J. Manickam

Ideal MHD stability calculations in axisymmetric toroidal coordinate systems

Abstract A scalar form of the ideal MHD energy principle is shown to provide a more accurate and efficient numerical method for determining the stability of an axisymmetric toroidal equilibrium than the usual vector form. Additional improvement is obtained by employing a class of straight magnetic field line flux coordinates which allow for an optimal choice of the poloidal angle in the minor cross section of the torus. The usefulness of these techniques is illustrated by a study (using a new code, PEST 2) of the convergence properties of the finite element Galerkin representation in tokamak and spheromak geometries, and by the accurate determination of critical β values for ballooning modes.

Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments

A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.

Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

Numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given. Iterative schemes are used to solve the elliptic nonlinear partial differential equation for the poloidal flux function psi. The principal emphasis is on solving the free boundary (plasma-vacuum interface) equilibrium problem where external current-carrying toroidal coils support the plasma column, but fixed boundary (e.g., conducting shell) cases are also included. The toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi. Examples of the application of the codes to tokamak design at PPPL are given.

IDEAL MHD STABILITY LIMITS OF LOW ASPECT RATIO TOKAMAK PLASMAS

The ideal magnetohydrodynamic (MHD) stability limits of low aspect ratio tokamak plasmas are computed numerically for plasmas with a range of cylindrical safety factors q*, normalized plasma pressures beta , elongations kappa and central safety factors q(0). Four distinct regimes are optimized, namely: (a) low-q* plasmas with q(0)=1.1 with and without a stabilizing wall, (b) low-q* plasmas with no wall and 1.1<q(0)<2, (c) high- beta , high bootstrap fraction plasmas at moderate kappa requiring a wall and edge current drive and (d) high- beta , very high bootstrap fraction plasmas with moderate to high kappa requiring a stabilizing wall but little external current drive. A stable equilibrium is found at an aspect ratio of A=1.4 and an elongation of kappa =3.0, with 99.3% of the current provided by the plasma pressure and beta =45%. Special attention is paid to the issues of numerical convergence and the proper definition of bootstrap current fraction

THE PROSPECTS FOR MAGNETOHYDRODYNAMIC STABILITY IN ADVANCED TOKAMAK REGIMES

Stability analysis of advanced regime tokamaks is presented. Here advanced regimes are defined to include configurations where the ratio of the bootstrap current, IBS, to the total plasma current, Ip, approaches unity, and the normalized stored energy, βN* = 80π〈p2〉1/2a/IpB0, has a value greater than 4.5. Here, p is the plasma pressure, a the minor radius in meters, Ip is in mega‐amps, B0 is the magnetic field in Tesla, and 〈⋅〉 represents a volume average. Specific scenarios are discussed in the context of Toroidal Physics Experiment (TPX) [Proceedings of the 20th European Physical Society Conference on Controlled Fusion and Plasma Physics, Lisbon, 1993, edited by J. A. Costa Cabral, M. E. Manso, F. M. Serra, and F. C. Schuller (European Physical Society, Petit‐Lancy, 1993), p. I‐80]. The best scenario is one with reversed shear, in the q profile, in the central region of the tokamak. The bootstrap current obtained from the plasma profiles provides 90% of the required current, and is well aligned with the...

n-dependence of ballooning instabilities

The critical β for stability against ideal hydromagnetic internal ballooning modes as a function of the toroidal mode number, n, is calculated for two different equilibrium sequences by use of a finite-element technique (n 20), and a WKB formalism (n 5). The agreement between the two methods is good in the overlap region 5 n 20. The WKB formula reduces to the 1/n correction at very high n, but is much more accurate at moderate n. The critical-β-versus-n curves exhibit oscillatory structure at low n, but in both sequences the lower bound on βc is set by n = ∞ modes at about βc ~ 5%.

Dependence of ideal-MHD kink and ballooning modes on plasma shape and profiles in tokamaks

Extensive numerical studies of ideal-MHD instabilities have been carried out to gain insight into the parametric dependence of critical βs in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate to both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that, for aspect ratio R/a ≈ 3, critical βs are of the order of 2% for circular cross-sections and 5% for plasmas with elongation K ≈2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analysed to compare critical β as a function of toroidal mode number n. It is concluded that the infinite-n analytic ballooning theory provides a sufficient condition for ideal-MHD internal-mode stability. Low-n free-boundary modes appear to set a lower limit.

Role of the stabilizing shell in high- beta , low-q disruptions in PBX-M

The characteristics of high- beta , low-q disruptions have been studied in PBX-M, a device with a nearby conducting shell. The coupling between the wall and the plasma was varied by choosing different plasma shapes, including nearly circular plasmas, D-shaped plasmas and bean-shaped plasmas (indented on the midplane), and by increasing the effective coverage of the plasma by the shell. Disruption precursors were observed to have a strong dependence on the coupling between the plasma and the shell. Measured mode growth times vary from between several times the Alfven time-scale (~100 mu s) to the L/R time-scale of the wall (~20 ms). The behaviour of observed disruption precursors is interpreted in terms of the resistive wall mode theory of ideal plasmas, and a detailed calculation of the stability of a strongly coupled bean configuration using the NOVA-W linear stability code is presented. The experimental observations are in good agreement with the theoretical predictions

Comparative Numerical Studies of Ideal Magnetohydrodynamic Instabilities

Stability properties associated with a specific analytic equilibrium have been calculated to compare the accuracy of three large computational programs that have been developed at Garching, Princeton, and Lausanne. All three use a Galerkin formulation of the variational principle for determining spectra. Good agreement is found, verifying the efficacy of all three codes.

Nonlocal properties of gyrokinetic turbulence and the role of E×B flow shear

The nonlocal physics associated with turbulent transport is investigated using global gyrokinetic simulations with realistic parameters in shaped tokamak plasmas. This study focuses on the turbulence spreading through a transport barrier characterized by an equilibrium E×B shear layer. It is found that an E×B shear layer with an experimentally relevant level of the shearing rate can significantly reduce, and sometimes even block, turbulence spreading by reducing the spreading extent and speed. This feature represents a new aspect of transport barrier dynamics. The key quantity in this process is identified as the local maximum shearing rate ∣ωEmax∣, rather than the amplitude of the radial electric field. These simulation studies also extend to radially local physics with respect to the saturation of the ion temperature gradient (ITG) instability, and show that the nonlinear toroidal couplings are the dominant k-space activity in the ITG dynamics, which cause energy transfer to longer wavelength damped mod...