Converging Cylindrical Shock Waves in a Nonideal Gas With an Axial Magnetic Field

Abstract

This paper analyses the propagation of converging cylindrical shock waves in a nonideal
gas, in the presence of an axial magnetic field. Chester-Chisnell-Whitham’s method has been
employed to determine the shock velocity and the other flow-variables just behind the shock
in the cases, when (i) the gas is weakly ionised before and behind the shock front, (ii) the gas
is strongly ionised before and behind the shock front, and (iii) nonionised gas undergoes intense
ionisation as a result of the passage of the shock. The effects of the nonidealness of the gas,
the conductivity of the gas, and the axial magnetic field have been investigated. It is found that
in the case (i), an increase in the value of parameter ( ) characterising the nonidealness of the
gas accelerates the convergence of the shock. In the case (ii), the shock speed and pressure
behind the shock increase very fast as the axis is approached; and this increase occurs earlier
if the strength of the initial magnetic field is increased. In the case (iii), for smaller values of the
initial magnetic field, the shock speed, and pressure behind the shock decrease very fast after
attaining a maximum; and for higher values of the initial magnetic field, the tendency of decrease
appears from the beginning. This shows that the magnetic field has damping effect on the shock
propagation. In the case (iii), it was also found that the growth of the shock in the initial phase
and decay in the last phase were faster when it was converging in a nonideal gas in comparison
with that in a perfect gas. Further, it has been shown that the gas-ionising nature of the shock
has damping effect on its convergence.