Differential algebraic method for aberration analysis of typical electrostatic lenses

Area of Science:

• Charged particle optics
• Electron optics
• Computational physics

Background:

• Accurate calculation of aberration coefficients is crucial for designing high-performance electron lenses.
• Traditional methods for calculating aberrations can be computationally intensive and complex.
• Differential algebraic (DA) methods offer a powerful alternative for analyzing charged particle optics.

Purpose of the Study:

• To calculate fifth-order geometric and third-order chromatic aberration coefficients for electrostatic lenses.
• To validate the differential algebraic (DA) method using established electron optics principles.
• To demonstrate the applicability of the DA method for analyzing numerically computed electron lenses.

Main Methods:

• Utilized the charged particle optics code, COSY INFINITY, which is based on the differential algebraic (DA) method.
• Calculated axial potential distributions for a two-tube immersion lens and a symmetric einzel lens using a FORTRAN program with the finite difference method.
• Computed aberration coefficients up to fifth-order geometric and third-order chromatic.

Main Results:

• Achieved good agreement between aberration coefficients calculated using the DA method and those evaluated by traditional aberration integrals.
• Successfully calculated high-order aberration coefficients for electrostatic lenses.
• Demonstrated the efficiency and accuracy of the DA method in charged particle optics.

Conclusions:

• The differential algebraic (DA) method, implemented in COSY INFINITY, is a reliable and efficient tool for calculating electrostatic lens aberrations.
• The DA method provides accurate results comparable to established methods in electron optics.
• This approach is readily extendable to analyze aberrations in other types of electron lenses, including magnetic lenses.