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Universität zu Köln
Mathematisch-Naturwissenschaftliche Fakultät
Fachgruppe Physik

I. Physikalisches Institut

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Modelling Multipole RF Traps


  • fanghaenel
  • schlemmer


An rf multipole trap uses a combination of static direct current (dc) and radio frequency (rf) oscillating electric fields to trap ions. The electrical potential of such a trap is determined by the geometry, dimension of it's rf electrodes and the applied voltages. To model the electrical and mechanical potential of a trap we make use of the boundary element method (BEM). To understand the effects of systematic changes of trap parameters (dimensions and shape of the electrodes) we express the solution by an appropriate multipole expansions. As a result, the quality of a trap can be characterized by a small set of parameters. Through this approach one can find the ''optimum'' geometry and alignment tolerances to reduce undesired effects which e.g. could heat up the stored ion cloud. One advantage of BEM is the possibility to set up realistic 3D trap-models with finite electrodes. Therefore the effect of misalignments or undesired manufacturing tolerances of electrodes to the potential can be investigated. Also geometries with a broken rotational symmetry can be simulated reliably.



Boundary Element Method (BEM)
To find the electric potential of an rf multipole trap we have to find a solution for the ''Laplace'' equation:
The movement of a particle in a rapidly oscillating field can described by an effective trapping potential. It is calculated by taking the time-average over one period of the fast oscillation rf field .
This effective potential can be expressed as:
Ueffective = qΦdc+ q²⁄(4mΩ²)·(∇Φrf
with Φdc the static part of the potential, Φrf the rf part, Ω the rf frequenz and m the mass of the particle.

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Recent Results

As an effect of the applied dc voltage at the entrance and exit lenses of an 22 pole ion trap, a minima in the simulated effective potential at r≈3mm appears around the middle of the trap. Simulations of a misalignment of only 0.15mm of 11 rods of a 22 pole trap shows that 10 minimas appear around a the center of the trap.

The upper plot shows a Contourplot of a simulated effective potential of a 22 pole trap in the x-z plane.

We have chosen ordinary values for the trap parameters. Vrf=15V, Vdc=1V, Ω=17Mhz, m=16amu.

The equipotential lines calculated in MeV.

The lower plot show the the cross section of the use CAD model for the electric field calculation.
The plot shows a cut through the minima of the effective potential in radial direction with different applied voltages on the entrance and exit lenses.
Contourplot of a simulated effective potential of a 22 pole trap in the x-z plane with a misalignment of 11 rods.

Vrf=15V, Vdc=0V, Ω=17Mhz, m=16amu

The equipotential lines calculated in MeV.