Expression of longitudinal third-order transport coefficient in terms of α parameters and its validity

The relation between the longitudinal third-order transport coefficient ω 3 contained in the continuity equation for electrons and α parameters defined by arrival-time spectra of an electron swarm is deduced. Values of ω 3 and the α parameters in CH4 gas and SF6 gas are calculated by Monte Carlo simulation, and then the values of ω 3 are compared with those of the longitudinal third-order transport coefficient ω'3 which are calculated from the α parameters to examine the validity of the deduced relation. The values of ω'3 are found to excellently agree with those of ω 3 below 500 Td in CH4 gas and from 150 Td to 700 Td in SF6 gas, where the values of the effective ionisation coefficient are nought or quite small. The results suggest that values of ω 3 can be obtained experimentally from arrival-time spectra measured by a double-shutter drift tube.