  We report measurements of GaAs/AlGaAs undoped field-effect transistors in
which two-dimensional electron gases (2DEGs) of exceptional quality and
versatility are induced without modulation doping. Electron mobilities at T=4.2
K and density 3 E11 /cm^2 exceed 4 E6 cm^2/Vs. At lower temperatures, there is
an unusually large drop in scattering, such that the mobility becomes too high
to measure in 100 micron samples. Below T=2.5 K, clear signatures of ballistic
travel over path lengths in excess of 160 microns are observed in magnetic
focusing experiments. Multiple reflections at the edges of the 2DEG indicate a
high degree of specularity.
