A Brief Introduction to Space Plasma Physics.pdf - Institute of ...

– Other frequently used distribution functions.
• The bi-Maxwellian distribution
⎡ 1
r r
ms
v − u
'
2
f ( ) = ⎢
s
, v As
exp −
⎢ kT
⎣
s
– where
s s s ⎜ s s ⎟
⎝ ⎠
– It is useful when there is a difference between the distributions
perpendicular and parallel to the magnetic field
• The kappa distribution
f
s
r
'
A
r
( r,
v)
=
A
Κ characterizes the departure from Maxwellian form.
– E Ts is an energy.
κs
⎡
⎢1
+
⎣
2
( ) ⎤ r r
⎡ 1
2
( ) ⎤
⎥⎦
1
2
m
s
⎥ exp⎢−
⎥
⎦ ⎣
( v − u )
sκ Ts
s
− u
– At high energies E>>κE Ts it falls off more slowly than a Maxwellian
(similar to a power law)
κ → ∞
⎛
⎜T
3
2
= A T
⊥
T
1
2
⎞
⎟
– For it becomes a Maxwellian with temperature kT=E Ts
r
E
r
2
2
⎤
⎥
⎦
m
s
v
−κ
−1
⊥
kT
⊥s
⊥s