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Recently the leptonic component of the cosmic ray spectrum has gained
new attention. New observations from ATIC, PAMELA and Fermi show a
deviation from a power-law in the form of an excess in both the
electron and positron spectra. Annihilating dark matter and nearby
pulsars (among other things) have been proposed as possible sources of
the excess leptons. Regardless of the source, a new propagation model
is needed to connect the energy spectrum measured on earth with the
injection spectra.
We present our numerical cosmic ray transport model in application to
the high energy electron transport in the ISM. Spatial and momentum
diffusion, particle escape, acceleration via Fermi I and continuous
energy losses were taken into account and their effects on the
steady-state energy spectrum analyzed. In solving the transport
equation we employed quasi-linear transport theory, the diffusion
approximation and a separation of the spatial and momentum problem to
obtain the leaky-box-equation, which was then solved numerically. The
spatial problem was solved analytically in cylindrical and prolate
spheroidal coordinates. We found that despite the many simplifications
we are able to reproduce the general shape of the high energy electron
spectrum.
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