Calculations of 3D mirror equilibria using a finite element vector potential representation

Several applications of plasma equilibrium models require a suitable continuous representation for the magnetic field. For example, numerical generation of single particle orbits in these fields requires that the continuum representation maintain del. B = 0 or at least keep it very small. Performing the interpolation analysis in terms of the vector potential A guarantees delxB = 0, whereas using the magnetic induction B does not. The code presented here uses A as the primary dependent variable. A finite element representation employing tricubic splines significantly reduces spatial truncation errors compared to conventional finite difference methods. The theoretical equilibrium model allows pressure functions of the form B(B,psi) = P(B)ω(psi). A modified long-thin approximation is derived which includes field line curvature effect; it agrees well with the results obtained from the code. Some results pertinent to the MFTF-B experiment are presented