\documentclass[../main.tex]{subfiles}
\graphicspath{{\subfix{../images/}}}

\begin{document}

\begin{abstract}
    We have studied the motion of singly-charged Calcium ions ($\text{Ca}^{+}$), inside an ideal Penning trap. With a numerical approach, studied the equations of motion by implementing the forward Euler method \(FE\) and the 4th order Runge-Kutta \(RK4\). We found that RK4 approximates the solution with smaller relative error than FE. In addition, we evaluated methods by rate of convergence. We found that RK4 has a higher convergence rate at approx. $4.0$, compared to FE at approx. $1.4$. Finally, we observed that for a time-dependent field, that there is an angular frequency that resonates with the particles in such a way that they escape the Penning trap.

    Freq.
\end{abstract}

\end{document}
