Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.