The successful operation of a Two-Beam accelerator based on extended relativistic klystrons hinges upon decreasing the cumulative dipole BBU growth from an exponential to a more manageable linear growth rate. We describe the theoretical scheme to achieve this, and a new experiment to test this concept. The experiment utilizes a 1-MeV, 600-Amp, 200-ns electron beam and a short beamline of periodically-spaced rf dipole-mode pillbox cavities and solenoid magnets for transport. Descriptions of the beamline are presented, followed by theoretical studies of the beam transportand dipole-mode growth.