multi-fluid/multi-scale simulations and their application in the...

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


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+)


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


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


Fluid Electrons

Reduced Numerical Resources –

Larger scale lengths and lower

frequencies, less particles


Hybrid Simulation – Particle Ions and Fluid Electrons

Ion Instability Problems

Magnetic Reconnection

Induced Magnetospheres

Smaller Planetary

Magnetospheres (Mars, Venus,

Mercury)

Important Applications:


Fluid Electrons


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



OnsetSouthward Turning

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