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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 nLi/nH ~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


   
   
e 2 ne 
c2
2
  E  (  E )  (ve  )(  B) / c 
E
4
me
 dne d

 
e 
c     c e 2 ne  
 eve
  qi ni vi 
( qi ni vi  B) 
(  B)  B  
 (  B),
dt dt i
cme  i
4
4

m

e
 
d

where
  (ve  )
dt t
Ignoring the velocity convection term:


   
e 2 ne 
c2
2
  E  (  E ) 
E
4
me

 ne
 
vi
e 
c     c e 2 ne  
 eve
  qi ni

( qi ni vi  B)  4 (  B)  B   4 m  (  B)
t

t
cm
i

e  i
e
Initial goal is to study process proposed by Ganguli et al. 2007
III. Simulation Results
• Simulation Initialization:
– Injected Lithium ion: ring velocity distribution
2
2
v  2 vmax
 (1   )vmin
vmax=7km/s, the orbit velocity at the ejection
ring energy=1.75eV
– ambient hydrogen ion and electrons: Maxwellian distribution
T=0.3eV
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 ()

Bo


Y
Z (||)
Time History of Field Energy
nLi/nH=0%
nLi/nH=10%
nLi/nH=5%
nLi/nH=20%
Saturation occurs after ~2.5*(2π/ linear growth rate)
Linear Growth Rate
nLi/nH=5%
ln( δ B2 /B o2 )
Linear Fit
-15.5
ln( δ E 2 /B o2 )
Linear Fit
-24.0
-16.0
-24.5
-16.5
-25.0
-17.0
-25.5
-17.5
-26.0
-18.0
Y = -20.59415 + 0.03173 * X
-18.5
-26.5
-19.0
-27.0
0
50
100
150
200
250
Y = -28.86699+ 0.03042 * X
50
100
150
ΩH t
ΩH t
Growth Rate γ/Ω H
nLi/nH=5%
0.01554
nLi/nH=10%
0.02202
nLi/nH=20%
0.03333
200
250
Frequency Spectrum Analysis: nLi/nH=5%:
Near Saturation
(Ω H t  80 ~ 161)
l(Ω Li )
l(Ω Li )
l(Ω Li )
After Satuaratio n
(Ω H t  260 ~ 341)
l(Ω Li )
l(Ω Li )
l(Ω Li )
k Spectrum Analysis: nLi/nH=5%
Near Saturation
E  ,k (Ω H t  160)
B  ,k (Ω H t  160)
B||,k (Ω H t  160)
After Satuaratio n
(Ω H t  260 ~ 341)
k z c/ω pH
k z c/ωpH
k z c/ωpH
After Satuaratio n
E  ,k (Ω H t  320)
k z c/ωpH
B ,k (Ω H t  260)
k z c/ωpH
B||,k (Ω H t  260)
k z c/ωpH
Lithium ion ring velocity phase: nLi/nH=5%
ΩH t  0
ΩH t  100
vx / vtH
vx / vtH
ΩH t  200
ΩH t  250
vx / vtH
vx / vtH
ΩH t  150
vx / vtH
ΩH t  400
vx / vtH
Lithium & Hydrogen ion velocity distribution: nLi/nH=5%
Li+
H+
1
0.1
Ht=0
Ht=100
Ht=250
Ht=400
0.8
0.6
0.06
0.4
0.04
0.02
0.2
0
ΩH t  0
ΩH t  150
ΩH t  250
ΩH t  400
0.08
0
0.5
1
1.5
v / vtH
2
2.5
3
0
-3
-2
-1
0
vx / vtH
1
2
3
Energy Extraction Efficiency
H+ KE change
Li+ KE change
Energy Extraction Efficiency=1-(Li+ kinetic energy)/(Li+ initial kinetic energy)
Energy efficiency
nLi/nH=5%
nLi/nH=10%
nLi/nH=20%
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
B||
Bx
By
2E-06
B2/B2o
1E-06
0
-1E-06
-2E-06
0
50
100
H t
150
200
Historical Plot of Electric Field
E||
Ex
Ey
4E-08
E2/B2o
2E-08
0
-2E-08
-4E-08
0
50
100
H t
150
200
Normalized Governing Equations
Fields:
Particles:
Where:
Numerical Implementation:
Predictor Corrector Scheme Leapfrog Particle Push; PCG Electric Field Solver
•
The basic procedure are in four steps: