  A 2+1-dimensional anisentropic magnetogasdynamic system with a polytropic gas
law is shown to admit an integrable elliptic vortex reduction when $\gamma=2$
to a nonlinear dynamical subsystem with underlying integrable
Hamiltonian-Ermakov structure. Exact solutions of the magnetogasdynamic system
are thereby obtained which describe a rotating elliptic plasma cylinder. The
semi-axes of the elliptical cross-section, remarkably, satisfy a
Ermakov-Ray-Reid system.
