Professor Felix Parra Diaz

Abstract:

A recent publication [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] warned against the use of the lower order gyrokinetic Poisson equation at long wavelengths because the long wavelength, radial electric field must remain undetermined to the order the equation is obtained. Another reference [W. W. Lee and R. A. Kolesnikov, Phys. Plasmas 16, 044506 (2009)] criticizes these results by arguing that the higher order terms neglected in the most common gyrokinetic Poisson equation are formally smaller than the terms that are retained. This argument is flawed and ignores that the lower order terms, although formally larger, must cancel without determining the long wavelength, radial electric field. The reason for this cancellation is discussed. In addition, the origin of a nonlinear term present in the gyrokinetic Poisson equation [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] is explained. © 2009 American Institute of Physics.

Abstract:

Traditional electrostatic gyrokinetic treatments consist of a gyrokinetic Fokker-Planck equation and a gyrokinetic quasineutrality equation. Both of these equations can be found up to second order in a gyroradius over macroscopic length expansion in some simplified cases, but the versions implemented in codes are typically only first order. In axisymmetric configurations such as the tokamak, the accuracy to which the distribution function is calculated is insufficient to determine the neoclassical radial electric field. Moreover, we prove here that turbulence dominated tokamaks are intrinsically ambipolar, as are neoclassical tokamaks. Therefore, traditional gyrokinetic descriptions are unable to correctly calculate the toroidal rotation and hence the axisymmetric radial electric field. We study the vorticity equation, ∇ J = 0, in the gyrokinetic regime, with wavelengths on the order of the ion Larmor radius. We explicitly show that gyrokinetics needs to be calculated at least to third order in the gyroradius expansion if the radial electric field is to be retrieved from quasineutrality. The method employed to study the vorticity equation also suggests a solution to the problem, namely, solving a gyrokinetic vorticity equation instead of the quasineutrality equation. The vorticity equations derived here only obtain the potential within a flux function as required. © 2009 IOP Publishing Ltd.

Abstract:

We first consider gyrokinetic quasineutrality limitations when evaluating the axisymmetric radial electric field in a non-turbulent tokamak by an improved examination of intrinsic ambipolarity. We next prove that the background ions in a pedestal of poloidal ion gyroradius scale must be Maxwellian and nearly isothermal in Pfirsch-Schlüter and banana regime tokamak plasmas, and then consider zonal flow behaviour in a pedestal. Finally, we focus on a simplifying procedure for our transport time scale hybrid gyrokinetic-fluid treatment that removes the limitations of gyrokinetic quasineutrality and remains valid in the pedestal. © 2009 IAEA, Vienna.

Abstract:

We compare two different derivations of the gyrokinetic equation: the Hamiltonian approach in Dubin D H E et al (1983 Phys. Fluids 26 3524) and the recursive methodology in Parra F I and Catto P J (2008 Plasma Phys. Control. Fusion 50 065014). We prove that both approaches yield the same result at least to second order in a Larmor radius over macroscopic length expansion. There are subtle differences in the definitions of some of the functions that need to be taken into account to prove the equivalence. © 2009 IOP Publishing Ltd.

Abstract:

For a tokamak, we consider gyrokinetic quasineutrality limitations when evaluating the axisymmetric radial electric field; a gyrokinetic entropy production restriction on the ion temperature pedestal; and a hybrid gyrokinetic-fluid treatment valid on transport time scales.