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Janitaws/latex setup #12

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coryab merged 24 commits from janitaws/latex-setup into develop 2023-10-24 20:43:04 +00:00
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latex/sections/abstract.tex
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\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. $1.4$.
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}
\end{document}