Propagation of a magnetized plasma beam in a toroidal filter

A two-fluid magneto-hydrodynamic model for the motion of a vacuum-arc-produced magnetized plasma beam in a toroidal magnetic filter is presented. The model takes into account in a self-consistent way electron-ion collisions and electrical, magnetic, centrifugal and pressure forces. An analytical solution is obtained that describes the distribution of the plasma density, the electron and ion velocities, the electric field and the current in the plasma. Analytical expressions for the filter efficiency as a 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 increases exponentially when the polarization field decreases. A decrease of the polarization field can take place when a current path outside the plasma short-circuits the electrical currents generated by the magnetic field in the plasma. When there is no polarization electric field, the filter efficiency η_c increases with the magnetic field as η_c = (1 + B²_c/B²)^-1 where B²_c = m_iΓ₀/(σ_⊥RR′ ²), m_i is the ion mass, Γ₀ is the total input ion flux, σ_⊥ is the transverse plasma conductivity and R and R′ are the major and minor radii of the torus, respectively.