Theory of cathode trajectory characterization by canonical mapping transformation

Area of Science:

• Electron Optics
• Charged Particle Beams

Background:

• Paraxial lens theory is inadequate for describing cathode trajectories within electron guns.
• This limitation hinders the interpretation of electron trajectories and the application of familiar optical concepts like focal length.

Purpose of the Study:

• To introduce a new method, Canonical Mapping Transformation (CMT), for describing electron trajectories inside electron guns.
• To establish a relationship between ray conditions on the cathode surface and those in the crossover plane.

Main Methods:

• The Canonical Mapping Transformation (CMT) method relates ray conditions on the cathode surface to those in the crossover plane.
• Ray conditions are defined using the distance along the surface and the sine of the ray angle relative to the surface normal.
• CMT is characterized by a few optical parameters, including an 'electron gun focal length'.

Main Results:

• The crossover size of a triode gun can be accurately calculated using the electron gun focal length and initial transverse energy spread.
• Calculations predict the dependence of crossover size on grid voltage, attributed to changes in electron gun focal length.
• Predictions show good agreement with experimental measurements.

Conclusions:

• Canonical Mapping Transformation (CMT) provides a practical framework for electron gun design.
• CMT allows for the calculation of essential source properties from representative trajectories.
• The method overcomes limitations of paraxial lens theory for electron guns.