Fast waves at frequencies far above the ion cyclotron frequency and approaching the lower hybrid frequency (also called 'helicons' or 'whistlers') have application to off-axis current drive in tokamaks with high electron beta. The high frequency causes the whistler-like behaviour of the wave power nearly following field lines, but with a small radial component, so the waves spiral slowly towards the plasma centre. The high frequency also contributes to strong damping. Modelling predicts robust off-axis current drive with good efficiency compared to alternatives in high performance discharges in DIII-D and Fusion Nuclear Science Facility (FNSF) when the electron beta is above about 1.8%. Detailed analysis of ray behaviour shows that ray trajectories and damping are deterministic (that is, not strongly affected by plasma profiles or initial ray conditions), unlike the chaotic ray behaviour in lower frequency fast wave experiments. Current drive was found to not be sensitive to the launched value of the parallel index of refraction n||, so wave accessibility issues can be reduced. Use of a travelling wave antenna provides a very narrow n||spectrum, which also helps avoid accessibility problems.