The neoclassical theory of ion transport in rotating axisymmetric plasmas is formulated. The flow speed is allowed to be of the order of the ion thermal speed. It is shown that the ion distribution function becomes Maxwellian, with temperature uniform on a magnetic surface, and the poloidal flow decays, in a few transit or collision times, in general. A drift kinetic equation is derived which is a simple generalization of the drift kinetic equation for nonrotating plasmas. The radial gradient of the toroidal angular velocity appears as a driving term like the temperature gradient. Both gradients drive the transport of toroidal angular momentum and energy, in general; Onsager relations for the two-by-two transport matrix are derived. The off-diagonal transport coefficients are shown to be zero if the magnetic field has up–down symmetry. A simple expression for the enhancement of the ion thermal conductivity in the banana regime, caused by rotation, is derived. The neoclassical viscosity is shown not to be enhanced by rotation in the banana regime, and to be small in the collisionality parameter in the collisional regime, assuming up–down symmetry. In the collisional regime, the thermal conductivity is shown to be suppressed by the effects of rotation.
Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wall limit but have little effect at lower beta. The discovery of an error field amplification has led to sustained operation above the no-wall limit through improved magnetic field symmetrization using an external coil set. The required symmetrization is determined both by optimizing the external currents with respect to the plasma rotation and by use of feedback to detect and minimize the plasma response to nonaxisymmetric fields as beta increases. Ideal stability analysis and rotation braking experiments at different beta values show that beta is maintained 50% higher than the no wall stability limit for durations greater than 1 s, and approaches beta twice the no-wall limit in several cases, with steady-state rotation levels. The results suggest that improved magnetic-field symmetry could allow plasmas to be maintained well above no-wall beta limit for as long as sufficient torque is provided.
Vertical poloidal asymmetries of hydrogen isotopes and low-Z impurity radiation in the PDX tokamak may be caused by poloidally asymmetric sources of these elements at gas inlet valves, limiters or vacuum vessel walls, asymmetric magnetic-field geometry in the region beyond the plasma boundary, or by ion curvature drifts. Low ionization states of carbon (C II to C IV) are more easily affected by edge conditions than is C V. Vertical poloidal asymmetries of C V are correlated with the direction of the toroidal field. The magnitude of the asymmetry agrees with the predictions of a quasi-fluid neoclassical model. Experimental data and numerical simulations are presented to investigate different models of impurity poloidal asymmetries.
A previous formulation of neoclassical transport for an axisymmetric plasma with arbitrary toroidal rotation is generalized to plasmas with impurity ions. Calculations in the banana regime for a two-ion species plasma for large aspect circular flux surfaces show significant enhancement of both particle and heat fluxes. The viscous part of the momentum flux remains small. A more detailed treatment of the electron equations reveals the importance of an assumption relating to the balancing of the toroidal torques on the electron fluids which is likely to require modification in practical situations.
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