1. 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

2. 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. 2

3. Interaction with Ionosphere

4. Ionosphere of Venus and Mars
From Chen et al., 1978
From Nagy et al., 1980

5. 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

6. Multi-Species Single-fluid MHD Equations
Continuity Equations:
Momentum Equation: ( )
Density change caused by chemical reactions
Momentum loss due to
ion-neutral elastic collisions
Momentum loss due to
chemical reactions 6

7. Multi-Species Single-fluid MHD Equations (2)
Magnetic Induction Equation:
Energy Equation ( )
Energy change due to
ion-neutral elastic collisions
Energy change due to chemical reactions 7

8. Numerical Method (BATSRUS)
2nd order finite-volume approach
Flux functions based on approximate Riemann solver from Linde et al. [2002]
2-stage explicit update scheme with point-implicit scheme for source terms to ensure stabilities.

9. 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 9

10. Examples
Simulation Results of Venus
Ma et al., 2013

11. 1D subsolar plots of densities, magnetic field and velocity.

12. B Cleaning
|B| in the XY plane
with hyperbolic B cleaning 12

13. 1D subsolar plots of densities, magnetic field and velocity for cases (without and with hyperbolic B cleaning.

14. 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]) 14 14 14

15. 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.

16. 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 16 16 16

17. 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). 17 17 17

18. Multi-Fluid MHD Model (Najib et al., 2011)
Continuity equation
Momentum equation
Pressure equation
Magnetic Induction equation
where the charge-averaged ion-velocity, and ue are defined as:
Causes flow separation in
convection electric field direction 18 18 18 18

19. Venus vs Mars (Multi-fluid model)
The multi-fluid effect is much stronger at Mars than at Venus.
Proton gyroradius
0.07RV at Venus,
0.4 RM at Mars.
The crustal field is not included for Mars for comparison. E
Mars E

20. 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. 20 20 20

21. Thank You 21 21 21