EGSnrc is an electromagnetic Monte Carlo radiation-transport code that can trace the interactions of electrons and positrons with matter down to 10 keV, and of photons down to 1 keV. I have used it to simulate a single mirroring of magnetospheric electrons in the upper atmosphere, to see what effect the magnetic field has on the energy spectra and angular distributions of the photons and electrons that come up from the atmosphere, and these webpages present preliminary results.
The atmosphere is represented by a mixture of nitrogen, oxygen, and argon varying with altitude from 0 to 200 km in 1 km steps, with partial pressures determined from the NRLMSISE-00 model averaged over the globe. I ran two sets of simulations, one without a magnetic field and one with a field corresponding to the footpoint of L = 3.8 in a centered dipole model (B magnitude is 0.505 Gauss, dip angle is 73 degrees, and derivatives of B magnitude are 2.3e-04 Gauss per km along the field line, -1.1e-04 Gauss per km in the toroidal direction, and -1.2e-04 Gauss per km in the poloidal direction). In each set, I simulated 20,000 monoenergetic incident electrons at each of 16 energies and at each of 19 angles from 0 to 90 degrees in 5 degree steps (pitch angles for the simulations with a magnetic field, zenith angles for simulations without); the output of the code was a list of the energy, velocity vector, and position for all particles (electrons, photons, and a few positrons) that exited the simulation heading upward. The incident electrons were gyrotropic for the simulations with a magnetic field, and the stepsize was limited to 2 percent of a particle's local gyroradius; supplementary runs with the atmosphere replaced by vacuum confirmed that numerical errors did not break the first adiabatic invariant, i.e., an electron that went in at one pitch angle came out at the same pitch angle (within a degree), down to 64 degrees incident pitch angle where the electrons ran out the bottom of the simulation volume (hit the ground!).
The pages of plots linked to the list at the bottom of this page are summaries of the exiting electrons and photons, for cases with and without the magnetic field, summed up over an isotropic distribution of electron incidence angles. Each of the four plots on each page shows the distribution of output particles with respect to angle and energy (pitch angle for the output electrons in the magnetic field, zenith angle for photons in both cases and for electrons without a magnetic field). The units are sort of nonphysical, a fractional response in each bin relative to the incident flux; that is, inputs and outputs are normalized by the solid angle of the respective pitch angle bins, but just counted up by energy bins (rather than per MeV, for example). The reason for this odd choice is that, in the case where all electrons mirror in the absence of an atmosphere, the output plot would be a solid column of 100% at all pitch angles in the energy bin corresponding to the incident energy, and zero elsewhere. The degree to which the results depart from this is a measure of the effect of the atmosphere.
The magnetic field's "mirror force" acts to lift electrons up and push them out of the atmosphere; thus it is not surprising that more electrons retain nearly all of their incident energy in the case with the magnetic field than in the case without. Only electrons that barely graze the atmosphere (incident zenith angles near 90 degrees) retain most of their energy in the absence of a magnetic field, while in the presence of a field, the response takes different forms at low and high incident energies. At the lowest energies, a nearly isotropic distribution of electrons with their full energies comes back up at a reduced flux, as scattering combines with the mirror force to enhance the "bouncing" behavior; I need to quantify this, but it looks like our old rule of thumb of "a fraction 1/e survives each bounce" isn't far off. At high energies, the electrons act more like ions, with a well-defined loss cone at about 75 degrees pitch angle. To my surprise, I don't see a lot of difference in the photon distributions coming out between cases in the presence and absence of a magnetic field, for any incident electron energy; it looks like somewhat fewer come up for the case with the magnetic field, but again I'll have to quantify this.
It takes weeks for our UNIX workstation to grind through a complete set of energies and pitch angles, so I will update these results rather slowly! I am currently redoing the simulations for the case with the magnetic field in order to tabulate the energy deposited in each layer of the atmosphere, for comparison with the deposition in the absence of a magnetic field. I would also like to try different configurations for the magnetic field, to investigate the effect of dip angle and field magnitude and gradients.
new 1 October 2003