By Ho-ming Mok
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Additional resources for Cosmic Rays: Climate, Weather and Applications
The narrow current sheet occurred in the magnetopause of the Earth is a typical example. 210) and Rm >> 1. This equation implies the physical phenomenon that the magnetic field lines in a highly conducting fluid move along with the parcel of the conducting fluid connecting with them as if they are frozen in it. In other words, any motion of the conducting fluid will carry with the magnetic field passing through them. To state it as a theorem, such "frozen-in magnetic flux" is the effect that the magnetic flux through a closed loop moving with the fluid of infinite conductivity remains constant over time.
In the statistical approach, the collective behaviour of particles is described by the distribution function. The single-particle distribution or just simply called the distribution function, fs(x,v,t) of a specific particle species s can be defined as the density of particles in an infinitestimal phase space volume elementΔV = ΔxΔyΔzΔvx Δvy Δvz = d3xd3v located at the phase space point (x,v,t). 90) 24 Ho-Ming Mok a = F/ms is the acceleration of the particle with mass ms. The associated phase space volume element of the particles will be changed from d3xd3v to d3x'd3v'.
209) The relationship shows that the characteristic decay time scale depends on the size of the concerned conducting body and its conductivity. For instance, d for a copper conductor with size of about 1 metre is less than 10 seconds while that of the Sun is about 1010 years. As indicated in the definition of the magnetic Reynolds number, if both values of u and L are small, the magnetic diffusion dominates the convection and results in smallness of Rm. The narrow current sheet occurred in the magnetopause of the Earth is a typical example.
Cosmic Rays: Climate, Weather and Applications by Ho-ming Mok