A kinetic theory of beam-induced plasma currents

Abstract

A Fokker-Planck treatment of the current induced by a beam of fast ions circulating in a toroidal plasma is developed. The electron Fokker-Planck equation is first reduced to an integro-differential equation which is then solved analytically in the limiting cases of: (a) a large plasma Z and (b) a large ratio of the electron thermal velocity ve to the fast ion velocity vb. In addition, a numerical solution was obtained for the complete range of values of ve/vb and for several values of Z. It is found that the resulting net plasma current has a very different functional dependence upon electron temperature than that given by the conventional theoretical treatment in which the electrons are assumed to be Maxwellian. In particular, for ve > vb and Z = 1, which is the limit appropriate to many present tokamak experiments, the net current is found to be in the opposite direction to the fast-ion current. The theory is compared with recent measurements of this current which were made by using the Culham Levitron, and agreement is found between theory and experiment.

Efficiency of current drive by fast waves

“…From this we can write down analytical expressions for the current-drive efficiency in various cases as given in Eqs. (27), (28), (30), (31), and (32).…”

“…The new term has no effect on the asymptotic form for the efficiencies Eqs. (27) because it is smaller by β 4 than another term in B, which had no effect. Connor and Hastie 21 also give an expression for collisions of high-energy particles off a fixed background.…”

Interaction of energetic particles with large and small scale instabilities

“…Beam drive of current has been predicted by theory (see e.g. [6][7][8] and observed in many experiments (e.g., in TFTR [9,10], DIII-D [11,12], JET [13,14], JT-60U [15][16][17], for an overview see [18]). In most of these experiments the beam driven current was located on-axis, including those with N-NBI [16,17].…”

Current-Drive Efficiency in a Degenerate Plasma

“…For the case of classical slowing down on both ions and electrons, a more accurate current-drive efficiency can be had by including kinetic effects of the slowed down beam distribution for different electron temperature [15]. However, a few observations can be made at once.…”