Electrons diffusion in gas with present of electric field

For research purposes, I am looking for a way to calculate how far the electrons "spread" perpendicularly to the electric field in a chamber of gas.

For example, if a beam of alpha particles ionize the gas in a chamber and leave a track of electron-postive ion pairs, is there a way to calculate how far the electrons move away from the point of ionization (perpendicular to the electric field). Note: also present in the gas chamber is an electric field, so the electrons and positive ions would move in opposite direction. I am reading W. R. Leo's Techniques for Nuclear and Particles Physics Experiments for hints on how to calculate this, but I haven't found any mention of this yet. The closest thing I found was about electron diffusion with the absent of an electric field. Please point me to articles, book chapters, equations, or links regarding information of this topic. Thanks in advance.

• one can see; Longitudinal and transverse diffusion of electrons in high-pressure xenon H. Kusano,a J.A.M. Lopes,b,c M. Miyajimaa and N. Hasebea a a Research Institute for Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan bDepartment of Physics, University of Coimbra, 3004-516 Coimbra, Portugal c Instituto Superior de Engenharia de Coimbra, 3030-199 Coimbra, Portugal E-mail: hiroki-kusano@akane.waseda.jp <iopscience.iop.org/article/10.1088/1748-0221/8/01/C01028/pdf> – drvrm Feb 17 '18 at 14:00

I have found the answer in the W. R. Leo's Techniques for Nuclear and Particles Physics Experiments. The equations that I needed are Eq. 6.18 $D=\frac1 3 v \lambda$ and Eq. 6.46 $\sigma=\sqrt{2Dx/\mu E}$.