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

Abstract

Theoretical and computational analyses of bootstrapped tokamaks with oscillating field current drive (OFCD) have been developed using a nonlinear magnetic helicity model. Assuming a rigid current profile, the conditions for optimal tokamak steady-state operation are derived and are shown to agree with the results of computer calculations. Generalized limit formulae for the toroidal plasma beta and bootstrap current fraction are also obtained. The results of the analyses indicate that steady-state bootstrapped tokamak operation with high toroidal plasma beta can best be achieved in tight aspect ratio A → 1 reactors with OFCD supplying as much as a quarter of the total toroidal plasma current.

Optimal condition for oscillating field current drive in a bootstrapped tokamak

“…First, in the large scaled driving frequency limit ω 1 relevant to the magnetic helicity model, the relationship between the rectified loop voltage V and the mean scaled bootstrap current fraction f bs takes on the inductive current drive form [1],…”

“…For example, if toroidal current oscillation amplitudes Î / I ≈ 10% can be tolerated for OFCD current fractions f OFCD ≈ 10%, then the optimal condition (11) requires only the very low scaled frequency value ω ≈ 40, in units of τ −1 nc . The reduction in the OFCD driving frequency ω is critical for successful penetration of the OFCD current to the tokamak plasma interior [1].…”

“…Suppose now that the required values for the toroidal current oscillation amplitude and the optimal toroidal flux association amplitude [1], ( Î / I ) min = √ 2 1opt , remain fixed. Then from (11), we see that f OFCD ∝ ω.…”

“…In a recent work [1], we showed that oscillating field current drive (OFCD) can be achieved in a bootstrapped tokamak with the minimum toroidal current oscillation amplitude…”

“…where ω is the OFCD oscillation driving frequency, σ (V ) is a dimensionless frequency reduction factor due to the bootstrap effect and τ nc is the neoclassical decay time, which is closely related to the plasma skin time. In addition to the scaling factor τ nc for the time t, the nonlinear magnetic helicity model of [1] employed scaling factors I S for the toroidal current I , V S for the loop voltage V , 0 for the toroidal magnetic flux , and bs for the bootstrap current fraction f bs . Working with these scaled units, the OFCD inputs are…”