Nonlinear Saturation of Cyclotron Maser Instability Associated with Energetic Ring-Beam Electrons

We study the cyclotron maser instability (CMI) driven by an energetic ring-beam distribution by a particle simulation to explain possible generation mechanisms of intense radiation phenomena observed in space. The main objective is to understand the nonlinear processes that control saturation of the emission process. Our study reveals new issues that have been overlooked in past literature. It is found that electrostatic wave modes excited by the electron beam instability compete with the electromagnetic waves excited by the CMI. Nonlinear effects of these electrostatic modes tend to redistribute the energy of the energetic electrons and make the physics more complicated. The CMI can be much less effective in a realistic case than it is anticipated theoretically.

Figure 1

A schematic illustration of the initial background (left) and energetic (right) electron distributions along with the pitch angle ${\varphi }_p$, wave propagation angle ${\theta }_B$, $u_{d\perp }$, and $u_{d\parallel }$. Here, in the momentum space, $u_{\perp 1}$ and $u_{\perp 2}$ are orthogonal axes perpendicular to ${\mathbf{B}}_{\mathbf{0}}$.

Figure 2

Energy histories of the longitudinal electric, transverse electric, transverse magnetic, and total kinetic energies for cases ${\varphi }_P=30°$, ${\omega }_{pe}/{\omega }_{ce}=0.2$, $u_d=0.67c$, and various propagation angles. Logarithmic scale is adopted except in the last panel, and the energies are normalized to the initial total energy.

Figure 3

Wave dispersion diagrams of (a) the electrostatic, (b) transverse electric, and (c) transverse magnetic components along with wave energy histories of (d) the electrostatic (ES) mode caused by the electron beam instability and (e),(f) $X$ and $Z$ modes for case $A$. The corresponding waves are designated by rectangles on the dispersion diagrams. All energies are normalized to the initial total energy. On the dispersion diagrams, the dotted horizontal lines and solid horizontal lines stand for ${\omega }_{pe}$ and ${\omega }_{ce}$, respectively, and the slope of the $\mathsf{V}$-like lines is the speed of light.

Figure 4

Particle distributions of the background and energetic electrons in the momentum space for (a) the initial condition, (b) case $A$ at $t=240{\omega }_{ce}^{-1}$, and (c) case $B$ at $t=480{\omega }_{ce}^{-1}$. The solid lines denoted by the letters $I$, $J$, $K$, $L$, $M$, and $N$ correspond to the cross-section plots in Figs. 5a, 5b, 5c, 5d, 5e, 5f, respectively. The presentation of energetic electron distribution (the right-hand part) is highlighted by multiplying a factor of 20.

Figure 5

Left-hand column: Cross-section plots of the energetic electron distribution at different times along $I$, $J$, and $K$ lines in Fig. 4b for case $A$. Right-hand column: Cross-section plots of the energetic electron distribution at different times along $L$, $M$, and $N$ lines in Fig. 4c for case $B$. Notice that here the magnitude of the distribution function is without the factor of 20, as considered in Fig. 4.

Figure 6

Wave dispersion diagrams of the transverse electric components (a) perpendicular (the $Z$ and $X$ modes) and (b) parallel (the $O$ mode) to the ambient magnetic field along with energy histories of (c),(d) the $Z$-, $X$-, and (e),(f) $O$-mode waves for case $B$.