latex/sections/results.tex

@@ -96,10 +96,10 @@ 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}. 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 $(1.0, 1.7)$ is effective in pushing the particles out of the Penning trap. 
+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 loss of particles for amplitude $f_{1} = 0.1$ in the range $\omega_{V} \in (1.3, 1.5)$, for $f_{2} = 0.4$ in the range $\omega_{V} \in (1.2, 1.6)$, and $f_{3} = 0.7$ in the entire range explored. When we introduce particle interaction, we observe the amplitude with higher value will result in a larger bound for the particle movement, and particles are easily pushed out. When we add particle interaction the angular frequencies, which result in particles being pushed out, are similar as in no interaction. As we see in figure \ref{fig:narrow_sweep_interactions} the particle's behavior, when interactions are added, is disrupted and add to the force resulting in the particle being pushed out of the Penning trap. We see that fewer particles tend to be left in the Penning trap, than without any particle interactions. We also see that the fraction of particles left is more unpredictable with particle interactions. 
 
-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, when we add particle interaction. As we see in figure \ref{fig:narrow_sweep_interactions} where $\omega_{V} \in (1.3, 1.4)$ is also effective for pushing out particles of amplitude $f_{1} = 0.1$. When particle interactions are added, we see that there tends to be fewer particles left in the Penning trap than without any interactions. We also see that the amount of particles left is more unpredictable when there are particle interactions.
-%The particles' behavior, when interactions are added, is disrupted and add to the force which result in the particle being pushed out of the Penning trap. 
 \begin{figure}[H]
     \centering
     \includegraphics[width=\linewidth]{images/particles_left_wide_sweep.pdf}