Energy Doubling in D.C. Accelerators

It is generally believed that charged particles cannot be accelerated from ground potential to ground potential unless they pass through a system which has associated iwth it a time varying magnetic field. D.C. electric fields must satisfy the equation {contour_integral} Eds = 0, while the time varying fields used in radio-frequency accelerators and betatrons are freed from this restriction of scalar potential theory. In 1932, AJ Dempster produced protons with an energy of 45 Kev, by passing them from an electrode at +22.5 kv dc to ground. The protons were first accelerated to ground potential, with an energy gain of 22.5 kev. A small fraction of the protons then picked up an electron from a residual gas molecule, and ''coasted'' to a second electrode at +22.5 kv. Then a small fraction of these neutral hydrogen atoms lost their electrons, and were accelerated to ground with a second gain in energy equal to 22.5 kev. An accelerator of this type is obviously impractical for several reasons. The probability of neutralizing a proton varies inversely with a high power of the particle velocity, so the scheme would not work at energies of interest to nuclear physicists. Even at the low energies where neutralization is not negligible, the energy spread of the beam would be wide because charge exchange could take place at all points along the beam trajectory