Transcript AGU2012_Eliasson

Outline
Motivation and observation
The wave code solves a collisional Hall-MHD model
based on Faraday’s and Ampere’s laws
respectively, coupled with the ion momentum equation
and the momentum equation for inertialess electrons
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Modulating electron pressure at F2 peak by HF heating, generating
ionospheric currents (Ionospheric Current Drive) and magnetosonic waves
Weakly collisional F region with magnetosonic and shear Alfven waves
Diffusive Pedersen layer 120-150 km
E-region supports weakly damped helicon/whistler waves
Nonconducting free space below 90 km (continuous parallel electric field
and normal magnetic field at plasma-free space boundary)
Konducting ground (zero parallel electric field and normal magnetic field)
Oblique magnetic field
Simulation Setup
• Source location
– L =1.5, Height =
• Source Dimension
• ULF waves: 2, 5, 10
Hz
• Ionosphere Condition
– Density Profile
Some background on Alfevn wave
EMIC
f = 2 Hz
f = 5 Hz
f = 10 Hz
The below figure shows a case with 10 Hz signal excited at the L=1.4 shell.
The below figure shows a case with 10 Hz signal excited at the L=1.57 shell.
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I have now made new setups at L=1.6, where the 10 Hz case will cross the resonance (this was not the case for
L=1.4). I have prepared runs for f=2Hz, 5Hz and 10Hz. Please see the attached zip file. While running, the program
makes a zoomed in view of the y-component of the B field so that one can monitor the details. Also the L=1.6 line is
plotted and a few contours of the EMIC wavelength, For 10 Hz one can see that the EMIC wavelength is relatively
constant up to near the resonance where it sharply drops to zero, while for 2 and 5 Hz the wavelength has a minimum
at the Alfven speed minimum and then rises due to decreasing plasma density at higher altitudes.
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In the radial direction I set the step size about 8 km and in the azimuthal direction about 20 km at Earth radius. I use
oxygen ions, and magnetic dipole field with 3.12e-5 Tesla at magnetic equator. The heating spot has a width (FWHM)
of about 40 km in radial direction and 80km in asimuthal direction, which is quite realistic. The Alfven minimum is at
around 500km which is somewhat high but not unreasonable.
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The simulation runs up to 12 seconds using 4e5 timesteps. On my laptop each timestep takes 1 second so the whole
simulation is 4-5 days. However you can probably interrupt the simulation earlier and use the data saved every 400
timesteps.
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My interpretation for 10Hz is as follows (based on the short run):
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The EMIC waves primarily propagates along the magnetic field lines directly from the source. Therefore I think these
waves are directly created at the pump location via interaction with the Hall term, which becomes important when the
"spot size" is comparable with or smaller than the ion inertial length.
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Somewhat below the L=1.6 lines are Alfven/whistler mode waves. These waves are not created at the pump location
but at the Hall region where magnetosonic waves have been mode converted to shear Alfven waves (the process
suggested by Dennis)
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The following maybe is for our internal notes for discussion for now (I am not completely sure of correctness):
The EMIC wave energy will pile up near the resonance. However this does not necessarily mean that the magnetic
field fluctuations will grow there. The wave energy density W consists of a sum of magnetic wave energy density
B^2/2mu0 and of ion kinetic energy density n0 m_i v_i^2/2. From Ampere's law we have that k B= mu_0 e n0 v_i
when c k/omega_pe>>1 (k is the parallel wavenumber). Therefore, instead of the energy density W=B^2/2mu0, we
will instead have W=n0 m_i v_i^2/2=(c^2 k^2/omega_pe^2)*B^2/2mu0. Energy conservation requires that (energy
density)x(group velocity)=constant. For c k/omega_pe>>1 we have the EMIC group velocity
v_g=omega_ci/k, hence constant =v_gr*W=(omega_ci/k)*(c^2 k^2/omega_pe^2)*B^2/2mu0
Solving for B, we find B ~ n0/sqrt(k) ~ n0*sqrt(lambda), where lambda is the wavelength.
Hence when lambda goes to zero at the resonance, then the wave magnetic field also goes to zero there, and all the
energy is dumped into kinetic energy of the ions.
It would be interesting to see a long run for 10Hz and see what happens near the resonance layer, if it increases or
decreases like above.
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This plot for 10 Hz I did quickly for the proposal writing. After this I changed
the code for
20 Hz and smaller domain. Unfortunately I didn't save the setup for 10 Hz
but I think you figured it out. I used somewhat larger domain for 10 Hz (total
domain pi/2 in phi direction and 10 000 km in r direction, with dr=16 km and
dphi=0.003, approximately).
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Yes the solid line is for gyrofrequency=10Hz. You can do this plot with the
command
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contour(X'/1000,Z'/1000,Babs_vec',1.0539e-005)
where 1.0539e-005 Tesla is the magnetic field for 10 Hz gyrofrequency and
Babs_vec is the total magnitude of the dipole geomagnetic field in the
simulation (see the code main.m).
• Maybe some pieces can be picked from the ICD
article with Dennis which I have
• attached. Section 4 contains some experimental
results. They essentially contained i)
Observations of shear Alfven waves by Demeter
above HAARP, ii) the skip-distance directly
under the heated region for ICD generated
waves, and iii) far propagation of guided
magnetosonic waves excited by ICD but not by
PEJ
• References:
• B. Eliasson, C.-L. Chang, and K. Papadopoulos (2012), Generation
of ELF and ULF electromagnetic waves by modulated heating of the
ionospheric F2 region, J. Geophys. Res., 117,
doi:10.1029/2012JA017935
• Papadopoulos, K., N. A. Gumerov, X. Shao, I. Doxas, and C. L.
Chang
• (2011), HF-driven currents in the polar ionosphere, Geophys. Res.
Lett.,
• 38, L12103, doi:10.1029/2011GL047368.
• Papadopoulos, K., C.-L. Chang, J. Labenski, and T. Wallace (2011),
First
• demonstration of HF-driven ionospheric currents, Geophys. Res.
Lett., 38,
• L20107, doi:10.1029/2011GL049263.