Scintillation Arc Brightness and Electron Density for an Analytical
  Noodle Model
  We show that narrow filaments or sheets of over- or under-dense plasma, or
"noodles," with fluctuations of scattering phase of less than a radian, can
form the scintillation arcs seen for many pulsars. The required local
fluctuations of electron density are indefinitely small. We assume a cosine
profile for the electron column and find the scattered field by analytic
Kirchhoff integration. For a large electron column, corresponding to large
amplitude of phase variation, the stationary-phase approximation is accurate;
we call this regime "ray optics". For smaller-amplitude phase variation, the
stationary-phase approximation is inaccurate or inapplicable; we call this
regime "wave optics". We show that scattering is most efficient when the width
of the strip equals that of one pair of Fresnel zones, and in the wave-optics
regime. We show that the resolution of present observations is about 100
Fresnel zones on the scattering screen. Incoherent superposition of strips
within a resolution element tends to increase the scattered field. We find that
observations match a single noodle per resolution element with phase of up to
12 radians; or many noodles per resolution element with arbitrarily small phase
variation each, for net phase of less than a radian. Observations suggest a
minimum radius for noodles of about 650 km, comparable to the ion inertial
scale or the ion cyclotron radius in the scattering plasma.
