A magnetically enhanced HDP-CVD plasma source includes a hollow cathode target and an anode. The anode and cathode form a gap. A cathode target magnet assembly forms magnetic field lines that are substantially perpendicular to a cathode target surface. The gap magnet assembly forms a cusp magnetic field in the gap that is coupled with the cathode target magnetic field. The magnetic field lines cross a pole piece electrode positioned in the gap. This pole piece is isolated from ground and can be connected with a voltage power supply. The pole piece can have a negative, positive, or floating electric potential. The plasma source can be configured to generate volume discharge. The gap size prohibits generation of plasma discharge in the gap. By controlling the duration, value and a sign of the electric potential on the pole piece, the plasma ionization can be controlled. The magnetically enhanced HDP-CVD source can also be used for chemically enhanced ionized physical vapor deposition (CE-IPVD). Gas flows through the gap between hollow cathode and anode. The cathode target is inductively grounded, and the substrate is periodically inductively grounded.