-ray bursts (GRBs) [7, 8].GRBs are among the most luminous events in the uni-verse, yet the precise nature of the emission remains un-resolved. It is commonly believed that GRBs result fromsynchrotron emission of relativistic particles energised atinternal shocks [9, 10]. In both the prompt and after-glow GRB emission, it is expected that filamentation-type kinetic beam-plasma instabilities [11–13] are respon-sible for the growth of magnetic fields associated with thesynchrotron emission [14, 15], and simulations have sug-gested that the required field strengths can be amplifiedin the kind of relativistic collisionless shocks expected tobe relevant to GRBs [16, 17]. Nevertheless, such studiesare constrained by the ability of numerical techniques tofully capture the extreme conditions in GRB outflows.This motivates the development of experimental plat-forms which can complement simulation studies in ex- ploring the non-linear aspects of beam-plasma instabil-ities for a range of compositions and densities of beamand background plasmas.In this paper, we introduce a previously unex-plored experimental scheme for generating electron-positron beams using 400 GeV/c protons available atfacilities such as HiRadMat [18] and AWAKE [19]at CERN. Preliminary Monte-Carlo simulations whichmodel this scheme indicate the possibility of gener-ating low-divergence beams of 10 − electron-positron pairs with sufficiently high densities to drivefilamentation-type beam-plasma instabilities on observ-able laboratory scales. This number of pairs is signifi-cantly higher (by several orders of magnitude) than pre-viously reported laser-produced quasi-neutral pair beams[20–24].As well as electron-positron pairs, the beams expectedto be generated contain a smaller density of hadrons suchas protons and pions. The scheme we introduce allows forthe possibility to control the density of these particles rel-ative to electron-positron pairs by several orders of mag-nitude. This is useful because jet composition remainsan important unresolved question surrounding the pow-ering of GRBs. In the fireball model of GRBs, baryon-loading of the jet is discussed as an important parameterin determining the Lorentz factor of the stream [7], andthe role of photoproduction of mesons (and also neutronsand neutrinos) at internal shocks of the fireball model hasbeen discussed as an explanation for anomalous spectralcomponents in the observed prompt emission [25, 26]. a r X i v : . [ phy s i c s . p l a s m - ph ] N ov Parameter HiRadMat AWAKEBeam momentum 440 GeV/c 400 GeV/c p + bunch intensity 1 . × × Bunch duration 375 ps 400 ps1 σ beam radius 0 . − . FIG. 1. Left: Beam parameters for 400 GeV/c proton facilities HiRadMat [18] and AWAKE [19]. Right: Proposed experimentalsetup. Beams composed of electrons, positrons, photons, protons and other hadrons are generated using a beryllium targetfollowed by a lead converter. Driving the beam into a gas cell will ionize the gas, forming a background plasma where the beam-plasma interaction can be studied. Since the bulk of the electrons and positrons in the beam have much smaller momentumthan the hadrons, dipole magnets can be used to deflect e + e − out of the beam to study their energy spectra, while the hadronsare deflected less and are absorbed by the beam dump. The effect of streaming ions on the growth and satura-tion of magnetic fields via filamentation-like instabilitieshas been investigated in Particle-in-cell (PIC) simula-tions [27], and can now be explored experimentally forthe first time.Furthermore, the generated beams have sufficient lon-gitudinal extent to observe obliquely-growing instabilitymodes that are otherwise suppressed in shorter beams[23]. This is important because obliquely-growing insta-bility modes that compete with transverse current fila-mentation instability are expected to affect the fractionof bulk kinetic energy of the beam which is convertedinto magnetic and electric fields, and hence is importantfor modelling radiative emission processes.This paper presents simulations and experimental fea-sibility of the introduced experimental setup. We showpreliminary results of Monte-Carlo simulations charac-terizing the generated electron-positron-hadron beams,and present PIC simulations modelling the propagationof these beams through a background plasma in the lab-oratory. These simulations demonstrate the developmentof kinetic instabilities and the growth of feasibly measur-able magnetic fields exceeding magnitudes of 0.1 T.
