Erdfernerkundung - Numerische Physik: Modellierung

5.5. CAWSES 267
Abbildung 5.35: Energy losses of 1–
500 MeV protons calculated with a
Monte Carlo simulation (circles) and
Bethe–Bloch (solid line) [217]
Orbiting Environmental Satellite) even suggest a slight preference for larger pitch angles
inside the polar cap at altitudes of 900 km (Bornebusch, priv. comm.).
§ 883 Energy spectra of precipitating SEPs can be described by a broken power law [74, 61,
114]: I(E) = I0 · (E/E0) −γ with I0 being the differential intensity at a reference energy E0,
E the energy, and γ the spectral index. Around some 100 MeV the spectrum flattens and
intensities increase due to the background of galactic cosmic rays [71]. Observed spectra are
fitted simultaneously by up to three power-laws; the breaks between the power laws are not
at fixed energies but are determined such that the best fit over the entire spectrum results.
Monte Carlo Simulation
§ 884 GEANT 4 [3, 67] allows for a multitude of interactions between the precipitating
particle and the absorber atmosphere. Our model considers as subset of particles protons,
electrons, positrons, αs, and photons. Interactions are limited to electromagnetic ones: multiple
scattering, Compton-scattering, ionization, photo electric effect, gamma conversion,
annihilation, pair production, and production of bremsstrahlung. Secondaries produced in
such interactions are tracked up to a cut-off length for particle propagation of 1 m. If particle
energies are lower, the model switches to continuous energy loss.
§ 885 Precipitating particles have an angular distribution and an energy spectrum. The
Monte-Carlo simulation itself is performed for mono-energetic pencil-beams of 100 particles;
angles of incidence vary between 0 ◦ and 80 ◦ in steps of 10 ◦ . The energies range from 1 MeV
to 500 MeV in 109 logarithmic equidistant steps for protons and 1 MeV to 50 MeV in 340
steps for electrons. Statistics are tested by increasing the number of incident particles by a
factor of 10 – the results are essentially the same.
§ 886 The total energy input into each layer is the sum of the energy depositions of the
individual particles; a division by the layer’s thickness yields the linear energy transfer (LET)
dE/dx. Thus the primary result of the simulation is the LET as function of altitude, initial
kinetic energy and impact angle.
§ 887 Ion pair production rates for individual particle events are obtained by folding the
LETs with the observed particle spectrum and angular distribution and assuming an average
ionization energy of 35 eV per ion pair [186].
c○ M.-B. Kallenrode 2. Juli 2008