No electromagnetic confinement? I may have missed something here, but the main problem with “beam fusion” has always been Coulomb collisions.

I offer to use focusing in a very strong self-magnetic field with only partial compensation of ions positive space charge. In this case the particle scattered at a small angle by Coulomb force will return to the axis magnetically. And this will be repeated and repeated before fusion event.

If you are using confinement, EM or otherwise, then we are back to talking about instability, especially in long-pulse. My guess is that you’ll see kink instability, especially at high beam densities.

Yes, thanks to the focusing the beam density will be very high. But there are a lot of types instabilities. Why obligatory kink instability?
In the text you can see:
Bennet and Budker have shown that in case of sufficient high relativism of electrons (relativistic factor) such beams should be steady enough against the majority types of instabilities (G.I. Budker, Collection of articles, The Stabilized Electronic Beam, M, Nauka, 1982)
And right now investigations of beams instabilities in case of very strong currents are under way as well.
And in Heavy Ions Fusion (HIF) program the currents equal to tens thousands amperes are used.
And then they are focused on a few mm sized target.