Transversally small-scale perturbations in arbitrary plasma configurations with magnetic surfaces

Abstract

It is shown that in arbitrary plasma systems with magnetic surfaces there are transversally small-scale (ballooning) perturbations with the vector of displacement lying in a magnetic surface. The equations of small oscillations for these perturbations are derived. It is shown that the spectrum of eigenmodes of these equations coincides with a continuous spectrum of resonant MHD modes (Cheng and Chance 1986 Phys. Fluids 29 3695-01). The case of a dipole magnetic field is analysed.

On ballooning instability in current sheets

“…Ballooning instability theory has been developed in detail for magnetic configurations employed in nuclear fusion devices [1][2][3][4]. There is a field in space research, however, where the ballooning instability is also widely used to explain the dynamics observed in plasma medium-physics of planetary magnetospheres.…”

Magnetospheric ULF waves driven by external sources

“…This field line resonance (FLR) mechanism was first suggested in [69] and later used in [66] and [10] to interpret observational results [57]. Recent analytical studies in [11,12,39] showed that in an dipole magnetic geometry an exact solution of small transverse and large longitudinal scales of perturbations can exist, which describes transversely small-scale perturbations with the displacement vector lying in a magnetic surface. It is established that in a dipole magnetic field the perturbations with just two polarizations can exist.…”

“…It is established that in a dipole magnetic field the perturbations with just two polarizations can exist. For poloidal polarization the equations of small oscillations are obtained coupled with magnetosonic component [11,12,14,33,34,38,70].…”

Comment on ‘Transversally small-scale perturbations in arbitrary plasma configurations with magnetic surfaces’

“…

Recently a paper appeared [1] with a main result described in its summary as a derivation of a 'set of exact equations of small oscillations (30)-( 32) for transversally small-scale perturbations in arbitrary three-dimensional spatially inhomogeneous plasma systems with magnetic surfaces'. It is regrettable that although much of this work draws on well-known results, only cursory respect was paid to the published literature.

…”

“…In addition, the claimed extensions are inconsistent with established results. The inconsistency arises due to the use of the MHD equations outside their range of applicability.In [1] the equations are derived from the standard magnetohydrodynamic (MHD) equations using the well-known technique and results described in detail, for example, in [2], in the review [3] and in the textbooks [4,5]. In particular, a ballooning ordering [2-5] has been used with a displacement vector presented in the form (equation ( 15) in [1])…”