Formulas

 

Lens aberrations

Miscellaneous formulas (ellipse, test planes, extrapolation of number of segments to infinity).

Inscribing correction

Surface charge Method equations

Planar Pierce gun 

Richardsons equation 

Fowler-Nordheim equation

Field at circular hole in flat sheet

Childs Law

Hemispherical deflection analyzer

Cylindrical deflection analyzer

Invertible randomization distributions

Conic sections, 1

Conic sections, 2

Relativistic equations, integrating

Space-charge spreading

Maximum current in converging beam 

Randomization