Mode properties of low‐frequency waves: Kinetic theory versus Hall‐MHD

Abstract

In fluid theory, the ordering of low‐frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documenting the dispersion and general mode properties of the low‐frequency waves (ω « (ΩciΩce)1/2, where Ωci, Ωce are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two‐fluid theory. Kinetic theory gives a separate Alfvén/ion‐cyclotron (A/IC) wave with phase speed ω/k ≈ υAcosθ for ω « Ωci, where υA is the Alfvén velocity and θ the angle of propagation between wave vector k and background magnetic field Bo. For a given wavenumber, the magnetosonic mode is a double‐valued solution with a singular point in θ, β parameter space, where β is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point θ ∼ 30°, β ∼ 3 and leading to larger β gives a practical and consistent separation of this double‐valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetosonic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at β ∼ 0.5. At larger β, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbations may become useless at high β, whereas the direction of the magnetic field perturbation with respect to k and Bo remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.