A model of plasma rotation in the Livermore spheromak for the regimes of large connection lengths

Abstract

A model is suggested that predicts the velocity and geometrical characteristics of the plasma rotation in the Livermore spheromak. The model addresses the "good confinement" regimes in this device, where the typical length of magnetic field lines before their intersection with the wall (this length is called "connection length" below) becomes large enough to make the parallel heat loss insignificant. In such regimes, the heat flux is determined by the transport across toroidally-averaged flux surfaces. The model is based on the assumption that, entering the good confinement regime, does not automatically mean that the connection length becomes infinite, and perfect flux surfaces are established. It is hypothesized that connection length remains finite, albeit large in regard to the parallel heat loss. The field lines are threading the whole plasma volume, although it takes a long distance for them to get from one toroidally-averaged flux surface to another. The parallel electron momentum balance then uniquely determines the distribution of the electrostatic potential between these surfaces. An analysis of viscous stresses shows that the toroidal flow is much faster than the poloidal flow. It is shown that the rotation shear usually exceeds by a factor of a few the characteristic growth rate of drift waves, meaning that suppression of the transport caused by the drift turbulence may occur, and a transport barrier with respect to this transport mechanism may be formed. The model may be useful for assessing the plasma rotation in other spheromaks and, possibly, reversed-field pinches and field-reversed configurations, provided a certain set of applicability conditions (Sec. II) is fulfilled.

Hybrid equilibria of field-reversed configurations

“…For example, in a plasma with neutral-beam injection, electrical shorting might prevent runaway ion spinup. 24 Shorting is especially likely in moderate to high-b plasmas such as spheromaks 25 and FRCs. 26 Their modest toroidal field gives rise to short connection lengths between magnetic surfaces, and, indeed, between the very core of the plasma and its periphery.…”

“…This serves to electrically short these surfaces in an axial Alfven time (a few ls in typical experiments). The gradient of the potential for quasi-steady shorting 25,26 is (e/k)!/ ¼ T e !n e /n e þ 1.71! T e .…”

An ion Doppler spectrometer instrument for ion temperature and flow measurements on SSPX

“…1 This makes ion temperature an important measurement. It has also been shown that sub-Alfvénic flow velocities have the potential to stabilize drift wave turbulence and improve energy confinement in spheromaks, 2 and hence warrants a measurement of flow inside sustained spheromak plasma experiment ͑SSPX͒. The spectral resolution of the system was chosen such that both temperature and flow could be measured simultaneously.…”