PHYSICAL REVIEW ACCELERATORS AND BEAMS 21, 081301 (2018) Quasimonoenergetic laser plasma positron accelerator using particle-shower plasma-wave interactions Aakash A. Sahai* Department of Physics and John Adams Institute for Accelerator Science, Blackett Laboratory, Imperial College London, SW7 2AZ, United Kingdom (Received 15 January 2018; published 8 August 2018) An all-optical centimeter-scale laser-plasma positron accelerator is modeled to produce quasimonoe- nergetic beams with tunable ultrarelativistic energies. A new principle elucidated here describes the trapping of divergent positrons that are part of a laser-driven electromagnetic particle-shower with a large energy spread and their acceleration into a quasimonoenergetic positron beam in a laser-driven plasma wave. Proof of this principle using analysis and particle-in-cell simulations demonstrates that, under limits defined here, existing lasers can accelerate hundreds of MeV pC quasi-monoenergetic positron bunches. By providing an affordable alternative to kilometer-scale radio-frequency accelerators, this compact positron accelerator opens up new avenues of research. DOI: 10.1103/PhysRevAccelBeams.21.081301 Monoenergetic positron accelerators intrinsic to positron- electron (eþ − e−) colliders at energy frontiers [1,2] have been fundamental to many important discoveries [3–6] that underpin the standard model. Apart from high- energy physics (HEP), monoenergetic eþ-beams of mostly sub-MeV energies are also used in many areas of material science [7,8], medicine [9] and applied antimatter physics [10]. Applications have however not had ready access to positron accelerators and have had to rely on alternative sources such as βþ-decay [11], (p,n) reaction [12] and pair- production [13] of MeV-scale photons from—fission reactors [14], neutron-capture reactions [15] or MeV-scale e−-beams impinging on a high-Z target [16]. Positron accelerators have evidently been scarce due to complexities involved in the production and isolation of elusive particles like positrons [2,16] in addition to the costs associated with the large size of radio-frequency (rf) accelerators [17]. The size of conventional rf accelerators is dictated by the distance over which charged particles FIG. 1. Schematic of all-optical centimeter-scale schemes of gain energy under the action of breakdown limited [18] quasimonoenergetic laser-plasma positron accelerator using the eþ − e− tens of MVm−1 rf fields sustained using metallic structures interaction of showers with plasma-waves. that reconfigure transverse electromagnetic waves into modes with axial fields. This limit also complicates thus produced have to be captured in a flux concentrator, efficient positron production [2,13], which has required a turned around and transported back [19] for reinjection into multi-GeV e−-beam from a kilometer-scale rf accelerator the same rf accelerator. [17] to interact with a target. Furthermore, the positrons Advancements in rf technologies have demonstrated 100 MVm−1-scale fields [20] but explorations beyond the eþ − e− *Corresponding author. standard model at TeV-scale center-of-mass ener- [email protected] gies still remain unviable. Moreover, the progress of non- HEP applications of eþ-beams has been largely stagnant. Published by the American Physical Society under the terms of Recent efforts on compact and affordable positron accel- the Creative Commons Attribution 4.0 International license. erator design based on advanced acceleration techniques Further distribution of this work must maintain attribution to ’ [21,22] have unfortunately been unsatisfactory. Production the author(s) and the published article s title, journal citation, þ − and DOI. of e − e showers using high-energy electrons from 2469-9888=18=21(8)=081301(7) 081301-1 Published by the American Physical Society AAKASH A. SAHAI PHYS. REV. ACCEL. BEAMS 21, 081301 (2018) þ þ 18 −3 FIG. 2. Energy spectra and p⊥ − pk phase-spaces of e -LPA accelerated e -beams modeled with n0 ¼ 10 cm using a 50 fs laser with a0 ¼ 1.4 and Full Width at Half Maximum (FWHM) spot-size of 40 μm. For Scheme A (Scheme B), the initial conditions are in (a),(c) [(e),(g)] and the eþ-beam at 2.2 mm (1.8 mm) in (b),(d) [(f),(h)]. compact laser-plasma accelerator (e−-LPA) [21–23] has The mechanism modeled in this paper uses two coupled been reported [24]. However, unlike eþ-“beams”, showers laser-plasma interaction stages. In the first (positron- are divergent and suffer from innately exponential energy production) stage, bremsstrahlung emission from laser- spectra. Moreover, the positron number in showers which driven electrons undergoes pair-production in the nuclear peaks around a few MeV [2,25], undergoes orders-of- Coulomb field inside a high-Z target and results in an magnitude drop at higher energies. Another work which electromagnetic-cascade particle-shower [13]. In scheme-A uses sheath fields driven by kilo-Joule (kJ) lasers in metal shown