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

Magnetic field profiles in fusion plasmas in the presence of equilibrium flow

“…[13], we will just mention here that the bootstrap current is expressed in terms of the equilibrium macroscopic quantities through the neo- as also reported in Ref. [15]. For the cases we have considered, we also observe that the total calculated bootstrap current will decrease slightly in the presence of toroidal rotation (see for example Fig.…”

Formation of edge pressure pedestal and reversed magnetic shear due to toroidal rotation in a tokamak equilibrium

“…The axisymmetric MHD equations in the presence of macroscopic poloidal and toroidal flows are derived in various forms by a number of authors [21][22][23][24][25]. Besides, several codes has been developed to compute equilibria with plasma flow, such as CLIO [26] DIVA [27], FINESSE [28], FLOW [23] and a version of FLOW that includes contributions from nonthermal populations [29]. The modified Grad-Shafranov equation due to toroidal flow is first given concisely by Hameiri [21].…”

The impact of anisotropy on ITER scenarios

“…The formulation of the anisotropic flowing equilibrium has been studied by many authors. [3,4,5,6,7,8,9,10,11] In one such formulation based on an enthalpy formulation [5], the flow-modified MHD equations read…”

“…This problem has been solved by the magnetic reconstruction code EFIT-TENSOR [9], the fixed boundary code HELENA+ATF [10], as well as the poloidal-flow enabled equilibrium code FLOW [7] and multi-specie code FLOW-M [8]. We have used these codes have been used to explore the impact of anisotropy and rotation in MAST.…”