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According to the reference below, the plasma in a planetary radiation belt increases its temperature anisotropy through radial diffusion; temperature perpendicular to the background magnetic field increases faster than that parallel to the magnetic field.

The question is why perpendicular energization is faster than parallel one?

As far as I know from textbooks, the betatron acceleration, due to the conservation of the first adiabatic invariant, increases the particle's kinetic energy perpendicular to the background magnetic field. On the other hand, the Fermi acceleration, due to the conservation of the second adiabatic invariant, increases the parallel kinetic energy.

If the competition of the two mechanisms is important to the anisotropy, why is the betatron stronger than the Fermi? Any reference mentioning about this will be helpful.

REFERENCES

http://www.nature.com/nphys/journal/v4/n4/full/nphys897.html

user1048419
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  • See my answer here. – honeste_vivere May 04 '15 at 11:56
  • @honeste_vivere I am afraid, but I don't see anything related to my question in your previous answer. You were mentioning about wave particle interaction in most of the answer. I know that wave particle interaction is important but that is not my interest. Besides, one of the reference I gave says "this anisotropy can excite very low frequency whistler mode chorus waves which resonate with electrons". My question is, how is the anisotropy generated? – user1048419 May 04 '15 at 12:18
  • I linked that answer because the particles in the radiation belts do not get their energies by simply conserving the first or second adiabatic invariants. The conservation of these invariants is what causes the particles to stay trapped for long periods of time in the radiation belts, but it is not generally considered the source for their energization. – honeste_vivere May 04 '15 at 12:37
  • Thank you, @honeste_vivere OK, I understand that adiabatic compression less contributes to the energization. But still I have a question about the origin of the anisotropy. There are several observation of electron and ion anisotropy. So I'll modify the question. – user1048419 May 04 '15 at 12:49
  • Unless the mirror points move (i.e., in the original idea for Fermi acceleration), the conservation of the 2nd adiabatic invariant should not change the total kinetic energy of the particle. Conservation of the 1st adiabatic invariant conserves kinetic energy as well (assuming no temporally- or spatially-varying processes), which is why I said that conserving these two invariants would not, alone, energize particles. – honeste_vivere May 04 '15 at 15:42
  • The idea of betatron and Fermi is in the context of radial diffusion, isn't it? So particle is transported to strong magnetic field and short bounce length region. Then it sounds plausible that conservation of 1st and 2nd adiabatic invariant gives perpendicular and parallel temperature. I think even if another effect, such as wave particle interaction, is stronger, there exists adiabatic compression somewhat. – user1048419 May 04 '15 at 15:52
  • Ah, yes, but there the energy gain comes from the 3rd adiabatic invariant. When the background field changes due to external forces (e.g., shock hits the magnetosphere), if this occurs slow enough that the particles can conserve the 3rd invariant then they will drift inwards. After the field recovers and the particles stay at lower altitudes, they can gain energy, yes. However, this is not the leading theory and has been shown to be too slow on several occasions. – honeste_vivere May 05 '15 at 11:46

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