Finite Temperature Effects on VLF-Induced Precipitation Praj Kulkarni, U.S. Inan and T. F. Bell MURI...
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Transcript of Finite Temperature Effects on VLF-Induced Precipitation Praj Kulkarni, U.S. Inan and T. F. Bell MURI...
Finite Temperature Effects on VLF-Induced Precipitation
Praj Kulkarni, U.S. Inan and T. F. BellMURI 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 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].
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:
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 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]
Sources Distributed in L-shell
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
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 concernres
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 reseffectively 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 vg can be determined from the refractive index surface,
The topology of changes if the wave frequency is above the lower hybrid resonance frequency, fLHR
fLHR at L = 2 is ~2.5 kHz
res exists if f > fLHR
vg
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 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
Thermal Effects
K: total dielectric tensorK0: cold plasma dielectric tensorK1: warm plasma correction2
2
10
/ mcTkq
q
KKK
b
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
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