A trapped-passing fluid model for tokamak neoclassical transport

Abstract

In the low collisionality banana regime, the response of the passing and trapped particles to toroidal forces is essentially distinct: Passing particles accelerate, whereas trapped particles drift radially. In order to model current drive and particle transport in a physically intuitive manner, a four-fluid model for a simple electron–ion plasma involving separate momentum equations for each of the trapped and passing species has been formulated. Because of relative drifts, the four fluids undergo collisional friction with each other and with neutrals; a radial electric field arises with the inclusion of momentum sources, particle sources, and the collisions with neutrals. Radial plasma transport, which conserves canonical angular momentum, is modeled by scattering the configurational component of trapped particle momentum into translational momentum of the passing particles at a rate related to the density and temperature gradients by standard neoclassical theory. For given radial temperature profile, the neoclassical differential equation for the density is obtained. This equation is integrated numerically to obtain the radial density profile. Over a broad range of parameters, the volume average density is close to the empirical Hugill–Murakami–Greenwald [Nucl. Fusion 28, 2199 (1988)] density limit n̄ (1020 m−3)=J̄ (MA m−2); although most plasmas operate below this density, the results suggest that near the density limit, plasma particle confinement may be neoclassical. In this case, it is shown explicitly, in the steady state, that Ohm’s law can be expressed very simply in terms of the classical Spitzer conductivity with no trapped particle correction, a fact first noted by Ware [Nucl. Fusion 13, 793 (1973)]. Alternately, the effect of the trapped particle correction on conductivity cancels the bootstrap current. Concomitantly, deposition of rf wave momentum on thermal, trapped particles in the direction so as to drive plasma current, will pinch the particles inward and result in toroidal current independent of the trapping effect.