Proton Acceleration with Relativistic Electromagnetic Shock

Abstract

Understanding the mechanisms behind the extreme energies of cosmic rays is crucial for unraveling fundamental physical processes in astrophysical environments. This study proposes a novel mechanism for accelerating cosmic-ray protons. By examining a high-velocity collision between an astrophysical object and static magnetic fields, the generation of an intense transverse electric field capable of trapping and accelerating protons are find to relativistic energies. Through Hamiltonian analysis, a scaling law that correlates the proton energy is derived to the minimum longitudinal thickness of the relativistic electromagnetic shock required for acceleration. One-dimensional (1D) Particle-In-Cell (PIC) simulations show that an electromagnetic shock driver with a given intensity can accelerate protons from 4.7 MeV to 13 GeV, driven by the transverse electric field induce by the compressed static magnetic field. These results suggest that this mechanism can be experimentally realized in magnetized laser-plasma systems, offering a novel approach for studying astrophysical phenomena in controlled laboratory experiments.

Keywords: intense laser pulse; proton acceleration; relativistic electromagnetic shock.

Figure 1

Schematic of Proton Acceleration. The astrophysical object colliding with magnetic fields compresses the field due to flux conservation, generating a transverse electric field that accelerates protons transversely. The colored circles show the trajectory of the accelerated proton.

Figure 2

The relationship between the proton's maximum acceleration distance and the initial magnetic field strength with the maximum energy. The lines show the relationship between the proton's maximum acceleration distance y _max and the magnetic field strength B _z0, with the velocity of the astrophysical object v _p = 0.925. The color area shows the representative magnetic field strengths and distance ranges for several astrophysical objects such as interstellar matter (ISM), pulsar wind nebulae (PWN), Gamma‐ray burst (GRB), active galactic nucleus (AGN), white dwarf stars (WD), and neutron stars (NS). The scale size of the magnetic fields of these objects is beyond the maximum acceleration distance y _max.

Figure 3

The trapped conditions and proton energy. a) The minimum longitudinal thickness d (shown by the color code) of the relativistic electromagnetic shock corresponding to different injected proton's initial momenta p_x0 and p _y0. b) The maximum proton energy E _max (shown by the color code) corresponding to different injected proton's initial momenta p _x0 and p _y0. The initial proton momentum with thickness of 10 µm (blue dashed line) and 50 µm (red dashed line) is marked on the plot, respectively.

Figure 4

The relativistic electromagnetic shock induced by compressing a static magnetic field through interaction with a strong laser (a ₀ = 150) at 295T₀.

Figure 5

The acceleration result and process of the trapped protons. a) The energy distribution of protons at 770T₀ after acceleration. The acceleration process of the trapped protons, with the color code representing the simulation time. b, c) The motion trajectories of the high‐energy protons in the x and ξ coordinate systems, separately. d) The energy source of the high‐energy protons.

Figure 6

Schematic diagram of relativistic electromagnetic shock cascaded acceleration. The direction of the magnetic field needs to change according to the direction of motion of the proton so that the transverse electric field is always in the y‐direction.