II. EXPERIMENTAL SCHEME
HiRadMat (High-Radiation to Materials) [18] andAWAKE (Advanced Proton Driven Plasma WakefieldAcceleration Experiment) [19] are facilities at CERNwhich can provide high-intensity 400 GeV/c protonbeams up to a maximum intensity of several 10 protonsper 400 ps pulse. A summary of the beam parameters ofthese facilities is given in Fig. 1.In proton-nucleon interactions with centre of massenergy, √ s , in excess of GeV, particles produced inhadronic interactions come mostly from the hadronisa-tion of quarks and gluons. A shower of protons, pions,kaons and other hadrons is observed. In particular, a sig-nificant component of this shower is a copious number ofneutral pions, each of which undergoes electromagnetic decay to two photons on a timescale O (10 − s) in the π rest frame. A highly-directional beam of GeV-energyphotons is produced in the target, which predominantlyloses energy via e + e − pair production. The generated e + e − lose energy via the generation of bremsstrahlungat a rate approximately proportional to their energy, andso a cascade of copious e + e − and γ develops. This rep-resents the dominant channel for production of electron-positron pairs initiated with a GeV/c proton beam [28].For ultra-relativistic streams such as the pair beamsystems we generate in this scheme, and those rele-vant to GRBs (in which Lorentz factors are expectedto be in the range γ b ∼ − ), transverse cur-rent filamentation instability (CFI) and oblique insta-bility (OBI) will be the dominant beam-plasma insta-bilities leading to growth of magnetic fields [15]. Thegrowth of these instabilities is observed when the physi-cal beam size exceeds the background plasma skin depth( c/ω p ), where ω p = (cid:112) πn e e /m e is the plasma fre-quency, n e is the background plasma density, e and m e are the electron charge and mass, and c is the speed oflight. Linear kinetic plasma theory gives estimates of thefastest growth rates of CFI and OBI in the cold distri-bution function limit [29] as Γ CFI ∼ β b (cid:112) α/γ b ω p andΓ OBI ∼ √ / / ( α/γ b ) / ω p , where β b and γ b are theLorentz factors of the beam, and α is the beam-plasmadensity ratio. Together, these set a requirement that thedensity of the e + e − pair beams must be sufficiently largethat collective plasma instabilities grow fast enough to beobserved on laboratory timescales, while the backgroundplasma is dense enough for the skin depth to be smallerthan the physical beam size.The easiest way to produce electron-positron pairsfrom a high-energy photon beam is the conversion pro-cess in a high-Z material, such as lead. In a scheme whichuses GeV/c protons, preliminary Monte-Carlo simula-tions indicate that we can increase the maximum pairbeam density above what can be obtained by a lead con-verter alone. We do this by preceding the converter witha beryllium target. Beryllium has a relatively short nu-cleon interaction length compared to its radiation length,such that a large number of high-energy γ can be gener-ated from π decays in the beryllium with minimal sub-sequent scattering. This additional flux of photons en-hances the densities of pairs that can be generated in thelead converter.A schematic demonstrating this idea is shown in Fig.1. To study the growth of beam-plasma instabilities asthe generated electron-positron-hadron beams propagatethrough a background plasma, we can drive the beamsimmediately into a gas cell. The gas in the cell will ion-ize (due to both photo-ionization and proton collisionswith the neutral atoms) to form a background plasmawhere beam-plasma instabilities discussed above can beobserved. III. MONTE-CARLO SIMULATIONS
To better understand the pair beams we create usingthis scheme, Monte-Carlo modelling was performed us-ing the particle transport code FLUKA [30, 31], whichcan accurately simulate hadronic interactions and elec-tromagnetic cascades as a 400 GeV/c proton beam prop-agates through a solid target of beryllium and lead. Asan input for the simulations, we assume a proton beamcorresponding to repeatable experimental conditions atHiRadMat. That is, a collimated proton beam with anessentially monochromatic spectral profile peaked at 440GeV/c (with width corresponding to 0.03% from the cen-tral energy), and a Gaussian transverse beam profile with σ = 0 . protons were simulated to inter-act with various combinations of thicknesses of berylliumtarget and lead converter. Beam characteristics such assize, divergence and energy spectra were recorded for thedifferent components of the generated beams escapingthe converter rear.The simulated beams are observed to contain a domi-nating fluence of 10 − electron-positron pairs and γ -rays, along with a smaller number (several tens of timessmaller) of protons and other hadron species, the mostnumerous of these being charged pions.The transverse radial beam profiles of differentbeam components are reasonably well-described by aLorentzian function, and fitting was used to obtainFWHM beam diameters and peak fluences. Estimates ofpeak volume densities were obtained from peak fluencesby assuming a beam duration of 375 ps.The dependencies of peak component densities on tar-get and converter thicknesses can be found in Fig. 2 forfour cases; (a) and (b) show the peak particle densitieswhen beryllium and lead are used on their own, while(c) and (d) show the sensitivities of particle densities toa change in thickness of beryllium or lead from a con-figuration which gives a high density of e + e − pairs (30cm beryllium target and 4 cm lead