We study experimentally and theoretically stable regimes and discharge disruptions in a helicon plasma source. At fixed input power and gas pressure, stable operation of the source is possible below some critical value of magnetic field B-cr. The plasma density increases with the magnetic field and reaches a maximum value n(max) at B-cr; after which the discharge disruption occurs. Both B-cr and n(max) increase almost linearly with the input power and the rate of increase is increasing with the pressure. Matching of the plasma load to the rf power source improves when approaching the disruption point, and becomes perfect at the critical field. The theory of discharge disruptions assumes the power absorption in a helicon source to arise from the linear conversion of helicon waves into electrostatic waves at the plasma edge. The calculated dependence of the absorbed power on the plasma density turns out to be nonmonotonic with minima at antiresonances of the electrostatic wave excitation. This explains qualitatively principal peculiarities of discharge disruptions. The calculated plasma impedance is in agreement with experimental value within a factor of 2.