Edge gyrokinetic theory and continuum simulations

Abstract

Abstract. The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code: (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells.Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are applicable to both neoclassical and turbulence simulations.

Conservative global gyrokinetic toroidal full-f five-dimensional Vlasov simulation

“…Eqs. (17) and (18) exactly conserve both f and f 2 provided that the discrete flows satisfy the incompressible condition, [Cont.] = 0.…”

“…In Section 4, the accuracy of the NDCFD defined in the cylindrical coordinates will be discussed through benchmark calculations against a particle code, which is essentially a mesh-free approach. The skew-symmetric operator (17) can be easily extended to higher-order accuracy by combining the second-order accurate operators. In this work, we use the fourth-order accurate operators,…”

“…In particular, global gyrokinetic simulations played important roles in studying the plasma size scaling of the turbulent transport and global profile effects on the turbulent transport [5][6][7][8]. So far, global toroidal gyrokinetic simulations have been developed either by particle (Lagrangian) approaches [9][10][11][12][13][14] or by mesh (Eulerian or semi-Lagrangian) approaches [15][16][17]. Most of particle simulations are based on a δ f Particle-In-Cell (PIC) method [18][19][20] which is valid for an isolated system without any sources and collisions.…”

“…In addition, δ f approach can not be applied to the edge turbulence where the perturbation amplitude reaches at δ f / f 0 ∼ O (1). From these backgrounds, recently, developments of global gyrokinetic full-f Vlasov simulations have been started [16,17].…”

Full f gyrokinetic method for particle simulation of tokamak transport

“…Fluid, Vlasov and particle approaches are used, the latter two being advantaged by a more precise kinetic description. Due to the need of full f kinetic simulations, a number of such gyrokinetic Vlasov and particle-in-cell codes based on the formalism in [8] have recently been developed [22][23][24][25][26]. A particular problem in the numerical implementation of gyrokinetic full f calculation is in the treatment of nonlinearities.…”