Dear all,

I’d like check with you to see if my calculations make sense if that’s OK? I’ll go straight into it if I may:

Without too much detail, my devices are shown in figure 1 (below), here electrons are drawn from the centre cathode by field emission and accelerated towards an anode. Under zero magnetic fields, an equal current strikes both anodes, and under a magnetic field the emitted e-beam is skewed making an imbalance of current proportional to applied field.




As seen from figure 1, under magnetic quiescent conditions the anode currents (Ia1 and Ia2) are equal – this assumes an equal electron beam (e-beam) width, yB.

Q. May the e-beam width be approximated by: 

yB = 2*l*tan(θa)? 


My justification for this is that the electron trajectory in the region marked l is linear, i.e. the electron is accelerated from the gate to the anode (in a simple condenser model) and I’ve just taken the tangent of the anode-current-angle: my aim is to have the e-beam width as a function of the anode-current-angle – then I can optimise conditions for minimal θa, giving minimal yB.

I have seen other models used in papers on SEM’s and they use horribly complicated de-Broglie wavelengths, etc, but I think these are overly complicated – the only other method I can think of for finding yB(θa, l) is to integrate the equations of motion for this model.. but again, this seems too complicated.

What do you think, is this (above) simplistic model for e-beam width justified?

Many thanks,

Paul French

p.s. email:
p.french@ee.ucl.ac.uk