converter). As ex-pected, we immediately see that e + e − density is muchmore sensitive to the thickness of the high-Z lead con- FIG. 2. The dependencies of peak densities of each beamspecies on Be target and Pb converter thicknesses is shownfor four configurations. (a) and (b) show the densities ob-tained for single-component targets of beryllium and lead,while (c) and (d) show the sensitivities of particle densities toa change in thickness of beryllium or lead from a configura-tion that generates a high density of e + e − pairs (that is, 30cm beryllium target with a 4 cm lead converter). The largestpair beam densities are only achieved by using a configurationthat contains both beryllium and lead, and the thickness oflead can be modified to alter the ratio of e + e − to hadronsin the beam. Densities are obtained assuming an incident p + beam with radius σ = 0.5 mm, and are presented in unitsper incident proton, so that the numbers can be scaled to thebunch intensity of the proton facility. A pulse duration of 375ps is assumed to obtain the peak density from the simulatedpeak fluence. verter. An increase in target thickness will only increasethe density of a beam component if additional particlegeneration is more significant than density decreases dueto beam divergence or depletion of particles in processessuch as decay, absorption, and annihilation. In all fourplots, proton density decreases with target thickness, asprotons scatter off the target nuclei. This is more notice-able in the beryllium thickness scans which cover morenuclear collision lengths than the lead scans. Density ofelectron-positron pairs increases as soon as high-energyphotons are generated and cascades initiated, but densi-ties of photons and e + e − pairs are higher in lead wherethe length scale associated with initiation of electromag-netic cascades is much smaller.By comparing the peak densities of pairs in these fourplots, we can see that the largest pair beam densities TABLE I. Summary of the characteristics of significant particle components of the beam, obtained from Monte-Carlo numericalsimulations for the case of a beryllium target and lead converter with thicknesses 30 cm and 4 cm, respectively. All quantitiesare calculated based on the particles which escape the rear surface of the lead converter. The peak fluence and beam diameterare obtained by fitting the transverse density profile of the escaping beam to a Lorentzian profile. Similarly the beam divergenceis the FWHM of the angular distribution of the escaping beam fitted to a Lorentzian profile. The peak fluence is used to inferthe peak volume density in the laboratory frame by assuming a 375 ps bunch duration. Yield and peak densities are given per10 incident protons with a beam radius σ = 0.5 mm. Species Yield per 10 p + Peak density per 10 p + (cm − ) Divergence (mrad) Beam diameter (mm) e − . × . × e + . × . × p + . × . × π + . × . × π − . × . × γ . × . × FIG. 3. Energy spectra (left) and angle-position phase space plots (right) obtained in the case of a 30 cm beryllium target and4 cm lead converter. The simulation setup is the same as the one mentioned in Table I. The energy spectra are displayed inthe ranges where their spectra are most significant, while insets display the spectra extending to much higher energies. Theangle-position phase space plots are normalized and displayed with a colour mapping that clearly depicts the half-maxima. and the largest ratios of pair density to hadron densitycan only be achieved by using a configuration that con-tains both beryllium and lead. Using a 30 cm berylliumtarget and 4 cm lead converter can lead to e + e − pairdensities in excess of 10 cm − (see column 3 of TableI). Higher densities are achievable with higher intensityproton pulses of smaller beam diameter. The thicknessof lead can be modified in an experiment to dramaticallyadjust the ratio of densities of e + e − to hadrons, withoutchanging the hadron density significantly. This can allowus to probe jets with a variety of compositions.For the case of a 30 cm beryllium target and 4 cm leadconverter, Fig. 3 shows the energy spectra and angle-position phase space plots for the significant beam com-ponents as they emerge from the rear of the converter.The e + and e − spectra are very similar, differing onlyat energies less than 10 MeV, where the annihilation crosssection of positrons becomes significant. The spectra are dominated by particles which have only 10’s of MeV, butextend up to tens of GeV in their high-energy tails. Thesecharacteristics are matched by the photon spectra, withthe addition of a spectral peak at 511 keV resulting fromelectron-positron annihilation.The proton spectra appears bimodal in distribution.We see a peak at 440 GeV corresponding to the pro-tons in the initial beam which have not lost a significantfraction of their energy, and we also see much lower en-ergy protons resulting from the inelastic hadronic scat-tering. Spectra with similar characteristics are seen forthe charged pions, except with the omission of the high-energy contribution from an initial beam.We can get an idea of the extent to which high beamdensities are maintained as the beam propagates by look-ing at its overall divergence (the distribution of the anglesbetween the beam axis and the particle trajectory of allthe particles of a species as they exit the rear of the con- FIG. 4. Simulation results of the interaction between an electron-positron-proton bunch and a static plasma with density10 cm − at a time t = 705 [1 /ω p ] = 1 .
