Electron-magnetized vacuum arc plasma transport in a magnetic toroidal duct is calculated numerically taking in account electron-ion collisions, electron and ion temperatures, and the high conductivity of the duct wall. The longitudinal magnetic field in the duct, the fully ionized plasma density and the electric potential distribution at the torus entrance are given, while the plasma density, electrical field and current, and macroscopic plasma velocity across the magnetic field inside the duct are calculated. Toroidal coordinates are used to describe plasma beam propagation. A Runge-Kutta routine is used for the calculations along the torus while a finite difference method is used across the torus cross section. It is found that plasma loss due to particle flux to the duct wall depends on the electron and ion temperatures and the plasma density distribution at the torus entrance cross section. With an electron temperature of Te = 20 000 K, 30 000 K and 50 000 K, an ion temperature Ti = 20 000 K and a Gaussian distribution of plasma density at the torus entrance with a maximum value n0 = 1019 m-3, we found that the duct efficiency was less than 10% for longitudinal magnetic field strengths of 10 mT and 20 mT. In the case where only the electrons are magnetized, filter efficiency depends only weakly on the magnetic field strength, on Te, and on Ti.