Self-Sustained Tokamak Reactor due to Bootstrap Current with Finite Banana-Width Effect

Abstract

The concept of a tokamak sustained only by the neoclassical bootstrap current is quite attractive. According to the conventional neoclassical transport theory, this completely bootstrapped tokamak is considered to be impossible since the bootstrap current vanishes at the magnetic axis and thus a seed current near the axis must be generated by an external source. However, several authors have suggested that the seed current can be generated through the anomalous radial diffusion of the bootstrap current and the inclusion of this effect may lead to the completely bootstrapped tokamak. Another suggestion for the possibility of the completely bootstrapped tokamak comes from the break-down of the conventional neoclassical transport theory near the magnetic axis. A particle orbit near the magnetic axis is quite different from the conventional banana orbit, and a thin-banana approximation in the conventional theory is broken down. The modification of the conventional neoclassical transport theory around the magnetic axis by the finite banana-width effect has been studied, and several expressions for the bootstrap current are presented. In these studies, the bootstrap current is found to remain finite on the magnetic axis. Therefore, this finite banana-width effect leads to the possibility of the completely bootstrapped tokamak. In order to calculate the bootstrapped tokamak equilibrium, we need the expression for the bootstrap current which can be used in entire region of plasma. Several formulae interpolating the expression at the magnetic axis and that of the conventional neoclassical transport theory have been presented. In a previous paper, the author obtained the bootstrap current at the magnetic axis by applying the Wang’s method, and proposed a more sophisticated interpolation formula between this bootstrap current at the axis and the conventional one. Our obtained expression for the bootstrap current reduces to the conventional one when the ratio 1=3 a = ffiffi p is much less than unity, where is the inverse aspect ratio, and a 1⁄4 2q0 a=kR0 with the major radius R0, the elongation parameter k, the safety factor q0 at the magnetic axis, and the Larmor radius a for species a. The finite banana-width effect is shown to modify the conventional bootstrap current around the magnetic axis satisfying the condition ffiffi p < 1=3 a . This modification is significant for high energy particles. In ref. 12, the author also obtained the expression for the bootstrap current due to fusion-produced alpha particles by taking into account the finite banana-width effect. In this paper, using the modified bootstrap current by the finite banana-width effect, we study a simple equilibrium model of completely bootstrapped tokamak. The bootstrap current Jbulk due to bulk particles is expressed as Jbulk 1⁄4 ðB=hBiÞðneTe=BpÞĴbulk with Ĵbulk 1⁄4 L1 pe pe þ 1