  We develop the theory of interstellar scintillation as caused by an irregular
plasma having a power-law spatial density spectrum with a spectral exponent of
4 corresponding to a medium with abrupt changes in its density. An ``outer
scale'' is included in the model representing the typical scale over which the
density of the medium remains uniform. Such a spectrum could be used to model
plasma shock fronts in supernova remnants or other plasma discontinuities. We
investigate and develop equations for the decorrelation bandwidth of
diffractive scintillations and the refractive scintillation index and compare
our results with pulsar measurements. We consider both a medium concentrated in
a thin layer and an extended irregular medium. We conclude that the
discontinuity model gives satisfactory agreement for many diffractive
measurements, in particular the VLBI meaurements of the structure function
exponent between 5/3 and 2. However, it gives less satisfactory agreement for
the refractive scintillation index than does the Kolmogorov turbulence
spectrum. The comparison suggests that the medium consists of a pervasive
background distribution of turbulence embedded with randomly placed discrete
plasma structures such as shocks or HII regions. This can be modeled by a
composite spectrum following the Kolmogorov form at high wavenumbers and
steepening at lower wavenumbers corresponding to the typical (inverse) size of
the discrete structures. Such a model can also explain the extreme scattering
events. However, lines of sight through the enhanced scattering prevalent at
low galactic latitudes are accurately described by the Kolmogorov spectrum in
an extended medium and do not appear to have a similar low-wavenumber
steepening.
