Formation of Planetary Magnetospheres
What can we learn from global hybrid
simulations?
X. Blanco-Cano (UNAM)
N. Omidi (UCSD),
C. T. Russell (UCLA)
H. Karimabadi (UCSD)
GEM, SNOWMASS 2003
Outline
-what is a global hybrid simulation?
-why are global hybrid simulations important?
-2D hybrid model
-scaling study  Phase transition of magnetospheres
as a function of dipole strength
Global Simulations to study the interaction of the
solar wind with a magnetized planet:
MHD
- Fluid ions and electrons + E B fields
- Very helpful to study global morphology of magnetosphere
- Do not resolve important ion physics
- Not suitable for studies of boundaries and discontinuities which occur on ion scales
- Not appropriate for the study of obstacles with scale size ~ c/p (Mercury, asteroids)
Hybrid simulation
Ions are macro-particles, fluid electrons
 resolves ion spatial scales (ion inertial length), and ion temporal
scales (gyroperiod)...allowing study of kinetic effects
Global hybrid simulations are now possible:
we can for the first time look at
the magnetosphere on ion scales
Importance of Global Hybrid Simulations
• Formation of boundaries occur on ion time scales
• The length scale of discontinuities is on ion spatial scales
• Hybrid code properly captures the scaling properties of
reconnection process
• Yields details about plasma distribution functions
• Can be used to study different types of magnetospheres
including asteroids
Challenges in Global simulations
Multi-scale Coupled Systems
- Spatial scales vary from centimeters to 200 RE 
- Temporal scales vary from less than milliseconds to days 
- Kinetic effects have large-scale consequences 
Multi-physics
- Electron physics: e.g., reconnection
- Ion physics: e.g., dominates formation of boundaries and transport 
- Coupling to the ionosphere
Hybrid simulations
particle ions, fluid electrons
spatial scales: ion inertial length c/p, ion
gyroradius i
(~10-100 km in solar wind)
temporal scales -1, p-1 (~ sec)
Ions
kinetic via particle -in - cell


d
v
p
v
p B 

mi
 q E  c 
dt


i
dxp  vp
dt
- move particles and collect moments
( ρi  qini, Ji  qimivi) on grid
Electrons
-massless, quasi-neutral fluid
ene=qni
-momentum eqn.

d
B     Pe
nemeve  0  -ene  E  ve 
c 

dt
-closure
 Scalar pressure pe=neTe,
Te= const, or adiabatic
Electromagnetic fields
-Faraday’s Law
B  c(  E)
t
Initialization
xi, vi
-Ampere’s Law (low freq. approx.)
  B  4c J  4c qini(vi  ve)
-E- field from electron momentum eq.
B  pe  B  (  B)  F(B, ni, vi)
E   vi 
c
qini
4qini
Sources
J, 
B, E
Lorentz force on
each particle
Details: Winske and Omidi, JGR 1996,
Winske and Omidi, Computer and Space Plasma Physics, 1993
Approach: 2D box, 3D fields
we study the interaction of the solar wind with dipoles of
different strength
Box size 40-1000 c/p
Cell size 0.1- 1 c/p
10 part/cell
Line dipole
(Ogino, 1993)
Vsw
t =0.0025 -1
Magnetic strength defines Dp, the distance
(in ion inertial lengths, c/p) from the dipole
at which Psw=Pm dipole
Dipole strength was varied from
Dp= 0.05  63 c/p
Uniform
Resistivity
L  0.03 c/p
No ionosphere
No planetary rotation
Dp
85 Mercury
640 Earth
5800 Jupiter
Scaling Study:
Phase transition
of model
magnetospheres
Dp

This exercise allows us to
learn how different
boundaries arise and how
they depend on ion scales
Very weak dipole
Dp <<c/p
No upstream changes,
the solar wind is not affected
Whistler wake
No Magnetospheric features
Possible sw-asteroid
interaction
Density, Temperature and B normalized to sw values
Whistler wake
Dp < c/p
Some flow deflection
n increases
and v decreases at r > Dp
Whistler wake
Fast and slow MS waves at
tail edges
Precursor of plasma tail
B=Boy
Bz
Density
Whistler
and MS wakes
MS wake
B=Boz
MS wakes are associated with density
enhancement (20%) and drop at
center of tail
Dp  c/p
Pileup at r Dp
Flow deflection
n, T, B increase
v decreases
Reflected ions
Fast mode bow wave upstream
Slow mode wake
Tail with hot plasma
Reconnection
Reflected ions,
foreshock (purely kinetic effect)
Plasma Tail,
slow wake
Ion acceleration?
Test Particle Runs:
Ions are accelerated mostly near dipole
Formation of plasma tail
Dp c/p
Reconnection
Northward IMF
Southward IMF
Reconnection
above cusp
Density hole at nose
Reconnection
at nose
Earth-like
magnetosphere forms
when Dp > 20 c/p
Flow modified at
bow shock, r >> Dp
n, t, B increase
v decreases
Magnetosheath
Magnetospheric
features:
Magnetopause
Cusp
Tail with plasma sheet
Radiation belts
Reconnection, leading to
ion acceleration and
magnetic island formation
Plasmoids at high latitude
Plasmoid at plasma sheet
Reconnection  ion acceleration
and magnetic island formation
Radiation Belts
Ion energies 40 KeV
Mercury
Dp=63
-Reconnection takes place above cusps
-Current sheet in flank is a rotational discontinuity with
a field minimum
Dp=63
For field approximately southward at
nose flux transfer events occur periodically
Summary: Global hybrid simulations show that magnetospheric structures
go through phase transitions as the dipole strength is increased,
and obstacle size Dp grows relative to ion scales:
Dp
Upstream Plasma Changes
Waves
Magnetospheric features
<<c/p None
Whistler
None
< c/p Some flow deflection
n increases, and v decreases at r>
Dp
Whistler wake
Fast and slow
magnetosonic waves
at wake edges
Fast mode bow wave
Upstream
Slow mode wake
Precursor of a plasma tail
 c/p Pileup at r  Dp
Flow deflection
n, T, B increase,
v decreases
Reflected ions
>>
Flow modified and deflected at
bow shock, r >> Dp
c/p
n, T, B increase,
v decreases
Magnetosheath
Bow shock
Particle acceleration at dipole
(Particle trapping at belts)
Tail with hot plasma
Reconnection precursor
Magnetospause
Cusp
Tail with plasma sheet
Radiation belts
Reconnection, leading to ion
acceleration
and magnetic island formation
An earth-like magnetosphere forms when Dp > 20 c/p
Of course, this is not the end of the story...
Kinetic processes are very important to the global structure
of the magnetosphere.
In practice these processes are tailored by features of each
planet such as the presence or absence of atmospheres and
moons creating a rich phenomenological environment and a
variety of magnetospheres
2D Global Hybrid simulations offer many
advantages and can be used to study the role of
kinetic effects in magnetosphere formation
Future:
-Larger Dp, closer to Earth
-Study particle distributions at different boundaries,
particle tracing
-3D simulations
-Different IMF geometries
New campaigns to study the solar wind-magnetosphere
interaction need to include global hybrid simulations to
get a better understanding of what kinetic effects do
to the system.