Space charge effect on the transport of a high-perveance He+ beam

Abstract

In the quasi-linear approximation of high perveance ion beam transport, the envelope equation for the beam radius r_b can be expressed by d²r_b/dz² = (K/r_b) + (ε_n²/r_b³), where K is the generalized perveance, r_b the beam radius, ε_n the normalized emittance, and z the direction of the beam. The perveance is a parameter for the space charge effect, and it is expressed using the characteristic beam current, I₀ 31 (A/Z) MA, as following: K = (I/I₀)(2β⁻³γ⁻³)(1−γ²f_e). The space charge, however, can be neutralized by electrons, which are produced through the beam induced ionization process in a residual gas. This effect is considered in the previous equation using the parameter f_e. The space charge neutralization becomes effective with the time constant τ_N, the mean ionization time of the residual gas of density n_g, τ_N = (n_gσ_iν)⁻¹, if the electron confinement time is much longer than τ_N.
In the transport of a low energy He⁺ beam, space charge neutralization effect is not obvious, because the ionization cross section is two orders of magnitude less than that of a proton beam in typical energy region of transport study, 30 − 100 keV. The ionization cross section of a He⁺ beam in a He gas and the mean neutralization time at the pressure 10⁻⁶ Torr are shown. The full neutralization can be expected only when the electron confinement time is longer than 200 ms.