Seong-Yeop Jeong
We develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a Gaussian wave packet. We show that the localized energy density of the Gaussian wave packet determines the velocity-space range in which the dominant wave-particle instability and counter-acting damping contributions are effective. Moreover, we derive a relation describing the diffusive trajectories of resonant particles in velocity space under the action of such an interplay between the wave-particle instability and damping. For the numerical computation of our theoretical model, we develop a mathematical approach based on the Crank-Nicolson scheme to solve the full quasi-linear diffusion equation. Our numerical analysis solves the time evolution of the velocity distribution function under the action of a dominant wave-particle instability and counteracting damping, and shows a good agreement with our theoretical description. As an application, we use our model to study the oblique fast-magnetosonic/whistler instability, which is proposed as a scattering mechanism for strahl electrons in the solar wind.
We argue that the unstable VDF is stabilized by the wave-particle instability. Therefore, we define the stabilisation as the process that creates the condition in which the quasi-linear diffusion does not occur anymore. For our analysis of a VDF stabilisation through a resonant wave-particle instability, we apply Eq. (1) to Boltzmann’s H-theorem and find the diffusive characteristics of the resonant particles in the stabilisation process.
Eq. (3) is a window function which determines the velocity region in which the quasi-linear diffusion of resonance particles is effective. Eq. (4) is the diffusive trajectory of resonant particles through the resonance in velocity space.
To support the theoretical description and simulate the VDF evolution through a resonant wave-particle instability quantitatively, a rigorous numerical analysis of Eq. (1) is necessary. For this purpose, we develop a mathematical approach based on the Crank-Nicolson scheme. We note that our mathematical approach is applicable to all general two-dimensional diffusion equations, including those with off-diagonal diffusion terms. Our numerical solution of Eq. (1) evolves the VDF under the action of multiple resonances with time.
We apply our model to the scattering of the electron strahl which is a field-aligned electron beam population in the solar wind. Our quasi-linear framework confirms that an instability of the fast-magnetosonic/whistler (FM/W) wave in oblique propagation with respect to the background magnetic field scatters the electron strahl into the electron halo. Fig. 5 shows the time evolution of the electron VDF under the action of the FM/W instability. The strahl electrons is scattered through the FM/W instability and its pitch-angle increases.