During major disruptions, an induced loop voltage accelerates runaway electrons (REs) towards high energy, being in the order of 1–100 MeV in present tokamaks and ITER. The stochastization mechanisms of such high-energy RE drift orbits are investigated by three-dimensional (3D) orbit following in tokamak plasmas. Drift resonance is shown to play an important role in determining the onset of stochastic drift orbits for different electron energies, particularly in cases with low-order perturbations that have radially global eigenfunctions of the scale of the plasma minor radius. The drift resonance due to the coupling between the cross-field drift motion with radially global modes yields a secondary island structure in the RE drift orbit, where the width of the secondary drift islands shows a square-root dependence on the relativistic gamma factor γ. Only for highly relativistic REs (γ ≫ 1), the widths of secondary drift islands are comparable with those of magnetic islands due to the primary resonance, thus the stochastic threshold becoming sensitive to the RE energy. Because of poloidal asymmetry due to toroidicity, the threshold becomes sensitive not only to the relative amplitude but also to the phase difference between the modes. In this paper, some examples of 3D orbit-following calculations are presented for analytic models of magnetic perturbations with multiple toroidal mode numbers, for both possibilities that the drift resonance enhances and suppresses the stochastization being illustrated.
A new matching scheme for linear magnetohydrodynamic (MHD) stability analysis is proposed in a form offering tractable numerical implementation. This scheme divides the plasma region into outer regions and inner layers, as in the conventional matching method. However, the outer regions do not contain any rational surface at their terminal points; an inner layer contains a rational surface as an interior point. The Newcomb equation is therefore regular in the outer regions. The MHD equation employed in the layers is solved as an evolution equation in time, and the full implicit scheme is used to yield an inhomogeneous differential equation for space coordinates. The matching conditions are derived from the condition that the radial component of the solution in the layer is smoothly connected to those in the outer regions at the terminal points. The proposed scheme is applied to the linear ideal MHD equation in a cylindrical configuration, and is proved to be effective from the viewpoint of a numerical scheme.
Kink instability and the subsequent plasma flow during the sustainment of a coaxial gun spheromak are investigated by three-dimensional nonlinear magnetohydrodynamic simulations. Analysis of the parallel current density λ profile in the central open column revealed that the n = 1 mode structure plays an important role in the relaxation and current drive. The toroidal flow (v t ≈ 37 km/s) is driven by magnetic reconnection occurring as a result of the helical kink distortion of the central open column during repetitive plasmoid ejection and merging.
The dynamics of spheromak plasmas in coaxial helicity injection (CHI) systems has been investigated using three-dimensional magnetohydrodynamic (MHD) numerical simulations. It was found that toroidal current is driven by repetitive asymmetric plasmoid injection, which is related to the n = 1 oscillations. In addition, we propose that multiple pulse operation of the helicity injection is effective for improving confinement because it reduces the n = 1 fluctuations. Keywords:coaxial helicity injection, spheromaks, repetitive plasmoid injection, MHD, simulation author's e-mail: skagei@elct.eng.himeji-tech.ac.jp Coaxial helicity injection (CHI) has demonstrated the ability to form and sustain spheromak and spherical tokamak (ST) plasmas on several devices [1,2]. In these experiments, magnetic field fluctuations with toroidal mode number n = 1 are observed during sustainment, and these fluctuations are considered responsible for the current drive. However, the detailed physical mechanism understanding this phenomenon is not yet well understood. Sovinec et al. demonstrated numerical simulations of helicity-driven spheromaks [3], but the detailed dynamics of toroidal current generation in the gun-driven-system was not clearly revealed. In order to reveal this, 3-D magnetohydrodynamic (MHD) numerical simulations for spheromak plasmas were executed.The simulation region consists of two cylinders, each with a center post: one is a gun region (0.175 ≤ r ≤ 0.65 and 0 ≤ z ≤ 0.5), the other a confinement region (0.15 ≤ r ≤ 1.0 and 0.5 ≤ z ≤ 2.0), as shown in Fig. 1. Grid sizes (N r × N θ × N z ) are (39 × 64 × 40) and (69 × 64 × 121) in the direction of the gun and the confinement regions, respectively. Bias magnetic flux penetrates electrodes at the inner and outer boundaries of the gun region. Boundaries of the confinement region are assumed to be perfectly conducting walls. The initial spheromak configuration is given by numerically solving ∇ × B = λ B (λ is the force-free parameter) under these boundary conditions. The governing equations are one-fluid MHD equations, as follows:In this simulation, the mass density is spatially and temporally constant for simplicity. All physical quantities are normalized by initial mass density ρ 0 , typical Alfvén speed V A , and maximum length of the cylinder radius L 0 . The conductivity κ , the resistivity η, and the viscosity ν are fixed to 1 × 10 -3 , 2 × 10 -4 , and 1 × 10 -3 in the normalized units (γ -1) -1 k n 0 L 0 V A , µ 0 L 0 V A , and ρ 0 L 0 V A , respectively. The simulation starts with the application of a toroidally symmetric radial electric field (E inj ) across a gap between two electrodes.The parameters used in this simulation are λ = 4.95
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