Signatures for strong-field QED in the quantum limit of beamstrahlung

W. L. Zhang, T. Grismayer, and L. O. Silva

Phys. Rev. A 108, 042816 – Published 20 October 2023

Abstract

Signatures for strong-field quantum electrodynamics are determined for collisions between round ultrarelativistic leptonic beams in the quantum limit of beamstrahlung. In the low-disruption regime, we derive the integrated beamstrahlung photon spectrum that features a characteristic peak close to the beam energy. The conditions to precisely observe this peak experimentally are given regarding the beam parameters. Moreover, the effects of electron-positron pair creation and beam disruption on the photon spectrum are discussed and explored with three-dimensional particle-in-cell QED simulations. The photon spectrum is associated with the emission of ultrashort and highly collimated $γ$ -ray beams with a peak spectral brightness exceeding $10^{30} photons / (s {mm}^{2} {mrad}^{2} 0.1 % BW)$ at the 100-GeV level of photon energy (close to the beam energy).

Received 31 January 2023
Revised 12 July 2023
Accepted 28 September 2023

DOI:https://doi.org/10.1103/PhysRevA.108.042816

Physics Subject Headings (PhySH)

Gamma-ray generation in plasmas Quantum electrodynamics

Electron-positron plasmas Lepton colliders Synchrotron radiation facilities

Monte Carlo methods Particle-in-cell methods

Accelerators & BeamsPlasma Physics

Authors & Affiliations

W. L. Zhang ^1,2,*, T. Grismayer ^2,†, and L. O. Silva ^2,‡

¹Engineering Research Center of Nuclear Technology Application, Ministry of Education, East China University of Technology, Nanchang 330013, China
²GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

^*wenlong.zhang@tecnico.ulisboa.pt
^†thomas.grismayer@tecnico.ulisboa.pt
^‡luis.silva@tecnico.ulisboa.pt

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Vol. 108, Iss. 4 — October 2023

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Figure 1
The $d N / d χ_{e}$ distribution of particles in leptonic beam-beam collisions. A Monte Carlo code is developed, where the colliding beams are represented by pseudoparticles created using random number generation. Each pseudoparticle is assigned with a weight given by the corresponding initial local density within the beam. The beams are set to cross each other at the speed of light. The $χ_{e} (r, t)$ of each particle is calculated based on the local fields from the oncoming beam. The $d N / d χ_{e}$ distribution shown here is taken at the peak interaction moment (when the centers of colliding beams cross) in a collision with $χ_{e \max} = 200$ . The distribution is normalized by the particle number of the beam ( $N_{0}$ ). For each colliding beam, $10^{6}$ pseudoparticles are initialized. Different beam profiles are compared here. The blue line is for Gaussian colliding beams with energy $E_{0} = 90$ GeV, longitudinal length $σ_{z} = 30.7 nm$ , transverse size $σ_{0} = 30.7$ nm, and particle number $N_{0} = 1.37 \times 10^{9}$ . The orange line is for the approximated uniform profile as specified in the text. The green dashed line represents the theoretical distribution for the approximated uniform profile, i.e., $d N / d χ_{e} = 2 χ_{e} / χ_{e \max}^{2}$ .
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Figure 2
The normalized energy spectrum $ξ S_{ω} (ξ)$ of photon radiation from a head-on collision between two identical, cold, round, and Gaussian electron beams with $χ_{e \max} = 200$ . The beam parameters are the same as those used in Fig. 1, i.e., $E_{0} = 90$ GeV, $σ_{0} = 30.7$ nm, $σ_{z} = 30.7$ nm, and $N_{0} = 1.37 \times 10^{9}$ . The blue line is for a 3D PIC simulation. The orange dashed line is for the analytical spectrum, Eq. (6). The green dashed line is for the direct numerical calculation of $S_{ω} (ξ)$ using the original Gaussian beam profile.
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Figure 3
The energy spectrum of photons from the same electron-electron collision in Fig. 2, but with stronger beamstrahlung by employing longer beams. Here, $σ_{z} = 230 nm$ , leading to $\bar{N_{γ}} = 1.5$ according to our theory [using Eq. (8)]. The initial disruption is weak with $D_{0} = 0.04$ . The other parameters, including $E_{0}, σ_{0}, n_{0}$ , and $χ_{e \max}$ , remain unchanged. Insets: Density maps at the $y − z$ slice across the beam axis, at the end of the collision. (a) Positrons from the created pairs in one colliding beam; (b) corresponding photons radiated from the same beam.
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Figure 4
The $d N / d χ_{e}$ distribution of particles in the same leptonic collision but with different misalignment $Δ_{0}$ (offset between the colliding beams). The beam parameters are the same as those used in Figs. 1 and 2, and the distribution is obtained using the same Monte Carlo method as in Fig. 1.
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Figure 5
Comparison between the differential probability rate of the nonlinear Compton process [ $d^{2} W / d t d ξ$ , given by Eq. (A1) and shown by the blue solid line] and its approximation proposed by this work [using Eq. (A6), shown by the orange dashed line]. The comparison is examined for different electron energy $E_{0}$ and field strength (electric field $E_{r}$ of the beams). The corresponding $χ_{e}$ of the electron under study is given by $χ_{e} = 2 (E_{0} / m c^{2}) E_{r} / E_{s}$ . Upper panels: An electron with $E_{0} = 10 GeV$ under fields of $1 \times 10^{14} V / m$ in panel (a), $4 \times 10^{14} V / m$ in panel (b), and $8 \times 10^{14} V / m$ in panel (c). Lower panels: an electron with $E_{0} = 100$ GeV under the same fields as the upper panels.
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