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High-current vacuum arc under axial magnetic field: Numerical simulation and comparisons with experimentsThe structure of slow shocks and intermediate shocks in the presence of a heat conduction parallel to the local magnetic field is simulated from the set of magnetohydrodynamic equations. This study is an extension of an earlier work ͓C. L. Tsai, R. H. Tsai, B. H. Wu, and L. C. Lee, Phys. Plasmas 9, 1185 ͑2002͔͒, in which the effects of heat conduction are examined for the case that the tangential magnetic fields on the two side of initial current sheet are exactly antiparallel ͑B y =0͒. For the B y = 0 case, a pair of slow shocks is formed as the result of evolution of the initial current sheet, and each slow shock consists of two parts: the isothermal main shock and the foreshock. In the present paper, cases with B y 0 are also considered, in which the evolution process leads to the presence of an additional pair of time-dependent intermediate shocks ͑TDISs͒. Across the main shock of the slow shock, jumps in plasma density, velocity, and magnetic field are significant, but the temperature is continuous. The plasma density downstream of the main shock decreases with time, while the downstream temperature increases with time, keeping the downstream pressure constant. The foreshock is featured by a smooth temperature variation and is formed due to the heat flow from downstream to upstream region. In contrast to the earlier study, the foreshock is found to reach a steady state with a constant width in the slow shock frame. In cases with B y 0, the plasma density and pressure increase and the magnetic field decreases across TDIS. The TDIS initially can be embedded in the slow shock's foreshock structure, and then moves out of the foreshock region. With an increasing B y , the propagation speed of foreshock leading edge tends to decrease and the foreshock reaches its steady state at an earlier time. Both the pressure and temperature downstreams of the main shock decrease with increasing B y . The results can be applied to the shock heating in the solar corona and solar wind.FIG. 4. The density ratio 2 / 1 across the slow shock is plotted as a function of ␦Q for the upstream shock parameters M A1 = 0.45, ␤ 1 = 0.04, and 1 = 60°.