Auxiliary material
Model field data used for detruding the observation
Table 2. Values of the model field at two points. Subscript 1 represents trajectory
position at y=-10, while subscript 2 represents trajectory at y=+10. The model field can
be assimilated as a straight line in such small scale compared with the scale of Saturn.
Components E7
E8
E9
E10
E11
E12
E13
Bx1
-0.8721
0.1203
-0.8890
0.3713
0.4329
0.1543
0.0818
By1
9.6138
15.7475
8.9057
8.8907
22.7045
6.6263
5.2984
Bz1
-317.87
-312.84
-313.47
-316.34
-320.70
-315.78
-316.28
Bx2
-0.8358
-0.0318
-0.7583
0.2502
0.1459
0.2431
0.3127
By2
10.6131
17.1229
9.7959
9.7588
19.3891
7.3680
5.9450
Bz2
-338.89
-333.62
-334.25
-337.40
-342.38
-337.24
-337.65
Multi-fluid MHD simulation of charged dust at Enceladus
The electron fluid is not tracked by the full continuity equation, rather it is defined by
the massive charges. The electron density is calculated by assuming charge neutrality:
ne   n s q s , where n is the number density. The gravity and electron pressure is
s
neglected. The electron velocity vector is calculated from the charge averaged velocity
between ions and dust:
ue 
 nqu
s
s s
ene
s
J
.
(1)
By neglecting the momentum of electrons, the convection electric field E is replaced
by
E  u e  B .
(2)
Thus the magnetic induction equation becomes:
B
   (u e  Β)  0 ,
t
(3)
which means the magnetic field is fronzen-in with the electron fluid.
In this simulation we neglect the charging process of dust, and assume uniform
mass/charge ratio of mD/qD = 104 amu/e, where e is the electron charge. In our multi-fluid
equations we model the conservation equations of ion fluid (subscript i) and dust fluid
(subscript D) respectively:
 s
   (  s u s )  Qs
t
(4)
(  su s )
   (  s u s u s  ps Ι )  ns qs (u s  u e )  B  Q sus
t
(5)
ps
   (  s u s )  (  1) ps (  u s )  Q ps ,
t
(6)
where , u and p are density, velocity vector, and pressure, respectively. Subscript s
is the index running over both fluids, qs = Zse is the total charge per particle,  = 5/3 is
the adiabatic index, and the source terms Q in each of the equations are written as mass
density source Qs, momentum source vector Qsus, and pressure source Qps, respectively.
Tensor I is a 33 unit tensor. Again, the electric field in equation (5) is replaced by the
term with electron velocity.
We isolate the effect of dust by temporarily neglecting the effect of the solid moon and
pickup ions from the plume neutrals. The dust cloud is defined by an arbitrary source rate
Qs = 1017/((2x)2 + (2y)2 + (z/3)2), which results in a number density contour of 8 cm-3
marked in Figure 3b and d. The upstream plasma has a number density ni = 70 cm-3, uix =
26 km/s and T = 40K. The magnetic field is Bz = 330 nT.
The very different mass/charge ratios in dust and ions have raised new phenomena,
because the dust fluid is demagnetized in the ion fluid. As the dust moves along the
convection field, the ions move in the opposite direction to maintain the original zero
momentum parallel to the convection electric field. However, the electrons follow the
combined motion of these heavy charges, which is different from the motion of the
momentum center. This difference hence raises additional convection of the magnetic
flux parallel to the initial electric field, which appears in increase/decrease of magnetic
field along the electric field.
Figure 3c shows the modeled Bz perturbation. The pile-up and decrease of the field
indicates slowing down of the plasma by picking up of the charged dust. This is also
supported by the bent field lines in the x-z plane in Figure 3a. Figure 3d shows that both
the southern and northern Alfvén wings are pushed to –y, breaking the symmetry across
the y=0 plane in an Io-type Alfven wing system. Consequently, a spacecraft traveling
from –x to +x above the momentum-loading center sees a negative By perturbation, which
is consistent with the 2008 data.
Observations along the 2009-2010 trajectories are not directly comparable with the 2D slices shown in Figure 3, but they are found consistent with the 3-D model result.
These comparisons are not shown here. Instead, we assemble all the important physics in
this interaction region into an improved multi-fluid MHD dusty plasma model as the next
step of our study.
In previous studies we have found that the observed By perturbations can be partly
modeled by adding a uniform flow in the +y direction [Jia et al., 2010c]. Our multi fluid
simulation indicates that charged dust provides observed By perturbations, which is
independent of the effect of the upstream flow. More modeling work is needed to
compare the difference of their effect.