Quasi-one-dimensional model equations for plasma flows in high-pressure discharges in ablative capillaries

Quasi-one dimensional hydrodynamic continuity, momentum and energy equations describing the plasma flow in high-pressure-discharge ablative capillaries are derived. To overcome the formidable difficulties arising in the solution of a fully two-dimensional system of equations, experimental information on the structure (geometry) of the generated plasma is used. Thus the two-dimensional hydrodynamic equations are averaged over the cross-section of the capillary to obtain a quasi-one-dimensional system of equations in which, however, the essential two-dimensional features are present. These include the radial outwards radiative transfer of energy and the radial inwards ablative mass flow. Some particular cases, including their thermodynamical aspects, are discussed. Illustrative analytical and numerical solutions of the equations are also presented.