27 ns. (a) Density filaments of electrons (blue) and protons (red). (b) Transversemagnetic fields ( B ⊥ ) filaments due to current filamentation. (c) Longitudinal electric fields ( E (cid:107) ), and (d) transverse electricfields ( E ⊥ ) attributed to space charge and inductive effects. Units are such that one plasma period [1 /ω p ] corresponds to[1 /ω p ] = 1 . c/ω p ] corresponds to [ c/ω p ] = 530 µ m, and magnetic and electric field units are[ m e ω p c/e ] = 3 . m e ω p c/e ] = GV m − respectively. verter). For e + e − and γ we observe that the emergingbeams have an overall divergence of 15 −
30 mrad (see col-umn 4 of Table I). The pions have divergence of 10 mrad,which means the ratio of beam density of pions to e + e − will not change much as the beam propagates. However,the lower divergence of the protons due to the direction-ality of the high energy component of the beam, meansthat care must be taken to position the gas cell close tothe converter rear in order to maximise the dominanceof e + e − pair density over proton density.For all beam components we find the beam diameter tobe mm-scale (see column 5 of Table I), meaning the back-ground plasma must exceed densities of 10 − cm − for the transverse beam size to be larger than the plasmaskin depth and for us to observe filamentation instabil-ities. Referring back to the theoretical growth rates ofCFI and OBI, we find that with these background plasmadensities, instability growth rates on the order of picosec-onds might be expected, given mean beam Lorentz fac-tors γ b ∼
100 and beam densities 10 − cm − .We also find that CFI and OBI have closely competinggrowth rates.For beams such as ours, which are relativistically hot( k B T > m e c ), the true scalings and growth rates will bedifferent from the cold beam approximations. So we haveperformed PIC simulations to better understand the non-linear growth of CFI and OBI in the case of our e − e + p + beams propagating through a background plasma. FromPIC simulations we can gain better insight into the com-petition between CFI and OBI growth, and better esti-mates of the timescales for instability growth and satu-ration. We can also obtain the magnitude of the energyexpected to be converted into magnetic and electric fields, and whether the generated fields are of a sufficiently highmagnitude that they might be measurable in an experi-ment. IV. PARTICLE-IN-CELL SIMULATIONS
The fully relativistic, massively parallel, PIC codeOSIRIS [32, 33], which has been used extensively tomodel relativistic beam-plasma interactions [34–36], wasused to perform two-dimensional PIC simulations of anelectron-positron-proton bunch through a backgroundplasma. The simulations used a moving window trav-elling at c , with absorbing boundary conditions, and di-mensions 800 ×
400 ( c/ω p ) divided into 8000 × × n b = n b exp( − r /σ r − z /σ z ),where the bunch peak densities are n b = 10 cm − for electrons and positrons, and n b ∼ cm − forthe protons. The bunch length and transverse waist are σ z = 7 . c/ω p and σ r = 0 .
