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Add part about resonance

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Cory Balaton 2023-10-24 21:09:50 +02:00
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@ -7,5 +7,8 @@ We studied the movement of particles confined by an ideal Penning trap, where we
We also compared iterative methods with the analytical solution, and found that the forward Euler \(FE\) method result in an approximation with larger relative error than the 4th order Runge-kutta \(RK4\) method. In addition to a small relative error, we also found that RK4 has a higher convergence rate at approx. $4.0$, compared to FE at approx. $1.4$. Which suggest RK4 ... We also compared iterative methods with the analytical solution, and found that the forward Euler \(FE\) method result in an approximation with larger relative error than the 4th order Runge-kutta \(RK4\) method. In addition to a small relative error, we also found that RK4 has a higher convergence rate at approx. $4.0$, compared to FE at approx. $1.4$. Which suggest RK4 ...
Resonance and freq? We finally looked at how the amount of particles that stay in the Penning trap
change when using different angular frequencies in a time-dependent field. We
observed that there seem to be a resonating frequency at around $1.4MHz$ that
makes the particles escape the Penning trap even at low amplitudes.
\end{document} \end{document}