Guiding center equations of high accuracy

Guiding center simulations are an important means of predicting the effect of resistive and ideal magnetohydrodynamic instabilities on particle distributions in toroidal magnetically confined thermonuclear fusion research devices. Because saturated instabilities typically have amplitudes of delta B/B of a few times 10(-4) numerical accuracy is of concern in discovering the effect of mode particle resonances. We develop a means of following guiding center orbits which is greatly superior to the methods currently in use. For full implementation, the method requires some breaking of axisymmetry, either through toroidal field ripple or magnetohydrodynamic instabilities. In the presence of ripple or time dependent magnetic perturbations both energy and canonical momentum are conserved in a time step to better than one part in 10(14), an improvement of nine orders of magnitude over standard Runge-Kutta integration, and the relation between changes in canonical momentum and energy is also conserved to very high order.