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\section{Conclusion}
We studied the movement of particles confined by an ideal Penning trap, where we used iterative methods to simulate the particle behavior. We included the magnetic and electric field of the Penning trap, in addition to simulating the particles behavior when interaction with other each other. When we introduced the interaction, the movement in both radial direction and z-direction changed. From a circular path, to a more elliptical path, where the particles initial condition determine how it is affecting other particles path. 

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?
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