Hisao Ashida

Neoclassical reversed-field pinch equilibrium with dominant self-induced plasma current

The neoclassical magnetohydrodynamic equilibrium of reversed-field pinch (RFP) is self-consistently solved considering the self-induced plasma current IϕSI in a reactor relevant parameter regime. The current IϕSI consists of bootstrap currents due to α particles as well as the bulk plasma, where the conventional neoclassical transport theory is applied without considering the finite banana-width effect, Pfirsch–Schluter current, and diamagnetic current. The neoclassical effect enhances IϕSI in a low-aspect-ratio RFP (aspect ratio A=2), when β is high. An IϕSI as high as 94.4% of the plasma current in the equilibrium with ellipticity κ=1.4 and triangularity δ=0.4 is obtained with a flat pressure profile, which provides a toroidal β of βt=63% (volume-averaged β, ⟨β⟩=66%) stable against both the ideal kink mode and Mercier mode. This dominant self-induced current makes the steady-state approach feasible. Its hollow current profile gives a strong magnetic shear and a high-stability β.

A 3-D Resistive MHD Simulation Analysis of Field Reversal Control in the Reversed Field Pinch

A three-dimensional (3-D) resistive MHD simulation code under the compressibility condition has been applied to analysis of the field reversal control in the reversed field pinch (RFP). Simulation results have shown that a loss of the field reversal at the wall leads to flattening of the toroidal field profile, and also to the rapid increase of the fluctuating magnetic energy due to nonlinear tearing modes with m =1. Moreover, the fluctuating magnetic energy spectrum for the m =1 and m =2 modes rapidly broadens toward high and low n , which is caused by the ( m =0; n =-1) mode. By deepening the field reversal at the wall, the reversal surface keeps away from the plasma surface, and safety factor becomes a narrow profile. As a result, a rapid growth and saturation of these tearing modes is suppressed by the field reversal control.

Monte Carlo Studies of Transport in a Reversed Field Pinch

Transport in a realistic reversed field pinch (RFP) configuration is studied numerically for neoclassical and MHD fluctuation transport mechanisms, by Monte Carlo simulation. The results indicate that neoclassical transport due to guiding center drift is one or two orders lower than classical transport due to finite gyro-motion and thus is not important for RFP plasmas. However, the electron diffusion coefficient corresponding to a typical MHD fluctuation configuration of the magnetic Reynolds number S =10 4 , and equilibrium β=8% is about 10 6 cm 2 /sec which is two orders higher than the classical transport, and thus is an important transport loss mechanism for RFP plasma confinement.

Low-aspect-ratio reversed field pinch plasma equilibria with finite surface toroidal current density

Low-aspect-ratio reversed field pinch (RFP) plasmas are expected to produce equilibria in which the resonant surfaces for tearing modes are well separated compared with high-aspect-ratio RFP plasmas. The profile of the safety factor, q, determines the mode separation of the resonant surfaces. The q profiles, the ratio of plasma pressure to magnetic energy, β, and the parallel current density to the magnetic field lines, μ, are studied with the varying aspect ratio, A. A new Mercier stable RFP plasma is proposed by introducing a finite surface toroidal current density at the plasma edge. The aim of this study is to investigate the effect of a finite surface toroidal current with a low-aspect-ratio (low A) on the profiles of q, μ, β and the ratio of plasma pressure to poloidal magnetic energy, β p . The investigation is performed using an equilibrium model with a finite pressure, in which unknown functions in the Grad-Shafranov (GS) equation are specified. Specified functions are composed of some numerical parameters that allow systematic variation of equilibria. The GS equation is solved in the toroidal coordinate for various A values, where the β limit of Mercier stable equilibria is determined. First we confirmed that q at the centre, q 0 , increases as A decreases. The result shows that the profiles of q, β and β p , strongly depend on A. The β and β p obtained decrease with decreasing A. In particular, the decrease in β differs from the case of a tokamak. The decrease in β is recovered, in spite of a low A, by setting the toroidal current to be finite at the plasma edge as a boundary condition.

