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Chorus emission in planetary magnetospheres is taken as working paradigm to motivate a short tutorial trip through theoretical plasma physics methods and their applications. Starting from basic linear theory, readers are first made comfortable with whistler wave packets and their propagation in slowly varying weakly nonuniform media, such as the Earths magnetosphere, where they can be amplified by a population of supra-thermal electrons. The nonlinear dynamic description of energetic electrons in the phase space in the presence of self-consistently evolving whistler fluctuation spectrum is progressively introduced by addressing renormalization of the electron response and spectrum evolution equations. Analytical and numerical results on chorus frequency chirping are obtained and compared with existing observations and particle in cell simulations. Finally, the general theoretical framework constructed during this short trip through chorus physics is used to draw analogies with condensed matter and laser physics as well as magnetic confinement fusion research. Discussing these analogies ultimately presents plasma physics as an exciting cross-disciplinary field to study.
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Resonant electron interaction with whistler-mode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasi-linear theory. However, recent statistics of parallel propagating chorus waves have demonstrated that 5-20% of the observed waves are sufficiently intense to interact nonlinearly with electrons. Such interactions include phase trapping and phase bunching (nonlinear scattering) effects not described by the quasi-linear diffusion. For sufficiently long (large) wave-packets, these nonlinear effects can result in very rapid electron acceleration and scattering. In this paper we introduce a method to include trapping and nonlinear scattering into the kinetic equation describing the evolution of the electron distribution function. We use statistics of Van Allen Probes and Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations to determine the probability distribution of intense, long wave-packets as function of power and frequency. Then we develop an analytical model of particle resonance of an individual particle with an intense chorus wave-packet and derive the main properties of this interaction: probability of electron trapping, energy change due to trapping and nonlinear scattering. These properties are combined in a nonlocal operator acting on the electron distribution function. When multiple waves are present, we average the obtained operator over the observed distributions of waves and examine solutions of the resultant kinetic equation. We also examine energy conservation and its implications in systems with the nonlinear wave-particle interaction.
Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.
This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring at spatial scales smaller than the ion gyroscale and in velocity space. Scaling relations for the resulting fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The importance of adequately modeling and resolving collisions in gyrokinetic simulations is biefly discussed, as well as the relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas.
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum-classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.
It is well-known that the resonance phenomena can destroy the adiabatic invariance and cause chaos and mixing. In the present paper we show that the nonlinear wave-particle resonant interaction may cause the emergence of large-scale coherent structures in the phase space. The combined action of the drift due to nonlinear scattering on resonance and trapping (capture) into resonance create a vortex-like structure, where the areas of particle acceleration and deceleration are macroscopically separated. At the same time, nonlinear scattering also creates a diffusion that causes mixing and uniformization in around the vortex.
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