Motion of magnetized vacuum arc plasma beam in a quarter-torus

An analytical solution is obtained that describes the distribution of plasma density, the electron and ion velocities, the electric field and the current in the magnetized plasma beam in a toroidal magnetic filter. Analytical expressions for the filter efficiency as function of the toroidal magnetic field are also derived. The effect of the centrifugal and diamagnetic ion drifts on the polarization electric field is studied. It is shown that the efficiency η_c increases exponentially when this field decreases. When the polarization electric field is absent, the filter efficiency increases with the magnetic field as η_c = (1 + B_c²/B²)^-1, where B_c² ≅ m_iΓ₀/(Zσ _⊥ RR′²), m_i and Z are the ion mass and charge state, Γ₀ is the input ion flux, σ_⊥ is the plasma transverse conductivity, and R, R′ are the major and minor radii of the torus, respectively.