Continuous transitions between discontinuous magnetohydrodynamic flows of plasma and its heating
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Continuous Transitions between Discontinuous Magnetohydrodynamic Flows of Plasma and Its Heating L. S. Ledentsov* and B. V. Somov** Sternberg Astronomical Institute, Universitetskii pr. 13, Moscow, 119992 Russia Moscow State University, Moscow, 119991 Russia *email: [email protected] **email: [email protected] Received June 25, 2013
Abstract—The possibility that the type of discontinuous flow changes as the conditions gradually (continu ously) change is investigated in connection with the problems arising when the results of numerical simula tions of magnetic reconnection in plasma are interpreted. The conservation laws at a discontinuity surface in magnetohydrodynamics admit such transitions, but the socalled transition solutions for the boundary con ditions that simultaneously satisfy two types of discontinuities should exist in this case. The specific form of such solutions has been found, and a generalized scheme of permitted transitions has been constructed on their basis. An expression for the jump in internal energy at discontinuity is derived. The dependence of the plasma heating efficiency on the type of discontinuity is considered. DOI: 10.1134/S1063776113140148
1. INTRODUCTION Discontinuous plasma flows in a magnetic field are present in various kinds of technical facilities and devices of practical significance [1–3], in laboratory and numerical experiments [4–6], and in astrophysi cal conditions—especially in connection with the magnetic reconnection effect [7–11]. The question about plasma heating to very high temperatures is gen erally important in this case [12]. For example, as applied to solar flares, the appearance of plasma in the solar corona whose electron temperature exceeds con siderably 10 keV [13] needs to be explained. Presentday numerical experiments simulating the reconnection process, for example, in the approxima tion of dissipative magnetohydrodynamics (MHD), demonstrate a slightly smoothed picture of discontin uous flows in the vicinity of a reconnecting current layer [14–17]. When the results of such calculations, especially threedimensional ones, are interpreted, it is difficult to unequivocally identify the type of a par ticular discontinuity by some incomplete and averaged set of attributes. If this difficulty has been successfully overcome, then a second problem arises; it consists in explaining the simultaneous presence of different types of discontinuities gradually transforming into one another in such experiments. In this case, the task of interpreting the picture of transitions is often com plicated by the appearance of nonevolutionary dis continuities [18]. From a theoretical point of view, the following facts play a fundamental role in investigating the properties of discontinuous plasma flows. The equations of ordi
nary hydrodynamics are known to have only two types of discontinuous solutions: a tangential discontinuity and a shock. In magnetohydrodynamics (MHD), the presence of a magnetic field in plasma leads to
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