The dynamic behaviour of a plasma produced by a helicon wave using exciting m=1 and -1 helical modes is investigated. The RF (radio frequency) power dependence, antenna-plasma coupling, and time evolution of plasma parameters and Ar line intensities are studied in relation to the density jump, i.e. a steep increase in density to a level of 1013 cm-3 by the application of an RP input power greater than 1 kW. Before the density jump, the excited wave is localized near the antenna, exhibiting a standing wave character. After the jump, this wave propagates outwards and a dispersion relation for the helicon wave is confirmed.