By Richard D. Gill
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9 EQUILIBRIUM IN A MAGNETIC FIELD From equation (41), and the steady state Maxwell equation we obtain the equilibrium condition INTRODUCTION TO PLASMA PHYSICS J_ c u r l Ä = __A . 51 (42 ) In a straight magnetic field this may be written as with solution B p, + 1 = constant , (43) 2y0 a result which could also have been deduced from the macroscopic MHD equations. Thus a magnetic field exerts a pressure (S 2 /2y 0 ), and magnetic con finement of a plasma transverse to the field direction is achieved by supporting the plasma pressure by an external magnetic pressure.
64) MAGNETOHYDRODYNAMICS 65 If there is a surface current density K then the lines of force of the magnetic field must lie in the interface to avoid infinite force densi ties on the surface, so we require, n ·B= 0 . (65) This is the boundary condition of interest in most considerations of confined plasma when gravitational forces can be ignored. 6 MAGNETOSTATIC EQUATIONS AND MHD EQUILIBRIA One relatively simple, but useful, application of magnetohydrodynamics is in the consideration of static plasma equilibria.
C. (1974). "Theory of Non-Neutral Plasmas", Benjamin, Reading, USA. Gamow, G. L. (1949). "Theory of Atomic Nucleus and Nuclear Energy Sources", Clarendon Press, Oxford. Gibson, A. W. (1969). Plasma Physics, 11, 121. Grad. H. (1962). In "Electromagnetic and Fluid Dynamics of Gaseous Plasma", (J. Fox and M. Crowell, eds). Polytechnic Press, New York. F. (1970). "Solid State Plasmas", Pion, London. A. F. (1973). "Plasma Engineering", Butterworth, London. A. W. (1973). "Principles of Plasma Physics", McGrawHill, New York.