Geoscience Reference
In-Depth Information
Time: 100
.
0
μ
s
Displacement
⊥
to
B
0.1
15
0.05
10
5
0
0
−0.05
−5
−0.1
−0.1
0.1
0
0
0.1
−0.1
−0.1 −0.05
0
0.05
0.1
y
-axis [m]
x
-axis [m]
x
-axis [m]
Displacement
to
B
15
10
5
0
−5
0
50
100
150
200
250
300
350
400
Time [
μ
s]
10
12
m
−
3
,
=
Fig. 4. Sample trajectory of an electron moving in an O+ plasma with density
N
e
z
25000 nT. Top left panel
depicts the trajectory in 3D space; projection on the
x
-
y
plane (the plane perpendicular to
B
)
is shown on the right; displacements parallel to
B
are depicted in the bottom plot (from Milla
& Kudeki, 2011).
=
T
i
=
1000 K, and an ambient magnetic field
B
=
temperatures
T
e
coefficients
D
needed in (43) take the forms derived by Rosenbluth et al. (1957)
which, for Maxwellian plasmas, have the Spitzer forms given in Milla & Kudeki (2011).
(
v
)
and
D
⊥
(
v
)
The velocity update equation (43) just described, along with its position counterpart
r
(
t
+
Δ
t
)=
r
(
t
)+
v
(
t
)
Δ
t
,
(44)
constitute our model equations for examining the effects of Coulomb collisions on incoherent
scatter response from magnetized plasmas. These equations are used to simulate particle
trajectories such as one shown in Figure 4 from which particle displacement statistics needed
in ISR spectral models are estimated as explained in Sections 7 and 8.
7. Coulomb collision effects on ion and electron trajectories
7.1 Statistics of ion displacements
First we use the update equations (43) and (44) to simulate sample trajectories
of an
ion, e.g., an oxygen ion O
+
, moving in an ionospheric plasma with suppressed collective
interactions but experiencing Coulomb collisions. Using the trajectory data, we can build up
the probability distributions of the displacements
r
(
t
)
r
in directions perpendicular and parallel
to the magnetic field for different time delays. Analyzing both distributions (parallel and
perpendicular), we notice that their shapes are in essence Gaussian for time delays smaller
than the inverse of the corresponding collision frequency.
Δ
In Figure 5, we show examples