15 cm = 2 . c/ω p re-spectively, with the skin depth of the background plasma c/ω p corresponding to a plasma density n p = 10 cm − .An ion-electron mass ratio m p /m e = 1836 is used.Studies which have investigated the effect of tempera-ture on growth of filamentation and oblique modes havefound that growth rates are strongly suppressed in beamswith large transverse temperature [37], but are less de-pendent on large longitudinal energy spreads [35]. There-fore, we set each beam component to propagate alongthe z-axis with Lorentz factor set by the mean longitudi- FIG. 5. Evolution of energies contained within transversemagnetic field (cid:15) B ⊥ (red), transverse electric field (cid:15) E ⊥ (green)and longitudinal electric field (cid:15) E (cid:107) (blue) as the beam prop-agates, normalized to the initial kinetic energy of the beam (cid:15) p = ( γ b − V where V is the volume of the beam. nal momentum (without a thermal momentum spread),while a thermal momentum spread is included in thetransverse direction that corresponds to the mean trans-verse momentum. For the electrons and positrons, wechoose a bulk Lorentz factor of γ ∼ (cid:104) p (cid:107) (cid:105) /m e c ∼ k B T ⊥ ∼(cid:104) p ⊥ (cid:105) c ∼ . γ ∼ (cid:104) p (cid:107) (cid:105) /m p c ∼
50 and k B T ⊥ ∼ (cid:104) p ⊥ (cid:105) c ∼
370 MeV for the protons.Simulation results are illustrated in Fig. 4, show-ing the spatial-temporal evolution of protons and elec-trons in the beam (Fig. 4a), the formation of transversemagnetic filaments (Fig. 4b), and the typical electricfield structure (Fig. 4c and 4d). In our simulations weobserve the breaking-up of the beam into current fila-ments (with width on the order of c/ω p ∼ µ m) asthe electron-positron-proton bunch enters into the back-ground plasma. Any charge separation in the beam gen-erates micro-currents which reinforces initial perturba-tions, causing the growth of electromagnetic plasma in-stability and the exponential growth of electromagneticfields. This is demonstrated in Fig. 5, where the tempo-ral evolution of the magnetic and electric field energiesis shown as a function of time, normalized to the initialbulk kinetic energy of beam.The fields saturate after t = 1000 [1 /ω p ] = 1 . ∼ − of the initial beam energy). Simultaneously,longitudinal and transverse electric fields are observedwith magnitudes exceeding 300 MV m − , which can beattributed to space charge and inductive effects [35]. Thisis contrary to the case of electron driven plasma wake-fields, where no filamentation of the beam is observed,nor the generation of strong magnetic fields [38–40]. Theprotons in the beam are not found to play a significantrole in the collective plasma dynamics, although they docontribute to space charge effects.Our simulations show the emergence of oblique modesand tilted filamentation, which reduces the growth of magnetic fields. This is seen in previous similar simu-lation studies [35]. Importantly, the effect of the growthof oblique modes on magnetic field generation can onlybe studied with beams that have a large enough longi-tudinal extent to allow coupling between transverse andlongitudinal beam instability modes. It cannot be stud-ied using quasi-neutral e + e − beams generated at laserfacilities [20–24], which are typically limited by havingmaximum beam durations of approximately 50 fs. V. SUMMARY
The growth of kinetic plasma instabilities of relevanceto astrophysical phenomena such as GRBs has been in-vestigated for a previously unexplored experimental plat-form in which low-divergence, ultra-dense, quasi-neutral,electron-positron pair beams are generated using 400GeV/c protons available at facilities such as AWAKE andHiRadMat at CERN.Monte-Carlo simulations demonstrate the possibilityof generating beams that contain 10 − electron-positron pairs along with a smaller number (10 − )of hadrons such as protons and pions. Particle-in-cellsimulations have shown that beams interacting with abackground plasma will exhibit collective plasma effectsand the generation of magnetic fields exceeding 0.1 T viafilamentation instabilities, which saturate after 50 cm ofbeam propagation.This platform represents a significant step