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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: