  The Aharonov-Bohm (AB) interference patterns in ring-shaped conductors are
usually dominated by random features. The amplitude of the oscillations is
random from sample to sample and from point to point on the magnetic field axis
owing to random scattering of the electron trajectories by impurities within
the wires. We report experiments on new devices made with wet etching and
global gates, which have shown major progress towards removing the random
features. In loops that exhibit ballistic conductance plateaux and cyclotron
orbit trapping at $4.2K$, the random pattern of AB oscillations (observed for
$T < 0.1K$) can be replaced by much more ordered one -- especially if only a
few transverse modes are populated in the ring. The amplitude and shape of the
oscillation envelope function change systematically as subbands are populated
in the wires forming the loops. Mechanisms governing the AB effect in the
ballistic regime are discussed. Correlation has been found between the
$G(V_{g},B=0)$ staircase and the ``beating period" of the envelope functions.
Quantum oscillations in $G(V_{g},B = 0)$ are consistent with direct
interference of paths of unequal length. Both the correlations and the quantum
oscillations in gate voltage are signatures of ballistic transport.
