A theoretical and simulation study of the contact discontinuities based on a Vlasov simulation code

Abstract

[1] Contact discontinuity (CD) is the simplest solution that can be obtained from the magnetohydrodynamics (MHD) Rankine-Hugoniot jump conditions. Due to the limitations of the previous kinetic simulation models, the stability of the CD has become a controversial issue in the past 10 years. The stability of the CD is reexamined analytically and numerically. Our theoretical analysis shows that the electron temperature profile and the ion temperature profile must be out of phase across the CD if the CD structure is to be stable in the electron time scale and with zero electron heat flux on either side of the CD. Both a newly developed fourth-order implicit electrostatic Vlasov simulation code and an electromagnetic finite-size particle code are used to examine the stability and the electrostatic nature of the CD structure. Our theoretical prediction is verified by both simulations. Our results of Vlasov simulation also indicate that a simulation with initial electron temperature profile and ion temperature profile varying in phase across the CD will undergo very transient changes in the electron time scale but will relax into a quasi-steady CD structure within a few ion plasma oscillation periods if a real ion-electron mass ratio is used in the simulation and if the boundary conditions allow nonzero heat flux to be presented at the boundaries of the simulation box. The simulation results of this study indicate that the Vlasov simulation is a powerful tool to study nonlinear phenomena with nonperiodic boundary conditions and with nonzero heat flux at the boundaries of the simulation box.

Possible observational evidence of contact discontinuities

“…Tsai et al . [] used different ratios of T e / T i (0.33, 1.25, and 5) on the two sides of a CD in Vlasov simulations. It is apparent that the values of T e / T i in these simulations were quite different from the ratios of T e / T i in the observations.…”

“…Tsai et al . [] also examined the steadiness of CD structure in MHD, the ion‐electron two‐fluid, and the Vlasov simulations. Their simulations indicated that the CD structure is steady under the out‐of‐phase profiles of the ion and electron temperatures and of the ion and electron thermal pressures.…”

Implicit predictor–corrector central finite difference scheme for the equations of magnetohydrodynamic simulations

“…Elimination-of-the-roundoff-error (ERE) technique [21] eliminates the errors generated from the accumulation of roundoff error due to subtraction during the modeling process. If the result of A minus B is less than a defined value, the result of A minus B is set to be equal to zero in all the subtraction.…”

“…Therefore we use the four staged fourth-order Runge-Kutta method [22,21] to obtain the first three steps U 1 , U 2 , U 3 . The fourth-order Runge-Kutta method can be represented as…”

“…The fourth-order explicit Adams-Bashforth formula serves as the predictor, while the fourth-order implicit Adams-Moulton formula serves as the corrector [22,21].…”