Space charge neutralization of positive and negative ion beams

After a brief review of the experimental methods, the present state of the theoretical works on the conditions to be fulfilled to reach charge neutrality and stability for a mixed positive and negative ion beam are described. Restriction is made to the case where the introduction of neutralizing ions is localized, the downstream mixed beam flying in a good vacuum, and where that mixed beam is current free. It is pointed out that one cannot hope to reach a final state of fine charge neutrality if a gross spatial mean neutrality is not ensured just downstream of the neutralizer, what requires severe restrictions for the possible values of the mean and thermal velocities of the two mixed fluids, at the neutralizer level. One of these necessary conditions is that the mixed fluids must both have supersonic mean velocities. When this condition is not fulfilled, there even is a possibility of joining the previous regime of mean neutrality through a sheath where the local electric field is a function of the local mean velocities. In the frame of a stationary model, this kind of solution is a mathematical singularity. However it was shown by numerical simulation to have a deep physical meaning : a self regulating sheath progressively modifies the distribution function of neutralizing ions as to provide at outgoing of the sheath a sonic mean velocity convenient for further mean neutrality, with a zero electric field. For the general problem of space charge neutralization of an ion beam by ions of opposite sign, a part of the present results are new