Geoscience Reference
In-Depth Information
i.e. the average distance between particles
is small in comparison with the
Debye radius. This condition can also be written as
Nr
3
D
r
1, i.e. a Debye
sphere should include many particles.
For the distribution function
f
α
of species
α
of the plasma particles in a
collisionless case, we have the Liouville theorem
df
α
dt
=
∂f
α
∂t
∂
r
∂t
+
∂
V
∂t
+
∇
r
f
α
·
∇
V
f
α
·
=0
.
(1.6)
Here d
/
d t is differentiating along the particle trajectory in the phase space
determined by the dynamic equations. Space and velocity gradients, respec-
tively,
∇
r
f
α
and
∇
V
f
α
, of the distribution function are
∂f
α
∂x
x
+
∂f
α
∂y
y
+
∂f
α
∇
r
f
α
=
∂z
z
,
∂f
α
∂V
x
x
+
∂f
α
∂V
y
y
+
∂f
α
∇
v
f
α
=
∂V
z
z
.
Let (
∂f
α
/∂ t
)
coll
be the rate of change of the distribution function caused
by collisions. (
∂f
α
/∂ t
)
coll
d
r
d
V
is the time variation of the number of par-
ticles in a time unit in the phase volume d
r
d
V
. For a plasma in the self-
consistently electromagnetic field the kinetic equations are
m
α
∇
V
f
α
=
∂f
α
∂f
α
∂t
∇
r
f
α
+
F
(
α
)
+
V
,
(1.7)
∂t
coll
where
F
(
α
)
(
r
,
V
,t
) is a force acting on the particles
α
. For charged particles,
F
(
α
)
is the Lorentz force
F
(
α
)
=
q
α
E
+
1
B
]
,
c
[
V
×
(1.8)
where
q
e
=
e
for electrons and
q
α
=
Z
α
e
for ions;
Z
α
e
is the charge of the
multiple charged ions.
Interaction between colliding neutral molecules is strongly localized be-
cause the interaction is ecient only for an impact parameter of the order of
atomic radius. Between neutral-neutral collisions, the motion of a neutral is
determined only by external fields. Contrary, charged particles interact simul-
taneously and hence collectively with many other nearby charged particles
because of long range Coulomb forces. They are shielded at distances of the
order of the Debye radius
r
D
that is, according to (1.5), larger than the spac-
ing
r
between particles. Thus, the interaction of two charged particles is a
collective effect from many particles at such distances. These forces should be
excluded from the collision integral in the right-hand side of (1.7).
Charged particles interact collectively in plasmas through their electro-
magnetic fields. To reveal collective interactions, let us present the microscopic
electric (
E
µ
) and magnetic (
B
µ
) fields acting at a charged particle as sums of
−
Search WWH ::
Custom Search