Magnetohydrodynamic waves within the medium separated by the plane shock wave or rotational discontinuity

Abstract

Abstract. Characteristics of small amplitude plane waves within the medium separated by the plane discontinuity into two half spaces are analysed. The approximation of the ideal one-fluid magnetohydrodynamics (MHD) is used. The discontinuities with the nonzero mass flux across them are mainly examined. These are fast or slow shock waves and rotational discontinuities. The dispersion equation for MHD waves within each of half space is obtained in the reference frame connected with the discontinuity surface. The solution of this equation permits one to determine the wave vectors versus the parameter c p , which is the phase velocity of surface discontinuity oscillations. This value of c p is common for all MHD waves and determined by an incident wave or by spontaneous oscillations of the discontinuity surface. The main purpose of the study is a detailed analysis of the dispersion equation solution. This analysis let us draw the following conclusions. (I) For a given c p , ahead or behind a discontinuity at most, one diverging wave can transform to a surface wave damping when moving away from the discontinuity. The surface wave can be a fast one or, in rare cases, a slow, magnetoacoustic one. The entropy and Alfvén waves always remain in a usual homogeneous mode. (II) For certain values of c p and parameters of the discontinuity behind the front of the fast shock wave, there can be four slow magnetoacoustic waves, satisfying the dispersion equation, and none of the fast magnetoacoustic waves. In this case, one of the four slow magnetoacoustic waves is incident on the fast shock wave from the side of a compressed medium. It is shown that its existence does not contradict the conditions of the evolutionarity of MHD shock waves. The four slow magnetoacoustic waves, satisfying the dispersion equation, can also exist from either side of a slow shock wave or rotational discontinuity. (III) The expressions determining the polarisation of the MHD waves are derived in the reference frame connected with the discontinuity surface. This form of presentation is much more convenient in investigating the interaction of small perturbations with MHD discontinuities. It is shown that the perturbations of the velocity and magnetic field associated with the surface magnetoacoustic wave have Correspondence to: A. A. Lubchich (lubchich@pgi.kolasc.net.ru) the elliptic polarisation. Usually the planes of polarisation for the perturbations of the velocity and magnetic field are not coincident with each other.

Magnetopause MHD surface wave theory: progress & challenges

“…Often surface waves are considered at discontinuities with the most studied being unbounded tangential discontinuities (TDs; Kruskal and Schwartzschild, 1954;Sen, 1963;Southwood, 1968;Goedbloed, 1971;Walker, 1981;Pu and Kivelson, 1983a;Pu and Kivelson, 1983b), pressure balanced surfaces with no threaded mass/magnetic flux-a reasonable approximation to the magnetopause in the absence of reconnection. Surface waves are, however, also supported by the other MHD discontinuities and shocks (Lubchich and Pudovkin, 1999;Lubchich and Despirak, 2005;Ruderman et al, 2018), as well as transition layers (Chen and Hasegawa, 1974;Lee and Roberts, 1986;Uberoi, 1989;De Keyser et al, 1999).…”

Relativistic magnetohydrodynamical simulations of the resonant corrugation of a fast shock front

“…The two remaining solutions are either fast modes, one of which can be discarded as it outruns the shock, i.e. | β g,2, x | > | β 2 | and β g,2, x β 2 < 0 (since −β 2 corresponds to the shock velocity relative to the downstream) or, two waves with complex wavenumbers, one of which is unphysical, as it diverges far from the shock, while the other describe a surface wave on the front (see LRG16 for further discussion on the number of degrees of freedom of the outgoing modes, see also Lubchich & Despirak (2005) for a detailed discussion on the nature of the modes). The resonance emerges at the transition between these two cases, when the velocity of the outgoing mode nearly coincides with the shock velocity in the downstream plasma frame.…”

On the stability of Alfvén discontinuity

“…They naturally arise when one tries to construct steady solutions of the magnetohydrodynamic ͑MHD͒ equations. [5][6][7][8] The simplest MHD flows with an Alfvén discontinuity are piecewise constant solutions of the MHD equations with a planar discontinuity surface. [2][3][4] They are used to model flows of astrophysical plasma and interpret observations of the behavior of Earth's magnetosphere and interplanetary medium.…”