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1971•The Physics of FluidsOpen access

Kinetic Theory of Plasma in a Magnetic Field

John C. Price

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Abstract

The Krylov-Bogoliubov transformation is used to simplify the guiding center equations for a charged particle in electric and magnetic fields. The resulting transformation of variables is then applied to the Vlasov distribution function, yielding a magnetic Vlasov equation which describes the low-frequency behavior of a system with no statistical effects. The equation is generalized to include effects of high- and low-frequency fluctuations by a procedure developed by Klimontovich and Dupree. A consistent treatment of the conservation laws and Maxwell's equations is given to complete the kinetic description.

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The Krylov-Bogoliubov transformation is used to simplify the guiding center equations for a charged particle in electric and magnetic fields. The resulting transformation of variables is then applied to the Vlasov distribution function, yielding a magnetic Vlasov equation which describes the low-frequency behavior of a system with no statistical effects. The equation is generalized to include effects of high- and low-frequency fluctuations by a procedure developed by Klimontovich and Dupree. A consistent treatment of the conservation laws and Maxwell's equations is given to complete the kinetic description.

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Available abstract

The Krylov-Bogoliubov transformation is used to simplify the guiding center equations for a charged particle in electric and magnetic fields. The resulting transformation of variables is then applied to the Vlasov distribution function, yielding a magnetic Vlasov equation which describes the low-frequency behavior of a system with no statistical effects. The equation is generalized to include effects of high- and low-frequency fluctuations by a procedure developed by Klimontovich and Dupree. A consistent treatment of the conservation laws and Maxwell's equations is given to complete the kinetic description.

Key concepts: Physics, Vlasov equation, Distribution function, Plasma modeling, Conservation law, Magnetic field, Guiding center, Transformation (genetics)

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