Simulation of shock size asymmetry caused by charge
exchange with pickup ions
H. Shimazu
Applied Research and Standards Division, Communications Research Laboratory,
Koganei, Tokyo 184-8795 Japan
Abstract. This paper considers the interaction between the solar wind and unmagnetized planets using computer
simulations. We used a three-dimensional hybrid code that treats kinetic ions and massless fluid electrons. The
results showed that the shock shape and magnetic barrier intensity are asymmetrical in the direction of the electric
field. The velocities of pickup ions and electrons differed near locations where charge exchange occurred. This
velocity difference caused an electric current and it generated a strong magnetic barrier on the side of the planet to
which the electric field was pointing. This magnetic barrier acted as an obstacle to the solar wind, and the shock
was inflated on this side. Application of these results to the interaction between the solar wind and the interstellar
medium near the heliopause is also discussed.
INTRODUCTION
electron dynamics in the hybrid code. In this study the
electron impact ionization is not considered. This study
is aimed at understanding the physical processes rather
than fitting simulation results to observations.
A hybrid code was used in a three-dimensional simulation of the interaction between the solar wind and
the dayside portion of an unmagnetized planet [14, 15].
Later, a magnetotail region was included in the simulation box and it was shown that the resultant magnetic
field configuration around Mars was consistent with observations [16].
There is asymmetry in the shock altitude around Venus
in the direction of the — vsw x Bsw convection electric
field (vsw: solar wind velocity observed at the planet; Bsw:
interplanetary magnetic field). Observations obtained by
the Pioneer Venus Orbiter (PVO) showed that the shock
is further away from the planet on the side of the planet
to which the convection electric field is pointing than on
the other side [17, 18]. However simulations using hybrid code showed that the shock is further away from
the planet on the opposite side [16, 19, 20, 21]. It was
shown that this asymmetry is caused by downstream oxygen ions of planetary origin that reduce the downstream
Alfven and fast mode velocities [22]. This is because the
shock cone angle depends on the ratio of the downstream
fast mode velocity to the upstream flow velocity. Unfortunately, the direction of the asymmetry in the simulation did not agree with the observations near Venus.
This discrepancy has been the subject of controversy. In
this study, we found that when charge exchange is included, the direction of simulated shock altitude asym-
Magnetohydrodynamics (MHD) simulations have been
useful to investigators studying the interaction between
the solar wind and planets with little or no magnetization (e. g., Venus) [1, 2, 3, 4, 5, 6]. Near Venus, ion
reactions such as electron impact ionization, photo ionization and charge exchange are of significant interest.
Electron impact ionization is a process in which neutral planetary particles are ionized by the impact of electrons. The electron impact ionization gives the highest
ion production rate of the three processes [7]. Photo ionization is a process in which neutral planetary particles
are ionized by the solar EUV flux. Charge exchange occurs between the solar wind and neutral planetary particles [8]. Many believe that these reactions have similar
effects on macro-scale structures such as a shock because
both reactions generate heavy ions (O+ ions). These oxygen ions are picked up by the solar wind [9, 10] and
then cause mass loading [11, 12]. This mass loading can
change the macro-scale structures, and MHD simulations
have shown that it can increase the shock height [13].
Unfortunately, MHD simulations cannot make allowance for changes in distribution functions caused by
ion reactions. The hybrid code (kinetic ions and massless electron fluid) is one of the most useful simulation methods for studying ion distribution functions. In
this study, the effects of photo ionization and charge
exchange are compared by using simulations of threedimensional global hybrid code. The electron impact ionization is also important, but it is difficult to include
CP598, Solar and Galactic Composition, edited by R. F. Wimmer-Schweingruber
© 2001 American Institute of Physics 0-7354-0042-3/017$ 18.00
329
metry agrees with observations near Venus. The process
in which charge exchange causes shock altitude asymmetry will also be described.
