The beams are a result of runaway particles in the dense plasma region. Runaway particles are ion and electrons that are accelerated well above the temperature of the system. For example, if you have a 1 keV plasma, you expect to find most of the particles with energies less than 10 keV. If you find an abundance of particles at 100 keV you have a runaway situation. The cause is complex but ions move away from the anode (center electrode) and electrons move toward it. While it is a nice diagram to show the two beams are truly separate, recent published articles show ions travel in both directions and electrons seldom let ions travel without tagging along. This means you have ions and electrons in both beams but the contributions are not equal.
If you get a fusion in another system, quite the same thing would happen then? At least if the fusion happen in a concentrated area, because the fused Ions and electrons must be so much hotter than the rest.
It doesn’t happen in every system. The ions from fusion are very energetic but they are distributed evenly in every direction. The reason the ions are directed because of the voltage difference between the anode and cathode.