Determination of Mathieu Stability Plot for Planar Trap With Circular Trapping Region

Area of Science:

• Physics
• Electrical Engineering
• Computational Physics

Background:

• Planar toroidal ion traps offer unique geometries for particle confinement.
• Accurate modeling of the electrostatic potential is crucial for predicting ion behavior.

Purpose of the Study:

• To investigate planar toroidal ion traps using a toroidal multipole representation.
• To validate analytical potential models against boundary element method (BEM) computations.
• To analyze ion dynamics and stability regimes within these traps.

Main Methods:

• Calculated multipole expansion coefficients for electrostatic potential.
• Validated analytical potential against BEM.
• Numerically simulated ion trajectories under varying RF and DC voltages.
• Mapped operating regimes onto Mathieu parameter space to create stability diagrams.

Main Results:

• Analytical potential model shows excellent agreement with BEM near the trapping circle.
• Mathieu stability diagrams reveal localized instability zones.
• Secular frequencies predicted from Mathieu parameters agree within 3% with trajectory simulations.

Conclusions:

• The toroidal multipole representation accurately models the electrostatic potential in planar toroidal ion traps.
• Nonlinear electric field components significantly influence ion dynamics, creating localized instabilities.
• The validated theoretical and numerical methods provide a reliable framework for designing and analyzing ion traps.