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Neoclassical transport: Difference between revisions
→Brief summary of the theory
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== Brief summary of the theory == | == Brief summary of the theory == | ||
The theory starts from the | The theory starts from the Kinetic Equation for the mean particle distribution function <math>f_\alpha(x,v,t)</math>: | ||
:<math> | :<math> | ||
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where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity, | where <math>\alpha</math> indicates the particle species, <math>v</math> is the velocity, | ||
<math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the | <math>F</math> is a force (the [http://en.wikipedia.org/wiki/Lorentz_force Lorentz force] acting on the particle) and <math>C_\alpha</math> the [[Collision operator|collision operator]]. | ||
If the chosen collision operator is the Fokker-Planck operator, the equation is called the [http://en.wikipedia.org/wiki/Fokker-planck Fokker-Planck Equation]. | |||
The derivation of this collision operator is highly non-trivial and requires making specific assumptions; | The derivation of this collision operator is highly non-trivial and requires making specific assumptions; | ||
in particular it must be assumed that a single collision has a small random effect on the particle velocity, | in particular it must be assumed that a single collision has a small random effect on the particle velocity, | ||