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Spherical Harmonic Reduction Of The Fokker Planck Equation


Spherical Harmonic Reduction Of The Fokker Planck Equation
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Spherical Harmonic Reduction Of The Fokker Planck Equation


Spherical Harmonic Reduction Of The Fokker Planck Equation
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Author : Thomas A. Oliphant
language : en
Publisher:
Release Date : 1965

Spherical Harmonic Reduction Of The Fokker Planck Equation written by Thomas A. Oliphant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Fokker-Planck equation categories.


The Fokker-Planck equation is reduced to aform that is useful from the viewpoint of doing practical calculations of problems involving configuration space as well as velocity space. The basic technique is a spherical harmonic decomposition in velocity space that reduces the number of independent variables by two. As an example, we show how to apply this method to a problem with theta-pinch geometry.



Tid


Tid
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Author :
language : en
Publisher:
Release Date : 1965

Tid written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Energy development categories.




Controlled Fusion And Plasma Research


Controlled Fusion And Plasma Research
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Author :
language : en
Publisher:
Release Date : 1965

Controlled Fusion And Plasma Research written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Controlled fusion categories.




Nuclear Science Abstracts


Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1971

Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Nuclear energy categories.




Scientific And Technical Aerospace Reports


Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.




Government Wide Index To Federal Research Development Reports


Government Wide Index To Federal Research Development Reports
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Author :
language : en
Publisher:
Release Date : 1966-10-10

Government Wide Index To Federal Research Development Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966-10-10 with Government publications categories.




Expansion Of The Fokker Planck Equation In Spherical Harmonics


Expansion Of The Fokker Planck Equation In Spherical Harmonics
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Author : Frederic A. Lyman
language : en
Publisher:
Release Date : 1965

Expansion Of The Fokker Planck Equation In Spherical Harmonics written by Frederic A. Lyman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Fokker-Planck equation categories.




Solution Of The Fokker Planck Equation With Mixing Of Angular Harmonics By Beam Beam Charge Exchange


Solution Of The Fokker Planck Equation With Mixing Of Angular Harmonics By Beam Beam Charge Exchange
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Author :
language : en
Publisher:
Release Date : 1989

Solution Of The Fokker Planck Equation With Mixing Of Angular Harmonics By Beam Beam Charge Exchange written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.


A method for solving the linear Fokker-Planck equation with anisotropic beam-beam charge exchange loss is presented. The 2-D equation is transformed to a system of coupled 1-D equations which are solved iteratively as independent equations. Although isotropic approximations to the beam-beam losses lead to inaccurate fast ion distributions, typically only a few angular harmonics are needed to include accurately the effect of the beam-beam charge exchange loss on the usual integrals of the fast ion distribution. Consequently, the algorithm converges very rapidly and is much more efficient than a 2-D finite difference method. A convenient recursion formula for the coupling coefficients is given and generalization of the method is discussed. 13 refs., 2 figs.



Wave Propagation In A Warm Magnetoplasma With Coulomb Interactions


Wave Propagation In A Warm Magnetoplasma With Coulomb Interactions
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Author : Robert J. Papa
language : en
Publisher:
Release Date : 1970

Wave Propagation In A Warm Magnetoplasma With Coulomb Interactions written by Robert J. Papa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Ionosphere categories.


Electromagnetic waves propagating through partially ionized gases can be severely attenuated and suffer distortion. This has important consequences in the design of any communication and radar system in which waves must propagate through an intervening plasma medium, such as in reentry communications and ionospheric propagation. In this report, formulas are derived that can predict such wave attenuation characteristics more accurately and for a wider range of plasma conditions than already existing theories. The conventional Appleton-Hartree equation used in ionospheric propagation studies gives the index of refraction of a wave travelling 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 cause nonlocal effects. Also, the energy dependence of the electron-neutral collision frequency can alter the nature of the wave attenuation process. In the report, a generalization of the Appleton-Hartree equation is made to include these effects. 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 electron-neutral collisions and Coulomb encounters are dominant, and spatial dispersion effects are weak.



Kinetic Theory And Transport Phenomena


Kinetic Theory And Transport Phenomena
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Author : Rodrigo Soto
language : en
Publisher: Oxford University Press
Release Date : 2016

Kinetic Theory And Transport Phenomena written by Rodrigo Soto and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Kinetic theory of matter categories.


One of the questions about which humanity has often wondered is the arrow of time. Why does temporal evolution seem irreversible? That is, we often see objects break into pieces, but we never see them reconstitute spontaneously. This observation was first put into scientific terms by the so-called second law of thermodynamics: entropy never decreases. However, this law does not explain the origin of irreversibly; it only quantifies it. Kinetic theory gives a consistent explanation of irreversibility based on a statistical description of the motion of electrons, atoms, and molecules. The concepts of kinetic theory have been applied to innumerable situations including electronics, the production of particles in the early universe, the dynamics of astrophysical plasmas, quantum gases or the motion of small microorganisms in water, with excellent quantitative agreement. This book presents the fundamentals of kinetic theory, considering classical paradigmatic examples as well as modern applications. It covers the most important systems where kinetic theory is applied, explaining their major features. The text is balanced between exploring the fundamental concepts of kinetic theory (irreversibility, transport processes, separation of time scales, conservations, coarse graining, distribution functions, etc.) and the results and predictions of the theory, where the relevant properties of different systems are computed. To request a copy of the Solutions Manual, visit http: //global.oup.com/uk/academic/physics/admin/solutions.