A cathodic arc plasma source equipped with a curved magnetic duct to filter macro-particles was used to study plasma transport through the duct. The optimal duct bias, at which the magnetic duct produces the maximum plasma output, for titanium cathodic arc plasma at 50, 100 and 150 A arc current was determined and the parametric effects of the arc current and guiding magnetic field on the optimal duct bias were investigated. The optimal bias decreased as the guiding magnetic field increased from 100 to 400 G and was almost independent of the guiding magnetic field when it was between 400 and 600 G, the upper limit for our equipment. The optimal duct bias at 400 G guiding magnetic field decreased with increasing arc current. Our results indicate that the optimal duct bias is related not only to the structure of the plasma source, but is also influenced by many other factors including cathode material and other plasma properties.