Temperature effects on the energy spreads in liquid metal ion sources

The energy spread of charged particles during beam propagation is calculated for liquid-metal ion sources. After acceleration, the particles have different energies originating from Coulomb interactions among them, which are randomly located due to the statistical fluctuations caused by the emission-surface temperature. The energy spreads are obtained in terms of the total current and emitter temperature. In particular, the energy spread is proportional to the square root of the emission-surface temperature. The results agree remarkably well with previously reported experimental data for the liquid-gallium ion beam.