Nonlinear self-similar boundary-value problem for a divergent plasma flow

A similarity transformation is given, which reduces the partial, nonlinear differential equations describing a compressible, polytropic plasma flow across an azimuthal magnetic field in a duct with plane inclined walls to an ordinary nonlinear differential equation of second order. The latter is solved rigorously in terms of a hyperelliptic integral. The form of the plasma flow fields in pure outflows (diffuser) is discussed analytically in dependence of the Reynolds $\mathrm{(R)}$ and Hartmann $\mathrm{(H)}$ numbers and the polytropic coefficient $\mathrm{(\gamma )}$ for given duct angles ${\theta }_0$ . The realizable Mach numbers are shown to be eigenvalues of the nonlinear boundary‐value problem, ${\mathrm{M\hspace{0.17em}=\hspace{0.17em}M(R,\hspace{0.17em}H,\hspace{0.17em}\gamma ,\hspace{0.17em}\theta }}_0)$ .