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Title: 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 ratemore » 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.« less

Authors:
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
908132
Report Number(s):
UCRL-JRNL-227066
Journal ID: ISSN 1070-664X; PHPAEN; TRN: US0703642
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas, vol. 14, no. 02, February 23, 2007, pp. 022506; Journal Volume: 14, no.; Journal Issue: 02
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; DISTRIBUTION; ELECTRONS; ELECTROSTATICS; HEAT FLUX; MAGNETIC FIELDS; MAGNETIC SURFACES; PLASMA; ROTATION; SHEAR; STRESSES; TRANSPORT; TURBULENCE; VELOCITY; TOKAMAK DEVICES; TOKAMAK TYPE REACTORS

Citation Formats

Ryutov, D. A Model of Plasma Rotation in the Livermore Spheromak for the Regimes of Large Connection Lengths. United States: N. p., 2007. Web. doi:10.1063/1.2435705.
Ryutov, D. A Model of Plasma Rotation in the Livermore Spheromak for the Regimes of Large Connection Lengths. United States. doi:10.1063/1.2435705.
Ryutov, D. Wed . "A Model of Plasma Rotation in the Livermore Spheromak for the Regimes of Large Connection Lengths". United States. doi:10.1063/1.2435705. https://www.osti.gov/servlets/purl/908132.
@article{osti_908132,
title = {A Model of Plasma Rotation in the Livermore Spheromak for the Regimes of Large Connection Lengths},
author = {Ryutov, D},
abstractNote = {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.},
doi = {10.1063/1.2435705},
journal = {Physics of Plasmas, vol. 14, no. 02, February 23, 2007, pp. 022506},
number = 02,
volume = 14, no.,
place = {United States},
year = {Wed Jan 03 00:00:00 EST 2007},
month = {Wed Jan 03 00:00:00 EST 2007}
}
  • We observe Doppler shifts of a CIII impurity line in a spheromak plasma showing toroidal rotation during the formation phase of the spheromak configuration but not during the equilibrium or decay phase. The evolution of the velocity fields is consistent with the estimated rate of cross helicity decay given the viscosity and resistivity of the plasma.
  • 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--Schlueter 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 changemore » 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--Schlueter regime are calculated. As examples, the cases of the rippled tokamak and the classical and helically symmetric stellarators are evaluated.« less
  • Dusty plasma experiments with flat dust clusters are often performed in the boundary sheath of radio frequency discharges at typical gas pressures of 1-100 Pa. The interaction of the dust grains is usually assumed to be of the Yukawa type, which is determined by the particle charge and the screening length. For the experimental determination of these quantities we present a method that does not require prior knowledge of the plasma parameters. The method is based on the application of centrifugal forces by means of a rotating electrode method (REM). The results are critically compared with an analysis of thermallymore » excited normal modes, which can be studied at pressures below 10 Pa. The REM has a wider range of applicability that can be extended to 100 Pa.« less
  • Experimental results are presented which verify the possibility, formerly predicted, of the self-formation of a closed, spheromak-like magnetic configuration (SLMC) in a plasma focus discharge.
  • The physical processes involved in the formation of a spheromak are studied. Using one-fluid axisymmetric resistive magnetohydrodynamic equations together with a temperature equation, investigations of the essential physics aspects of the formation specifically for the new Maryland Spheromak (MS) (J. Antoniades, C. Chin-Fatt, A. DeSilva, G. Goldenbaum, R. Hess, and R. Shaw, in Proceedings of the Sixth U. S. Symposium on Compact Torus Research, Princeton, 1984 (Princeton Plasma Physics Laboratory, Princeton, NJ, 1985), p. 65) have been performed. These studies elucidate the role of differential rotation in accelerating the penetration of toroidal field B/sub phi/ and in forcing Iequivalent rB/submore » phi/ to be a flux function. Another important aspect of the formation is the magnetic reconnection that occurs at the X point between the two reversal coils. A strong toroidal current is generated by the reconnection, and the X point is converted into an O point that finally becomes the magnetic axis of the spheromak. In this latter phase of reconnection, the plasma is heated very strongly. Studies have also been done on the effect of the difference in phase and time scales for the reversal and I/sub z/ banks for the purpose of optimization.« less