On approximations involved in the theory of charged particle transport in gases in electric and magnetic fields at arbitrary angles

Various approximations and computer codes for the calculation of charged particle transport in gases in electric and magnetic fields have found their may into mainstream applications of various types. Some of these codes/approximations avoid the mathematical complexity associated with an accurate solution of Boltzmann's equation, but because of assumptions of symmetry and/or near isotropy in velocity space they may be incorrect. Using an accurate multiterm solution of Boltzmann's equation for electric and magnetic fields oriented at arbitrary angles with respect to each other, we highlight the inadequacies of such assumptions. In addition we explore the validity of Tonks' theorem and the effective field approximation as applied to the more general case of arbitrary orientation angles.