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The KArlsruhe TRItium Neutrino (KATRIN) experiment aims at a measurement ofthe neutrino mass with a 90 % confidence limit (C.L.) sensitivity of 0.2eV/c$^2$ by measuring the endpoint region of the tritium $\beta$ decay spectrumfrom a windowless gaseous molecular tritium source using an integratingspectrometer of the MAC-E-Filter type. We discuss the idea of using theMAC-E-Filter in a time-of-flight mode (MAC-E-TOF) in which the neutrino mass isdetermined by a measurement of the electron time-of-flight (TOF) spectrum thatdepends on the neutrino mass. MAC-E-TOF spectroscopy here is a very sensitivemethod since the $\beta$-electrons are slowed down to distinguishablevelocities by the MAC-E-Filter. Their velocity depends strongly on theirsurplus energy above the electric retarding potential. Using MAC-E-TOF, astatistical sensitivity gain is expected. Because a small number ofretarding-potential settings is sufficient for a complete measurement, incontrast to about 40 different retarding potentials used in the standardMAC-E-Filter mode, there is a gain in measurement time and hence statisticalpower. The improvement of the statistical uncertainty of the squared neutrinomass has been determined by Monte Carlo simulation to be a factor 5 for anideal case neglecting background and timing uncertainty. Additionally, twoscenarios to determine the time-of-flight of the $\beta$-electrons arediscussed, which use the KATRIN detector for creating the stop signal anddifferent methods for obtaining a start signal. These comprise the hypotheticalcase of an `electron tagger' which detects passing electrons with minimalinterference and the more realistic case of `gated filtering', where theelectron flux is periodically cut off by pulsing the pre-spectrometerpotential.

Neutrino mass sensitivity by MAC-E-Filter based time-of-flight spectroscopy with the example of KATRIN