D. A. Monticello

Saturation of the tearing mode

A quasi‐linear analytical model is used to describe the nonlinear growth and saturation of tearing modes with mode number m⩾2. The saturation of the magnetic island growth is the quasi‐linear development of a single mode rather than a mode coupling process. The saturation amplitude, which is dependent on the form of the resistivity, is in good agreement with results obtained previously by numerically advancing the full set of nonlinear equations.

Reconnection rates of magnetic fields including the effects of viscosity

The Sweet–Parker and Petschek scalings of the magnetic reconnection rate are modified to include the effect of the viscosity. The modified scalings show that the viscous effect can be important in high‐β plasmas. The theoretical reconnection scalings are compared with numerical simulation results in a tokamak geometry for three different cases: a forced reconnection driven by external coils, the nonlinear m=1 resistive internal kink, and the nonlinear m=2 tearing mode. In the first two cases, the numerical reconnection rate agrees well with the modified Sweet–Parker scaling when the viscosity is sufficiently large. When the viscosity is negligible, a steady state which was assumed in the derivation of the reconnection scalings is not reached and the current sheet in the reconnection layer either remains stable through sloshing motions of the plasma or breaks up to higher m modes. When the current sheet remains stable, a rough comparison with the Sweet–Parker scaling is obtained. In the nonlinear m=2 teari...

Theory of mode-induced beam-particle loss in tokamaks

Large‐amplitude rotating magnetohydrodynamic modes are observed to induce significant high‐energy beam particle loss during high‐power perpendicular netural beam injection on the poloidal divertor experiment (PDX). A Hamiltonian formalism for drift orbit trajectories in the presence of such modes is used to study induced particle loss analytically and numerically. Results are in good agreement with experiment.

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...

Stability of high-beta tokamaks to ballooning modes

Fixed-boundary ballooning modes are found to possess a second globally stable regime for high-beta flux-conserving equilibria. This confirms a conjecture of several authors based on local analysis of the instability in the vicinity of the magnetic axis. The range of unstable beta values depends on the details of the equilibrium and, in particular, on shear. Very high shear can decrease the width of the unstable region.

Nonlinear drift tearing modes

It is shown analytically and with a numerical code that the nonlinear growth and saturation of magnetic islands in tokamaks are not affected by diamagnetic corrections. Diamagnetic effects change the linear growth and introduce mode rotation, which persists in the nonlinear regime. The analysis is used to construct a model for the effect of feedback stabilization schemes in the nonlinear regime.

Non-linear saturation of the internal kink mode

A numerical study shows that in a cylindrical tokamak the internal kink mode (m = 1) develops non-linearly into a helical equilibrium state that possesses a singular current sheet. In the large-aspect-ratio limit, the neighbouring equilibria obtained agree well with the asymptotic analytic theory of Rosenbluth et al.

Magnetic coordinates for equilibria with a continuous symmetry

Magnetic coordinates for hydromagnetic equilibria are defined which treat toroidal and ‘‘straight’’ helical plasmas equivalently and yet exploit the existence of a continuous symmetry to derive relations between various geometrical and physical qualities. This allows the number of equilibrium quantities which must be known to be reduced to a minimal, or primitive, set. Practical formulas for various quantities required in hydromagnetic stability calculations (interchange, ballooning, and global) are given in terms of this primitive set.

Heliac parameter study

Helical axis stellarators (heliacs) with zero net current are found to possess very good stability properties. Helically symmetric or ‘‘straight’’ heliacs with bean‐shaped cross sections have a first region of stability that reaches to 〈u2009β〉 of 30% or more. Those with circular cross sections have a second region of stability to Mercier modes. In addition, the stability properties of these plasma configurations as functions of pressure profile, helical aspect ratio, and helical period length are also reported.

Three-dimensional stellarator equilibrium as an ohmic steady state

A stable three‐dimensional stellarator equilibrium can be obtained numerically by a time‐dependent relaxation method using small values of dissipation. The final state is an Ohmic steady state which approaches an Ohmic equilibrium in the limit of small dissipation coefficients. A method to speed up the relaxation process and a method to implement the B⋅∇p=0 condition are described. These methods are applied to obtain three‐dimensional heliac equilibria using the reduced heliac equations.