Modeling the effect of anisotropic pressure on tokamak plasmas normal modes and continuum using fluid approaches

Extending the ideal MHD stability code MISHKA, a new code, MISHKA-A, is developed to study the impact of pressure anisotropy on plasma stability. Based on full anisotropic equilibrium and geometry, the code can provide normal mode analysis with three fluid closure models: the single adiabatic model (SA), the double adiabatic model (CGL) and the incompressible model. A study on the plasma continuous spectrum shows that in low beta, large aspect ratio plasma, the main impact of anisotropy lies in the modification of the BAE gap and the sound frequency, if the q profile is conserved. The SA model preserves the BAE gap structure as ideal MHD, while in CGL the lowest frequency branch does not touch zero frequency at the resonant flux surface where $m+nq=0$, inducing a gap at very low frequency. Also, the BAE gap frequency with bi-Maxwellian distribution in both model becomes higher if $p_perp > p_parallel$ with a q profile dependency. As a benchmark of the code, we study the m/n=1/1 internal kink mode. Numerical calculation of the marginal stability boundary with bi-Maxwellian distribution shows a good agreement with the generalized incompressible Bussac criterion [A. B. Mikhailovskii, Sov. J. Plasma Phys 9, 190 (1983)]: the mode is stabilized(destabilized) if $p_parallel < p_perp (p_parallel > p_perp)$.

Analysing the impact of anisotropy pressure on tokamak equilibria

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 $p_parallel/p_perp approx 1.5$, $p_perp$ 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 $p^*=(p_parallel + p_perp)/2$, the average of parallel and perpendicular pressure, is taken as the approximate isotropic pressure. We find the reconstructions of the same MAST discharge with $p_parallel/p_perp approx 1.25$, using isotropic and anisotropic model respectively, to have a 3% difference in toroidal field but a 66% difference in poloidal current.