Simulation of weak electron beam injection into plasma with open boundary conditions

Institute of Solar-Terrestrial Physics SB RAS, 664033 Irkutsk, Russia

^⋆ Corresponding author; annenkov.phys@gmail.com

Received: 1 August 2024
Accepted: 19 December 2024

Abstract

Context. Different high-energy events lead to the generation of electron beams in the solar atmosphere as well as in planetary magnetospheres. The propagation of these beams through space plasma becomes a main source of non-thermal emission, primarily on the harmonics of the fundamental plasma frequency. Due to the high level of non-linearity and the complexity of such systems, theoretical studies of them are largely based on numerical simulations. However, it is still common practice to use a simplified model in which periodic boundary conditions for fields and particles are used to simulate an infinite plasma.

Aims. In this work, the first attempt at high-resolution studies of the dynamics of a weak beam in space plasma using a model with open boundary conditions is reported. The general results of the simulations are compared with those obtained previously using the approximation of infinite plasma.

Methods. The continuous injection of an electron beam with an average velocity of v_b = 0.25c (c – speed of light) and a relative density of n_b/n₀ = 5 ⋅ 10⁻⁴ (n₀ – plasma density) into an unmagnetised plasma was simulated in a quasi-1D approximation using a collisionless electromagnetic particle-in-cell code. The background plasma was initially homogeneous and consisted of electrons and protons with the real mass ratio. The total simulation time was 10 000 ω_p0⁻¹, where ω_p0 is the Langmuir frequency for the given n₀.

Results. The present simulations demonstrate the formation of a spatially localised Langmuir turbulence in the close vicinity of the beam injection site. The continuous injection of fresh beam particles increases the amplitude of the plasma waves to values larger than those possible when simulating the same parameters in a simplified model. Plasma waves in this region turn out to be unstable against the modulation instability, so the formation of density wells followed by plasma wave trapping is observed. Some of the beam particles are significantly accelerated by previously arisen plasma waves. On average, only 10% of the beam energy gets lost in the system, but the distribution function is transformed into a flat-top form with a supra-thermal tail.

Conclusions. The obtained results demonstrate several significant differences from the results of simulations using the approximation of infinite plasma. This fact emphasises the importance of using of a more realistic model for simulations of beam-plasma systems. In addition, using the model with open boundaries, in contrast to the simplified model, will allow us to correctly investigate the influence of not only random gradients of the plasma parameters, but also regular ones.