A cathodic arc plasma source equipped with a curved magnetic duct to filter macro-particles was used to studyplasma diffusion and transport in the duct. We determine the optimal duct bias, at which the magnetic duct producesthe maximum plasma output, for titanium cathodic arc plasma at 50, 100 and 150 A arc current, and we investigate theparametric effects of the arc current and guiding magnetic field on the optimal duct bias. The optimal bias decreases asthe guiding magnetic field increases from 0.01 to 0.04T and is almost independent of the guiding magnetic field whenthe magnetic field strength ranges from 0.04 to 0.06T, the upper limit for our equipment. The optimal duct bias at0.04T guiding magnetic field decreases with increasing arc current.