Author: Kenneth Donald MarxPublisher:
ISBN:
Category :
Languages : en
Pages : 296
Book Description
Solution of a Spatially Dependent Fokker-Planck Equation for Mirror-confined Plasmas
Author: Kenneth Donald MarxRadial Fokker-Planck Model for Plasmas Confined by Magnetic Mirror Fields
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
A time-dependent computer model has been developed for the spatially dependent distribution function f(r, v, t). An orbit averaged Fokker-Planck equation treats Coulomb collisions and various atomic physics processes. The motivation for the present code is to provide an accurate treatment of gyro-radius effects and realistic beam geometries which have been neglected in previous Fokker-Planck codes. Finite width beams may be offset from the plasma center to determine beam injection for build-up studies. The inclusion of a finite gyro-radius is essential for studying radial transport due to both quasilinear fluctuations and charge exchange collisions. Charge exchange with energetic beam atoms and plasma erosion due to charge-exchange collisions with thermal gas are both included. Quasilinear diffusion terms include the effects of turbulent diffusion in the model. The model has been used to study particle and energy confinement times in the 2XIIB experiment and in the mirror plug of the TMX experiment. Calculated values of T/sub e/ decrease from classical Fokker-Planck values (1000 eV for 2XIIB) to the 50 eV to 200 eV range observed in 2XIIB and TMX experiments. Radial density profiles and n tau scaling with plasma radius and magnetic field agree with experimental data.
Nuclear Science Abstracts
Author: Extension of Dougherty's Model Fokker-Planck Equation for a Plasma
Author: Robert J. PapaPublisher:
ISBN:
Category : Electromagnetic waves
Languages : en
Pages : 64
Book Description
Electromagnetic waves can be severely attenuated and suffer distortion as they propagate through partially ionized gases. These facts must be considered in the design of any communication system in which waves must propagate through an intervening plasma medium, such as in reentry communications and ionospheric propagation. In this report, formulas are given that can predict such wave attenuation characteristics more accurately and for a much wider range of plasma conditions than previous theories. The conventional Appleton-Hartree equation used in ionospheric propagation studies gives the index of refraction of a wave traveling through a plasma in a magnetic field in terms of the properties of the plasma. This conventional Appleton-Hartree formula neglects important effects such as the random thermal motion of the particles, which can produce nonlocal effects. Also, the energy dependence of the electron-neutral collision frequency can alter the nature of the wave attenuation process. A generalization of the Appleton-Hartree equation is made to include these effects and to account for the Coulomb forces between charged particles. A kinetic equation is solved which includes the effects of energy-dependent electron-neutral collisions, Coulomb encounters and spatial dispersion. The perturbation method used in solving the kinetic equation assumes that the effects of Coulomb encounters and spatial dispersion are dominant, and electron-neutral collisions are relatively infrequent.
Nuclear Science Abstracts
Author: Computational Methods for Kinetic Models of Magnetically Confined Plasmas
Author: J. KilleenPublisher: Springer Science & Business Media
ISBN: 3642859542
Category : Science
Languages : en
Pages : 208
Book Description
Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.
Numerical Solution of the Fokker--Planck Equations for a Multi-species Plasma
Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Two numerical models used for studying collisional multispecies plasmas are described. The mathematical model is the Boltzmann kinetic equation with Fokker-Planck collision terms. A one-dimensional code and a two-dimensional code, used for the solution of the time-dependent Fokker-Planck equations for ion and electron distribution functions in velocity space, are described. The required equations and boundary conditions are derived and numerical techniques for their solution are given.
Scientific and Technical Aerospace Reports
Author: Computational Mathematics
Author: Andrzej WakuliczPublisher:
ISBN:
Category : Computational mathematics and applications
Languages : en
Pages : 804
Book Description
Controlled Fusion
Author: John KilleenPublisher: Elsevier
ISBN: 0323149367
Category : Science
Languages : en
Pages : 465
Book Description
Methods in Computational Physics, Volume 16: Controlled Fusion considers the full variety of computer models needed for the simulation of realistic fusion devices. These computer models include time-dependent magnetohydrodynamics, plasma transport in a magnetic field, MHD and guiding-center equilibria, MHD stability of confinement systems, Vlasov and particle models, and multispecies Fokker-Planck codes. This volume is divided into 11 chapters. The first three chapters discuss various aspects of the numerical solution of the equations of magnetohydrodynamics (MHD). The subsequent chapters present the more realistic models, including the thermal conductivity and electrical resistivity. Other chapters describe two-dimensional codes with varies choice of coordinate systems, such as fixed Eulerian grid, Lagrangian descriptions, and the use of magnetic flux surfaces as coordinate surfaces. The discussion then shifts to models on the inclusion of neutrals and impurities, as well as the use of empirical transport coefficients. A chapter surveys the development of time-dependent codes to support the design and operation of major CTR experiment. The final chapters explore the electromagnetic codes in the nonradiative limit (Darwin model) where the equations are nonrelativistic and displacement currents are neglected. This book is an invaluable source for geoscientists, physicists, and mathematicians.