where X is the free path length. The numerical coefficient a in this case is equal to 1/2; a more systematic treatment can show that its value is somewhat different. An acceleration of charged particles, therefore, occurs in a shear flow of a collisionless plasma, and the rate of energy increase is proportional to the square of the curl of the hydrodynamic velocity of a plasma (in the analyzed case (rot u)2 ~ (du/dy)2).
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