Toon Weyens, Ph.D.

Numerically accurate expressions are critical for the evaluation of 3-D MHD plasma stability, as the conventional formulas generally suffer from large numerical problems. In this work, we present new expressions for the quantities of interest, namely the parallel current density , the local shear and the normal and geodesic components of the curvature .

High accuracy is achieved in these expressions by employing strategies such as avoiding as much as possible the computation of… Meer weergeven

Numerically accurate expressions are critical for the evaluation of 3-D MHD plasma stability, as the conventional formulas generally suffer from large numerical problems. In this work, we present new expressions for the quantities of interest, namely the parallel current density , the local shear and the normal and geodesic components of the curvature .

High accuracy is achieved in these expressions by employing strategies such as avoiding as much as possible the computation of derivatives in the direction normal to the flux surfaces, and avoiding cancellation errors by subtracting large numbers. The result is a set of equations that have been found to be important for the calculation of MHD stability of axisymmetric equilibria, and essential for the assessment of 3-D ones.

Minder weergeven

The calculation of the perturbed vacuum potential energy in an ideal Magnetohydrodynamical (MHD) system consisting of plasma surrounded by vacuum is a crucial ingredient for the treatment of peeling modes. In this work, detailed theoretical expressions are derived to describe this, making use of the potential representation of the magnetic field in the vacuum, which leads to a Laplace equation that can be solved through the boundary element method. The complications that arise from the singular… Meer weergeven

The calculation of the perturbed vacuum potential energy in an ideal Magnetohydrodynamical (MHD) system consisting of plasma surrounded by vacuum is a crucial ingredient for the treatment of peeling modes. In this work, detailed theoretical expressions are derived to describe this, making use of the potential representation of the magnetic field in the vacuum, which leads to a Laplace equation that can be solved through the boundary element method. The complications that arise from the singular integrals that appear are studied thoroughly. Special attention is also given to the case of axisymmetric equilibria, which leads to more accurate but also more complicated analytical expressions than the general 3D expressions. In the near future, the resulting expressions will be used directly in 3D ideal MHD stability codes such as PB3D so that it can treat all 3D ideal high-n MHD stability, including peeling modes.
Minder weergeven

A new numerical code PB3D (Peeling-Ballooning in 3-D) is presented. It implements and solves the intermediate-to-high-n ideal linear magnetohydrodynamic stability theory extended to full edge 3-D magnetic toroidal configurations in previous work [1]. The features that make PB3D unique are the assumptions on the perturbation structure through intermediate-to-high mode numbers n in general 3-D configurations, while allowing for displacement of the plasma edge. This makes PB3D capable of very… Meer weergeven

A new numerical code PB3D (Peeling-Ballooning in 3-D) is presented. It implements and solves the intermediate-to-high-n ideal linear magnetohydrodynamic stability theory extended to full edge 3-D magnetic toroidal configurations in previous work [1]. The features that make PB3D unique are the assumptions on the perturbation structure through intermediate-to-high mode numbers n in general 3-D configurations, while allowing for displacement of the plasma edge. This makes PB3D capable of very efficient calculations of the full 3-D stability for the output of multiple equilibrium codes. As first verification, it is checked that results from the stability code MISHKA [2], which considers axisymmetric equilibrium configurations, are accurately reproduced, and these are then successfully extended to 3-D configurations, through comparison with COBRA [3], as well as using checks on physical consistency. The non-intuitive 3-D results presented serve as a tentative first proof of the capabilities of the code. Minder weergeven

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions… Meer weergeven

Ideal magnetohydrodynamics theory is extended to fully 3D magnetic configurations to investigate the linear stability of intermediate to high n peeling-ballooning modes, with n the toroidal mode number. These are thought to be important for the behavior of edge localized modes and for the limit of the size of the pedestal that governs the high confinement H-mode. The end point of the derivation is a set of coupled second order ordinary differential equations with appropriate boundary conditions that minimize the perturbed energy and that can be solved to find the growth rate of the perturbations. This theory allows of the evaluation of 3D effects on edge plasma stability in tokamaks such as those associated with the toroidal ripple due to the finite number of toroidal field coils, the application of external 3D fields for elm control, local modification of the magnetic field in the vicinity of ferromagnetic components such as the test blanket modules in ITER, etc. Minder weergeven