I was looking through the various nuclear fusion approaches and it struck me that they all suffered from one of two problems. Either they wasted a lot of energy trying to accelerate fusion fuel to the needed speed by using heat, which produced a distribution of particle energies instead of a single energy, or they couldn't get the needed particle density for the reaction to progress fast enough to burn all the fuel before it flies apart.
The reactor that comes closest in terms of accelerating fusion fuel efficiently is the polywell, because it uses an electrostatic potential difference to get the fuel to the needed speed for fusion. However, since the nucleii are ions, it is very hard to get the densities (150 g/cm^3) for rapid fuel burn.
So a thought came to me. Why can't an electrostatic accelerator accelerate deuterium ions to fusion energies, and have the accelerators arranged to have the ion beams converge to a focal point. However, after accelerating the ions, and moving them towards the focus, neutralize the ions using an electron beam, so the particle beam is both at high speed, and neutral to allow compression without electrostatic repulsion.
I think this might, work and googled it and couldn't find anyone having attempted this. Am I missing something fundamental here? If so, what is it? Why wouldn't this work?