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 m e = 0 and n e = n i Field equations: Modified Ohm’s law:

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 gyrofrequency  i = qB/m i c  12 rad/s; f ci -1  0.5 s (solar wind at 1 AU, B = 5 nT) Velocity scale – Alfvén velocity v A =  i  i  51 km/s (sound speed  21 km/s, T e = 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 R E period: 28 days atmosphere: none magnetic field: no internal dipole (however, surface fields exist with B ~ 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: L x  L y = 3200  x  1280  y  53 R L  26 R L grid spacing:  x = 0.2  i and  y = 0.25  i (  i = c/  pi = R L /12) time step:  t =  ci -1 solar wind speed : v sw = 6 v A (~ 400 km/s); plasma beta :  i = 0.6 and  e = 0.4 uniform constant resistivity:  = 0.02  v A /  ci IMF direction ( with respect to the solar wind flow ) :  = 45 o and 90 o

Density Profiles  = 90 o  = 45 o x/R L

Ion phase space perp. parallel  = 45 o

 B fluctuations T  /T || anisotropy contours  = 45 o

 B FFT Spectrum (28R L < x < 40R L ;  4.4R L < y < 4.4R L )

WIND Lunar flyby ~25 R L 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 28R L < x < 40R L, 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