This paper is the summary of my paper [23] ("Effects
of charge exchange and photo ionization on the interaction between the solar wind and unmagnetized planets", /. Geophys. Res.) but application of the results to
the shock shape near the heliopause was added.
MODEL
The simulation code used was the same as that used
by [22], except that the effects of photo ionization and
charge exchange were included. The three-dimensional
Cartesian coordinate system (x, j, and z) was used in the
simulation. There were 64 equally spaced grid cells in
each direction. The average number of particles in each
cell was 16. The solar wind was emulated by using a
super-Alfvenic plasma (velocity vsw = 4.0V^, where VA
is the upstream Alfven velocity) continuously injected
into the simulation system from the x = 0 plane. The
solar wind ions were protons. The bulk velocity of the
solar wind was parallel to the x axis, and the solar wind
protons were removed from the simulation system when
they reached the other boundary.
Planetary oxygen ions, distributed uniformly in a
sphere of radius R = L/8, were placed at the center of
the simulation box (L: box size). R was set to 6.4r/, =
25c/cOp/, where ri = v5W/coa is the Larmor radius of protons, coc/ is the upstream proton cyclotron frequency, and
(Op/ is the upstream proton plasma frequency. Under a
typical upstream condition (vsw = 500 km/s and coc/ =0.5
Hz), R (6.4 x 103 km) corresponds to that of Venus. The
proton inertial length c/(%/ equals VA/O)C/, which is approximately the Larmor radius of shocked solar wind
protons. This fact also means that a pickup oxygen ion
has a Larmor radius of 16 c/<%.
The sphere was also a source of planetary ions. This
source corresponds to an ion generation process in Venusian ionosphere. The supply rate of these ions was assumed to be uniform and constant, and was the same
as that used by [22]. This supply is needed to maintain the gaseous planet and is limited to the sphere. Ions
added outside the planet by photo ionization or charge
exchange will be discussed later. This uniform supply assumption was not realistic, but the resolution was not fine
enough to include ionospheric processes such as plasma
transport.
In this study, the ion flux from the ionosphere across
the ionopause was low, and the ionosphere was not diffused on the upstream side.
330
The initial ambient magnetic field B was given by the
potential field:
TT U
B=
(r>R)
(1)
0
where £0/(47im^o)1/2 = VA = 1.0 x 10~4c, r2 = (jcL/2) 2 + (j-L/2) 2 + (z-L/2) 2 , mt is the proton mass, n$
is number density, and c is the speed of light. Electrical
resistivity was not artificially introduced. In the upper
ionosphere, gravity can be ignored because it is much
weaker than the electromagnetic force exerted by the
solar wind. In this study gravity was ignored because we
only considered the upper part of the ionosphere.
We assumed that the temperature of the solar wind and
that of the planetary plasma were the same and that the
initial temperature of the ions was the same as that of
the electron fluid. The electron temperature was constant
in space and time. It was confirmed that the results did
not depend so much on the electron temperature. We
also assumed that the ratio of the ion thermal pressure
to magnetic pressure of the solar wind (i.e., P/) was 1.0.
Thus p (= p/ + pg; $e is p for electrons) was 2.0. The
sonic Mach number of the solar wind flow is 2.8. Under
the initial conditions, the dynamic pressure of the solar
wind was in balance with the thermal pressure of the
planetary plasma at the subsolar point.
The ion production rate for photo ionization is given
by
(2)
where a is the ionization cross section of atomic oxygen, <|) is the ionization photon flux outside the atmosphere, a<|) = 13.5 x 10~7/s at the heliocentric distance
of Venus for solar maximum [7], and n\ is the number density of the ionizable constituent. However, in this
photo-ionization simulation, the ionization rate was assumed to be constant. Oxygen ions were added to the
dayside portion of the 1.0 - 1.3R region at the same
total rate as the planetary ions described earlier. The
total production rate corresponds to 2.85 x 1024/s and
qphoto = 2.17 x 10"3 s"1 cm"3. Thus n\ is 1.61 x 104
cm~3. The total ion production rate from photo ionization for Venus is 3.4 x 1024/s [7]. This value is close to
our value. The temperature of the newly added ions was
the same as that of the planetary oxygen ions.
