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Register a new userAnalysing the impact of anisotropy pressure on tokamak equilibria
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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.
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The Hall term has often been neglected in MHD codes as it is difficult to compute. Nevertheless setting it aside for numerical reasons led to ignoring it altogether. This is especially problematic when dealing with tokamak physics as the Hall term cannot be neglected as this paper shows.
We have used the local-$delta{f}$ gyrokinetic code GS2 to perform studies of the effect of flux-surface shaping on two highly-shaped, low- and high-$beta$ JT-60SA-relevant equilibria, including a successful benchmark with the GKV code. We find a novel destabilization of electrostatic fluctuations with increased elongation for plasma with a strongly peaked pressure profile. We explain the results as a competition between the local magnetic shear and finite-Larmor-radius (FLR) stabilization. Electromagnetic studies indicate that kinetic ballooning modes are stabilized by increased shaping due to an increased sensitivity to FLR effects, relative to the ion-temperature-gradient instability. Nevertheless, at high enough $beta$, increased elongation degrades the local magnetic shear stabilization that enables access to the region of ballooning second-stability.
A new force balance model for the EFIT magnetohydrodynamic equilibrium technique for tokamaks is presented which includes the full toroidal flow and anisotropy changes to the Grad-Shafranov equation. The free functions are poloidal flux functions and all non-linear contributions to the toroidal current density are treated iteratively. The parallel heat flow approximation chosen for the model is that parallel temperature is a flux function and that both parallel and perpendicular pressures may be described using parallel and perpendicular temperatures. This choice for the fluid thermodynamics has been shown elsewhere to be the same as a guiding centre kinetic solution of the same problem under the same assumptions. The model reduces identically to the static and isotropic Grad-Shafranov equation in the appropriate limit as different flux functions are set to zero. An analytical solution based on a modified Soloviev solution for non-zero toroidal flow and anisotropy is also presented. The force balance model has been demonstrated in the code EFIT TENSOR, a branch of the existing code EFIT++. Benchmark results for EFIT TENSOR are presented and the more complicated force balance model is found to converge to force balance similarly to the usual EFIT model and with comparable speed.
We report on the impact of anisotropy to tokamak plasma configuration and stability. Our focus is on analysis of the impact of anisotropy on ITER pre-fusion power operation 5~MA, $B=1.8$~T ICRH scenarios. To model ITER scenarios remapping tools are developed to distinguish the impact of pressure anisotropy from the change in magnetic geometry caused by an anisotropy-modified current profile. The remappings iterate the anisotropy-modified current profile to produce the same $q$ profile with matched thermal energy. The analysis is a step toward equilibria that are kinetically self-consistent for a prescribed scenario. We find characteristic detachment of flux surfaces from pressure surfaces, and an outboard (inboard) shift of peak density for $T_{parallel}>T_perp$ ( $T_{parallel}<T_perp$). Differences in the poloidal current profile are evident, albeit not as pronounced as for the spherical tokamak. We find that the incompressional continuum is largely unchanged in the presence of anisotropy, and the mode structure of gap modes is largely unchanged. The compressional branch however exhibits significant differences in the continuum. We report on the implication of these modifications.
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof here to arbitrary aspect ratio, using a variant of the virial theorem to derive a relatively simple integral constraint on the equilibrium. However, this constraint does not, by itself, exclude equilibria with non-nested flux surfaces, or equilibria with singular fields and/or hollow pressure profiles that may be spontaneously generated.
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