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

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 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.

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. 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. 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. My interpretation for 10Hz is as follows (based on the short run): 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. 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) 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.

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 km in r direction, with dr=16 km and dphi=0.003, approximately). Yes the solid line is for gyrofrequency=10Hz. You can do this plot with the command contour(X'/1000,Z'/1000,Babs_vec',1.0539e-005) where e-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: /2012JA 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: /2011GL Papadopoulos, K., C.-L. Chang, J. Labenski, and T. Wallace (2011), First demonstration of HF-driven ionospheric currents, Geophys. Res. Lett., 38, L20107, doi: /2011GL