Oscillating field current drive and nonlinear plasma response in bootstrapped tokamaks

Abstract

The nonlinear response of bootstrapped tokamaks to oscillating field current drive (OFCD) is studied with the aid of a formal mathematical solution. The tokamak plasma response to OFCD is shown to be similar to that of a driven inductor–resistor (LR) circuit, but the effective plasma resistance can be negative. A physical picture is constructed in which the tokamak bootstrap effect is viewed as a nonlinear amplification of the plasma magnetic helicity. The bootstrap amplifier can rectify the toroidal plasma current. The importance of the tokamak thermal instability for peaking the plasma current and creating a plasma dynamo is stressed. Estimates are made which suggest that steady-state tokamak fusion reactors operating with OFCD may be achievable with moderate amplitude toroidal magnetic flux and loop voltage oscillations and oscillation driving frequencies significantly below the audible frequency range.

A nonlinear magnetic helicity model of a tight aspect ratio bootstrapped tokamak with oscillating field current drive

“…where L e is the energy inductance and the volume averaged internal inductance i = B 2 θ /B 2 θa , with B θa the poloidal magnetic field at the plasma edge. For a rigid current profile, we also showed in [2] that the resistance reduction factor ξ bs has the form…”

“…Finally, we complete our specification of the magnetic helicity model by assuming that the plasma current profile is rigid, as was already mentioned in the introduction. That is, we assume that the circuit elements L h and R nc are fixed [2], dL h /dt = 0 and dR nc /dt = 0. From definitions (35) and (41), the helicity inductance and the neoclassical resistance can then be approximated as…”

“…In several recent works [1,2], we have suggested that an alternative tokamak current drive scheme may exist which maintains the attractive features of inductive drive, but which also allows for steady-state tokamak operation. This scheme, called oscillating field current drive (OFCD) [3], involves simultaneously oscillating the loop voltage and the plasma toroidal magnetic flux in phase,…”

“…In this work, we present theoretical and computational analyses of bootstrapped tokamaks with OFCD using a nonlinear magnetic helicity model [2]. Similar analyses for reversed field pinch (RFP) devices with OFCD have been given in [4].…”

“…The current viscosity can create poloidal magnetic flux, but conserves the plasma magnetic helicity [7]. Because of nonlinear tokamak plasma response, the current viscosity and the bootstrap current together can maintain an approximately rigid current profile, with λ large in a region about the magnetic axis [1,2]. The rigid current profile approximation is a fundamental assumption used throughout this work.…”