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Neoclassical transport: Difference between revisions
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→Brief summary of the theory
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The theory starts from the (Markovian) Fokker-Planck Equation for the particle distribution function <math>f_\alpha(x,v,t)</math>: | The theory starts from the (Markovian) Fokker-Planck Equation for the particle distribution function <math>f_\alpha(x,v,t)</math>: | ||
<math> | :<math> | ||
\frac{\partial f_\alpha}{\partial t} + v\cdot \nabla f_\alpha + F \frac{\partial f_\alpha}{\partial v} = C_\alpha(f) | \frac{\partial f_\alpha}{\partial t} + v\cdot \nabla f_\alpha + F \frac{\partial f_\alpha}{\partial v} = C_\alpha(f) | ||
</math> | </math> | ||
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Once the collision operator is decided, the moments of the Fokker-Planck equation can be computed: | Once the collision operator is decided, the moments of the Fokker-Planck equation can be computed: | ||
<math> | :<math> | ||
n u = \int{v f d^3v} | n u = \int{v f d^3v} | ||
</math> | </math> | ||
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(particle flux) | (particle flux) | ||
<math> | :<math> | ||
P = \int{m v \cdot v f d^3v} | P = \int{m v \cdot v f d^3v} | ||
</math> | </math> | ||
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(stress tensor) | (stress tensor) | ||
<math> | :<math> | ||
Q = \int{\frac{m v^2}{2} v f d^3v} | Q = \int{\frac{m v^2}{2} v f d^3v} | ||
</math> | </math> | ||