Hybrid Simulation of Ion-Cyclotron Turbulence Induced by Artificial Plasma Cloud in the

MagnetosphereW. Scales, J. Wang, C. Chang

Center for Space Science and Engineering Research

Virginia Tech

Progress Report:

OutlineOutline

• I. Introduction

• II. Hybrid PIC Simulation Model

• III. Simulation Results

• IV. Summary and Conclusion

I. IntroductionI. Introduction

• Objective:– To study the process and efficiency of energy extraction from a chemical release that

may produce plasma turbulence which ultimately interacts with radiation belt electrons

• Overview of Progress:– Developed and implemented a new EM hybrid PIC algorithm which incorporates finite

electron mass– Developing a new ES hybrid PIC algorithm which incorporates finite electron mass– Simulated plasma turbulence generated by the injection of a velocity ring distribution

of Li ions– Simulation results show that the excitation of Lithium cyclotron harmonics which

extracts about ~20% to ~15% of the Lithium ring energy (for nLi/nH ~5% to 20% injection)

• Basic Assumption:– Quasi-neutral plasma; particle ions; fluid electrons;

– displacement current ignored

• Governing Equations:– Fields:

– Fluid Electrons:

– Particle Ions

II. EM Hybrid PIC Simulation ModelII. EM Hybrid PIC Simulation Model

Electric field equation incorporating finite-mass electron mass

)(

),(4

)(4

)(

/))(()(4

2

22

2

e

e

e

iiii

eiiii

ee

e

ee

vtdt

dwhere

Bm

necBB

cBvnq

cm

evnq

dt

d

dt

dnve

Em

necBvEE

c

)(4

)(4

)(

)(4

2

22

2

Bm

necBB

cBvnq

cm

e

t

vnq

t

nve

Em

neEE

c

e

e

iiii

ei

iii

ee

e

e

Ignoring the velocity convection term:

Initial goal is to study process proposed by Ganguli et al. 2007

III. Simulation ResultsIII. Simulation Results

• Simulation Initialization: – Injected Lithium ion: ring velocity distribution

vmax=7km/s, the orbit velocity at the ejection

ring energy=1.75eV

– ambient hydrogen ion and electrons: Maxwellian distribution

T=0.3eV

2 2min

2max )1( vvv

Simulation Cases:nLi/nH=0%, 5%, 10%, 20%

• Simulation domain – 2-D, Z is parallel to Bo , X is perpendicular to Bo

– Zmax=182.42 km, 100 cells in the domain

– Xmax=0.58 km, 50 cells in the domain

– The Lithium Larmor radius=0.126 km. Xmax~ 4.6 times Larmor radius (11 cells for one Larmor radius)

)(X

(||)Z

Y oB

Time History of Field EnergyTime History of Field Energy

Saturation occurs after ~2.5*(2π/ linear growth rate)

nnLiLi/n/nHH=10%=10% nnLiLi/n/nHH=20%=20%

nnLiLi/n/nHH=0%=0% nnLiLi/n/nHH=5%=5%

Linear Linear Growth Rate

tΩH

FitLinear )/BB ln(δ 2

o2

0 50 100 150 200 250

-19.0

-18.5

-18.0

-17.5

-17.0

-16.5

-16.0

-15.5

Y = -20.59415 + 0.03173 * X

Growth Rate

nnLiLi/n/nHH==5% 0.01554

nnLiLi/n/nHH==10% 0.02202

nnLiLi/n/nHH==20% 0.03333

nnLiLi/n/nHH=5%=5%

50 100 150 200 250

-27.0

-26.5

-26.0

-25.5

-25.0

-24.5

-24.0

Y = -28.86699+ 0.03042 * X

tΩH

FitLinear )/BE ln(δ 2

o2

Hγ/Ω

)l(ΩLi

Frequency Spectrum Analysis: nnLiLi/n/nHH=5%: =5%:

)l(ΩLi

)l(ΩLi

)l(ΩLi

)l(ΩLi

341)~260t(Ω

nSatuaratioAfter

H 161)~80t(Ω

SaturationNear

H

)l(ΩLi

k Spectrum Analysis: nnLiLi/n/nHH=5%=5%

SaturationNear

341)~260t(Ω

nSatuaratioAfter

H

pHzc/ωk pHzc/ωk pHzc/ωk

160)t(Ω E Hk, 160)t(Ω B Hk, 160)t(Ω B Hk,||

nSatuaratioAfter

pHzc/ωkpHzc/ωk pHzc/ωk

)203t(Ω E Hk, 260)t(Ω B Hk, 260)t(Ω B Hk,||

Lithium ion ring Lithium ion ring velocity phase: nnLiLi/n/nHH=5% =5%

0tΩH

/x tHv v

100tΩH

/x tHv v

150tΩH

/x tHv v

/x tHv v

200tΩH

/x tHv v

250tΩH

/x tHv v

400tΩH

Lithium & Hydrogen ion Lithium & Hydrogen ion velocity distribution: nnLiLi/n/nHH=5%=5%

Li+ H+

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

Ht=0Ht=100Ht=250Ht=400

/ tHv v

-3 -2 -1 0 1 2 30

0.02

0.04

0.06

0.08

0.1

150tΩH 250tΩH 400tΩH

tHx vv /

0tΩH

Energy Extraction EfficiencyEnergy Extraction Efficiency

Energy Extraction Efficiency=1-(Li+ kinetic energy)/(Li+ initial kinetic energy)

Li+ KE change H+ KE change

nnLiLi/n/nHH==5% nnLiLi/n/nHH==10% nnLiLi/n/nHH==20%

Energy efficiency 18% 15% 13%

V. Summary and Future Plans

• Significant progresses have been made in developing a simulation model of ion cyclotron turbulence generated by a velocity ring distribution– Initial simulation predictions of energy extraction efficiency are consistent with predictions from previous work

(Mikhailovskii et al., 1989)– Model may be used to study a variety of velocity ring EM instability mechanisms from various chemical releases (Li, Ba,

ect.)

• Future work– Refine the current electromagnetic EM hybrid PIC code for more direct comparisons of the NRL mechanism– Complete the implementation of a electrostatic ES hybrid PIC model with electron inertia for studying energy extraction

associated with lower hybrid turbulence from chemical release (both Ba and Li).

Historical Plot of Magnetic Field

Ht

B2 /B

2 o

0 50 100 150 200

-2E-06

-1E-06

0

1E-06

2E-06

B||

Bx

By

Historical Plot of Electric Field

Ht

E2 /B

2 o

0 50 100 150 200

-4E-08

-2E-08

0

2E-08

4E-08

E||

Ex

Ey

Fields:

Particles:

Normalized Governing Equations

Where:

Numerical Implementation:Predictor Corrector Scheme Leapfrog Particle Push; PCG Electric Field Solver

• The basic procedure are in four steps: