Parallel magnetic field perturbations in gyrokinetic simulations

Abstract

At low ␤ it is common to neglect parallel magnetic field perturbations on the basis that they are of order ␤ 2 . This is only true if effects of order ␤ are canceled by a term in the ٌB drift also of order ␤ ͓H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 ͑1977͔͒. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2 ͓Kotschenreuther et al., Comput. Phys. Commun. 88, 128 ͑1995͔͒ to investigate whether the compressional magnetic field perturbation B ʈ is required for accurate gyrokinetic simulations at low ␤ for microinstabilities commonly found in tokamaks. The kinetic ballooning mode ͑KBM͒ demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient ͑ETG͒ driven modes do not typically exhibit this behavior; the effects of B ʈ are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with e . The effect of B ʈ on the ETG instability is shown to depend on the normalized pressure gradient ␤Ј at constant ␤.

Progress in simulating turbulent electron thermal transport in NSTX

“…(A summary of the influence of B || on different microinstabilities, along with the relation of the equilibrium pressure gradient, has recently been given in [81].) We also note that similar hybrid TEM/KBM behavior has been predicted in GS2 simulations further out in radius near the top, and inside of, the pedestal region of similar NSTX discharges [35].…”

“…This is due to the strong low-k cutoff provided by the large E B shearing rate [79,80]. For physical accuracy, the simulations include kinetic deuterium and carbon ions consistent with the experimental Z eff =1.7, collisions, , A || , B || perturbations (although electromagnetic effects are not very important for ETG simulations [80,81]), and E B shear. Figure 6 shows that the predicted nonlinear ETG heat flux for the experimental parameters (Q e,sim~1 .5 MW) is a significant fraction of the experimental transport (Q e,exp~2 MW).…”

Magnetic compressibility and ion-temperature-gradient-driven microinstabilities in magnetically confined plasmas

“…Thus, if the plasma pressure is increased whilst the magnetic curvature is kept fixed, then the drift velocity is reduced and the instability is weakened. As has been discussed in the literature [5,13,14,23], this effect from the ions partly cancels that from δB , but it is important to keep in mind that this cancellation only holds if κ, rather than ∇ ⊥ B, is held constant. A simple mathematical argument for the cancellation is given in an Appendix.…”

“…Waltz and Miller reported on such a cancellation, resulting in a substitution rule for the magnetic drift: magnetic compressibility could be dropped if the magnetic drift were replaced by the curvature drift [11]. While this fact now seems to be common knowledge in part of the gyrokinetic community [14,20], the picture that emerges from systematic electromagnetic gyrokinetic simulations of the ITG mode is more complicated [13] and difficult to disentangle. A simple analytical explanation is therefore helpful.…”

“…With some notable exceptions [4][5][6][7][8][9][10], electromagnetic perturbations have been considered mainly from a numerical standpoint [11][12][13][14][15], and the attempt to understand their role in ITG stability has resulted in a patchy collection of numerical findings rather than in a coherent physical picture. Moreover, most studies have neglected magnetic compressibility and have thus neglected the magnetic perturbations parallel to the equilibrium magnetic field, δB , that are generated by the instability to maintain perpendicular pressure balance.…”