Time-Focusing Time-of-Flight, a new method to turn a MAC-E-filter into a quasi-differential spectrometer

Abstract

Spectrometers based on the magnetic adiabatic collimation followed by an electrostatic filter (MAC-E-filter) principle combine high angular acceptance with an excellent energy resolution. These features make MAC-E-filters very valuable for experiments where the kinetic energy of ions or electrons from rare processes has to be measured with utmost sensitivity and precision. Examples are direct neutrino mass experiments like KATRIN which investigate the energy of electrons in the endpoint region of the tritium $\beta$-spectrum. However, the MAC-E-filter is a very sharp energy high-pass filter but not a differential spectrometer. To determine a spectral shape of a charged particle source, different electric retarding potentials have to be used sequentially, reducing the statistics. In a previous work we have shown that the advantages of the standard MAC-E-filter can be combined with a measurement of the time-of-flight (TOF), allowing to determine spectral information over a certain energy range with one retarding potential only, with the corresponding gain in statistics. This TOF method requires to know the start time of the charged particles, which is not always possible. Therefore, we propose a new method which does not require the determination of the start time and which we call "time-focusing Time-of-Flight" (tfTOF): By applying a time dependent acceleration and deceleration potential at a subsequent MAC-E-filter, an energy dependent post-bunching of the charged particles is achieved.