Drift‐compressional modes generated by inverted plasma distributions in the magnetosphere

Abstract

[1] The polarization and field-aligned structure of drift-compressional modes and the corresponding plasma instability are studied in a gyrokinetic framework in the axisymmetric model of the magnetosphere with isotropic plasma. The plasma is assumed to be composed of core cold particles and an admixture of hot protons, with an inverted distribution of hot protons. Such plasma experiences a compressional resonance when the wave frequency is equal to an eigenfrequency of the drift-compressional mode. In this resonance, the wave is dominated by the field-aligned and azimuthal magnetic field components and is narrowly localized along the field line at the equator, the same as the plasma to magnetic pressure ratioˇ. The plasma instability occurs when the temperature diamagnetic drift velocity is less than the magnetic drift velocity or opposite in direction. Furthermore, the narrower the inverted distribution, the higher the instability growth rate and the smaller the value ofˇrequired for the instability to occur. The growth rate reaches its highest values when a positive radial temperature gradient and a negative radial density gradient occur simultaneously.

Drift-compression waves propagating in the direction of energetic electron drift in the magnetosphere

“…In this case, we get sets of eigenfunctions b N and eigenvalues  N in the integral equation, which determine the field-aligned structure and eigenfrequencies of drift-compressional modes. As shown in [Mager et al, 2013], drift-compressional modes are localized in the vicinity of the geomagnetic equator. This agrees with satellite data on compressional Pc5 pulsations [Higuchi, Kokubun, 1988].…”

“…In the approximation in which the wave frequency is much less than the bounce frequency of particles, an equation describing the drift-compressional mode can be derived from the gyrokinetic equations presented in [Chen, Hasegawa, 1991]. However, unlike previous works [Crabtree et al, 2003, Klimushkin, Mager, 2011Mager et al, 2013] which took a wave whose direction of propagation coincided with the proton direction k 2 <0, i.e. to the west, we consider the case where the wave propagates east, in the electron drift direction k 2 >0.…”

“…Then, in Equation (4) we can take  outside the integrals. Next, we can carry out a number of transformations, as in [Mager et al, 2013], and obtain a second-kind homogeneous Fredholm integral equation with a symmetric kernel. This equation can be solved numerically.…”

“…They are the most common compressional modes in kinetics since they demand for their existence only finite plasma pressure and inhomogeneity across magnetic shells. In this case, the instability of the drift-compressional modes can arise from spatial gradients of hot plasma density [Crabtree et al, 2003;Klimushkin, Mager, 2011], inverted distribution of hot proton energy [Mager et al, 2013], or from the coupling with the Alfvén mode due to magnetic field line curvature [Klimushkin et al, 2012]. By the inverted distribution is meant the nonmonotonic velocity distribution with its maximum in the highenergy part of spectrum, by analogy with [Hughes et al, 1978].…”

“…As temperature increases and particle density decreases with distance away from Earth, this can cause instability and a spontaneous increase in waves whose phase velocity direction coincides with the proton drift direction [Mager et al, 2013]. The instability threshold is lowered if the proton distribution function is inverted.…”