Professor Felix Parra Diaz

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.

Abstract:

Simulating electrostatic turbulence in tokamaks on transport time scales requires retaining and evolving a complete turbulence modified neoclassical transport description, including all the axisymmetric neoclassical and zonal flow radial electric field effects, as well as the turbulent transport normally associated with drift instabilities. Neoclassical electric field effects are particularly difficult to retain since they require evaluating the ion distribution function to higher order in gyroradius over background scale length than standard gyrokinetic treatments. To avoid extending gyrokinetics an alternate hybrid gyrokinetic-fluid treatment is formulated that employs moments of the full Fokker-Planck kinetic equation to remove the need for a higher order gyrokinetic distribution function. The resulting hybrid description is able to model all electrostatic turbulence effects with wavelengths much longer than an electron Larmor radius such as the ion temperature gradient (ITG) and trapped electron modes (TEM). © 2008 IOP Publishing Ltd.

Abstract:

We present a new recursive procedure to find a full f electrostatic gyrokinetic equation correct to first order in an expansion of gyroradius over magnetic field characteristic length. The procedure provides new insights into the limitations of the gyrokinetic quasineutrality equation. We find that the ion distribution function must be known at least to second order in gyroradius over characteristic length to calculate the long wavelength components of the electrostatic potential self-consistently. Moreover, using the example of a steady-state -pinch, we prove that the quasineutrality equation fails to provide the axisymmetric piece of the potential even with a distribution function correct to second order. We also show that second order accuracy is enough if a more convenient moment equation is used instead of the quasineutrality equation. These results indicate that the gyrokinetic quasineutrality equation is not the most effective procedure to find the electrostatic potential if the long wavelength components are to be retained in the analysis. © 2008 IOP Publishing Ltd.

Abstract:

Time-centering algorithms to increment the temporal accuracy of the state of macroparticles in the hybrid code HPHall-2 are presented. As a result, one orderof-magnitude increment in temporal precision is achieved. Errors in the conservation of mass flow along the chamber are reduced by one order-of-magnitude too. In a second part, the algorithm controlling the population of particles per cell is improved with the aim of reducing both the statistical oscillations and the computational cost.