Analytical Approximate Solution of a Coupled Two Frequency Hill\'s Equation

Abstract

Abstract: A coupled two frequency Hill's equation is solved. Analytically approximate solution correct up-to first order is derived using modified Lindstedt-Poincare perturbation method. For a wide range of controlling parameters, we compare the numerical and analytical solutions. The solution is the first step towards developing a comprehensive understanding of the electrodynamics of charged particles in a combinational ion trap utilizing both electrostatic DC and RF fields along with a constant static magnetic field with prospects of confining antimatter such as anti-hydrogen for a reasonably long durations of time.