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Positron beam acceleration driven by laser-accelerated electron beam

A positron beam, produced in copper target based on laser-accelerated energetic electrons, is accelerated from a few MeVs to several hundred MeVs in strong longitudinal electric field induced by the co-propagating high-density electron beam. This new acceleration scheme for positron beams is demonstrated by two-dimensional particle-in-cell simulation and Monte-Carlo code. The electron beam after passing through the copper target keeps its high density ~10^17cm-3 for 0.7 m propagation distance, with the guiding from an external longitudinal magnetic field of 30 T and provides a strong acceleration field of GV/m for the positrons. Simulation results indicate that a positron beam with an initial Maxwellian-energy-spectrum of Tp = 24.1 MeV is accelerated to quasi-monoenergetic peaks up to 796.5 MeV with energy spread of 18.7% when 10 PW laser pulse is employed. The angular divergence of the positron beam is 2.3 mrad and the charge is 12 pC. This proposed method resolves the creation, injection and acceleration of positrons in a single set-up, which offers a new way to accelerate high-energy positrons for potential modest-sized all-optical electron-positron colliders.

what breaks the mechanism of electroweak symmetry [1]. Discovering the Higgs boson at the Large Hadron Collider (LHC) in the European Organization for Nuclear Research (CERN) is one of the most remarkable achievements obtained by particle collisions [2]. Electron-positron collisions, whose events are much cleaner than proton-proton collisions because there are only elementary particles involved, are being widely considered based on big machines, such as International Linear Collider (ILC) [3] and Compact Linear Collider (CLIC) [4]. However, the acceleration gradient of these conventional accelerators is limited to ~100 MV/m mainly because of material damage threshold, and the acceleration distance reaches a few tens of kilometers in order to realize energy frontier up to TeV-class [4], which generates enormous expense. Thus, it is essential to look for other acceleration mechanisms to accelerate electrons and positrons. In the past forty years, electron acceleration driven by femtosecond relativistic laser pulse has made remarkable progress since the concept of laser wakefield acceleration (LWFA) being first proposed [5]. The electron energy has reached 4 GeV [6] and even 7.8 GeV with small energy spread reported recently [7]. Nowadays, the electron beam with short pulse duration of a few femtoseconds [8], small angular divergence of less than 1.5 mrad [9] and beam charge up to 10 nC [10] can be readily obtained. These high-quality laser-driven electrons have been successfully used to generate Maxwellian-energy-spectrum positron beam with maximum energies up to hundreds MeVs [11][12][13][14] at sufficiently low emittance [15].
Realization of electron-positron collisions requires mono-energetic GeV-class or even TeV-class positrons. Besides the expensive conventional acceleration method, several new methods have been proposed to accelerate positrons in plasma, such as particle driven wakefield acceleration (PWFA) [16], laser driven sheath field acceleration [17,18] and LWFA [19]. In order to overcome the problem of transverse defocusing of positrons in the wakefield driven by electrons [20], plasma channel [21] , hollow electron beam [22] and two electron driven beams [23] have been applied. Donut shaped wakefield driven by Laguerre-Gaussian (LG) laser pulses also helps to avoid the defocusing of positron beam. [24] Despite the impressive beam quality that is able to be achieved by these methods, positron acceleration is still challenging and has been less studied experimentally due to the lack of suitable driving beams and positron sources [25][26][27]. Therefore, finding a practical approach to generate and accelerate positrons to higher energy is still an open research area.
In this letter, we propose a novel scheme to create positron source and further accelerate it to GeVs in vacuum, driven directly by the laser-accelerated electron beam, as shown in FIG. 1. The scheme is composed of three stages, stage Ⅰ is the generation of high-charge high-energy electrons in LWFA. Stage Ⅱ is the positron generation in copper targets via the routine Bethe-Heitler (BH) process [28] and stage Ⅲ is the acceleration process for positrons. In stage Ⅲ, the energetic electron beam drives the intense longitudinal electric field to accelerate the co-propagating positrons.
Our combined simulations (EPOCH-Geant4-EPOCH) confirm that an quasi-monoenergetic position beam peaking at 796.5 MeV with 18.7% energy spread, 2.3 mrad angular divergence, 12 pC beam charge and 6.4 fs pulse duration can be obtained by a 20 2 1.37 10 W/cm  , 223 J driving laser pulse, while the initially generated positrons are of a Maxwellian energy spectrum with Tp = 24.1 MeV. The laser-driven electron beam provides an acceleration gradient of several GV/m, which is between the conventional accelerators (~100 MV/m) [3,4] and PWFA (~100 GV/m). But the set-up is far less demanding than conventional accelerators and does not require special injection designs or high-quality positron sources as in PWFA.
Therefore, the proposed method is a promising candidate for high-energy positron sources in the future to develop modest-sized all-optical electron-positron colliders. The acceleration process of high-charge energetic electron bunch, favorable for accelerating positrons, has been studied by two dimensional (2D) particle-in-cell (PIC) simulation code EPOCH [29]. The simulation window, moving at the light speed c, is This high-charge energetic electron beam impinges onto a 1 mm-thick copper target, and triggers the generation of high-energy Gamma photons via bremsstrahlung [30] and further the production of electron-positron pairs via the BH process.
Numerical simulations performed by the Monte-Carlo code Geant4 [31] are able to account for the positron generation process and provide the energy and angular spectrum of both electrons and positrons after they exit the copper target. Electrons generated from stage I are sampled at 4 5. 34 10   ratio by reserving the energy and angular spectrum, and input into the copper target in the Monte-Carlo simulations.
The copper target with thickness of 1 mm is set 0.5 mm away from the gas target. For the sampled 10 7 electrons, we obtain where ()  is the normalized scalar potential of longitudinal field with where "+" stands for  increasing with time and "-" stands for  decreasing with time.
To exemplify the general property of the system with Hamiltonian 0 ( , ) we show its phase portrait Fig. 4, which represents the motion of the positrons whose initial kinetic energy at 0    Therefore most of them easily get trapped into the acceleration field and gain energy.
The peak energy in typical simulation at 0.7 m is 796.5 MeV and the cutoff energy is 2.5 GeV, which is lower than theoretical results (9.2 GeV, black solid line in FIG. 4.).
Because the theoretical line describes the whole positron acceleration process including the dephasing part and the positrons will overtake the electric field, while the positrons at 0.7 m in the PIC simulation are far away from reaching the maximum energy gain in this acceleration scheme. Moreover, the pulse duration of driving electron beam elongates due to the energy loss. Its density will reduce because of initial divergence and Coulomb expansion and thus the amplitude of acceleration field decreases during propagation. Therefore positron beam will be further accelerated to even higher energy if stronger external magnetic field is applied. Figure 4 also shows that positrons with lower initial energy and can be captured by the electric field experience a longer relative displacement and thus, they will get more energy gain than those with higher initial energies, which can be calculated by Eq. (5).