Abstract. Neutral beam injection or ion cyclotron resonance heating induces pressure anisotropy. The axisymmetric plasma equilibrium code HELENA has been upgraded to include anisotropy and toroidal flow. With both analytical and numerical methods, we have studied the determinant factors in anisotropic equilibria and their impact on flux surfaces, magnetic axis shift, the displacement of pressures and density contours from flux surface. With p /p ⊥ ≈ 1.5, p ⊥ can vary 20% on s = 0.5 flux surface, in a MAST like equilibrium. We have also re-evaluated the widely applied approximation to anisotropy in which p * = (p + p ⊥ )/2, the average of parallel and perpendicular pressure, is taken as the approximate isotropic pressure. We show that an isotropic reconstruction can infer a correct p * , only by getting an incorrect RBϕ. We find the reconstructions of the same MAST discharge with p /p ⊥ ≈ 1.25, using isotropic and anisotropic model respectively, to have a 3% difference in toroidal field but a 66% difference in poloidal current.
The stepped-pressure equilibrium code (SPEC) [Hudson et al., Phys. Plasmas 19, 112502 (2012)] is extended to enable free-boundary, multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', D, is computed, and the virtual-casing principle is used iteratively to compute the normal field on D so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.
Abstract.Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose existence is determined by the fast particles, is investigated in cases where these particles do not move freely and their motion is bounded to restricted orbits. An equilibrium oscillating potential, which creates different orbit topologies of energetic particles, is included into the bump-on-tail instability problem of a plasma wave. With respect to fast particles dynamics, the extended model captures the range of particles motion (trapped/passing) with energy and thus represents a more realistic 1D picture of the long range sweeping events observed for weakly damped modes, e.g. global Alfven eigenmodes, in tokamaks. The Poisson equation is solved numerically along with bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate that the shape and the saturation amplitude of the nonlinear mode structure depends not only on the amount of deviation from the initial eigenfrequency but also on the initial energy of the resonant electrons in the equilibrium potential. Similarly, the results reveal that the resonant electrons following different equilibrium orbits in the electrostatic potential lead to different rates of frequency evolution. As compared to the previous model [Breizman B.N. 2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower rates. The additional physics included in the model enables a more complete 1D description of the range of phenomena observed in experiments.Hard nonlinear evolution in the presence of particle orbits 2
A phase-space version of the ideal magnetohydrodynamic (MHD) Lagrangian is derived from first principles and shown to give a relabeling transformation when a cross-helicity constraint is added in Hamilton's Action Principle. A new formulation of time-dependent "relaxed" magnetohydrodynamics is derived using microscopic conservation of mass and macroscopic constraints on total magnetic helicity, cross helicity, and entropy under variations of density, pressure, fluid velocity, and magnetic vector potential. This gives Euler-Lagrange equations consistent with previous work on both ideal and relaxed MHD equilibria with flow, but generalizes the relaxation concept from statics to dynamics. The application of the new dynamical formalism is illustrated for short-wavelength linear waves, and the interface connection conditions for Multiregion Relaxed MHD (MRxMHD) are derived. The issue of whether E þ u  B ¼ 0 should be a constraint is discussed.
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