ABSTRACT
This Letter presents the first numerical verification for the bounce-harmonic (BH) resonance phenomena of the neoclassical transport in a tokamak perturbed by nonaxisymmetric magnetic fields. The BH resonances were predicted by analytic theories of neoclassical toroidal viscosity (NTV), as the parallel and perpendicular drift motions can be resonant and result in a great enhancement of the radial momentum transport. A new drift-kinetic δf guiding-center particle code, POCA, clearly verified that the perpendicular drift motions can reduce the transport by phase-mixing, but in the BH resonances the motions can form closed orbits and particles radially drift out fast. The POCA calculations on resulting NTV torque are largely consistent with analytic calculations, and show that the BH resonances can easily dominate the NTV torque when a plasma rotates in the perturbed tokamak and therefore, is a critical physics for predicting the rotation and stability in the International Thermonuclear Experimental Reactor.
ABSTRACT
The confinement of plasmas by magnetic fields with nonaxisymmetric shaping can be degraded or destroyed by the breakup of the magnetic surfaces through effects that are intrinsic to the shaping. An efficient perturbation method of determining this drive for islands was developed and applied to stellarator equilibria.
ABSTRACT
Small nonaxisymmetric perturbations of the magnetic field can greatly change the performance of tokamaks through nonambipolar transport. A number of theories have been developed, but the predictions were not consistent with experimental observations in tokamaks. This Letter provides a resolution, with a generalized analytic treatment of the nonambipolar transport. It is shown that the discrepancy between theory and experiment can be greatly reduced by two effects: (1) the small fraction of trapped particles for which the bounce and precession rates resonate; (2) the nonaxisymmetric variation in the field strength along the perturbed magnetic field lines rather than along the unperturbed magnetic field lines. The expected sensitivity of the International Thermonuclear Experimental Reactor to nonaxisymmetries is also discussed.
ABSTRACT
The sensitivity of tokamak plasmas to very small deviations from the axisymmetry of the magnetic field |deltaB/B| approximately 10{-4} is well known. What was not understood until very recently is the importance of the perturbation to the plasma equilibrium in assessing the effects of externally produced asymmetries in the magnetic field, even far from a stability limit. DIII-D and NSTX experiments find that when the deleterious effects of asymmetries are mitigated, the external asymmetric field was often made stronger and had an increased interaction with the magnetic field of the unperturbed equilibrium. This Letter explains these counterintuitive results. The explanation using ideal perturbed equilibria has important implications for the control of field errors in all toroidal plasmas.
ABSTRACT
A magnetic evolution is ideal if it is consistent with the field being embedded in a perfectly conducting fluid. Faraday's law implies the evolution is ideal when the parallel component of the electric field is the derivative of a scalar potential, a condition that generically holds in any local region of space. Reconnection requires the non-existence of such a potential. In systems with two periodic directions, non-existence focuses reconnection onto the surfaces in which the magnetic field lines close on themselves, the rational surfaces. This rational surface effect does not arise in astrophysics but does appear in periodic simulation codes. Effects that could give astrophysical reconnection are discussed.
ABSTRACT
The confinement of a nonneutral plasma in a magnetic-surface, or stellarator, configuration is explored. The fluid equilibrium equations are derived and are found to be fundamentally different from previous results. Diocotron modes are predicted to be stable. The collisional confinement time can be very long. Possible applications include positron trapping and confinement of positron-electron plasmas. The basic physics can be addressed experimentally in the simple tabletop stellarator planned for construction at Columbia University.
ABSTRACT
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current. (c) 2001 American Institute of Physics.
