Finite Temperature Effects on VLF-Induced Precipitation

1. Finite Temperature Effects on VLF-Induced Precipitation Praj Kulkarni, U.S. Inan and T. F. Bell MURI Review February 18, 2009

2. Outline • Motivation • Review of published results • Refractive index surface • Importance of ions • Open/closed refractive index surfaces • Thermal Corrections • Conclusions

3. Motivation and Procedure • Resonant interactions with waves are responsible for the acceleration and loss of radiation belt electrons. • In the inner belt and slot region, different types of waves (whistlers, hiss, VLF transmitters) are important drivers of precipitation. • Abel and Thorne [1998a] • The possibility of controlled precipitation of electrons by waves injected in-situ has been suggested by Inanet al. [2003] • Our purpose is to quantitatively investigate the precipitation of energetic electrons as a result of in-situ injection of whistler-mode waves. • Utilize the Stanford 2D VLF Raytracing program • Diffusive equilibrium model. • Electrons plus 3 species of ions: O+, H+, He+. • 6 injection sites: L = 1.5, 2.0, 2.5 and λs = 0˚, 20˚ • Consider a range of frequencies and wave normal angles. • Account for Landau damping along ray path. • Calculate energetic electron precipitation based on method of Bortnik et al. [2005a, 2005b].

4. Illumination of the Plasmasphere • If f < fLHR, vg moves outwards, f > fLHR, vg moves inwards • Modulating the wave frequency can be used to target specific regions • Landau damping affects this result:

5. Cavity Enhancement Factor

6. Equatorial Source at L=2 • We can use the cavity enhancement factor to determine which L-shells are maximally targeted • Different wave frequencies and wave normal angles are effective at different L-shells

7. Sources Distributed in L-shell • With each source radiating three wave frequencies close to the local fLHR, 3 sources can fill most of the inner magnetosphere with wave energy • Use these results as input to precipitation calculation • Published in Kulkarni et al. [2006]

8. Energetic Electron Precipitation • Choose 3 central wave frequencies • For each launch rays from θres θres + 3˚ • Calculate pitch angle change for a range of resonance modes and electron energies • Apply calculated pitch angle change to loss cone electrons to determine precipitated flux

9. Simulation Results We have results for sources at L = 1.5, 2.0, and 2.5, at l = 0, 20o for each L-shell

10. Variation of q along Raypath • q impacts the effectiveness of the wave-particle interaction • For a wide variety of input parameters, q approaches the resonance cone • As q approaches the resonance cone, previous work has concluded that the wave-particle interaction becomes less effective • Especially for > 100 keV electrons • Inan et al. [2003] raised this concern p/2 - qres

11. Sensitivity of Precipitation on q • Few > 100 keV electrons are precipitated because there are relatively few electrons at those energies • A constant distribution function demonstrates that waves propagating with q -> qreseffectively precipitate > 100 keV electrons

12. Sensitivity of Precipitation on q • For controlled precipitation, >100 keV and especially >1 MeV electrons are of primary interest • Distribution in L-shell is also important Propagation at high q induces strong > 1 MeV precipitation at a restricted range of L-shells Published in Kulkarni et al. [2008]

13. The Refractive Index Surface p/2 - qres • The direction of the vg can be determined from the refractive index surface, m(q) • The topology of m(q) changes if the wave frequency is above the lower hybrid resonance frequency, fLHR • fLHR at L = 2 is ~2.5 kHz • qresexists if f > fLHR Free Space: m =1 vg

14. Importance of Ions • At the frequencies of interest (1 – 5 kHz), ions are essential in calculating the refractive index • Above the local fLHR, including ions does not change the topology of the refractive index surface • The importance of ions is also manifested when thermal effects are accounted for

15. Thermal Effects Basic Equations: K: total dielectric tensor K0: cold plasma dielectric tensor K1: warm plasma correction • Thermal effects are especially important near resonances • 3 approaches: • Scalar pressure • “Fully adiabatic” theory retains tensor pressures, but neglects heat flux • Hot plasma theory—most complete • Fully adiabatic theory good approximation to hot plasma theory

16. Finite Ion Temperature At the frequencies of interest (1 – 5 kHz), a finite ion temperature more strongly closes the refractive index surface than a finite electron temperature

17. Heavy Ions Parallel Refractive Index Perpendicular Refractive Index

18. Conclusions • Thermal effects do change the refractive index surface for f > fLHR • A finite ion temperature impacts the refractive index surface more than a finite electron temperature • This effect needs to be investigated more deeply to determine whether the conclusions presented in Kulkarni et al. [2006] and Kulkarni et al. [2008] will change

19. Temperature Corrections