  Experimental and theoretical studies of the effects of weak radio-frequency
electric fields on Rydberg-Stark states with electric dipole moments as large
as 10000 D are reported. High-resolution laser spectroscopic studies of Rydberg
states with principal quantum number $n=52$ and $53$ were performed in pulsed
supersonic beams of metastable helium with the excited atoms detected by pulsed
electric field ionisation. Experiments were carried out in the presence of
sinusoidally oscillating electric fields with frequencies of 20~MHz, amplitudes
of up to 120~mV/cm, and dc offsets of up to 4.4~V/cm. In weak fields the
experimentally recorded spectra are in excellent agreement with the results of
calculations carried out using Floquet methods to account for electric dipole
couplings in the oscillating fields. This highlights the validity of these
techniques for the accurate calculation of the Stark energy level structure in
such fields, and the limitations of the calculations in stronger fields where
$n-$mixing and higher-order contributions become important.