In the charge-exchange simulations, the reaction
(3)
was assumed. Part of the solar wind protons that reached
a distance of 1.37? from the center of the planet disappeared, and oxygen ions were added at this location. The
temperature of the newly added ions was the same as that
(a) photoionization: Vex/V A
of the planetary oxygen ions. The charge exchange ionization rate is given by
qCE = npvpGcn\,
200
(4)
where np is the solar wind (or magnetosheath) proton
density, vp is the solar wind (or magnetosheath) proton
bulk velocity, and oc (8 x 10~16 cm2) is the cross section
for charge exchange with atomic oxygen. In this study,
however, the charge-exchange rate was assumed to be
constant. This rate corresponds to 2.36 x 1023/s and qcE
is 1.80 x 10~4 s"1 cm"3. When npvp is assumed to be
108 s"1 cm"2, n\ becomes the order of 103 cm"3. The
ion production rate from charge exchange for Venus is
1 x 1024/s [7]. This is larger than the value we used.
Because the charge exchange effect was more than that of
photo ionization, as shown later, we used a lower charge
exchange rate.
In the photo ionization model, heavy ions are added
to the flow, whereas in the charge exchange model, they
replace the solar wind protons. The momentum required
for heavy ions must be supplied immediately when ions
appear in the charge exchange model. Therefore the
charge exchange process is more abrupt than the photo
ionization process.
We used 1.3R for the ion reaction region, which is
based on the estimates in [7]. Their estimates showed
that both rates decrease at near exponential rates as the
distance from the planet increases. They are the highest
by far in the region of 1.0 - 1.3R.
0
50
100
x/(c/wpi;
150
200
vsw
(b) charge exchange: Vex/VA
200
RESULTS
Figures la and Ib show the x components of the electron velocity for the y = L/2 plane when photo ionization and charge exchange were included. They are cross
sections of the y = L/2 plane, cutting through the center
of the planet. The simulation results shown here are for
t = 37.5/coc/, at which the solution is nearly stabilized.
The period 37.5/coa corresponds to almost one gyro period of oxygen ions near the ionosheath/magnetosheath.
Because the mass of an oxygen ion is 16 times that
of a proton, and because the magnetic field is nearly
three times that of the solar wind, the gyro frequency
of an oxygen ion is (3/16)coc/. Therefore the period is
2jc/(3(0C|/16) = 34/Q)C|. In this period, a pickup oxygen ion, which has an average velocity of v5W, moves
I36c/(£>pi (0.66L). Thus we can see the effects of the
mass loading at the time 37.5/coc/.
The electron velocity ve in the hybrid code is given by
+ en0+v0+ - j)/e(nH+
(5)
where j is electric current, e is the unit charge, VH+
and VQ+ are bulk velocities of protons and oxygen ions,
FIGURE 1. The x component of electron velocity for y =
L/2 plane at ooc/f = 37.5 when (a) photo ionization was included and (b) charge exchange was included. Circles with
the radii 1.07? and 1.3R are shown. The x axis is directed to
upstream solar wind velocity vsw, y axis to upstream magnetic
field Bsw, and z axis to vsw x Bsw.
respectively, and nH+ and no+ are densities of protons
and oxygen ions, respectively.
As shown, the velocity decreased sharply upstream
of the planet, and a bow shock was generated. Downstream of the planet, the shocked solar wind flow near
jc = 150c/G)pi and z = 140c/(0p/ (upper side) is accelerated by the Lorentz force to a speed greater than that
upstream. On the other side (lower side), the flow decelerated because of the mass loading of the planetary oxygen ions escaping from the planet. A magnetotail formed
downstream of the planet, and the tail region was filled
mainly with planetary ions. These are consistent with
those of the hybrid simulation that had no photo ionization or charge exchange [22].
