Constant-temperature magneto-gasdynamic channel flow

In the course of investigating boundary-layer flow in continuous plasma accelerators with crossed electric and magnetic fields, it was found advantageous to have at hand simple closed-form solutions for the magneto-gas dynamic flow in the duct which could serve as free-stream conditions for the boundary layers. Nontrivial solutions of this sort are not available at present. and in fact, as in the work of Resler and Sears, the variation of conditions along the flow axis must be obtained through numerical integration. Consequently, some simple solutions of magneto-gasdynamic channel flow were sought, possessing sufficient algebraic simplicity to serve as free-stream boundary conditions for analytic investigations of the boundary layer in a physically reasonable accelerator. In particular, since the cooling of the accelerator tube is likely to be an important physical problem because of the high gas temperatures required to provide sufficient gaseous conductivity, channel flow with constant temperature appears interesting. Some simple algebraic solutions for the case of a constant temperature plasma are developed in the following paragraphs.