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

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

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 Inan et 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 λ s = 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].

Illumination of the Plasmasphere  If f f LHR, v g moves inwards  Modulating the wave frequency can be used to target specific regions  Landau damping affects this result:

Cavity Enhancement Factor

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

 With each source radiating three wave frequencies close to the local f LHR, 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] Sources Distributed in L-shell

Energetic Electron Precipitation  Choose 3 central wave frequencies  For each launch rays from θ res  θ res + 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

Simulation Results We have results for sources at L = 1.5, 2.0, and 2.5, at  o for each L-shell

Variation of  along Raypath   impacts the effectiveness of the wave-particle interaction  For a wide variety of input parameters,  approaches the resonance cone   s  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  res

Sensitivity of Precipitation on   Few > 100 keV electrons are precipitated because there are relatively few electrons at those energies  A constant distribution function demonstrates that waves propagating with  res  effectively precipitate > 100 keV electrons

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

The Refractive Index Surface  The direction of the v g can be determined from the refractive index surface,   The topology of  changes if the wave frequency is above the lower hybrid resonance frequency, f LHR  f LHR at L = 2 is ~2.5 kHz   res exists if f > f LHR vgvg Free Space:  =1  res

Importance of Ions  At the frequencies of interest (1 – 5 kHz), ions are essential in calculating the refractive index  Above the local f LHR, 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

Thermal Effects K: total dielectric tensor K 0 : cold plasma dielectric tensor K 1 : warm plasma correction Basic Equations: 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

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

Heavy Ions Perpendicular Refractive Index Parallel Refractive Index

Conclusions  Thermal effects do change the refractive index surface for f > f LHR  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

Temperature Corrections