A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
A Brief Introduction to Space Plasma Physics.pdf - Institute of ...
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• The second adiabatic invariant<br />
– The integral <strong>of</strong> the parallel momentum over one<br />
complete bounce between mirrors is constant (as<br />
long as B doesn’t change much in a bounce).<br />
J<br />
= ∫<br />
s<br />
s<br />
1<br />
2<br />
2mv<br />
ds<br />
= const.<br />
– Using conservation <strong>of</strong> energy and the first<br />
adiabatic invariant<br />
J<br />
= ∫<br />
s<br />
s<br />
1<br />
2<br />
B<br />
2<br />
2mv(1<br />
− )<br />
1<br />
ds<br />
B<br />
here B m is the magnetic field at the mirror point.<br />
m<br />
= const.