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taken as individual test particles and electrons as fluid will provide a more realistic
picture (Motschmann and Kuehrt
2006
). As the cometary outgassing rate increases
when r decreases below 2 AU, both models would give similar results according to
the recent works by M. Rubin and C. Koenders (private communication, 2014).
10.2
Diamagnetic Ionospheric Cavity
All cometary ions have their source from the neutral gas coma via photoionization,
solar wind charge exchange, and electron impact ionization. In the inner region of
the cometary ionosphere, the plasma dynamics is controlled by collisional effect
with the neutral molecules in radial expansion from the central nucleus. It is so much
so that the ions have the same radial velocity as the neutral gas up to a boundary
where they will be decoupled from the gas stream because of the Lorentz force.
What is the size of the ionospheric cavity containing the unmagnetized plasma?
That was the question asked prior to the Giotto mission to comet Halley (Ip and
Axford
1982
).
A simple approximation can be obtained by considering that the collisional
drag force on the cometary ions from the neutral gas is counteracted by the
curvature force of the bent magnetic field lines, namely,
j
B
/
c
D
kmn
i
n
g
v
,
where
k
(
2
10
9
cm
3
s
1
) is the rate coefficient of ion-molecule reaction (e.g.,
H
2
O
C
C
H
2
O
!
H
3
O
C
C
OH), m is the mass of the water molecule, n
i
is the ion
number density,
n
g
is the neutral gas number density, and
v
(
1kms
1
)isthe
expansion speed of the neutral gas. For steady-state and spherically symmetric
condition,
n
g
at cometocentric distance
R
can be expressed in terms of the gas
production rate (
Q
)as
n
g
D
Q
/4
vR
2
. In turn, the ion number density will be
determined by equating the ion production rate via photoionizatio
n to the i
on loss
rate via electron dissociative recombination. As a result, n
i
D
q
n
g
=Ǜ
i
,where
Ǜ (
D
10
7
cm
3
s
1
) is the electron dissociative recombination rate and
i
is the
photoionization rate taken to be
i
D
10
6
r
2
s with the heliocentric distance in AU
to account for the radial variation of the ionizing photon flux.
At the radial position (
R
D
R
max
)where
B
reaches the maximum value (
B
max
), the
force balance equation can be written as
B
max
2
4R
max
D
Km
n
i
n
g
v;
(10.1)
from which we obtain
R
max
1:34
10
17
Q
3=4
=B
max
=
p
r
cm;
(10.2)
with
B
max
in nT and
r
in AU. For comet Halley near the Giotto encounter,
Q
8
10
29
H
2
Os
1
and
B
max
90 nT, we can find
R
max
4,000 km.
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