Yeah, RHIC is "conventional", but WOW! Quark-gluon plasmas... tiny black holes...
As for using electrons, this is somewhat of a holy-grail in some circles. The concept is simple; take some electrons from a plasma, separate them from the ions, and there will be an electrostatic field that is so huge that the ions will reach high energies in 10's of microns. This is what is done (routinely) in many laser labs, mostly in the Northern Hemisphere. Fire a very powerful laser at an extremely thin piece of solid. The laser "heats" the electrons predominantly in the forward direction, they leave the target and set up this short-lived field that accelerates ions.
The electrons have a "temperature" of order of MeV, as you said, and, if the ions are protons, their energies are coming out at 20-50 MeV. For higher Z ions, the energies can be > GeV. But one must look at the energy per nucleon before one is impressed or not! For medical applications, protons at 200 MeV are needed to get to ~ center of a human body. So, for applications, think of 200 MeV per nucleon, roughly.
I'm not sure what you are referencing in you initial comment, but ions can be accelerated by electrons to GeV energies in 10-100 microns and 10-100 psec. But take care of which ion and, for my example, there is a rather large laser used to make the electrons.