From 978616f7d94f85ad277dcb612a31664f70d76258 Mon Sep 17 00:00:00 2001 From: Cory Date: Tue, 24 Oct 2023 21:12:45 +0200 Subject: [PATCH] Add resonance part for the abstract --- latex/sections/abstract.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/latex/sections/abstract.tex b/latex/sections/abstract.tex index cb358a8..3632e5e 100644 --- a/latex/sections/abstract.tex +++ b/latex/sections/abstract.tex @@ -4,9 +4,9 @@ \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} \ No newline at end of file +\end{document}