  Plasma lensing is the refraction of low-frequency electromagnetic rays due to
free electrons in the interstellar medium. Although the phenomenon has a
distinct similarity to gravitational lensing, particularly in its mathematical
description, plasma lensing introduces other additional features, such as
wavelength dependence, radial rather than tangential image distortions, and
strong demagnification of background sources. Axisymmetrical models of plasma
lenses have been well-studied in the literature, but density distributions with
more complicated shapes can provide new and exotic image configurations and
increase the richness of the magnification properties. As a first step towards
non-axisymmetrical distributions, we study two families of elliptical plasma
lens, softened power-law and exponential plasma distributions. We perform
numerical studies on each lens model, and present them over a parameter space.
In addition to deriving elliptical plasma lens formulae, we also investigate
the number of critical curves that the lens can produce by studying the lens
parameter space, in particular the dependence on the lensing ellipticity. We
find that the introduction of ellipticity into the plasma distribution can
enhance the lensing effects as well as the complexity of the magnification map.
