Transcript Immersed Finite Element Solution to the Field Problem
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: