Effects of Heat and Momentum Addition Inside and Outside the Compound Sonic Point of the Solar Wind

We consider the effect of heat and momentum addition to the solar wind for a model including the effects of Alfven waves and plasma pressure (proton plus electron pressure). The mass flux per unit area in 1D flow maximizes when the flow speed equals the compound sound speed, including the effects of the Alfven wave pressure. We discuss the analogue of the Laval nozzle for the solar wind flow, and the dependence of the effective nozzle area as a function of radial distance, and the relationship of the nozzle area to the momentum equation and the Mach number of the flow. An analysis is carried out of the effects of heat and momentum addition to the wind, using a thin slice approximation, which leads to Rankine Hugoniot relations for weak deflagrations and detonations (i.e. the combustion Hugoniot). The linearized Hugoniot is used to analyze the effects of small momentum and energy addition to the wind in the thin slice approximation. We obtain the fully nonlinear Rankine Hugoniot equation solutions. The analysis also holds in the presence of Alfven waves, in which the wave energy exchange equation yields the wave action flux conservation law when their contribution to the compound sound speed is taken into account. The effective polytropic index γgamma and flow speed relative to the compound flow speed ahead of the slice play crucial roles in determining whether local acceleration or deceleration results. Some results are at first sight unexpected since γgamma for Alfven waves ranges from -1/2 (in sub-Alfvenic flow) to 3/2 in super-Alfvenic flow.