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Janita Willumsen
2023-10-24 21:44:56 +02:00
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latex/sections/results.tex
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@@ -96,26 +96,28 @@ In figure \ref{fig:two_particles_radial_interaction} we see the movement in radi
\label{fig:3d_particles}
\end{figure}
Finally, by subjecting the system to a time-dependent field, making the replacement in \ref{eq:pertubation}, we study the fraction of particles left at different amplitudes $f$. We can see how the different amplitudes lead to loss of particles, at different angular frequencies $\omega_{V}$ in \ref{fig:wide_sweep}. % Something
Finally, by subjecting the system to a time-dependent field, making the replacement in \ref{eq:pertubation}, we study the fraction of particles left at different amplitudes $f$. We can see how the different amplitudes lead to loss of particles, at different angular frequencies $\omega_{V}$ in \ref{fig:wide_sweep}. We study frequencies in the range $\omega_{V} \in (0.2, 2.5)$ MHz, with steps of $0.02$ MHz, and find that angular frequencies in the range $(1.0, 2.5)$ is effective in pushing the particles out of the Penning trap.
We explore the range $\omega_{V} \in (1.0, 1.7)$ MHz closer in figure \ref{fig:narrow_sweep}, and observe a gradual loss of particles for amplitude $f_{1} = 0.1$. Since they are additive, a greater amplitude will result in a larger bound for the particle movement, and particles are easily pushed out. Certain angular frequencies are more effective in pushing particles out of the Penning trap, as we see in figure \ref{fig:narrower_sweep} where $\omega_{V} \in (1.3, 1.4)$ is also effective for pushing out particles of amplitude $f_{1} = 0.1$. % Something
When we study the angular frequency $\omega_{V} \in [1.1, 1.7]$ closer, in figure \ref{fig:narrow_sweep}, we observe that there are a few spots where more particles will escape. The most prominent one is where $\omega_V \in [1.1, 1.7]$, and when looking closer to the range, it seems like there's a resonating frequency at around $1.4MHz$ where All the particles will escape no matter the amplitude. When looking at the different angular frequencies with particle interaction like in \ref{fig:narrow_sweep_interactions}, we see that the amount of particles left is roughly the same as when there are no particle interactions, but that it's less predictable.
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{images/particles_left_wide_sweep.pdf}
\caption{Exploring particles}
\caption{Exploring the behavior of particles, where the amplitude of time-dependent potential $f = [0.1, 0.4, 0.7]$, for angular frequency $\omega_{V} \in (0.2, 2.5)$ MHz.}
\label{fig:wide_sweep}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{images/particles_left_narrow_sweep.pdf}
\caption{Exploring different angular frequencies more closely}
\includegraphics[width=\linewidth]{images/particles_left_wide_sweep.pdf}
\caption{Exploring the behavior of particles, where the amplitude of time-dependent potential $f = [0.1, 0.4, 0.7]$, for angular frequency $\omega_{V} \in (1.0, 1.7)$ MHz.}
\label{fig:narrow_sweep}
\end{figure}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{images/particles_left_narrow_sweep_interactions.pdf}
\caption{Exploring particles}
\label{fig:wide_sweep_interactions}
\includegraphics[width=\linewidth]{images/particles_left_wide_sweep.pdf}
\caption{Exploring the behavior of particles, where the amplitude of time-dependent potential $f = [0.1, 0.4, 0.7]$, for angular frequency $\omega_{V} \in (1.3, 1.4)$ MHz.}
\label{fig:narrower_sweep}
\end{figure}
\end{document}