In this series, we outline a strategy for analyzing electrons and muons in gases in crossed electric and magnetic fields using the straightforward transport equations of momentum-transfer theory, plus empirical arguments. The method, which can be carried through from first principles to provide numerical estimates of quantities of experimental interest, offers a straightforward, physically transparent alternative to "off-the-shelf" simulation packages, such as Magboltz and GEANT. In this first article, we show how swarm data for electrons in helium gas subject to an electric field only can be incorporated into the analysis to generate electron swarm properties in helium gas in crossed electric and magnetic fields and to estimate the Lorentz angle in particular. The subsequent articles in the series analyze muons in crossed fields using similar transport theory, though the absence of muon swarm data requires empiricism of quite a different nature.
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