Physics of kinetic Alfvén waves: a gyrokinetic theory approach

Abstract

The transverse shear Alfvén wave (SAW) is a fundamental anisotropic electromagnetic oscillation in plasmas with a finite background magnetic field. In realistic plasmas with spatial inhomogeneities, SAW exhibits the interesting spectral feature of a continuous spectrum. That is, the SAW oscillation frequency varies in the non-uniform (radial) direction. This continuum spectral feature then naturally leads to the phase-mixing process; i.e., time asymptotically, the effective radial wave-number increases with time. Any initial perturbation of SAW structures will, thus, evolve eventually into short-wavelength structures; termed as kinetic Alfvén wave (KAW). Obviously, one needs to employ kinetic theory approach to properly describe the dynamics of KAW; including effects such as finite ion-Larmor radius (FILR) and/or wave–particle interactions. When KAW was first discovered and discussed in 1975–1976, it was before the introduction of the linear electromagnetic gyrokinetic theory (1978) and nonlinear electromagnetic gyrokinetic theory (1982). Kinetic treatments then often involved the complicated procedures of taking the low-frequency limit of the Vlasov kinetic theory and/or employing the drift-kinetic theory approach; forsaking, thus, the FILR effects. In recent years, the powerful nonlinear gyrokinetic theory has been employed to re-examine both the linear and nonlinear physics of KAWs. This brief review will cover results of linear and nonlinear analytical theories, simulations, as well as observational evidences. We emphasize, in particular, that due to the enhanced electron–ion de-coupling in the short-wavelength regime, KAWs possess significantly enhanced nonlinear coupling coefficients and, thereby, play important roles in the heating, acceleration, and transport processes of charged particles in magnetized plasmas.

Kinetic Alfven Waves Near a Dissipative Layer

“…In particular, we have, in the two limiting cases, As we will see from further calculations, the small parameters in the tensor (Equation ) determine the square of the characteristic KAW dispersion length: , which agrees with its definition in Chen et al. (2021). It is easy to verify that the ratio is equivalent to the condition , where is a parameter characterizing the gas‐kinetic to magnetic plasma pressure ratio.…”

“…Note that the same solution of the inhomogeneous Airy equation, which describes the structure of resonant KAW near the resonance surface was obtained in Goertz (1984) and Chen et al. (2021).…”

“…As was shown in Chen et al. (2021), in close proximity to the turning point the wave structure in this case is described by the Airy function .…”

“…i.e., in the transparency region (to the right of  A E x x ), the resonant kinetic Alfven wave has the form of a wave running away from the resonance surface, and in the opacity region (to the left of  A E x x ), it monotonically decreases as 1/( ) x x A  . Note that the same solution of the inhomogeneous Airy equation, which describes the structure of resonant KAW near the resonance surface was obtained in Goertz (1984) and Chen et al (2021).…”

“…If the dissipation of such waves is small, their structure across magnetic shells is then determined by other small dispersion effects (Dmitrienko, 2010; Hasegawa & Chen, 1976). Such Alfven oscillations have the form of waves running across magnetic shells at much smaller velocities than the Alfven velocity, and are called kinetic Alfven waves (KAWs) (Chen et al., 2021; Pucci et al., 2016). These dispersion effects determine the Alfven wave length across magnetic shells.…”