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Multi-Fluid/Multi-Scale Simulations and their application in
the Terrestrial Magnetosphere: Substorm Onset
R. M. Winglee
Is Earth Special with only limited heavy ion influence
OR
Do Heavy Ions Strongly the Influence Dynamics of the
Terrestrial System similar to other systems?
Heavy Ions dominate at many Planetary Magnetospheres
Including:
• Jupiter and Saturn at the Outer Planets
• Mercury, Mars and Venus at the Inner Planets
Heavy Ions dominate at Most Induced Magnetospheres
Including:
• Enceladus and Titan at Saturn
• Io, Europa, Ganymede and Callisto at Jupiter
Simulation Methodologies
Multi-Fluid/Multi-Scale Simulation Code :
In’s and Out’s
A Substorm Example
Future Directions
Talk Outline
Simulation Methodologies
Full Particle Simulation – Particle Ions and Electrons
Max. Frequencies that need to
be Resolved:
ωpe, Ωe, EM radiation
Min. Distance Scales to be
Resolved:
Debye Length
Requires sufficient particle
statistics accurately determine
bulk density and velocity to
solve Maxwell’s EquationsProtons Heavy Ions (O+)
Electrons
Protons Heavy Ions (O+)
Simulation Methodologies
Electrons
Full Particle Simulation – Particle Ions and Electrons
Very Powerful Tool for
Local instability analysis
Reconnection Studies –
Initial Value Problems
High Frequency, Small Scales
Presently Prevents Usage for
Realistic Global Simulations
Simulation Methodologies
Hybrid Simulation – Particle Ions and Fluid Electrons
Max. Frequencies that need to
be Resolved: Whistler
Frequency
Min. Distance Scales to be
Resolved: Order of Ion Skin
Depth c/ωpi
Properties of the Electrons
Derived from Fluid Equations
and Known for Each Grid Point
Protons Heavy Ions (O+)
Fluid Electrons
Reduced Numerical Resources –
Larger scale lengths and lower
frequencies, less particles
Simulation Methodologies
Hybrid Simulation – Particle Ions and Fluid Electrons
Ion Instability Problems
Magnetic Reconnection
Induced Magnetospheres
Smaller Planetary
Magnetospheres (Mars, Venus,
Mercury)
Important Applications:
Protons Heavy Ions (O+)
Fluid Electrons
Simulation Methodologies
Fluid Simulations – Fluid Ions and Fluid Electrons
Starting Point is to first take the
moments of the Vlasov Equation,
so that all quantities are know on
the grid and these quantities are
moved in time.
Fluid Quantity
Advantage: Don’t have to track
the ensemble of particles- saves
compute time and can handle
large dynamics ranges – global
magnetosphere order of 106.
Disadvantage: Some loss of
physics – how much is dependent
on assumptions made.
Vlasov Eqn: 0
va
xv
ff
t
fwhere a = (q/m)(E + v×B),
vd 3Zero Moment: ( )
t0)(
V
Conservation of Mass
First Moment: ( )
Pnqdt
d ))(( rBVE
V
Momentum Equationv3
vd
Second Moment: ( )23 v vd Pressure Equation
P
t (P V ) ( 1)V P
At this point all wave modes are included, but Resonant Particle Interactions
(Landau Damping) and Temperature Anisotropies are Neglected.
The Fluid Equations
The MHD Equations ( ≠ Fluid Equations)
Make Additional (One Fluid) Simplifying Assumptions:
Single ion species
Assume Ve ~ Vi Te~Ti Ne ~Ni
ADD the electron and ion equations together
0)(
V
t
Pdt
d BJ
V
PPt
P
VV )1()(
+ Ohms Law
Because of the assumption of the one fluid, all cyclotron
and mass dependent processes are neglected.
The MHD Equations ( ≠ Fluid Equations)
Advantages: Full global simulations of planetary
magnetospheres and many features are seen in spacecraft
observations.
Disadvantages: Many plasma effects including ion skin
depth and ion gyro-radius effects are neglected.
Question: Are the neglected effects
important?
Current Sheet Scale Sizes at the Earth
Field Strength of 5-20 nT
H+ Gyroradius : 600-150 km
O+ Gyroradius : 2400-600 km
H+ Skin Depth : 600 - 200 km 30 km
O+ Skin Depth : larger by a factor of ~ 10
Densities: Tail ~ 0.1 - 1 cm-3 MPause ~40 cm-3
Observed Current Sheet Thicknesses:
•Tail - ~ 800 -1200 km
• MPause 80-200 km
Significant Regions
within the Terrestrial
Magnetosphere have
conditions that
violate the MHD
Assumptions
t0)(
V
Pnqdt
d ))(( rBVE
V
P
t (P V ) ( 1)V P
The Multi-Fluid Equations
Ion Prescription α: H+, O+Inner Boundary
• Radius :2.7 RE
• Density: 100 cm-3
• 5% O+
O+ is gravitationally bound
and magnetospheric
forcing is required to
produce net heavy ion
outflow
Electron Prescription
eeeee PPt
P
VV )1()(
0/0 eeee enP
dt
dBVE
V
BJJ
VV 0e
1,
en ,
i
i
e
iie
i
iie
en
nq
e
nqn
Modified Ohm’s Law
Modified Ohm’s Law
J BJ
BVEe
)(1
xPenenen
nqe
ei
i
e
ii
Different Ion Species
couple through their
contributions to E
Hall and GradP corrections
which scale as Ion skin
depth/Spatial Scale
Collisional
Resistivity in
Ionosphere only
2
22
pee
ck
Max. Frequency: Whistler
Protonspic max/~ Min Spatial Scale: Ion Skin Depth
Time Step: Fraction of ΩProtons
Doable with variable gridding but the code is very much
slower than an MHD code.
Kidder et al. 2008
MercuryHybrid Multi-Fluid
Solar Wind Conditions
A Terrestrial Application
onset
Solar Wind Conditions
A Terrestrial Application
Solar Wind Conditions
onset
A Terrestrial Application
CIS
OnsetSouthward Turning
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