A negatively biased collecting plate was used to collect the ion current of the cathodic arc plasma transported through a curved magnetic duct. The optimal duct bias at which the duct has the maximum efficiency for plasma transport was measured for C, Ti, Mo, and W plasmas as a function of the arc current and guiding magnetic field. The optimal bias decreased with the magnetic field and was almost steady when the field was above 400G. The optimal bias at 400G and above increased with the arc current for C plasma but the opposite relationship was observed for Ti, Mo, and W plasmas. The effects of the plasma density, ion mass, ion kinetic energy, and magnetic field on the optimal bias are discussed.