M.G. McCoy

ICRF fusion reactivity enhancement in tokamaks

A systematic study of ICRF fusion reactivity enhancement has been conducted, using a new bounce-averaged two-dimensional Fokker-Planck code. Second-harmonic heating of deuterium in a 50–50 DT plasma is assumed, and the results are obtained as a function of background plasma density and temperature. An enhancement factor of ten is achieved at low Q (= fusion power/RF power), which is important for ion-tail diagnostics, but at Q = 0.5 the enhancement is 2. Significant poloidal variations in ion density (up to 14%) and in fusion reactivity (by a factor up to 2.5) are found.

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. Transport loss of electron energy is simulated according to a model of stochastic-magnetic-field effects. Results are obtained for waves with phase velocity normalized to electron thermal velocity in the range from 0.175 to 4.0. Scaling to a tokamak reactor is considered.

FPPAC94: A two-dimensional multispecies nonlinear Fokker-Planck package for UNIX systems☆

Abstract FPPAC94 solves the complete nonlinear multispecies Fokker-Planck collison operator for a plasma in two-dimensional velocity space. The operator is expressed in terms of spherical coordinates (speed and pitch angle) under the assumption of azimuthal symmetry. Provision is made for additional physics contributions (e.g. rf heating, electric field acceleration). The charged species, referred to as general species, are assumed to be in the presence of an arbitrary number of fixed Maxwellian species. The electrons may be treated either as one of these Maxwellian species or as a general species. Coulomb interactions among all charged species are considered This program is a new version of FPPAC. FPPAC was last published in Computer Physics Communications in 1988. This new version is identical in scope to the previous version. However, it is written in standard Fortran 77 and is able to execute on a variety of Unix systems. The code has been tested on the Cray-C90, HP-755 and Sun Sparc-1. The answers agree on all platforms where the code has been tested. The test problems are the same as those provided in 1988. This version also corrects a bug in the 1988 version.

Three-dimensional simulations of electron cyclotron heating

Many heating problems in tokamaks are inherently three-dimensional, involving the velocity coordinates parallel and perpendicular to the ambient magnetic field and the plasma radial coordinate. We will describe a new three-dimensional, Fokker-Planck/rf quasilinear code. This code is based upon a two-dimensional in velocity space Fokker-Planck code which solves for the distribution evaluated at the outer equatorial plane (π = 0) of each flux surface in radial mesh. The rf energy density ϵk satisfies the transport equation ▿·(νgϵk)= −Pabs , where νg is the group velocity of the ordinary or extraordinary wave and pABS is power absorption obtained using results of the Fokker-Planck code. The rf quasilinear operator is a functional of the wave polarization. Warm plasma relations are used for the group velocity and polarizations. With knowledge of Pabs, the transport equation is employed to obtain ϵk, which is used update the quasilinear diffusion coefficients and resume the Fokker-Planck calculation on the various flux surfaces. The procedure of alternately solving the Fokker-Planck equation and the transport equation is repeated to steady state.

Three‐dimensional model of electron cyclotron heating

To address heating problems in tokamaks, we have implemented a 3‐D Fokker‐Planck/rf code. This code uses a 2‐D bounce‐averaged Fokker‐Planck package to solve for the distribution on a radial mesh. The rf energy density ξk is determined as a solution to a transport equation involving the local power absorption and the group velocity of the wave. Once ξk is determined it is used to update the quasi‐linear diffusion coefficients and resume the Fokker‐Planck calculation. A fast procedure for simulating a tokamak diagnostic, the soft‐x‐ray analyzer, is presented.

Collision broadened resonance localization in tokamaks excited with ICRF waves

Abstract Collisions mediate the absorption of rf energy by maintaining velocity space gradients to drive resonant diffusion and by limiting wave-particle interaction coherence through the process of gyro phase diffusion. A code is constructed to evolve the local spectral energy absorption rate which can be exploited to ensure consistency in associated or concurrent wave propagation calculations.

SIGV5D: a routine to compute the reaction rates of interacting distribution functions

Abstract We present a package which computes reaction rates 〈σv〉 based on interactions whose cross-sections σ are functions of relative velocity. The reacting distribution functions are expressed in terms of spherical coordinates in velocity space and are assumed to be independent of the azimuthal angle. A Legendre expansion method is used. One may compute 〈σv〉 for several different reactions simultaneously and for several sets of distribution functions. The user must supply subprograms for setting up the mesh, defining the distribution functions and computing the reaction cross-sections. A test problem is supplied within the source deck.

3D bounce averaged Fokker-Planck calculation of electron cyclotron current drive efficiency

Electron cyclotron current drive heating efficiency in tokamak is calculated using 3D bounce averaged Fokker‐Planck equation. A computer code has been assembled which predicts the profiles of heating and current drive. (AIP)

FOKKER-PLANCK/TRANSPORT ANALYSES OF FUSION PLASMAS IN CONTEMPORARY BEAM-DRIVEN TOKAMAKS

The properties of deuterium plasmas in experimental tokamaks heated and fueled by intense neutral-beam injection are evaluated with a Fokker-Planck/radial transport code coupled with a Monte Carlo neutrals treatment. Illustrative results are presented for the Poloidal Divertor Experiment at PPPL as a function of beam power and plasma recycling coefficient, R/sub c/. When P/sub beam/ = 8 MW at E/sub b/ = 60 keV, and R/sub c/ = 0.2, then approximately 0.5, (/sup 2///sub 3/ ) = 22 keV approximately 6, and the D-D neutron intensity is 10/sup 16/ n/sec.