SHOCK STRENGTH IN SPACE AND ASTROPHYSICAL PLASMAS

The Rankine–Hugoniot (R–H) jump conditions are the most important and frequently used equations in studies of the properties of space and astrophysical plasmas during their passage through shock discontinuities. This paper revisits the R–H conditions for shocks, develops the formulation of the compression ratio, and examines its range of values and properties. The analysis expresses the downstream thermodynamic variables and the compression ratio as functions of the upstream thermodynamic variables, either for equal or different polytropic indices upstream and downstream of the shock. In the general case of space plasmas with an oblique magnetic field, the compression ratio is given by a quartic polynomial, which is reduced to a cubic trinomial when the upstream/downstream polytropic indices are equal. The special cases of magnetic fields that are perpendicular or parallel to the shock normal are also examined. In any case, the compression ratio polynomial has one degree larger order, when the upstream/downstream polytropic indices are different. Emphasis is placed on the maximum value of the compression ratio, which is known to be ∼4 for adiabatic polytropic index ∼5/3. However, the compression ratio can be much larger if the upstream/downstream polytropic indices are not equal to each other and less than one. Several other issues are investigated: (i) the entropic condition, showing that statistical mechanics and thermodynamics lead to the same relation of entropy variation; (ii) the effect of kappa distributions on jump conditions; and (iii) the upper limit of the upstream temperature for a shock to exist