10.02.2014 Views

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 ...

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

• 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.

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!