Generalization of cylindrical spheromak solution to finite beta and large reversed shear

Abstract

The well-known analytic solution for a spheromak in a cylindrical flux conserver is generalized to the situation of finite β with the shape of the flux conserver now being a dependent quantity. Analytic expressions are found for the poloidal flux surfaces, beta, the safety factors at both the magnetic axis and the wall, and the wall profile. A large reversed shear (i.e., ratio of safety factor on magnetic axis to safety factor at the wall) can be obtained at finite beta. This feature may be important because reversed shear in the core of tokamaks has been shown to permit stable operation at high β.