Interaction of a spatially uniform electron beam with a rotational magnetic hole in a form of a Harris current sheet

TL;DR

The paper investigates why bump-on-tail electron beams in solar wind plasmas can exhibit longer quasi-linear relaxation times than predicted by classical theory. It uses fully kinetic 2D PIC simulations with a Harris current sheet modeled as a rotational magnetic hole to study beam interactions across a range of magnetic hole widths, thereby tuning the ratio $r_L/R_{MH}$. A key finding is that narrow magnetic holes (small $\delta$) with $r_L/R_{MH}\gtrsim 1$ hinder quasi-linear relaxation via non-conservation of electron magnetic moment $\mu$, preserving a positive slope in the VDF and suppressing Langmuir growth, while wider holes allow plateau formation and Langmuir activity. This mechanism offers a potential explanation for the extended propagation distance of some solar wind electron beams along current sheets and highlights the role of kinetic effects in inhomogeneous magnetic structures. The results emphasize that beam transport in the heliosphere is affected by the local magnetic topology and nonadiabatic particle dynamics, beyond standard quasi-linear theory.

Abstract

In this work we use particle-in-cell (PIC) numerical simulations to study interaction of a spatially uniform electron beam with a rotational magnetic hole in a form of a Harris current sheet. We vary width of the Harris current sheet to investigate how this affects the quasi-linear relaxation, i.e. plateau formation of the bump-on-tail unstable electron beam. We find that when width of the Harris current sheet approaches and becomes smaller than the electron gyro-radius, quasi-linear relaxation becomes hampered and a positive slope in the electron velocity distribution function (VDF) persists. We explain this by the effects of non-conservation of electron magnetic moment, which, as recent works suggest, can maintain the positive slope of the VDF. In part, this can explain why some electron beams (the ones that interact with narrow magnetic holes with sharp boundaries, represented in our study by a Harris current sheet) in the solar wind travel much longer distances than predicted by the quasi-linear theory, at least in those cases when the electron beams slide along the current sheets that are abundant when the different-speed solar wind streams interact with each other.

Figures (10)

• Figure 1: Time evolution of different physical quantity profiles across the middle ($y=y_{\rm max}/2$) of the Harris current sheet: (a) plot of $B_y(x,y=y_{\rm max}/2,t)/B_0$ (please note this panel is zoomed-in the x-range), (b) background electron number density $n_e(x,y=y_{\rm max}/2,t)/n_0$, (c) the total magnetic field squared $\sum_{i=x,y,z}[B_i^2(x,y=y_{\rm max}/2,t)]/B_0^2$, which shows the depth of the magnetic hole, (d) out-of-plane current $J_z(x,y=y_{\rm max}/2,t)/J_{z0}$, (e) electron beam number density $n_b(x,y=y_{\rm max}/2,t)/n_0$, (f) background ion number density $n_i(x,y=y_{\rm max}/2,t)/n_0$. The data is for Run 1, the narrowest current sheet $\delta/ x_{\rm max}=0.05$. See table \ref{['t1']} for details. Black, Red, Green, Blue, Cyan, and Gold lines correspond to time instances of $t=0,0.2,0.4,0.6,0.8,1.0~t_{\rm END}$.
• Figure 2: The same as in Fig.(\ref{['fig1']}), but for the Run 5, a wide current sheet with $\delta/ x_{\rm max}=0.5$.
• Figure 3: Time evolution of the sum of background and beam VDF parallel to the magnetic field component, i.e. $f_e(p_\parallel)\equiv f_e(p_y)$. (a) is for Run1, (b) is for Run2, (c) is for Run3, (d) is for Run4, (e) is for Run5, (f) is for Run6. Here, again Black, Red, Green, Blue, Cyan, and Gold lines correspond to time instances of $t=0,0.2,0.4,0.6,0.8,1.0~t_{\rm END}$. Note that $t_{\rm END}$ is different for each run.
• Figure 4: The same as in Fig.(\ref{['fig3']}), but for the background and beam VDF perpendicular to the magnetic field component $f_e(p_\perp)\equiv f_e(p_x)$.
• Figure 5: Time evolution of electric field component parallel to the background magnetic field, i.e. electric field associated with Langmuir waves, $E_y$. The data is for Run 1, the narrowest current sheet $\delta/ x_{\rm max}=0.05$. Panels (a), (b), (c), (d), (e), (f) correspond to time instances of $t=0.01,0.2,0.4,0.6,0.8,1.0~t_{\rm END}$. The electric field is normalized to $E_0=0.25 \omega_{\rm pe} m_e c /q_e$. See text for details.