Erdfernerkundung - Numerische Physik: Modellierung

264 KAPITEL 5. DIE ERWEITERTE PERSPEKTIVE: CAWSES
Abbildung 5.32: Bastille Day event: Particle intensities (left) and ionization rates (right) [189]
time for interaction decreases with increasing speed. dE/dx becomes minimum around the
particles rest energy, afterwards it increases slightly due to relativistic effects (interval 4).
Since this is a general behavior, Fig. 5.31 also can be applied to other particle species as long
as the horizontal axis is scaled in units of the particle’s rest energy (938 MeV in case of the
proton) instead of its energy.
§ 873 The specific energy loss is maximum at low energies (interval 2). In consequence,
the specific energy loss becomes largest close to the end of the particle’s range. Thus the
deposited energy as well as the resulting ion–pair production becomes maximum at the end
of the range, the so-called Bragg peak. For very low energies (interval 1), the Bethe–Bloch
equation is no longer valid: here the main physical processes are collisions between thermal
particles and attachment of the electron to an ion. Both processes are not described by the
Bethe–Bloch equation.
§ 874 The energy loss of a particle along its track can be calculated by numerical integration
of (5.3). Figure 5.32 shows in its right panel the calculated ion–pair production rates (that is
specific energy loss divided by average ionization energy) for three subsequent 12 h intervals,
the first one starting at the time marked by the left horizontal line in the left panel. During
this interval (blue curve), ion–pair production occurs down to about 15 km because particle
energies are rather high (the magenta curve has already acquired its maximum while the
blue curve still is rising). With increasing time (going from blue to red to green), the ion–pair
production rate shifts to higher altitudes because the intensities at higher energies already are
decreasing. In addition, ion–pair production at altitudes around 70 km is increased because
the intensities in the lower proton energies (blue curve in the left panel) still are increasing.
§ 875 For the total model chain, these data now are fed into the model atmosphere. Figure
5.33 shows the modeled (left) and observed (right) NOx production (top) and ozone
depletion (bottom). Although the modeled results tend to overestimate both the NOx production
and the ozone depletion, the overall temporal and spatial pattern is reproduced quite
well.
5.5.2 Monte Carlo Simulation of Atmospheric Ionization
§ 876 Sofar, we have used a direct numerical integration of (5.3). But that approach has two
disadvantages. First of all, the Bethe–Bloch equation is an empirical law derived from observations
at the ground, that is in a standard atmosphere. And secondly, it neither allows to
track the secondary electrons correctly nor to calculate ionization rates for incident electrons.
The reason for this is simple: if a proton ionizes an atom, the collision is between a heavy
2. Juli 2008 c○ M.-B. Kallenrode