forwardfor experiments aimed at exploring relativistic pair-plasma phenomena in a laboratory setting. We havedemonstrated the experimental feasibility of isolatingand studying the non-linear evolution of several key in-stabilities that are presently limited to numerical experi-ments, allowing for the possibility of observing the effectsof obliquely-growing filamentation modes and the role ofhadrons on magnetic field generation in the developmentof kinetic plasma instabilities. By changing experimentalparameters such as incident proton density, target thick-ness and density of background plasma, different configu-rations corresponding to fireballs traversing an overdenseor underdense background medium can be examined, andthe composition of different astrophysical scenarios canbe studied.The research leading to these results has received fund-ing from AWE plc., the Central Laser Facility (Sci-ence and Technology Facilities Council of the UnitedKingdom), the European Research Council (throughgrant ERC-2015-AdG, GA No. 695088), Funda¸c˜ao paraa Ciˆencia e a Tecnologia (through grant EXPL/FIS-PLA/0834/2012), and the Department of Energy Officeof Fusion Energy (DE-SC0017950). FLUKA simulationswere performed using the Science and Technology Facili-ties Council Scientific Computing Department’s SCARFcluster, and OSIRIS simulations were performed at theMarconi-Broadwell (CINECA, Italy). [1] P. Goldreich and W. H. Julian, Pulsar electrodynamics,The Astrophysical Journal , 869 (1969).[2] J. Arons, Pair creation above pulsar polar caps-geometrical structure and energetics of slot gaps, TheAstrophysical Journal , 215 (1983).[3] R. D. Blandford and R. L. Znajek, Electromagnetic ex-traction of energy from kerr black holes, Monthly Noticesof the Royal Astronomical Society , 433 (1977).[4] M. C. Begelman, R. D. Blandford, and M. J. Rees, The-ory of extragalactic radio sources, Reviews of ModernPhysics , 255 (1984).[5] H. R. Miller and P. J. Wiita, Active galactic nuclei ,Vol. 30 (1988).[6] J. Wardle, D. Homan, R. Ojha, and D. Roberts,Electron–positron jets associated with the quasar 3c279,Nature , 457 (1998).[7] P. Meszaros and M. Rees, Relativistic fireballs andtheir impact on external matter-models for cosmologi-cal gamma-ray bursts, The Astrophysical Journal ,278 (1993).[8] T. Piran, The physics of gamma-ray bursts, Reviews ofModern Physics , 1143 (2005).[9] A. Gruzinov, Gamma-ray burst phenomenology, shockdynamo, and the first magnetic fields, The AstrophysicalJournal Letters , L15 (2001).[10] P. Chang, A. Spitkovsky, and J. Arons, Long-term evo-lution of magnetic turbulence in relativistic collision-less shocks: electron-positron plasmas, The Astrophys-ical Journal , 378 (2008).[11] S. Bludman, K. Watson, and M. Rosenbluth, Statisticalmechanics of relativistic streams. ii, The Physics of Fluids , 747 (1960).[12] R. Lee and M. Lampe, Electromagnetic instabilities, fil-amentation, and focusing of relativistic electron beams,Physical Review Letters , 1390 (1973).[13] B. B. Godfrey, W. R. Shanahan, and L. E. Thode, Lineartheory of a cold relativistic beam propagating along anexternal magnetic field, The Physics of Fluids , 346(1975).[14] M. V. Medvedev and A. Loeb, Generation of mag-netic fields in the relativistic shock of gamma-ray burstsources, The Astrophysical Journal , 697 (1999).[15] A. Bret, Weibel, two-stream, filamentation, oblique, bell,buneman... which one grows faster?, The AstrophysicalJournal , 990 (2009).[16] J.-I. Sakai, R. Schlickeiser, and P. Shukla, Simulationstudies of the magnetic field generation in cosmologicalplasmas, Physics Letters A , 384 (2004).[17] M. V. Medvedev and A. Spitkovsky, Radiative coolingin relativistic collisionless shocks: Can simulations andexperiments probe relevant gamma-ray burst physics?,The Astrophysical Journal , 956 (2009).[18] I. Efthymiopoulos, D. Grenier, M. Meddahi, P. Trilhe,S. Evrard, H. Vincke, C. Theis, N. Charitonidis,C. Hessler, A. Pardons, et al. , HiRadMat: a new irra-diation facility for material testing at CERN , Tech. Rep.(2011).[19] E. Gschwendtner, E. Adli, L. Amorim, R. Apsimon,R. Assmann, A.