Numerical studies of toroidicity simulation in a linear heliac

The High Beta Q Machine (HBQM) is a three-meter theta-pinch that can be configured with an iota = 1 compression coil set and an axial hardcore center conductor to form linear high beta heliac plasmas. A critical issue in a toroidal heliac is the predicted degradation of magnetic flux surfaces by magnetic island formation owing to the loss of helical symmetry. Finite plasma pressure can drive currents in these magnetic islands and degrade confinement. Approximate analytical expressions for the first order corrections to the vacuum linear heliac magnetic fields have been derived for two cases: large aspect ratio toroidicity and a radial translation (shift) of the hardcore conductor. A magnetic field line following code, HELIK, shows the similarity of field line puncture plots for the toroidal, and shifted hardcore cases. These expansions are also found to possess similar Roozer harmonic spectra of the magnetic flux coordinate system Jacobian (1/B2). This similarity is so great that toroidal effects can be coupled with a shifted hardcore in such a way as to heal the magnetic flux surfaces, partially restoring the situation of helical symmetry