# Dynamics of Ions in the Electrostatic Ion Beam Trap (EIBT)

## Topics

Ion Bunching | Mass Selection| Transverse motion

### Ion Bunching

During the last four years, our group has developed and studied a new type of ion trap, in which fast (keV) ions are stored between two electrostatic mirrors, much like photons in an optical resonator.

Recently, we have found that a certain type of ordering can be achieved in such a device with ions at high temperature (~1 eV). In this paper, we present a short overview of this new phenomenon which is related to the dynamics of small bunches of ions oscillating between the trap mirrors. The effect, which manifests itself as a synchronization of the motion of the ions, leads to the interesting possibility of keeping the size of a packet of ions constant for a practically unlimited time, i.e., eliminating the de-bunching usually observed for ion bunches.

In the following, we show that the fact that a bunch of positive ions oscillating between two mirrors say "localized" is due to the Coulomb repulsion between the ions! Although this might seems to be counter-intuitive, we would like to show this using a little movie, which shows the result of a classical calculation (Newton equations) for the motion of two charged particles (both positively charged) between two mirrors. The situation is pretty much like in our ion trap. The initial velocities of the two particles are slightly different (the red one is faster than the blue one), so that if there is no Coulomb interaction between them, they will separate after several oscillations (as their period of oscillation are different). We show here two situation: On the left side there is NO Coulomb interaction between the ions, while on the right side, the Coulomb interaction is taking into account in solving the equation of motion.

## Wait for the movie to load

As can be seen, the two particles on the right side stay "glued" together, even though there is a repulsive interaction between them!

If you want to understand why this is happening, read the following papers:

1. H. B. Pedersen, D. Strasser, S. Ring, O. Heber, M. L. Rappaport, Y. Rudich, I. Sagi, and D. Zajfman, Ion Motion Synchronization in an Ion-Trap Resonator, Phys. Rev. Lett., pp. 055001-055004, 87 (2001).

2. H. B. Pedersen, D. Strasser, B. Amarant, O. Heber, M. L. Rappaport, and D. Zajfman, Diffusion and synchronization in an Ion-Trap Resonator, Phys. Rev. A, pp. 042704, 65 (2002).

### Mass Selection in the EIBT

As opposed to other ion trapping techniques, the ion trajectories in the EIBT are independent of their mass and thus very large molecules (amino acids etc.) can be stored. On the other hand the ion oscillation period does depend on their mass, and by measuring the ion frequency, the mass spectrum of the trapped ion species can be deduced. By relying on the EIBT can be used for mass selection. The method, which we refer to as the kickout mass selection, relies on the phenomena of ion bunching .

The principle of operation is as follows: Since the EIBT is completely electrostatic, ions of equal energy but different masses are moving on the same trajectories, however, their oscillation period is proportional to the square root of their mass. By applying to the deflector a voltage pulse with the oscillation frequency of the mass to be retained, which is zero whenever the bunch containing the desired ions passes through the deflector but high otherwise, ions of different masses will be deflected out of the trap after a certain dwell time. The time span of the kickout technique needed to select a certain mass depends on the resolution of the mass separation, e.g. for Δm/m~10-3, 20 ms are required. This technique has the advantages of having no upper mass limit and can be easily employed to existing EIBT.

The experimental setup:

Proof of principle:

A pickup electrode is mounted a few cm off-center towards the exit mirror of the trap (see Fig 1). The image current created by an ion bunch passing through the electrode is amplified and then recorded by a digital scope. After Fourier transforming the signal and converting frequency to mass, the mass spectrum displaying the composition of the stored ion beam can be deduced. In an example, the figure below displays the mass spectrum of Xe9+ clusters before and after mass selection using the kick out technique. The mass selector was used for 550 oscillation, being on for 19.3 ms.

### Transverse motion in ion trap

In addition to parallel movement of the ions between the electrostatic mirrors, the trapped ions also move transversely with respect to the optical axis. This topic was studied in our lab by D. Attia and published. See the following article for further details:
• "Transverse kinematics of ions stored in an electrostatic ion beam trap", D. Attia, D. Strasser, M. L. Rappaport, and D. Zajfman, Nucl. Ins. and Methods in Physics Reaserch A, 547, pp 279-286 (2005).