Evolution of the plasma rotation and the radial electric field for a toroidal plasma in the Pfirsch–Schlüter and plateau regimes subject to a biased electrode

Abstract

In this paper, the fluid equation approach is used to analyze the time evolution of the plasma rotation and the ambipolar electric field in a nonsymmetric toroidal plasma subject to an external biasing voltage induced by a probe. Under consideration is a plasma with low rotation speed in the Pfirsch–Schlüter or the plateau regime that includes the effects of a background neutral gas. A time-dependent charge conservation equation is used to determine the ambipolar electric field as a function of time. It is found that, after the application of the biasing voltage, the electric field and the plasma rotation change quickly and reach steady-state after a time inversely proportional to the sum of the momentum damping rates due to parallel viscosity and ion–neutral collisions. The steady state is characterized by a radial electric field and a plasma rotation that are proportional to the electric current flowing through the biasing probe. The direction of the plasma flow is determined by the relative magnitude of the momentum damping rates on the flux surface. From the steady-state solution, an expression for the radial electric conductivity is obtained, which includes the effect of collisions with neutrals as well as viscosity. Axisymmetric systems without neutrals are also discussed, which is a special case since there is no momentum damping in the toroidal direction. Here, the toroidal velocity increases continuously in time with the bias and never reaches steady state. Finally, a model for nonsymmetric magnetic fields is presented and the viscous damping rate, the radial conductivity and the spin-up rate for a plasma in the Pfirsch–Schlüter regime are calculated. As examples, the cases of the rippled tokamak and the classical and helically symmetric stellarators are evaluated.

Neoclassical momentum transport in a collisional stellarator and a rippled tokamak

“…This problem is not new and has been studied in Refs. [29][30][31][32][33][34], but none of these treatments is completely satisfactory. As discussed in the Appendix of this paper, Ref.…”

Electrode and Langmuir probe tools used for flow damping studies in the Helically Symmetric Experiment

“…Simply speaking, the flow appears to rise with a time scale of ϳ300 s. A more detailed inspection of the flow speed and direction evolution reveals that there are two time scales present in the flow rise; a fast time scale of ϳ20 s or faster, and a longer time scale of ϳ300 s. A two time scale flow evolution in response to a biased electrode has been predicted based on neoclassical theory, 31 and the rapid response of the probes allows detailed comparisons between neoclassical modeling and experiment. Data have also been collected in different configurations of HSX, allowing the study of how magnetic geometry impacts flow damping.…”

Theory of Enhanced Reversed Shear Mode in Tokamaks

“…The other possible cause is the magnetic stress associated with the MHD activity observed after bifurcation. The effect of neutral change exchange momentum loss [29] on the value of U pm can be important because for high temperature plasmas, nonlinear viscosity is weak. These issues will be addressed separately.…”