in Fig. 1(a),ane−-LPA produces multi-GeVelectrons targets has obtained quasimonoenergetic 10 MeV positrons [30]. In scheme-B shown in Fig. 1(b), a kJ laser [26] [26] although with inherently high temperatures. Both produces an MeV electron flux in the pre-plasma of a solid scaling to higher energies and cooling of positrons using target. The eþ − e− shower from the target propagates into this mechanism is yet unexplored. Beam-driven plasma the second (positron-acceleration) stage where a significant acceleration of positrons [27,28] although compact by number of shower particles are trapped in a laser-driven itself, depends upon unviable kilometer-scale GeV rf accel- plasma-wave. The fields of the plasma-wave accelerate erators. Additionally, obtaining an appropriately spaced a quasimonoenergetic eþ-“beam” with typical energy drive-witness bunch pair for beam-plasma acceleration spectra from particle-in-cell (PIC) simulations shown in methods is technologically difficult. Figs. 2(b) and 2(f). This groundbreaking quasimonoener- þ In this paper, all-optical quasimonoenergetic e -beam getic eþ-beam acceleration model defines the key principles production is proposed using a centimeter-scale positron as well as the limits of eþ-LPA. Recent efforts have shown accelerator (as shown in Fig. 1). This laser-plasma positron that it is possible to overcome single-stage limits of electron þ accelerator invention (e -LPA) uses the interaction between acceleration using multistage e−-LPAs albeit with a few þ − laser-driven e − e particle showerspffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi[25] and laser-driven technological challenges [31]. 18 −3 −1 þ plasma waves that support 100 n0ð10 cm Þ GVm A proof of the principle of the above described e -LPA −3 fields [21,22] (n0 is the plasma electron density in cm ). is developed below using analysis and PIC simulations. þ − This letter models the trapping of divergent positrons that are The first stage laser-driven e − e showers are below part of laser-driven particle showers and their acceleration modeled with characteristics that depend upon peak elec- into a quasimonoenergetic eþ-beams, of tunable energy, in a tron energy and net charge in scheme-A [25], laser energy laser-driven plasma wave. in scheme-B [26] in addition to the target properties. This novel compact eþ-LPA opens up an affordable In scheme-A the particle-shower is modeled with an pathway for the application of ultrarelativistic quasimo- anisotropic relativistic Maxwellian distribution [32,33] noenergetic eþ-beams outside HEP as much as it invigor- consistent with experiments [2,25]. This distribution in ates research in advanced collider concepts [29]. momentum space (normalized to mec), p ¼ðp⊥;pkÞ is 081301-2 QUASIMONOENERGETIC LASER PLASMA … PHYS. REV. ACCEL. BEAMS 21, 081301 (2018) h qiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 ω0 k fðpÞ¼C ðp⊥ þ pkÞ exp −β⊥ 1 þ p⊥ þ Apk ð1Þ E0 ¼ γ ð1 − β β Þ − 1 m c2: ð Þ sh ω sh sh ϕ e 2 pe where pk is along the axis of laser propagation and p⊥ in 2 −1 −1 Positrons with negative relative velocities in the wave frame the transverse directions, β⊥ ¼ mec T⊥ , A ¼ TkT⊥ , at E0 are trapped only when a lower-limit of wave frame transverse T⊥ and longitudinal Tk temperatures are in sh potential Ψ0 is exceeded eV and C normalizes the distribution [33]. Using exper- imental evidence [2,25], the peak particle number is at eΨ0 ≥ E0 ð Þ sh 3 2.3 MeV (dfðpÞ=dpk ¼ 0) with T⊥ ¼ 0.2 MeV and A ¼ 25. The shower positron densities here lie between Lorentz transformation of the four potential ðΨ0; A0Þ (A0 is 15 17 −3 þ − 10 –10 cm with e -to-e density ratio (feþ =fe− )of the wave vector potential) back to the lab-frame under Ψ ψ between 0.1 to 0.4 [25]. gauge invariance gives the threshold potential and th eþ − e− Experiments on laser-driven showers, which ω observed 109 positrons over 1 MeV [25] using 0.6 GeV Ψ ¼ pe Ψ0 þ c A β ω · ϕ peak energy, 100 pC e−-LPA electrons (with a 10 J, 50 fs, 0 ω eΨ λ0 ¼ 0.8 μm wavelength laser) incident on 5-10 millimeter ψ ≥ γ ð1 − βk β Þ − pe ; ψ ¼ ;A ¼ 0: ð Þ th sh sh ϕ 2 k 4 Pb target, showed excellent agreement with Monte-Carlo ω0 mec particle simulations (GEANT4/FLUKA). These simula- tions predict many times higher eþ-yield [34] using The longitudinal trapping condition in Eq. (4) is necessary multi-GeV e−-LPA electrons [30] but the innate distribution but not sufficient, because particles may still transversely of showers in Eq. (1) is retained. escape. A threshold potential is therefore necessary to In scheme-B, sheath-accelerated eþ − e− shower is here constrain the divergent positrons within a transverse escape 10 momentum contour. This potential is derived by Lorentz modeled on experiments in [26] that observed 10 posi- cβk trons using a 305 J, λ0 ¼ 1.054 μm, τp ∼ 10 ps laser transforming to the shower frame at sh where the longitudinal momentum contracts and the average particle incident on millimeter-scale Au targets.