A Global Hybrid Simulation Study of the Solar Wind

Interaction with the Moon

David Schriver

ESS 265 – June 2, 2005

Solar Wind – Plasma from the Sun

Goal and Approach

• Examine global kinetic aspects of the solar wind interaction with the Moon– Moon has no internal dipole and no ionosphere– wake-tail forms on the nightside

• Use hybrid simulations of solar wind flow over a non-conducting, unmagnetized object– include ion kinetic effects – invoke realistic spatial scales and parameters

Global Simulation Techniques

• Magnetohydrodynamic (MHD)– 3D fluid modeling on global scales – does not include kinetic effects

• Particle in cell (PIC)– includes kinetics for both electrons and ions– requires unrealistic parameters (i.e., mass ratio)

• Hybrid– includes ion kinetics (fluid electrons)– use realistic parameters for some global systems– does not include electron kinetics

Hybrid Code Methodology• Ion equations (full particles):

• Electron equations (massless fluid):

let me = 0 and ne = ni

• Field equations:

• Modified Ohm’s law:

ii

dt

dv

r ][ B v E

v i

i

ii

m

q

dt

d

E B

tJ B o

eBee TknP eeee

ee Pendt

dmn B J E

u

B BJBB

E )()(1

eioe

Pen

Hybrid Code Normalization

• Spatial scale – ion inertial length i = c/pi 102 km(solar wind at 1 AU, n = 5 cm-3)

• Time scale – ion gyrofrequencyi = qB/mic 12 rad/s; fci

-1 0.5 s(solar wind at 1 AU, B = 5 nT)

• Velocity scale – Alfvén velocityvA = i i 51 km/s (sound speed 21 km/s, Te = 5 eV)

Allows small global systems to be simulated on parallel supercomputers (i.e., Moon, Mercury, Mars, etc.)

Earth’s Moon

radius: 1738 km

orbit: 59.6 RE

period: 28 days

atmosphere: none

magnetic field: no internal dipole (however, surface fields exist with B ~ 1-100 nT)

interior: essentially non-conducting

Solar Wind – Moon Interaction

• Lunar surface absorbs particles on dayside– lack of atmosphere eliminates local lunar plasma

source

• Solar wind IMF diffuses through lunar interior– crustal magnetic fields on lunar surface may form

mini-magnetospheres, but effects are localized

• Plasma cavity forms on nightside region – examine structure of the wake-tail – understand plasma refilling processes

Lunar Prospector Data

Wind flyby summary [Bosqued et al., 1996]

THE LUNAR PLASMA WAKE… [1996]

Plasma waves during flyby [Farrell et al., 1996]

Refilling of Moon’s Wake-Tail

Kinetic processes in Moon’s wake tail are observed:

• streaming and anisotropic ion distributions

• plasma waves of various types

Lunar Wake-Tail Refilling Studies

• Fluid interaction with obstacle– rarefaction and trailing shock wave form down tail [Michel,

1968; Wolf, 1968; Spreiter et al., 1970]

• Particle studies – ions removed along Sun-Moon line [Whang, 1968]– electrons removed along the IMF direction [Bale et al., 1997]

• Kinetic studies – 1D PIC simulations show streaming and charge separation

instabilities [Farrell et al., 1997; Birch and Chapman, 2001]– few global kinetic self-consistent studies [e.g. Lipatov, 2002]

Hybrid Simulation Setup

• code: current advance method – cyclic leapfrog (CAM-CL) [Matthews, 1994]• 2D system size: Lx Ly= 3200x 1280y53 RL 26 RL

• grid spacing: x = 0.2 i and y = 0.25 i (i = c/pi = RL/12)

• time step: t = 0.005 ci-1

• solar wind speed: vsw = 6 vA (~ 400 km/s); plasma beta: i = 0.6 and e = 0.4

• uniform constant resistivity: = 0.02vA/ci

• IMF direction (with respect to the solar wind flow): = 45o and 90o

Density Profiles

= 90o

= 45o

0 10 20 30 x/RL

Ion phase space

perp.

parallel

= 45o

B fluctuations

T/T|| anisotropy contours

= 45o

= 45o

B FFT Spectrum (28RL < x < 40RL; 4.4RL < y < 4.4RL )

WIND Lunar flyby ~25 RL

wave spectra

ion energy

B components

|B|

density

Conclusions

• Cavity refilling is described by a magnetized plasma to vacuum expansion; the electron pressure gradient at the cavity’s edge provides a parallel electric field

• The rate of the plasma refilling process depends on the orientation of the IMF

• The density cavity is filled with counterstreaming ion beams and highly anisotropic plasma

• Left-hand polarized electromagnetic VLF waves are generated in the region 28RL < x < 40RL, probably generated by an anisotropy and/or heat flux instability

Future Research

• Perform more two and three-dimensional Moon runs– vary solar wind speed, density, IMF intensity– use upstream solar wind data to drive simulation– examine plasma environment in Earth’s magnetosphere

• Add surface magnetic field sources– examine the formation and effects of mini-magnetospheres

(surface shielding)

• Simulations of Mercury’s magnetosphere– preparation for Messenger, Bepi-Colombo missions

Density Comparison:Data with Simulations