Theoretical discussion for electron-density distribution in multicuspion source

By introducing some ideas of magnetohydrodynamics (MHD) and kinetic theories, some useful solutions for electron-density distribution in the radial direction in multicusp ion source are obtained. Therefore, some conclusions are made in this perspective: 1, the electron-density distributions in a specific region in the sheath are the same with or without magnetic field; 2, the influence of magnetic field on the electron density obeys exponential law, which should take into account the collision term as well if the magnetic field is strong; 3, the result derived from the Boltzmann equation is qualitatively consistent with some given experimental results.