Numerical and Experimental Investigation of the Stability Region for a Cylindrical Ion Trap

The stability diagram provides a useful tool for determining the appropriate AC biased potential to confine ions in an ion trap. Since no analytic solution exists for the cylindrical ion trap\u27s (CIT\u27s) equations of motion, the CIT\u27s stability region is not well known. The objective of this thesis is to determine the stability region for a CIT numerically and experimentally. The equations of motion for ions confined in a CIT are derived and found to be similar to the Mathieu equation, i.e. the equation that describes ion motion in a hyperbolic ion trap (HIT). Because of the similarities in the equations of motion for the two traps, and since the stable region for a HIT is well known, the HIT is used as a guide for the determination of the CIT\u27s stable region. The HIT stability region is determined by numerical calculations for comparisons with the analytic HIT stable region in order to test the validity of the numerical method. In this investigation, the ion kinetic energy is found to influence the shape of the CIT\u27s stable region. The locations of the CIT\u27s βz=0 and βr=0 stability boundaries, i.e. for unstable trajectories in the axial and radial directions respectively, are experimentally determined through measuring the number density of N+ at multiple locations in the stability diagram. The experimentally determined boundaries for βz=0 and βr=0 are found to lie consistently between the 0.01eV and 0.1eV numerically calculated energy dependent boundaries for the CIT