Estimation of width of electron energy loss region in cusp magnetic field in negative ion sources

The loss width of electron energy in the cusp magnetic field in negative ion sources is investigated analytically. Energy equation and continuity equation for electrons are solved with heat flux and particle flux parallel and perpendicular to the magnetic field. Electron energy and density perpendicular to the magnetic field are assumed to decrease exponentially with each decay length and the cusp loss width is defined by the doubling of the decay length. An expression of the ratio of the cusp loss width of electron energy to that of electron density is obtained. The ratio of the cusp loss width depends on electron collision frequencies across the magnetic field and a heat transmission coefficient defined by the ratio of the heat flux to the particle flux multiplied by the electron temperature along the magnetic field. The heat transmission coefficient is related to the sheath potential on the wall surface. Both parameter dependence and the calculated value of the cusp loss width of electron energy derived from our analysis are in good agreement with Horiike et al.'s experimental result for the magnetic multipole ion source.