An Optimal Magnetic Coordinate system for High-Beta ST configurations

In the study of magnetohydrodynamics of magnetically confined systems, it is well known that both analysis and computation are facilitated by an appropriate coordinate system. Specifically, a magnetic coordinate system,$(\Psi,\theta,\zeta)$,where $\Psi$ is a flux label, $\theta$ a poloidal angle and $\zeta$ a generalized toroidal angle, such that magnetic field lines are straight in $(\theta,\zeta)$ space. The generalized toroidal angle, $\zeta$, can be related to the Cartesian angle $\phi$, by introducing a periodic function $\delta(\Psi,\theta)$. This function depends on the choice of Jacobian, and is identically zero when the Jacobian is proportional to $x^2$. This coordinate is commonly referred to as PEST coordinates. A more general approach to straight field line coordinates is obtained when the Jacobian is defined as $J = X^i/\alpha(\Psi) |\nabla\dot\Psi|^j$. Commonly used coordinate systems are: PEST, with i=2 , j=0; Equal Arcs, with i=j=1; and Hamada with i=j=0. Each of these coordinates has its own merits, but for high beta spherical tori, we identify a new coordinate system, i=0, j=1, which is optimal to this regime. We present results comparing the different coordinate systems in different parameter regimes.