331
The shock is located at a distance of 1.93R in Figure
la and 2.15R in Figure Ib at the subsolar point from the
center of the planet. The position of the shock was determined as the distance from the center of the planet
to the nose point where the velocity suddenly changes.
When neither photo ionization nor charge exchange were
included, the shock was located at a distance of 1.33R
from the center (the other conditions were the same.)
[22]. Thus, when photo ionization or charge exchange is
included, the shock is inflated. This is because the additional oxygen ions play the role of a larger obstacle. The
Venera 9 and 10, and the PVO observations showed that
the distance to the nose of the bow shock of Venus is 1.1
- 1.6R [24, 25, 26, 27]. Our results are larger values than
those observed. The distance, however, depends on the
Mach number of the solar wind flow. Because we used a
smaller Mach number than that in the observations, the
distance is larger. This smaller Alfven Mach number is
used for numerical convenience. Although the height of
the shock changed with the Mach number, it was confirmed that there were few differences in the physical
structures when the Alfven Mach numbers are 4 or 8. The
different total ionization rates at Venus (that depends on
the solar activity) and at this simulation may also cause
the difference.
Figures 2a and 2b show the magnetic field intensity
for the x = L/2 plane when photo ionization and charge
exchange are included. These figures show asymmetry
in the magnetic barrier in the direction of the convection
electric field (—z direction). The intensity of the magnetic barrier is larger on the side of the planet to which
the electric field is pointing than on the other side. This
agrees with the previous observations [28] and simulations [16, 22]. When these figures are compared, we find
that the intensity of the magnetic barrier is larger when
charge exchange is included (Figure 2b).
These figures show the penetration of the magnetic
field into the obstacle especially under photo ionization. The penetration of the magnetic flux into the planet
may result in small magnetic field compression in the
ionosheath/magnetosheath. This compression is prominent when compared with that presented in Figure 2 of
[5]. The penetration may change physical quantities near
the planet less than those in reality. Thus a penetrable
obstacle may decrease the asymmetries.
Figures 2a and 2b clearly show shock altitude asymmetry in the direction of the convection electric field
(—z direction). Figure 2a shows that the shock height is
7.98% smaller on the side of the planet to which the electric field is pointing than on the other side when photo
ionization is included. The shock height was determined
as the distance from the center of the planet to the point
where the magnetic field intensity suddenly changes. The
direction of the asymmetry agrees with that of previous
simulations in which neither photo ionization nor charge
332
(a) photoionization: |B|/BQ
200 -
50
100
150
200
(b) charge exchange: |B|/BQ
200 -
FIGURE 2. Magnetic field intensity for x = L/2 plane at
oodr = 37.5 when (a) photo ionization was included and (b)
charge exchange was included.
exchange were included [16]. This asymmetry in shock
altitude was explained by lower downstream Alfven and
fast mode velocities due to heavy ions on the side of the
planet to which the electric field was pointing than on the
other side [22]. The shock cone angle depends on the ratio of the downstream fast-mode velocity to the upstream
flow velocity. However the direction of the asymmetry
does not agree with observations near Venus [17,18].
When charge exchange is included, the direction of
the shock altitude asymmetry reverses (Figure 2b) and
agrees with the observations. The shock height is 7.79%
larger on the side of the planet to which the electric field
is pointing than on the other side. These figures also show
that when the charge exchange is included, the shock
is further away from the planet than when the photo
ionization is included. This is true in all directions.
(a) photoionization: j x /en 0 V
proximately 30v/coC|, where v is the local flow speed. The
separation between the peaks in Figure 3b is consistent
with this value.
The cycloidal motion of pickup ions can generate both
jx and jz currents. It was confirmed that the distributions
of the jx and jz currents are coincident. Thus it is reasonable to consider that the currents responsible for the magnetic barrier are the jz current on the side of the planet to
which the electric field was pointing. The region where
jx is large in Figure 3b (which also corresponds to the region where jz is large.) agrees with the magnetic barrier
region. This magnetic barrier acted as an obstacle to the
solar wind, and the shock was inflated on this side when
the charge exchange was included.
