Transcript Models

Non-magnetic Planets
Yingjuan Ma, Andrew Nagy, Gabor Toth,
Igor Sololov, KC Hansen, Darren
DeZeeuw, Dalal Najib, Chuanfei Dong,
Steve Bougher
SWMF User Meeting
Oct. 14, 2014
Introduction
• Both Venus and Mars do not have
global internal magnetic field but
with substantial atmosphere. As a
result, solar wind plasma flow
interact more directly with the
atmosphere/ionosphere system as
compared with Earth.
• The upstream plasma flow interact
not only through electric-magnetic
forces with the ionosphere, but also
through collisions with neutral
atmosphere.
Interaction with Ionosphere
Ionosphere of Venus and Mars
From Nagy et al., 1980
From Chen et al., 1978
Interaction with Atmosphere
-Collisions are important
• Elastic collisions: momentum and energy loss of the plasma
• Inelastic collisions
– Photoionization: A + h  A+ + e
Increase the plasma number density
Decrease the average flow speed and temperature
– Charge exchange: A + B+  A+ + B
Usually increase the plasma mass density
Decease the total momentum and energy of the plasma
– Recombination:
A+ + e  A
Decease the number density, momentum and energy of the plasma
Multi-Species Single-fluid MHD Equations
Continuity Equations:
Density change caused by chemical reactions
 i
    i u   Si  Li
t
Si  mi ni ( ph,i   imp,i 
Li  mi ni ( R ,i ne 
Momentum Equation:
k
s ions
si
k n )
it t
t  neutrals
(

ns )
Momentum loss due to
ion-neutral elastic collisions
 i )
Momentum loss due to
chemical reactions
i ions


( u)
B2
1
   uu  pI 
I  BB G   i  itu   Liu
t
20
0 

i ions t neutrals
i ions

Multi-Species Single-fluid MHD Equations (2)
Magnetic Induction Equation:
B
   (uB  Bu)  0
t
1 2
1
1 2
Energy Equation (   u 
p
B )
2
 1
20
 


1 2 1
    u   p 
B   ( B  u)B  
t
2  0  0
 

Energy change
due to chemical
reactions

u  G 
 
i ions t  neutrals
 i it
mi  mt
Energy change
due to
ion-neutral
elastic collisions
[3k (Tn  Ti )  mi u 2 ]
 SiTn  LiTi  i

1
k
2

  Li u 
  R ,i neTe 

2 i ions
  1 i ions 
mi
mi

Numerical Method (BATSRUS)
1.
2nd order finite-volume approach
2.
Flux functions based on approximate Riemann solver
from Linde et al. [2002]
3.
2-stage explicit update scheme with point-implicit
scheme for source terms to ensure stabilities.
Simulation Details
 Four ion species: H+, O2+, O+, CO2+; two
background neutrals: CO2, O; and eight
chemical reactions.
 Spherical grids:
 Computational domain: –24RV ≤ X ≤ 8
RV, –16RV ≤ Y, Z ≤ 16 RV ;
 Radial resolution varies from 5 km in
the ionosphere to 3000 km further
away;
 Angular resolution is 2.50 ;
 5 million cells, ~5,000 CPU hours.
 Inner Boundary Conditions
 Inner boundary at 100 km;
 [O2+] , [O+] and [CO2+] are in
photochemical equilibrium (SZA and
optical depth considered);
 Absorbing boundary condition for U
and B.
Illustration of the grid system used in the
calculation
Examples
Ma et al., 2013
Simulation Results
of Venus
1D subsolar plots of densities, magnetic field and velocity.
B Cleaning
|B|
in the XY plane
with hyperbolic B cleaning
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1D subsolar plots of densities, magnetic field and velocity for cases
(without and with hyperbolic B cleaning.
Simulation Results of Mars (Ma et al., 2014)
B=B0, where B0 is the crustal magnetic field (60-order spherical
harmonic model of Arkani-Hamed [2001])
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Effects Diurnal Rotation of the Crustal Field
B and Field lines
Crustal Field (B0)
As the planet rotates, the size and shape of the obstacle to the solar wind varies, as a
results, the induced magnetic field also varies with time.
Comparison with MGS
observations on May 16, 2005
*Overall good agreement
between model results and
MGS observations.
*The agreement is the best for
B magnitude (corr. Coeff =0.88,
RMSE = 10.9 nT).
*The corr. Coeff for components
of magnetic field is not as good
mostly due to IMF direction
change during the day.
IMF condition used in the MHD model
BX =1.6 nT, BY=-2.5 nT
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Zoom in view of the comparison with
MGS observations on May 16, 2005,
over-plotted with local time.
*Good agreement near strong
crustal field region indicates that the
crustal field model included in the
MHD model is quite accurate.
*Around dayside weak crustal field
region, the induced field is needed
to fit with the data.
*In some region, it is hard to
distinguish what is the cause for the
discrepancy (IMF, crustal source, or
model limitation).
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Multi-Fluid MHD Model (Najib et al., 2011)
Continuity equation
Momentum equation
Pressure equation
Causes flow separation in
convection electric field direction
pe  s ps
Magnetic Induction equation
where the charge-averaged ion-velocity, and ue are defined as:
ue  u  
J
ne
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Venus vs Mars (Multi-fluid model)
Venus
•The multi-fluid effect
is much stronger at
Mars than at Venus.
E
•Proton gyroradius
0.07RV at Venus,
0.4 RM at Mars.
•The crustal field is
not included for Mars
for comparison.
Mars
E
Summary
• BATSRUS is the best existing tool in simulating plasma
interaction with non-magnetic planets.
Future work
•
•
•
•
Improve efficiency for multi-fluid MHD code;
Couple between SPICE and BATSRUS;
Couple between BATSRUS with MGITM;
Extend the simulation domain inside the planet to take into
account effects of subsurface conducting layer.
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Thank You
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