Immersed Finite Element Solution to the Field Problem

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/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 c2 e 2 ne 2 E (E ) (ve )(B) / c E 4 me dne d e

c c e 2 ne eve qi ni vi cm (i qi ni vi B) 4 (B) B 4 m (B), dt dt i e e d where (ve ) dt t Ignoring the velocity convection term: c2 e 2 ne 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 i e 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 () Z (||) Y Bo Time History of Field Energy nLi/nH=0% nLi/nH=10% nLi/nH=5%

nLi/nH=20% Saturation occurs after ~2.5*(2/ linear growth rate) Linear Growth Rate nLi/nH=5% ln( B2 /Bo2 ) Linear Fit -15.5 ln( E 2 /Bo2 ) 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 Ht H t Growth Rate / 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 ( H t 80 ~ 161) l( Li ) l( Li ) l( Li ) After Satuaration ( H t 260 ~ 341) l( Li ) l( Li ) l( Li )

k Spectrum Analysis: nLi/nH=5% Near Saturation E ,k ( H t 160) B , k ( H t 160) B||,k ( H t 160) After Satuaration ( H t 260 ~ 341) k z c/ pH k z c/ pH k z c/pH After Satuaration E ,k ( H t 320) k z c/ pH B , k ( H t 260) k z c/ pH

B||,k ( H t 260) k z c/pH Lithium ion ring velocity phase: nLi/nH=5% H t 0 H t 100 vx / vtH vx / vtH H t 200 H t 250 vx / vtH vx / vtH H t 150 vx / vtH

H 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 H t 0 H t 150 H t 250 H 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 2 2 B /Bo 1E-06 0 -1E-06

-2E-06 0 50 100 Ht 150 200 Historical Plot of Electric Field E|| Ex Ey 4E-08 2 0 2

E /Bo 2E-08 -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:

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