We have examined the charge exchange caused by
oxygen atoms. We also performed simulations that included the following charge exchange reaction:
200
(b) charge exchange: J
(6)
The simulation results showed that the direction of the
shock altitude asymmetry was the same as that when
oxygen was used. The charge exchange affected the
shock altitude asymmetry in the same manner.
APPLICATION TO THE HELIOSPHERE
Shock shape asymmetry near the heliopause is considered in this section. The shock shape is important when
we consider behavior of pickup ions near the heliopause.
Properties near Venus and those near the heliopause
are compared. According to the table of properties near
the heliopause [29], the magnetic field intensity near the
heliopause is less than that near Venus by the order of 1,
and the Larmor radius near the heliopause is larger than
that near Venus. However the size of the heliosphere is
much larger than that of the Venusian magnetosheath,
and the ratio rL/Lsystem, where Lsystem is the size of the
system, is probably much smaller near the heliopause
than that near Venus. Thus the finite Larmor radius effect
would be less near the heliopause than that near Venus.
No significant asymmetries associated with the finite
Larmor radius effect would be found at the heliopause.
Since charge exchange changes the macro-scale electric current and also momentum near the shock as shown
earlier, charge exchange may affect the macro-scale
structure even when the ratio ri/Lsystem is small. However charge exchange ionization rate near the heliopause
is lower than that near Venus by the order of 8, because
density near the heliopause is much less than that near
Venus (see Eq. (4)) [29]. When we consider the lower
charge exchange rate and smaller ratio of ri/Lsystem, no
significant asymmetries of the bow shock shape would
be expected near the heliopause.
FIGURE 3. The x component of the electric currents for
y = L/2 plane at ooaf = 37.5 when (a) photo ionization was
included and (b) charge exchange was included.
To investigate the cause of this difference in shock altitude, we consider the x component of the electric current
jx. Figures 3a and 3b show it. When we compare both
figures, we find that the magnitude of jx is larger when
the charge exchange is included (Figure 3b). The current
jx was generated by the difference in the velocities between the ions and electrons when charge exchange occurred. One would see first a negative then a positive jx
current in the cycloidal motion of newly picked up ions
on the lower side of Figure 3b. The newly picked up ions
move at twice the solar wind speed at the maximum of
their cycloidal motion and are at rest at the minimum.
It is worth noting that the pickup ion Larmor radius is
(l6/3)c/(Qpi as shown earlier, and the ion travels 2n times
the Larmor radius in one gyro-period. Thus the peaks of
negative and positive current should be separated by ap-
333
CONCLUSIONS
REFERENCES
We compared the effects of photo ionization and charge
exchange by using three-dimensional hybrid code simulations of the interaction between the solar wind and
Venus.
When either photo ionization or charge exchange were
included, the shock was inflated because of the presence
of additional oxygen ions. The shock shape asymmetry
in the direction of the convection electric field when the
photo ionization was included was opposite to actual
observations. However, when the charge exchange was
included, the direction of the shock shape asymmetry
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Future work will include the electron impact ionization,
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We applied the results to the shock near the heliopause. The shock shape is important when we consider
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the heliopause than that near Venus. Moreover since the
charge exchange ionization rate near the heliopause is
much lower than that near Venus by the order of 8, charge
exchange may not affect asymmetry of the bow shock
shape near the heliopause.
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ACKNOWLEDGMENTS
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The author thanks Dr. Shinobu Machida (Kyoto University), Dr. Motohiko Tanaka (National Institute for Fusion Science), Dr. Takashi Tanaka (Communications Research Laboratory), and Dr. Katsuhide Marubashi (Communications Research Laboratory) for their stimulating and insightful comments and suggestions during the
course of this work. The author also appreciates the referee's valuable comments. Parts of this paper have appeared in [23] and were modified by permission of the
American Geophysical Union.
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