A study of tearing instability in the presence of a pressure anisotropy

Abstract

The effects of pressure anisotropy on the tearing mode in a current sheet are studied based on a linear compressible MHD code. It is found that in the presence of a small pressure anisotropy (Pc > Pll)' tearing mode dominates the unstable modes except that the growth rates are enhanced, which is consistent with the recent results; for a large pressure anisotropy the growth rates of unstable modes become even larger, and a mixed mirror-tearing configuration is formed for large k• (wave number along current sheet) implying that mirror instability is responsible for the enhancement of growth rate and modification of the tearing mode. In the presence of a large pressure anisotropy, a new oscillating tearing mode is observed when the wave number k• is small. Furthermore, a large 1/component of the magnetic field is found to be able to cancel the effect of pressure anisotropy, with the resultant mode being the same as that of isotropic tearing instability. 1975, 1978; Drake and Lee, 1977; Killeen and $hestakov, 1978;White, 1983; Lee and It& 1986]. Plasma processes developed in the current sheet may provide an effective mechanism for the conversion of magnetic energy into kinetic energy of particles. The occurrence of current filamentation in the current sheet relaxes the configuration to a lower energy state, which in turn leads to the formation of magnetic islands. This process, known as tearing instability, violates the basic topological restfictions of the infinite conductivity assumption; namely, the process consists of "breaking"and reconnection of the magnetic lines of force. For the tearing mode to occur, a finite resistivity is necessary. In case of collisionless plasma, the role of this resistivity is provided by the inertia of current carriers [$peiser, 1970; Vas•tliunas, 1975; $onnerup, 1979], tearing mode-particle resonance or by microinstabilities driven by the strong currents or gradients in the diffusion region. Reviews of several microinstabilities that are suggested as possible anomalous transport mechanisms in current sheets have been given by $onnerup [1979].For nearly two decades, the tearing instability has been considered as a possible candidate responsible for the reconnection in the magnetotail and magnetopause [Coppi et al., 1966;Galeev and Zelenyi, 1978;Schindler, 1974; •uest and Coroniti, 1981; Lee and Fu, 1985]. As early as 1963, Furth et al. systematically studied the problem of tearing instability analytically by MHD approach. Since then, a substantial amount of research has been done on the linear and nonlinear stages of the instability [ Coppi, 1964; Laval and Pellat, 1967; Dobrowoln•l, 1968; Drake and Lee, 1977; Galeev and gelen•ti, 1975; Terasawa, 1981; Ghen and Palmadesso, 1984; Ambrosiano et al., 1986]. Generally, the tearing instability falls into three regimes which are referred to as collisionless, semicollisionless, and collisional [Drake and Lee, 1977]. In the collisionless regime, anisotropy

Proton Temperature Anisotropy and Magnetic Reconnection in the Solar Wind: Effects of Kinetic Instabilities on Current Sheet Stability

“…On the other side, they also suggested that the tearing instability can be strongly suppressed if the opposite anisotropy T ⊥ < T is present in the current sheet. This picture has been confirmed by numerical studies in a hybrid (Ambrosiano et al 1986) and fluid (Shi et al 1987) framework.…”

MHD modeling of magnetotail instability for anisotropic pressure

“…Shi et al [1987], for example, considered the linear evolution of the resistive tearing instability in a current sheet model with anisotropic pressure in the initial condition. Therefore we included an anisotropic pressure model in the investigation described in this paper.…”

Pressure anisotropy in global magnetospheric simulations: A magnetohydrodynamics model

“…First of all, the anisotropic pressure equations are formulated equivalently to the double adiabatic equations. However, the double adiabatic approximation is not applicable to some processes, for example mirror instability [ Kulsrud , 1982; Shi et al , 1987]. Although the pressure relaxation term mimics the effect of instabilities on pressure, it is still an approximation.…”