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Carbon and titanium plasmas are used to investigate the effects of duct bias on the plasma transport through the magnetic duct of a cathodic-arc plasma source as a function of the magnetic-field strength and arc current so as to determine the optimal duct bias, at which the magnetic duct produces the maximum efficiency for plasma transport. The influence of the guiding magnetic field and arc current on the optimal duct bias is investigated. The optimal duct bias increases with the plasma density for carbon plasma, while the relationship is the opposite for the titanium plasma. The carbon-plasma behavior can be explained by a plasma-diffusion model presented in this paper, since the electron-ion collision frequency νei is less than the electron-cyclotron frequency νc,e. On the other hand, in a titanium plasma, νei is larger than νc,e, so this model is inaccurate. Our result shows that different kinds of plasmas have different transport behavior through the magnetic duct and thus, the duct parameters must be carefully chosen in order to achieve the optimal transport efficiency.