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

Center for Space Science & Engineering ResearchVirginia 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

ΩLi

• coalescence of two such short wavelength plasmons leads to a long wavelength plasmon with

• to calculate the energy transfer rate

||kk

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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

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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

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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%

• 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

)(X

(||)Z

Y oB

• The initial growth rate γ/ΩcH is around 0.038, which is consistent with linear theory.

• After tΩcH=400, the cyclotron waves decay radiating lower frequency and corresponding longer wavelength Alfven waves due to nonlinear effects.

Field Energy: nLi/nH=30%

Li Cyclotron Waves

Alfven Waves

• The dominate frequency is around the 2nd Li cyclotron harmonic, as described by linear theory.

Frequency Power Spectrum: nLi/nH=30%

Linear Growth Period (0 < ΩcHt < 150)

Li Cyclotron Waves

Temporal variation of spectrum: nLi/nH=30%

Alfven Waves

Li cyclotron waves

Li cyclotron waves

Alfven Waves

Li cyclotron waves

0 < ΩcHt < 900

0 < ΩcHt < 400

0 < ΩcHt < 150

• Frequency power spectrum showing decay of cyclotron waves into Alfven waves at late times.

Li Cyclotron Harmonic Modes (l=1 and l=2)

Wave Number Power Spectrum: nLi/nH=30%

• kx >> kz and the wave number value is consistent with linear theory.

Linear Growth Period

Ex,k2(ΩcHt=100) By,k

2(ΩcHt=100)

Wave Number Power Spectrum: nLi/nH=30%

• Over time, the wavenumber spectrum shows perpendicularly propagating Li cyclotron waves (kx >> kz ) decaying into Alfven waves.

Li Cyclotron Harmonic Modes (l=1 and l=2)

Alfven Mode

Li Cyclotron Modes Alfven Mode

100cH t 400cH t 900cH t

Lithium Ring Velocity Phase: nLi/nH=30%

ΩcHt=0

ΩcHt=700ΩcHt=200

ΩcHt=100

Hydrogen Velocity Phase: nLi/nH=30%

ΩcHt=0

ΩcHt=700ΩcHt=200

ΩcHt=100

Li Ring and H+ Velocity Distribution Functions

Li+ H+

• The cold ring is bulk heated while the hydrogen background is tail heated.• There is negligible heating of the hydrogen.

Energy Extraction Efficiency: nLi/nH=30%

• The energy extraction efficiency of lithium is 20%-25%.

Field energy variation with ring density

• The growth rate γ/ΩcH 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.