  V407 Vul and RX J0806.3+1527 are X-ray emitting stars with X-ray light curves
that are 100% modulated on periods of 569 and 321 seconds respectively. These
periods and no others are also seen at optical and infra-red wavelengths. These
properties have led to the suggestion that the periods are the orbital period
of ultra-compact pairs of white dwarfs. There are two main double white dwarf
models: the unipolar inductor model analogous to the Jupiter-Io system and the
direct impact model analogous to Algol. In this paper we consider geometrical
constraints on the unipolar inductor model, in particular what parameter values
(component masses, orbital inclination and magnetic co-latitude) can describe
the X-ray and optical light curves. We find that for a dipole field on the
primary star, the unipolar inductor model fails to match the data on V407 Vul
for any combination of parameters, and can only match RX 0806.3+1527 if the
sparser set of observations of this star have been unluckily timed.
