Neoclassical toroidal viscosity and error-field penetration in tokamaks

Abstract

A model for field error penetration is developed that includes nonresonant as well as the usual resonant field error effects. The nonresonant components cause a neoclassical toroidal viscous torque that tries to keep the plasma rotating at a rate comparable to the ion diamagnetic frequency. The new theory is used to examine resonant error-field penetration threshold scaling in ohmic tokamak plasmas. Compared to previous theoretical results, the plasma is found to be less susceptible to error-field penetration and locking, by a factor that depends on the nonresonant error-field amplitude.

Advances in understanding the generation and evolution of the toroidal rotation profile on DIII-D

“…In that sense, the NRMF torque can still be considered a drag, provided one appreciates that the drag is towards a finite-rotation condition. The local torque density has been computed as the time derivative of the angular momentum density dl/dt, which exhibits the offset linear relationship as expected from theory [23,26]. In the cases where the initial plasma rotation is small, the acceleration of the plasma by the applied n = 3 NRMF results in an improvement in the global energy confinement.…”

“…The offset rotation is thus of the same order as the ion diamagnetic speed, and pointed in the direction counter to the plasma current, I p . In specific collisionality limits, equation (1) can be written as [23] …”

Observation of Peak Neoclassical Toroidal Viscous Force in the DIII-D Tokamak

“…Second, on a longer transport timescale roughly of order [v ti /R 0 (δB n /B 0 ) 2 ] −1 , with v ti ≡ 2T i /m i the ion thermal speed, the NA magnetic fields damp the toroidal component of plasma flow to a rotation rate Ω * (ν i , E r ) = [(c t + c p )/(Z i e)]dT i /dχ, where c t is a number of order unity. In this two-stage successive determination of the plasma flows, the NTV damping rate has the form [3,6,7] …”

Spectral Asymmetry Due to Magnetic Coordinates

“…A number of papers have discussed the resonant Fourier harmonics of magnetic field δB ≡ δ B ·n instead of Φ, assuming the Fourier spectrum is little changed by going to magnetic coordinates [11][12][13][15][16][17][18][19]. But this assumption can be very inaccurate in toroidal plasmas.…”

“…The spectral asymmetry is important in practical applications, such as studies of tokamaks subjected to magnetic perturbations [8][9][10][11][12][13][14][15][16][17][18][19]. Magnetic coordinate systems can be defined by the Jacobian, which for the standard coordinate systems can be written as [20] …”