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Modeling Generation and Nonlinear Evolution of Plasma Turbulence for Radiation Belt Remediation

Modeling Generation and Nonlinear Evolution of Plasma Turbulence for Radiation Belt Remediation. W.A. Scales, J.J. Wang and O. Chang. Center for Space Science & Engineering Research Virginia Polytechnic Institute and State University. Overall Objective:

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Modeling Generation and Nonlinear Evolution of Plasma Turbulence for Radiation Belt Remediation

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  1. Modeling Generation and Nonlinear Evolution of Plasma Turbulence for Radiation Belt Remediation W.A. Scales, J.J. Wang and O. Chang Center for Space Science & Engineering ResearchVirginia Polytechnic Institute and State University

  2. Overall Objective: • To study the characteristics of plasma turbulence that may be utilized for scattering radiation belt particles using numerical simulations. • Questions to be Considered • What types of free energy sources may generate appropriate plasma turbulence (with emphasis on chemical releases)? • What plasma wave modes and plasma instabilities are involved in producing the turbulence ? • What is the nonlinear evolution of the corresponding plasma turbulence and the impact on steady state turbulence characteristics? • How much of the initial free energy can be transferred to the plasma wave energy? • How much wave energy can be transferred to pitch angle scattering of trapped electrons?

  3. Outline Two topics to be discussed: • I. EM Hybrid PIC Simulations of Ion-Cyclotron Turbulence • Induced by Li Release in the Magnetosphere • II. EM Full Particle PIC Simulations of Non-Linear Evolution • of Whistler Turbulence

  4. EM Hybrid PIC Simulations of Ion Cyclotron Turbulence Induced by Li Release • Outline: • Introduction • Algorithm: EM Hybrid PIC with Finite Electron Inertia • Simulation Results • Conclusions

  5. Radiation Belt Remediation by Plasma Turbulence Induced by Chemical Release in Space • The Process: • Release easily ionized chemicals in the equatorial plane to form an artificial plasma cloud • the released plasma forms a ring velocity distribution perpendicular to the geomagnetic field • The orbital kinetic energy (v~7km/s) provides free energy to excite plasma waves through micro-instabilities • The plasma instabilities transfer a fraction of the orbital kinetic energy for wave-particle interactions with the energetic electrons and protons

  6. Introduction • Intense ion cyclotron turbulence can be generated by shaped release of Li. • Nonlinear evolution of the turbulence converts the quasi-electrostatic waves into electromagnetic waves which can pitch angle scatter trapped electrons • Specific Objectives: • to verify and demonstrate of the theoretical predictions of the following turbulence evolution: • Waves are initially highly oblique: • Short wavelength shear Alfven waves amplified around harmonics of ΩLi • coalescence of two such short wavelength plasmonsleads to a long wavelength plasmonwith • to calculate the energy transfer rate

  7. Electromagnetic Ion Cyclotron Instability(Ganguli et al. 2007) • Linear theory describes initial generation of highly oblique shear Alfven waves near lithium cyclotron harmonics by a Lithium velocity ring plasma

  8. Linear Growth Rate Calculations

  9. II. EM Hybrid PIC Simulation Model • Basic Assumptions: • Quasi-neutral plasma; particle ions; fluid electrons; • Displacement current ignored • Governing Equations: • Fields: • Particle Ions • Finite Mass Fluid Electrons

  10. Field Equation

  11. III. Simulation Results • Simulation Initialization: • Injected Lithium ions: cold ring velocity distribution • vper=7km/s, the orbit velocity at the ejection • TLi=1.79eV • Ambient hydrogen ion and electrons: Maxwellian distribution • β=4.0e-5, Bo=0.04G, TH=Te=0.53eV • Artificial resistivity η is 1.0e-7 • Simulation Cases Considered: • nLi/nH=5%, 10%, 30%

  12. Simulation domain (nLi/nH=30%) • 2-D, Z is parallel to Bo , X is perpendicular to Bo • LZ = 234km = 64c/ωpi = 56.14c/ωpH , 128 cells in the domain • LX = 4.7km = 1.28c/ωpi = 1.12c/ωpH , 128 cells in the domain

  13. Field Energy: nLi/nH=30% Li Cyclotron Waves Alfven Waves • The initial growth rate γ/ΩcH is around 0.038, which is consistent with linear theory. • After tΩcH=400, the cyclotron waves decay radiatinglower frequency and corresponding longer wavelength Alfven waves due to nonlinear effects.

  14. Frequency Power Spectrum: nLi/nH=30% Linear Growth Period (0 < ΩcHt < 150) Li Cyclotron Waves • The dominate frequency is around the 2nd Li cyclotron harmonic, as described by linear theory.

  15. Temporal variation of spectrum: nLi/nH=30% 0 < ΩcHt < 150 Li cyclotron waves • Frequency power spectrum • showing decay of cyclotron • waves into Alfven waves at • late times. Alfven Waves Li cyclotron waves 0 < ΩcHt < 400 Alfven Waves Li cyclotron waves 0 < ΩcHt < 900

  16. Wave Number Power Spectrum: nLi/nH=30% Linear Growth Period Ex,k2(ΩcHt=100) By,k2(ΩcHt=100) Li Cyclotron Harmonic Modes (l=1 and l=2) • kx>> kzand the wave number value is consistent with linear theory.

  17. Wave Number Power Spectrum: nLi/nH=30% Alfven Mode Li Cyclotron Harmonic Modes (l=1 and l=2) Li Cyclotron Modes Alfven Mode • Over time, the wavenumber spectrum shows perpendicularly propagating Li cyclotron waves (kx >> kz ) decaying into Alfven waves.

  18. Lithium Ring Velocity Phase: nLi/nH=30% ΩcHt=0 ΩcHt=100 ΩcHt=200 ΩcHt=700

  19. Hydrogen Velocity Phase: nLi/nH=30% ΩcHt=0 ΩcHt=100 ΩcHt=200 ΩcHt=700

  20. Li Ring and H+ Velocity Distribution Functions H+ Li+ • The cold ring is bulk heated while the hydrogen background is tail heated. • There is negligible heating of the hydrogen.

  21. Energy Extraction Efficiency: nLi/nH=30% • The energy extraction efficiency of lithium is 20%-25%.

  22. Field energy variation with ring density Li Cyclotron Wave Alfven Waves • The growth rate γ/ΩcH of each density-ratio case is consistent with linear theory.

  23. Energy extraction variation with ring density • Increasing the ring density from 5% to 30% shows a relatively modest increase in extraction efficiency.

  24. Summary The simulation shows good agreement with linear theory predictions for frequency spectrum and wave-number spectrum of the initially generated Li ion cyclotron waves. Simulations indicate nonlinear wave-wave processes during the non-linear period resulting in the development of longer wavelengths and lower frequency Alfven waves. Simulations show energy extraction from the Li ring kinetic energy to the wave energy in the range of 20-25% with only modest increases going from 5% to 30% ring density Ongoing work is investigating the generation of the relatively long wavelength Alfven waves after initial saturation of the cyclotron instability in more detail. IV. Summary and Future Plans

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