[en] Helix-controlled collective ion acceleration involves the use of a helical slow wave structure to control the propagation velocity of an intense relativistic electron beam front, in which ions could be trapped and accelerated to high energy. Experimental and theoretical studies of the propagation of an IREB inside both cylindrical and helical conducting boundary systems have been conducted. In the experiments, an IREB (1 MeV, 30 kA, 30 ns, confined by an applied axial magnetic field) is injected from a 1 cm diameter hollow stainless steel cathode through a 2.4 cm diameter hole in a stainless steel anode into either cylindrical or helical downstream drift chambers. Beam propagation in the cylindrical systems is in good qualitative agreement with theoretical calculations based on a modified Bogdankevich, Rukhadze beam model. When a helical slow wave structure is used as the conducting boundary, the beam front velocity is significantly reduced to values approaching those associated with the helix pitch angle