Hisaya Sugimoto

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.

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...

Friction coefficient and correlation length of stochastic magnetic field lines

An averaged transverse velocity of stochastic magnetic field lines between two tearing modes is presented by using the renormalized weak turbulence theory. The averaged velocity gives the friction coefficient of moving magnetic field lines which is expressed in terms of a renormalized propagator. A correlation length (time) of magnetic field lines, which is the time integrated renormalized propagator, is presented with respect to various parameters. The diffusion coefficient given in a previous paper (Sugimoto et al 1994 Plasma Phys. Control. Fusion 36 383) and the friction coefficient obtained here are related to each other by the so-called Einstein relation. Although the renormalized propagator given here involves more effects such as collision and friction types than that in the previous paper, which has the term of the diffusion type effect alone, the former effects do not greatly modify the renormalized propagator. Effects of collision and friction types do not play an important role in the propagator and the diffusion type effect alone is essential.

Magnetohydrodynamic Instability in Axisymmetric Spherical Plasma with Parallel Flow to Magnetic Field.

The instability of the axisymmetric spherical force free plasma with the parallel plasma flow to the magnetic filed is studied by using the MHD equations under the condition of incompressibility. The linear growth rate of the unstable mode with the fixed toroidal mode number n =1 is obtained and it decreases with the increase of Alfven Mach number C A in the rage of C A <1 in the case of the free boundary. The nonliner numerical analysis in the free boundary case shows that the tilting mode plays a main role, and the damping rate of the original helicity and the toroidal flux decreases with the increase of C A .