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For a while I have been fascinated with the real science behind some of the most common sci-fi weaponry out there, and I always like to find out which ones make any sense (although we cease discussions when fictional science is used to explain the weaponry itself). However, I am still not getting the concept behind ion cannons, because they have only a very general concept: a beam or focused missile of something which is shot straight at a target and disables all electronic equipment on it.

When I look at this, I think only of the proton beam, used in cancer treatment today, and which uses energized charged particles, such as protons or other forms of radiation, that pass near orbiting electrons and where the positive charge of the protons attracts the negatively charged electrons pulling them out of their orbits and causing ionization. So at the moment, when someone talks about and ion cannon, I read proton beam. Is this scientifically sound or am I missing something?

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The kind of thing you are looking for is the MARAUDER

The first MARAUDER experiment was motivated by RACE, or the Ring Accelerator Experiment, which took place in 1991 at Lawrence Livermore National Laboratory.[3][4] The ultimate goal of the MARAUDER program was to accelerate highly dense toroids containing plasma to high speeds. Such a system could be used for “hypervelocity projectiles,” x-ray production, and electrical power amplification. The stated goals of the program included studying the “formation, compression, and acceleration of magnetized plasma rings.”[3]

Specifically, objective of the program was the acceleration of a toroid of 0.5-2.0 mg plasma to a kinetic energy level on the order of megajoules using a 5-10 MJ coaxial gun design