7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Particle acceleration by a relativistic shock interacting with an inhomogeneousmedium
1Kanji Morikawa1 and Yutaka Ohira1
Department of Earth and Planetary Science, The University of Tokyo physics
e-mail (speaker): kanji.m1029@eps.s.u-tokyo.ac.jp

Cosmic Rays (CRs) are coming from both inside andoutside our galaxy. Their highest energy reaches to 1020
eV, which is called Ultra-High-Energy Cosmic Rays(UHECRs). UHECRs are thought to come fromextragalactic sources, but we do not know the origin ofUHECRs.
In the Hillas plot, some candidates of the UHECRs
source have relativistic shocks driven by relativistic jets,
such as gamma-ray bursts or active galactic nuclei.
Therefore, UHECRs are expected to be accelerated by
the relativistic shock, where they go back and fortharound the shock many times. However, in aperpendicular relativistic shock which has a uniform andperpendicular magnetic field to the shock normal,
particles cannot cross the shock front at most one time
because they are swept away to the far downstream
region [1]. On the other hand, it is shown that if particles
are scattered in the downstream region, particles cancross the shock front many times because of theturbulence [2]. This the reason we must consider theturbulence around the shock front.
In this work, we consider density clumps in the shock
upstream region. When they interact with the relativistic
shock, some shear motion is driven. Then, in thedownstream region, a turbulent field is generated by thisshear. In this turbulence, particles are scattered, and theirdirection is changed to the upstream region. After all, theparticles can cross the relativistic shock front several
times and gain much energy by the 1st-order Fermi
process. Although this mechanism of the turbulence

generation is well confirmed in the case of a nonrelativistic shock [3], this does not work efficiently in thecase of a relativistic shock due to the Lorentz contraction[4]. In order to confirm whether this mechanism canmake the downstream region turbulent enough forparticles to be scattered and go back to the upstream
region in the relativistic shock or not, we must calculate
the numerical simulations. Then, we performed 3D
relativistic MHD simulations and test-particle
simulations and confirmed that particles are accelerated
by these processes.
In this talk, we argue the parameters in the simulations
that particles can gain their energy by the 1st-order Fermi
process in a relativistic shock. We found that theamplitude of the density fluctuation is important forparticles to be scattered in the downstream region.
Furthermore, we found that the peak of the energy
spectrum moves to higher energy, as the amplitude of thedensity fluctuation get larger. This might be the effect ofthe 2nd-order Fermi acceleration in the turbulent
downstream region.

References[1] M. Lemoine et al, ApJL, 645, L129 (2006)[2] M. Lemoine and B. Revenu, MNRAS, 366, 635(2006)[3] T. Inoue et al, ApJ, 734, 77 (2011)[4] S. Tomita et al, ApJL, 936, L9 (20222)

Figure 1 (left). The energy spectrum of the particles in the shock rest frame. The case (a) is the amplitude of the densityclumps 𝛿𝑛/𝑛 = 1, (b) is the case of the amplitude 𝛿𝑛/𝑛 = 10, and (c) is the case of the no density fluctuation.
Figure 2 (right). The trajectory of the highest-energy particle in the test-particle simulations. The horizontal axis is thespatial coordinate in the x direction and the vertical axis is the energy of the particle. The particle crosses the shock front
many times and gain their energy by 1st-order Fermi process.