Skip to main content Accessibility help

Reevaluation of the Braginskii viscous force for toroidal plasma



The model by Braginskii [1] (Braginskii, S. I. 1965 Transport processes in plasma. In: Review of Plasma Physics, Vol. 1 (ed. M.A. Leontovich). New York, NY: Consultants Bureau, pp. 205–311) for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation, which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force, which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium, which indicates qualitative agreement between theory and measurement for impure plasma discharges with strong toroidal flow.



Hide All
[1]Braginskii, S. I. 1965 Transport processes in plasma. In Review of Plasma Physics, Vol. 1 (ed. Leontovich, M. A.). New York, NY: Consultants Bureau, pp. 205311.
[2]Stacey, W. M., Johnson, R. W. and Mandrekas, J. 2006 A neoclassical calculation of toroidal rotation profiles and comparison with DIII-D measurements. Phys. Plasmas 13 (6), 062508.
[3]Stacey, W. M. and Sigmar, D. J. 1985 Viscous effects in a collisional tokamak plasma with strong rotation. Phys. Fluids 28 (9), 28002807.
[4]Stacey, W. M., Bailey, A. W., Sigmar, D. J. and Shaing, K. C. 1985 Rotation and impurity transport in a tokamak plasma with directed neutral beam injection. Nucl. Fusion 25 (4), 463477.
[5]Mikhailovskii, A. B. and Tyspin, V. S. 1984 Viscosity of a collisional plasma in a curvilinear magnetic field and drift equilibrium (rotation) of a plasma. Sov. J. Plasma Phys. 10, 51.
[6]Simakov, A. N. and Catto, P. J. 2003 Drift-ordered fluid equations for field-aligned modes in low-beta collisional plasma with equilibrium pressure pedestals. Phys. Plasmas 10 (12), 47444757.
[7]Catto, P. J. and Simakov, A. N. 2004 A drift-ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy. Phys. Plasmas 11 (1), 90102.
[8]Catto, P. J. and Simakov, A. N. 2005 Evaluation of the neoclassical radial electric field in a collisional tokamak. Phys. Plasmas 12 (1), 012501.
[9]Ramos, J. J. 2005 General expression of the gyroviscous force. Phys. Plasmas 12 (11), 112301.
[10]Hinton, F. L. and Wong, S. K. 1985 Neoclassical ion transport in rotating axisymmetric plasmas. Phys. Plasmas 28 (10), 30823098.
[11]Wong, S. K. and Chan, V. S. 2007 Fluid theory of radial angular momentum flux of plasmas in an axisymmetric magnetic field. Phys. Plasmas 14 (11), 112505.
[12]Connor, J. W., Cowley, S. C., Hastie, R. J. and Pan, L. R. 1987 Toroidal rotation and momentum transport. Plasma Phys. Control. Fusion 29 (7), 919931.
[13]Solomon, W. M., Burrell, K. H., Andre, R., Baylor, L. R., Budny, R., Gohil, P., Groebner, R. J., Holcomb, C. T., Houlberg, W. A. and Wade, M. R. 2006 Experimental test of the neoclassical theory of impurity poloidal rotation in tokamaks. Phys. Plasmas 13, 056116.
[14]Stacey, W. M. 2006 Rotation velocities and radial electric field in the plasma edge. Contrib. Plasma Phys. 46 (7–9), 597603.
[15]Luxon, J. L. 2002 A design retrospective of the DIII-D tokamak. Nucl. Fusion 42, 6114.
[16]Lao, L. L., St.John, H., Stambaugh, R. D., Kellman, A. G. and Pfeiffer, W. 1985 Reconstruction of current profile parameters and plasma shapes in tokamaks. Nucl. Fusion 25 (11), 16111622.
[17]Huba, J. D. 2004 NRL Plasma Formulary. Washington, DC: Naval Research Laboratory.
[18]Sivia, D. S. 1996 Data Analysis: A Bayesian Tutorial (Oxford Science Publications). Oxford, UK: Oxford University Press.
[19]Stacey, W. M. and Bae, C. 2009. Representation of the plasma fluid equations in “Miller equilibrium” analytical flux surface geometry. Phys. Plasmas 16 (8), 082501.
MathJax is a JavaScript display engine for mathematics. For more information see

Reevaluation of the Braginskii viscous force for toroidal plasma



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.