Progress Report:

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

W. Scales, J. Wang, C. Chang Center for Space Science and Engineering Research Virginia Tech

Outline

•

I. Introduction

•

II. Hybrid PIC Simulation Model

•

III. Simulation Results

•

IV. Summary and Conclusion

I. 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 n Li /n H ~5% to 20% injection)

II. EM Hybrid PIC Simulation Model

• •

Basic Assumption:

– –

Quasi-neutral plasma; particle ions; fluid electrons; displacement current ignored Governing Equations:

–

Fields:

–

Fluid Electrons:

–

Particle Ions

Electric field equation incorporating finite-mass electron mass

c

2 4     2 

E

    (   

E

)  ( 

v e

    )(   

B

) /

c

   

e



v e where dn e dt d dt

 

dt



d



t

 

i q i n i



v i

( 

v e

   ) 

e cm e

  ( 

i q i n i



v i e

2

n e m e

 

B

)  

E c

4   (   

B

)  

B

  

c

4 

e

2

n e

  (   

B

),

m e

Ignoring the velocity convection term:

c

2 4     2 

E

   

e v e



n e



t

(   

E

)  

e

2

n e m e

 

i q i n i

 

v i



t



e cm e



E

  ( 

i q i n i



v i

 

B

) 

c

4  (   

B

)  

B

  

c

4 

e

2

n e

 (   

B

)

m e

Initial goal is to study process proposed by

Ganguli et al.

2007

III. Simulation Results

•

Simulation Initialization:

–

Injected Lithium ion: ring velocity distribution

v

  2 2

v

max  ( 1   2 )

v

min

v max =7km/s, the orbit velocity at the ejection ring energy=1.75eV

–

ambient hydrogen ion and electrons: Maxwellian distribution T=0.3eV

Simulation Cases: n Li /n H =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

n Li /n H =0% Time History of Field Energy n Li /n H =5% n Li /n H =10% n Li /n H =20% Saturation occurs after ~2.5*(2 π/ linear growth rate)

Linear Growth Rate n Li /n H =5%

-15.5

-16.0

-16.5

-17.0

-17.5

-18.0

-18.5

-19.0

0 50 100 ln( δ B 2 Linear /B 2 o Fit ) -24.0

Y = -20.59415 + 0.03173 * X -24.5

-25.0

-25.5

-26.0

-26.5

-27.0

150 Ω H t 200 250 Growth Rate γ/Ω H n Li /n H =5% n Li /n H =10% n Li /n H =20% 0.01554

0.02202

0.03333

50 100 ln( δ E 2 Linear /B 2 o Fit ) Y = -28.86699+ 0.03042 * X 150 Ω H t 200 250

Frequency Spectrum Analysis: n Li /n H =5%:

Near Saturation (Ω H t  80 ~ 161) After Satuaratio n (Ω H t  260 ~ 341) l(Ω Li ) l(Ω Li ) l(Ω Li ) l(Ω Li ) l(Ω Li ) l(Ω Li )

Near Saturation E  , k (Ω H t  160)

k Spectrum Analysis: n Li /n H =5%

B  , k (Ω H t  160) B || , k (Ω H t  160) k z c/ω pH After Satuaratio n E  , k (Ω H t  3 20 ) k z c/ω pH B  , k (Ω H t  260) After Satuaratio n (Ω H t  260 ~ 341) k z c/ω pH B || , k (Ω H t  260) k z c/ω pH k z c/ω pH k z c/ω pH

Lithium ion ring velocity phase: n Li /n H =5%

Ω H t  0 Ω H t  100 Ω H t  150

v x

/

v tH

Ω H t  200

v x

/

v tH

Ω H t  250

v x

/

v tH

Ω H t  400

v x

/

v tH v x

/

v tH v x

/

v tH

Lithium & Hydrogen ion velocity distribution: n Li /n H =5% Li+ H+

1 0.8

0.6

0.4

0.2

0 0 0.5

1 1.5

v

 /

v tH

2 0.1

 H t=0  H t=100  H t=250  H t=400 0.08

0.06

0.04

0.02

2.5

3 Ω H t Ω H t   0 150 Ω H t Ω H t   250 400 0 -3 -2 -1 0

v x

/

v tH

1 2 3

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

Energy efficiency n Li /n H =5% 18% n Li /n H =10% 15% n Li /n H =20% 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).

2E-06

Historical Plot of Magnetic Field

B || B x B y 1E-06 0 -1E-06 -2E-06 0 50 100  H t 150 200

Historical Plot of Electric Field

4E-08 2E-08 0 -2E-08 -4E-08 0 50 100  H t 150 200 E || E x E y

Fields: Particles: Where:

Normalized Governing Equations

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

•

The basic procedure are in four steps: