Plasma Dictionary - Definition of Term Klimontovich Equation
 

 

 
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Term : Klimontovich Equation
Definition : Describes space-time evolution of the microscopic distribution function. It is derived from the Klimontovich distribution function, which is just the microscopic density of particles in the phase space (position and velocity) and is represented by six-dimensional delta functions. One must be careful when deriving the Klimontovich equation, because the electric and magnetic fields entering the derivation must include both the external and the fine-grained fields. The Klimontovich equation describes the whole system one particle at a time. Since this is often impossible to compute in practice, one typically takes a statistical average, and by doing so obtains the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations, which are a coupled set of equations that provide the basis for the kinetic theory of plasmas.
 
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