Fokker-Planck and Quasilinear Codes

  title={Fokker-Planck and Quasilinear Codes},
  author={Charles F. F. Karney},
  journal={Computer Physics Reports},
On the fundamental solution of the Fokker–Planck–Kolmogorov equation
The Fokker–Planck–Kolmogorov parabolic second-order differential operator is considered, for which its fundamental solution is derived in explicit form. Such operators arise in numerous applications,
Images of electron kinetics during electron-cyclotron current drive in tokamak plasmas using Gaussian short-time propagators
A path-sum approach, based on Gaussian short-time propagators, is used to solve a two-dimensional Fokker-Planck model of the electron kinetics during electron-cyclotron current drive of tokamak
Studies on electron cyclotron heating at the Wendelstein VII-A/AS stellarators
The absorption of ECF power launched nearly perpendicular to the magnetic field, ECF current drive and generation of suprathermal electrons is analysed using a 3-D ray tracing code in combination
Self-consistent modelling of ion cyclotron resonance heating
A one-dimensional model is presented for the study of RF heating of tokamak plasmas in a fully self-consistent way. It involves the simultaneous description of the temporal evolution of the heated
A Formulation of Nonlinear Collision Operator for the Monte Carlo Code in Toroidal Plasmas
A nonlinear collision operator is formulated in order to study the effect of collisions among high-energy particles on their confinements in toroidal plasmas. The Monte Carlo collision operator is
Impact of radial transport on the quasilinear plateau formation due to electron cyclotron wave absorption
Numerical simulations using a three‐dimensional Fokker–Planck code show that for small tokamaks the transport of electrons across the magnetic surfaces at a level consistent with anomalous transport


Runaway electrons in a plasma
r a uniform electric field is calculated by solving the Fokker-Planck equation numerically. Comparison with other theoretical and experimental results is made. (auth)
Efficiency of current drive by fast waves
The Rosenbluth form for the collision operator for a weakly relativistic plasma is derived. The formalism adopted by Antonsen and Chu can then be used to calculate the efficiency of current drive by
Currents driven by electron cyclotron waves
Certain aspects of the generation of steady-state currents by electron cyclotron waves are explored. A numerical solution of the Fokker-Planck equation is used to verify the theory of Fisch and
Current in wave-driven plasmas
A theory for the generation of current in a toroidal plasma by radio‐frequency waves is presented. The effect of an opposing electric field is included, allowing the case of time varying currents to
Non-linear Fokker-Planck studies of RF current drive efficiency
A two-dimensional, non-linear Fokker-Planck code coupled to a quasi-linear diffusion term is used to calculate the ratio of RF current excited to power consumed by travelling waves in the plasma.
Kinetic theory and simulation of multispecies plasmas in tokamaks excited with electromagnetic waves in the ion-cyclotron range of frequencies
A description of a bounce‐averaged Fokker–Planck quasilinear model for the kinetic description of tokamak plasmas is presented. The nonlinear collision and quasilinear resonant diffusion operators
Relativistic theory of electron cyclotron resonance heating
The formal theory of the interaction of mildly relativistic electrons with a cyclotron resonant applied electromagnetic field described by geometric optics is developed. The electron distribution
Radio frequency current generation by waves in toroidal geometry
The quasilinear generation of current by rf wave fields is investigated in toroidal geometry. A general expression is derived for the amount of current generated for a given wave‐induced flux of