Effect of Longitudinal Electric Field on Toroidal Diffusion

Abstract

critical temperature (but by less than a part in a thousand) without significantly altering the form of the specific heat singularity.We are indebted to F. J. van Kann for his assistance with the data analysis and one of us (J.A.L.) wishes to thank the Commonwealth

Linearized model Fokker–Planck collision operators for gyrokinetic simulations. I. Theory

“…These are, in fact, just the standard correction expressions used for the model pitch-angle-scattering operator 19,20 and for more complex operators including energy diffusion. 21 Note that the numerical implementation of our collision operator documented in Paper II 10 achieves exact satisfaction of the conservation laws by choosing the discretization scheme that exactly captures the differential identities ͑6͒ and ͑7͒ and the double integration by parts needed in deriving Eqs.…”

“…18 In the ␦f kinetics, we would naturally consider the linearized Landau operator. [20][21][22] This course of action is, indeed, eminently sensible: from Eq. Consequently, several simplified model collision operators have been developed, both for analytical and computational convenience, that try to capture the qualitative essence, if not the quantitative de-tail, of the physics involved.…”

“…19,20 However, in kinetic turbulence, there is no reason that small-scale velocity-space structure should be restricted to pitch angles. 19,20 However, in kinetic turbulence, there is no reason that small-scale velocity-space structure should be restricted to pitch angles.…”

Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests

“…5,23,24,26 These range in complexity from the Krook operator 27 to the RutherfordKovrizhnikh operator 28 to the Catto-Tsang operator, 29 all of which have previously been implemented in GS2. The most advanced of these operators ͑Catto-Tsang͒, implemented using a split-implicit method, 4,26 consists of the linearized Landau test-particle operator ͑both pitch-angle scattering and energy diffusion͒ with a model field-particle operator designed to satisfy conservation properties.…”

Neoclassical Drift of Circulating Orbits Due toToroidal Electric Field in Tokamaks

“…This is especially valid for runaway electrons. Rutherford et al [18] pointed out that that to study neoclassical transport effect, collisions need to be considered, and the collisional friction between particles perturbs the orbit in a similar way to the electric field. The conclusion was that for the banana regime, the inward flux is roughly the Ware pinch velocity times the density of trapped electrons.…”