  Diffusive Synchrotron Radiation (DSR) is produced by charged particles as
they random walk in a stochastic magnetic field. The spectrum of the radiation
produced by particles in such fields differs substantially from those of
standard synchrotron emission because the corresponding particle trajectories
deviate significantly from gyration in a regular field. The Larmor radius,
therefore, is no longer a good measure of the particle trajectory. In this
paper we analyze a special DSR regime which arises as highly relativistic
electrons move through magnetic fields which have only random structure on a
wide range of spatial scales. Such stochastic fields arise in turbulent
processes, and are likely present in pulsar wind nebulae (PWNe). We show that
DSR generated by a single population of electrons can reproduce the observed
broad-band spectra of PWNe from the radio to the X-ray, in particular producing
relatively flat spectrum radio emission as is usually observed in PWNe. DSR can
explain the existence of several break frequencies in the broad-band emission
spectrum without recourse to breaks in the energy spectrum of the relativistic
particles. The shape of the radiation spectrum depends on the spatial spectrum
of the stochastic magnetic field. The implications of the presented DSR regime
for PWN physics are discussed.
