A plasma weapon doesn't expand because of its charge, it expands due to its internal pressure and temperature. Any macroscopic-scale plasma stream has to be electrically neutral, with equal numbers of free positive charges and free electrons. If a plasma discharge was non-neutral, whoever was firing the plasma would accumulate a huge negative or positive charge... which would soon become large enough to overwhelm the accelerating potential and cause the plasma to come right back to its source. (not to mention being very harmful to the shooter)
For example, every ion thruster used in real-world spacecraft contains separate accelerating elements for positive ions and negative electrons. The resulting plasma is electrically neutral.
Electrostatic ion thruster - Wikipedia, the free encyclopedia
You're confusing plasma weapons with electron beam weapons. Electron beams are very commonly used for food sterilization and radiation therapy so their physics is well understood. Their mutually repulsive charge spreads them out very widely over a distance of a few meters, and they also create an electrical circuit between the beam and the target.
On the other hand, a plasma weapon would attempt to use some form of confined plasma, usually based on the same plasma technology used to create fusion power. Fusion plasmas are electrically neutral, with magnetic fields that simultaneously confine the positive nuclei and the associated electrons. This also means that a fusion plasma is extremely electrically conductive. Tokamaks only work because the confined fusion plasma carries an extremely strong electrical current; up to 15 megaamperes in ITER according to Wikipedia. (
Tokamak - Wikipedia, the free encyclopedia)
I'd imagine that any civilization with a high prevalence of fusion power would have a much better understanding of hot-plasma magnetohydrodynamics than what we have today. It's at least partially plausible that super-advanced plasma physics could produce a free-floating plasmoid that remains stable for milliseconds... If that plasmoid is moving at a substantial percentage of c, that would give a "plasma weapon" an effective range of tens of kilometers.