By Ho-ming Mok
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Additional info for Cosmic Rays: Climate, Weather and Applications
However, the pressure of a conducting inviscid fluid in the presence of strong magnetic field is anisotropic such that the scalar field assumption is no longer valid. Suppose the cyclotron frequency frequency is much greater than the collision frequency, the charged plasma particles gyrates around the magnetic field lines many times before collision occurs. The particle kinetic energy associated in the direction parallel to the magnetic field is different from that perpendicular to it. Consequently, the pressure in the plane normal to the magnetic field is also not the same as that along the field.
The relative significance of the reconnection and diffusion processes can be described by the ratio of their corresponding time scales known as the Lundquist number S. 241) Apart from replacing u by VA, the Lundquist number has the same mathematical form as the magnetic Reynolds number. The condition for magnetic reconnection requires the characteristic time scale of the resistive plasma lies between A and d as A << << d such that the magnetic flux annihilation by reconnection has a faster rate than diffusion in plasma.
More elaborated understanding on the nature of collision term requires discussions on the correlation between the interacting particles. 106) Since the distribution function f k (x, v, t) describes the probability of a particle of species k staying at a point in the phase space at a moment of time t, if the k type particle does not interact with the l type, their distributions will not depend on each other. 108) That means there is no particle distribution correlation. 109) The number of particles leaving the infinitestimal phase space volume at is simply the total number of collisions of the particles travelling at velocity with all other particles in the time intervalΔt.
Cosmic Rays: Climate, Weather and Applications by Ho-ming Mok
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