-M. Bachmann, F. Batsch, J. Bauche,V. B. Olsen, M. Bernardini, et al. , Awake, the advancedproton driven plasma wakefield acceleration experiment at cern, Nuclear Instruments and Methods in Physics Re-search Section A: Accelerators, Spectrometers, Detectorsand Associated Equipment , 76 (2016).[20] G. Sarri, K. Poder, J. Cole, W. Schumaker, A. Di Piazza,B. Reville, T. Dzelzainis, D. Doria, L. Gizzi, G. Grittani, et al. , Generation of neutral and high-density electron–positron pair plasmas in the laboratory, Nature commu-nications , 1 (2015).[21] G. Williams, B. Pollock, F. Albert, J. Park, andH. Chen, Positron generation using laser-wakefield elec-tron sources, Physics of Plasmas , 093115 (2015).[22] T. Xu, B. Shen, J. Xu, S. Li, Y. Yu, J. Li, X. Lu, C. Wang,X. Wang, X. Liang, et al. , Ultrashort megaelectronvoltpositron beam generation based on laser-accelerated elec-trons, Physics of Plasmas , 033109 (2016).[23] J. Warwick, T. Dzelzainis, M. E. Dieckmann, W. Schu-maker, D. Doria, L. Romagnani, K. Poder, J. Cole,A. Alejo, M. Yeung, et al. , Experimental observation ofa current-driven instability in a neutral electron-positronbeam, Physical review letters , 185002 (2017).[24] G. Williams, H. Chen, J. Kim, S. Kerr, and H. Khater,Comment on “table-top laser-based source of femtosec-ond, collimated, ultrarelativistic positron beams”, Phys-ical Review Letters , 179501 (2020).[25] K. Asano, S. Guiriec, and P. Meszaros, Hadronic modelsfor the extra spectral component in the short grb 090510,The Astrophysical Journal Letters , L191 (2009).[26] K. Asano, S. Inoue, and P. M´esz´aros, Prompt high-energyemission from proton-dominated gamma-ray bursts, TheAstrophysical Journal , 953 (2009).[27] N. Shukla, A. Stockem, F. Fi´uza, and L. Silva, Enhance-ment in the electromagnetic beam-plasma instability dueto ion streaming, Journal of Plasma Physics , 181(2012).[28] N. Charitonidis, private communication (2020).[29] A. Bret and C. Deutsch, Stabilization of the filamentationinstability and the anisotropy of the background plasma,Physics of plasmas , 022110 (2006).[30] A. Ferrari, P. R. Sala, A. Fasso, J. Ranft, U. Siegen, et al. , FLUKA: a multi-particle transport code , Tech.Rep. (Stanford Linear Accelerator Center (SLAC), 2005).[31] T. B¨ohlen, F. Cerutti, M. Chin, A. Fass`o, A. Ferrari,P. G. Ortega, A. Mairani, P. R. Sala, G. Smirnov, andV. Vlachoudis, The fluka code: developments and chal-lenges for high energy and medical applications, Nucleardata sheets , 211 (2014).[32] R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk,W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Kat-souleas, et al. , Osiris: A three-dimensional, fully rela-tivistic particle in cell code for modeling plasma basedaccelerators, in
International Conference on Computa-tional Science (Springer, 2002) pp. 342–351.[33] R. Fonseca, S. Martins, L. Silva, J. Tonge, F. Tsung, andW. Mori, One-to-one direct modeling of experiments andastrophysical scenarios: pushing the envelope on kineticplasma simulations, Plasma Physics and Controlled Fu-sion , 124034 (2008).[34] L. O. Silva, R. Fonseca, J. Tonge, J. Dawson, W. Mori,and M. Medvedev, Interpenetrating plasma shells: near-equipartition magnetic field generation and nonthermalparticle acceleration, The Astrophysical Journal Letters , L121 (2003).[35] N. Shukla, J. Vieira, P. Muggli, G. Sarri, R. Fonseca,and L. O. Silva, Conditions for the onset of the cur-rent filamentation instability in the laboratory, Journalof Plasma Physics , 905840302 (2018).[36] N. Shukla, S. Martins, P. Muggli, J. Vieira, and L. Silva,Interaction of ultra relativistic e+e- fireball beam withplasma, New J. Phys , 013030 (2020).[37] A. Bret, L. Gremillet, and M. E. Dieckmann, Multidi-mensional electron beam-plasma instabilities in the rela-tivistic regime, Physics of Plasmas , 120501 (2010). [38] P. Chen, J. Dawson, R. W. Huff, and T. Katsouleas, Ac-celeration of electrons by the interaction of a bunchedelectron beam with a plasma, Physical review letters ,693 (1985).[39] P. Chen, J. Su, T. Katsouleas, S. Wilks, and J. Dawson,Plasma focusing for high-energy beams, IEEE transac-tions on plasma science , 218 (1987).[40] K. Lotov, Acceleration of positrons by electron beam-driven wakefields in a plasma, Physics of plasmas14