 Electrostatic acceleration energy gain

For a fixed electric charge $q$, a time-independent electric potential $\Phi$ and negligible collisions or radiation losses, conservation of energy givesHere $V$ is the signed potential drop along the trajectory. A proton starting nearly at rest at $+V$ and arriving at ground gains $eV$: a chosen $500\mathrm{kV}$ gives $500\mathrm{keV}$, by the definition of the electronvolt. Several intermediate electrodes can distribute that drop along a tube, but the gains telescope to the same endpoint difference. Passing through more electrodes does not multiply the available kinetic energy beyond $qV$.

This is the distinction from a cyclotron. In a static electric field, a closed trip gives zero net work. A cyclotron changes the gap electric field between successive visits, so correctly timed particles repeatedly gain kinetic energy. Its limit involves the cyclotron resonance condition and relativistic detuning of a cyclotron; a single-pass electrostatic accelerator instead requires the full accelerating electric potential difference to be sustained at once. Neither machine's beam energy by itself specifies the energy released by a nuclear reaction.