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

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?

Outline 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 Two topics to be discussed:

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

Radiation Belt Remediation by Plasma Turbulence Induced by Chemical Release in Space The Process: 1.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 2.The orbital kinetic energy (v~7km/s) provides free energy to excite plasma waves through micro- instabilities 3.The plasma instabilities transfer a fraction of the orbital kinetic energy for wave-particle interactions with the energetic electrons and protons

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 Ω Li coalescence of two such short wavelength plasmons leads to a long wavelength plasmon with to calculate the energy transfer rate

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

Linear Growth Rate Calculations

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

Field Equation

III. Simulation Results Simulation Initialization: –Injected Lithium ions: cold ring velocity distribution v per =7km/s, the orbit velocity at the ejection T Li =1.79eV –Ambient hydrogen ion and electrons: Maxwellian distribution β=4.0e-5, B o =0.04G, T H =T e =0.53eV –Artificial resistivity η is 1.0e-7 Simulation Cases Considered: n Li /n H =5%, 10%, 30%

Simulation domain (n Li /n H =30%) –2-D, Z is parallel to B o, X is perpendicular to B o –L Z = 234km = 64c/ω pi = 56.14c/ω pH, 128 cells in the domain –L X = 4.7km = 1.28c/ω pi = 1.12c/ω pH, 128 cells in the domain

The initial growth rate γ/Ω cH is around 0.038, which is consistent with linear theory. After tΩ cH =400, the cyclotron waves decay radiating lower frequency and corresponding longer wavelength Alfven waves due to nonlinear effects. Field Energy: n Li /n H =30% Li Cyclotron Waves Alfven Waves

The dominate frequency is around the 2 nd Li cyclotron harmonic, as described by linear theory. Frequency Power Spectrum: n Li /n H =30% Linear Growth Period (0 < Ω cH t < 150) Li Cyclotron Waves

Temporal variation of spectrum: n Li /n H =30% Alfven Waves Li cyclotron waves Alfven Waves Li cyclotron waves 0 < Ω cH t < < Ω cH t < < Ω cH t < 150 Frequency power spectrum showing decay of cyclotron waves into Alfven waves at late times.

Li Cyclotron Harmonic Modes (l=1 and l=2) : n Li /n H =30% Wave Number Power Spectrum: n Li /n H =30% k x >> k z and the wave number value is consistent with linear theory. Linear Growth Period E x,k 2 (Ω cH t=100)B y,k 2 (Ω cH t=100)

: n Li /n H =30% Wave Number Power Spectrum: n Li /n H =30% Over time, the wavenumber spectrum shows perpendicularly propagating Li cyclotron waves (k x >> k z ) decaying into Alfven waves. Li Cyclotron Harmonic Modes (l=1 and l=2) Alfven Mode Li Cyclotron ModesAlfven Mode

: n Li /n H =30% Lithium Ring Velocity Phase: n Li /n H =30% Ω cH t=0 Ω cH t=700Ω cH t=200 Ω cH t=100

: n Li /n H =30% Hydrogen Velocity Phase: n Li /n H =30% Ω cH t=0 Ω cH t=700Ω cH t=200 Ω cH t=100

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

Energy Extraction Efficiency: n Li /n H =30% The energy extraction efficiency of lithium is 20%-25%.

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

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

IV. Summary and Future Plans 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.