  Recently cosmic ray electrons and positrons, i.e. cosmic ray charged leptons,
have been observed. To understand the distances from our solar system to the
sources of such lepton cosmic rays, it is important to understand energy losses
from cosmic electrodynamic fields. Energy losses for ultra-relativistic
electrons and/or positrons due to classical electrodynamic bremsstrahlung are
computed. The energy losses considered are (i) due to Thompson scattering from
fluctuating electromagnetic fields in the background cosmic thermal black body
radiation and (ii) due to the synchrotron radiation losses from quasi-static
domains of cosmic magnetic fields. For distances to sources of galactic length
proportions, the lepton cosmic ray energy must be lass than about a TeV.