Stochastic diffusion of magnetic field lines

A renormalized diffusion coefficient for magnetic field lines is presented by using the renormalized weak turbulence theory. It is defined on locally destroyed magnetic surfaces caused by two tearing modes. The renormalized diffusion coefficient is given in terms of a renormalized propagator expressed by the integral of the Bessel function of the first kind, J1. It is free from delta -function-type divergence. An averaged renormalized propagator is introduced whose imaginary part represents the behaviour of the memory of the initial condition. Numerical calculation shows that the averaged propagator decreases within a correlation damping time.

Magnetohydrodynamic Simulation of Pulsed Poloidal Current Drive in Reversed Field Pinch Plasmas

Numerical simulations using magnetohydrodynamic (MHD) equations are performed for the pulsed poloidal current drive (PPCD) in reversed field pinch (RFP) plasmas. The PPCD is simulated by reducing the toroidal magnetic field at the wall, B z ( a ), in the short period. The simulations take into account the values of reduced B z ( a ), the period of changing B z ( a ) and the start time as the characteristic parameters of the PPCD. The effects of the parameters on m =1 resistive modes, which play the main role in the sustainment of RFP configurations, are calculated. The PPCD has stabilizing effect for the m =1 modes over a wide range of the parameters. The dependence on the parameters for the formation of quasi-single helicity after the PPCD and for the growth of the m =0 mode is calculated. The stabilizing factor due to the enhanced magnetic shear for the resistive modes is also analyzed by the linear growth rate in the equilibrium model of the transient configuration during the period of the PPCD.

Reversed field pinch plasma equilibria with shear flow

The Grad–Shafranov equation with flow, which is derived by a variational method, involves unknown functions such as the dynamic pressure, P(Ψ). These functions are specified by minimizations of free energies under the constraints of constant P′(Ψ), magnetic helicity, flow helicity, and cross helicity in reversed field pinch (RFP) plasmas. New flow and cross helicities are introduced based on the analogy of the magnetic helicity, which are different from those used in fluid mechanics. The constraint of constant flow helicity provides flow with profiles from high- to low-shear flow. The Suydam-stable RFP equilibria obtained with flows are extremely different in β and βp from RFP equilibria without flow. The high-shear flow can extend the Suydam limit, allowing higher β and βp.

A field‐reversal mechanism in a reversed‐field pinch

A field‐reversal mechanism in a reversed‐field pinch (RFP) is studied through a three‐dimensional resistive compressible magnetohydrodynamic (MHD) simulation of the single‐ and multiple‐helicity modes. As the magnetic Reynolds number increases, the m=1 fluctuating magnetic field grows exponentially and extends radially, and then the flow begins to form the vortex structure around the core of the plasma. This radial flow acts such as to push out the toroidal magnetic field. As the dynamo electric field induced by this interaction increases near the core of the plasma, the toroidal magnetic field at the wall decreases toward the negative value and the toroidal magnetic field reverses. As a result, it is found that the field reversal is achieved by the single‐helicity evolution of the m=1 mode alone, without the (m=0; n≠0) modes, and the interaction of the radial flow and the toroidal magnetic field is the most dominant source for the dynamo action on the field‐reversal process.

Effects of Impurities and Neutrals on Setting-Up Phase of Reversed Field Pinch

Two-dimensional MHD pinch simulation code, “TOPICS”, which includes the effects of the impurity ions, the neutral atoms and anomalous resistivity, has been applied to the investigation of the RFP-plasmas at the setting-up phase of the TPE-1R. Results from the simulations are compared with the typical two cases of the experiment: (a) the lower initial bias field and the higher plasma current density and (b) the higher initial bias field and the lower plasma current density. By comparing the simulated and experimental results, it is found that the magnetic field profiles at the early phase of the RFP setting-up strongly depend on the ionization degree of the initial plasma and the largest increase is obtained by assuming the 50% ionization degree and the presence of 10% oxygen. It is also found from this study that the radiation loss due to 5 to 10% impurities is the dominant loss mechanism of the electron energy. The toroidal magnetic field profile inside the plasma calculated by using the isotropic anomal...

Rotations of reversed field pinch plasma due to the resistive tearing modes

Poloidal and toroidal rotations of the reversed field pinch plasmas induced by the magnetohydrodynamic resistive tearing modes are numerically studied by using the ohms law with the ion inertia te...