A four-field model for tokamak plasma dynamics

A generalization of reduced magnetohydrodynamics is constructed from moments of the Fokker-Planck equation. The new model uses familiar aspect-ratio approximations but allows for (i) evolution as slow as the diamagnetic drift frequency, thereby including certain finite Larmor radius effects, (ii) pressure gradient terms in a generalized Ohm's law, thus making accessible the adiabatic electron limit, and (iii) plasma compressibility, including the divergence of both parallel and perpendicular flows. The system is isothermal and surprisingly simple, involving only one additional field variable, i.e., four independent fields replace the three fields of reduced magnetohydrodynamics. It possesses a conserved energy. The model's equilibrium limit is shown to reproduce not only the large-aspect-ratio Grad-Shafranov equation, but also such finite Larmor radius effects as the equilibrium ion parallel flow. Its linearized version reproduces, among other things, crucial physics of the long mean-free-path electron response. Nonlinearly, the four-field model is shown to describe diffusion in stochastic magnetic fields with good qualitative accuracy.