Energetically Resolved Multiple-Fluid Equilibria of Tokamak Plasmas

Abstract

In many magnetically confined fusion experiments, a significant fraction of the stored energy of the plasma resides in energetic, or non-thermal, particle populations. Despite this, most equilibrium treatments are based on MHD: a single fluid treatment which assumes a Maxwell-Boltzmann distribution function. Detailed magnetic reconstruction based on this treatment ignore the energetic complexity of the plasma and can result in model-data inconsistencies, such as thermal pressure profiles which are inconsistent with the total stored kinetic energy of the plasma. Alternatively, ad hoc corrections to the pressure profile, such as summing the energetic and thermal pressures, have poor theoretical justification. Motivated by this omission, we generalize ideal MHD one step further: we consider multiple quasi-neutral fluids, each in thermal equilibrium and each thermally insulated from each other - no population mixing occurs. Kinetically, such a model may be able to describe the ion or electron distribution function in regions of velocity phase space with a large number of particles, at the expense of more weakly populated phase space, which may have uncharacteristically high temperature and hence pressure. As magnetic equilibrium effects increase with the increase in pressure, our work constitutes an upper limit to the effect of energetic particles. When implemented into an existing solver, FLOW (Guazzotto et al 2004 Phys. Plasmas 11, 604-14), it becomes possible to qualitatively explore the impact of resolving the energetic populations on plasma equilibrium configurations in realistic geometry. Deploying the modified code, FLOW-M, on a high performance spherical torus configuration, we find that the effect of variations of the pressure, poloidal flow and toroidal flow of the energetic populations is qualitatively similar to variations in the background plasma. We also study the robustness of the equilibrium to uncertainties in the current profile and the energetic toroidal rotation or energetic pressure profile. For constant toroidal current and stored energy, the change in the poloidal flux with changes in the current profile is similar irrespective of whether the toroidal rotation or pressure was changed, indicating insensitivity to whether uncertainties lie in the pressure or toroidal rotation profiles. We conclude that to a first approximation, lumping the energetic and thermal fluids together, as is done for many equilibrium solvers, qualitatively produces correct results.