By Ho-ming Mok
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Extra resources for Cosmic Rays: Climate, Weather and Applications
86) The equation indicates that the magnetic moment remains constant in a magnetic field that has small spatial variation compared with its magnitude. In this case, the magnetic moment is known as the first adiabatic invariant. 87) Plasma Physics 23 where rL = mv٣/qB. Since the magnetic moment is an invariant, the magnetic flux enclosed by the particle orbit is also unchanged throughout the motion. The invariant property of magnetic moment and the constancy of particle kinetic energy produce the so called magnetic mirror effect.
Pairs of oppositely directed field lines will be broken at the neutral line and reconncted with each other and such process let the field lines of the solar wind and the Earth combine together. The magnetic field frozen in the high speed moving solar wind then behaves as being dragged behind by the Earth's magnetic field when moving across the Earth's magnetosphere with the field lines stretched and combined to the Earth through the magnetic reconnection. The transport of the charged particles across the neutral line also allows the flowing of solar wind plasma in the magnetospheric cavity.
111) where b stands for the impact parameter of collision and g = | v1 - v| is the relative velocity between the two colliding particles. The term b(db)(dψ) is the base area of the element while gΔt is the height. 112) If the particle collision process is reversible, the particles scattered into the phase space volume is just the inverse of the particles scattered out from the same phase space volume. 115) The primed variables refer to the inverse of the unprimed variables. 121) The Boltzmann equation becomes an integro-differential equation involving both the integrals and partial derivatives of the distribution function.