Modification of magnetohydrodynamic waves by the relativistic Hall effect

Abstract

This study shows that a relativistic Hall effect significantly changes the properties of wave propagation by deriving a linear dispersion relation for relativistic Hall magnetohydrodynamics (HMHD). Whereas, in nonrelativistic HMHD, the phase and group velocities of fast magnetosonic wave become anisotropic with an increasing Hall effect, the relativistic Hall effect brings upper bounds to the anisotropies. The Alfvén wave group velocity with strong Hall effect also becomes less anisotropic than non-relativistic case. Moreover, the group velocity surfaces of Alfvén and fast waves coalesce into a single surface in the direction other than near perpendicular to the ambient magnetic field. It is also remarkable that a characteristic scale length of the relativistic HMHD depends on ion temperature, magnetic field strength, and density while the non-relativistic HMHD scale length, i.e., ion skin depth, depends only on density. The modified characteristic scale length increases as the ion temperature increases and decreases as the magnetic field strength increases.

Relativistic-amplitude electromagnetic waves—Beating the “magnetic” barrier

“…Here, we wish to emphasize that the model studied herein contains relativistic MHD 2,3,32 as a limiting case [33][34][35] . Our results encompass, to varying degrees, some of the previous analyses of linear and non-linear relativistic magnetofluid waves [36][37][38][39][40][41][42][43][44] .…”

Yet Another Modification of Relativistic Magnetohydrodynamic Waves: Electron Thermal Inertia

“…The nal term in the right hand side of (1c) is a Hall term, while the terms multiplied by ℎ e and in (1b) and (1c) are originated from the electron thermal and rest mass inertiae. In our previous paper [36], we neglected the electron inertia e ects and focused on the Hall e ect by assuming that the electron temperature is modestly-or non-relativistic, i.e., e ∕ e 2 ≲ 1, and wavelength is in proton inertial scales, i.e., i ∼ 1, where i = ( i 2 ∕4 0 2 ) 1∕2 is the proton skin depth. In this study, we consider electrons with ultrarelativistic temperature while the wavelength is slightly shorter than i but much larger than the electron inertial length e = 1∕2 i .…”

“…where ȟe = ℎ e ∕ e 2 , i = ℎ i0 ∕[(4 0 ℎ i0 + 2 0 ) 2 ] 1∕2 is the modi ed proton skin depth [36], A = 0 ∕[4 ( 0 ℎ i0 + 2 0 )] 1∕2 is the Alfvén speed, and S = (Γ i0 ∕ 0 ℎ i0 ) 1∕2 is the sound speed. The subscript ‖ (⟂) denotes the parallel (perpendicular) component to 0 .…”

“…One nds that ȟe is always multiplied by ( i ) 2 in (4), and ȟe ( i ) 2 is ∼ 1 because ℎ e ∼ −1∕2 and i ∼ −1∕4 . Ignoring the ETI e ect by ȟe → 0, one retrieves the relativistic Hall MHD dispersion relation [36]…”

“…strongly anisotropic, i.e., it primarily propagates in the direction parallel to the background magnetic eld. In our previous work [36], we explored the wave properties in relativistic Hall MHD (RHMHD), in which the electron temperature is modestly-or non-relativistic, and thus ETI is negligible in ion inertial scales. We demonstrated that relativistic Hall e ect and non-relativistic Hall e ect change the wave properties di erently.…”