Self-similar expansion of a warm dusty plasma—II. Magnetized case

The self-similar transverse expansion into vacuum of a warm, magnetized dusty plasma filling semi-infinite half-space is investigated. The analysis is carried out using a MHD model wherein the plasma expansion preserves quasi-neutrality and the magnetic field lines are frozen to the plasma. As the nature of the study is quite complex, for simplicity the analysis is restricted to a one-dimensional expansion of a collisionless plasma in which the dust particles have constant charge. The self-similar governing equations obtained from the model equations are reduced to a quadrature. Analytical solutions for a number of cases of practical interest are obtained both for the isothermal as well as for the adiabatic expansions. The qualitative nature of the density and the velocity profiles during the expansion has been discussed. The magnetic field is found to constrain the transverse expansion of the plasma. For sufficiently strong magnetic fields, the dust density falls off to nearly zero at much shorter distances from the initial plasma-vacuum boundary whereas the expansion velocity is substantially reduced.