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

– Momentum equation
r
∂us
r r r
r r r
ρ
s
( + us
⋅∇us
) + msus
( Ss
− Ls
) = −∇ps
+ ρqsE
+ J
s
× B + ρsF
∂t
ρ
= q
n
r
J =
where qs s s is the charge density, s s s s is the
current density, and the last term is the density of nonelectromagnetic
forces
∂ r
– The operator ( + u s
⋅∇)
is called the convective derivative
∂t
and gives the total time derivative resulting from intrinsic
time changes and spatial motion.
– If the fluid is not moving (u s =0) the left side gives the net
change in the momentum density of the fluid element.
– The right side is the density of forces
• If there is a pressure gradient then the fluid moves toward lower
pressure.
• The second and third terms are the electric and magnetic
forces.
q
n
r
u
g
m
s