The results of the experimental study of the magnetic configurations in the H-1 heliac are presented. The shape of the flux surfaces and the rotational transform in H-1 can be controlled by varying external coil currents. Electron beam magnetic mapping has been performed to show the existence of closed nested flux surfaces and to observe the effect of small errors in coil alignment on the vacuum magnetic structure in H-1. Langmuir probes have been used to study the electron density profiles in a current-free collisional RF-sustained plasma (ne ≤ 4×1012 cm-3, Te ≤ 15 eV). In standard magnetic configuration and for the present moderate RF power levels, the highest central density is achieved at rather low magnetic field (0.07 T). This regime is characterised by peaked density profiles that appear to have a maximum coincident with the position of the vacuum magnetic axis. When a lowest-order m = 1, n = 1 resonance is introduced inside the outermost magnetic surface a strong asymmetry in both the vacuum magnetic structure and the plasma density profiles is observed. We observed low frequency (2–3 kHz) density fluctuations having low radial mode numbers and internal parallel plasma current localised in the regions of highest density gradient. These fluctuations are effectively suppressed by an increase of the magnetic field.