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Heat pinch: Difference between revisions
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→Fick versus Fokker Planck
(Created page with 'The concept of heat pinch is related to the convective term proportional to ''V'' in the (electron) heat transport equation: :<math>q_e = -n_e\chi \nabla T_e + n_e V T_e</math> …') |
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In inhomogenous systems (such as fusion plasmas), the ''Fokker-Planck'' formulation seems more appropriate. | In inhomogenous systems (such as fusion plasmas), the ''Fokker-Planck'' formulation seems more appropriate. | ||
<ref>[[doi:10.1088/0741-3335/47/12B/S56|B.Ph. van Milligen, B.A. Carreras and R. Sá́nchez, ''The foundations of diffusion revisited'', Plasma Phys. Control. Fusion '''47''' (2005) B743–B754]]</ref> | <ref>[[doi:10.1088/0741-3335/47/12B/S56|B.Ph. van Milligen, B.A. Carreras and R. Sá́nchez, ''The foundations of diffusion revisited'', Plasma Phys. Control. Fusion '''47''' (2005) B743–B754]]</ref> | ||
Within the Fokker-Planck formulation, the radial gradient of the heat conductivity produces a 'natural' heat pinch ''V = - | Within the Fokker-Planck formulation, the radial gradient of the heat conductivity produces a 'natural' heat pinch. | ||
By way of simplified example, one may write the Fokker-Planck heat transport equation | |||
:<math>q_e = - \nabla(n_e \chi T_e) + n_eUT_e</math> | |||
Setting ''U = 0'' and assuming ''∇ n<sub>e</sub> = 0'', comparison with the above 'Fickian' heat transport equation shows that | |||
:<math>V = -\nabla \chi</math> | |||
I.e., the gradient of the heat conductivity produces a 'natural' pinch. | |||
== Mesoscopic and microscopic mechanisms == | == Mesoscopic and microscopic mechanisms == | ||