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A brief discussion of ion trapping

The Penning Trap

The Penning trap uses a set of three specially shaped electrodes (two endcaps and a ring) to set up an electrostatic quadrupole potential when a dc voltage (U0) of typically a few volts is applied between them. The electrodes have a typical internal diameter on the order of a few mm. Their shapes correspond to the shape of a pure quadrupole potential in three dimensions and this means that the motion of ions trapped in them is harmonic. The sign of the potential is such that ions are repelled by both endcap electrodes, leading to stable confinement in the axial direction at a frequency wz which depends on U0 and the size of the electrodes. In the radial (x,y) plane the motion would be unstable because the ions are attracted to the (negatively charged) ring electrode. However, if a static magnetic field B is applied along the axis, the ion motion is forced into a circular orbit so that the ions are not lost to the ring electrode (so long as there are no collisions - for this reason the trap is operated under UHV conditions). We end up with two radial oscillation frequencies, the fast modified cyclotron frequency (wc) and the slow magnetron frequency (wm). The resulting motion is stable except that if there are collisions with background gas molecules this can cause the radius of the magnetron motion to increase without limit, leading to loss of particles. This is because the magnetron motion has a negative amount of energy associated with it, i.e. it is unstable. This has profound implications for laser cooling.

Radiofrequency (RF) trap

This trap (also called a Paul trap) uses the same electrodes as the Penning trap but here the radial confinement is obtained by applying a radio frequency voltage to the electrodes instead of having a magnetic field. This gives stable confinement in all directions in an effective potential called a pseudopotential which is set up as a result of the driven motion of the ions at the applied RF frequency. The oscillation frequencies in the pseudopotential depend on the values of the RF voltage and any DC voltage which can also be applied, as well as the trap size and the value of the RF drive frequency. Many RF traps have internal diameters of several mm, but if they are designed for use with a single ion they are much smaller in order to obtain very tight confinement. In this case the internal diameter is less than 1 mm.

The Combined Trap

The combined trap is a device which brings together some of the advantages of both the Penning trap and the Paul (or radiofrequency) trap. It thus has both a DC and a radiofrequency potential applied between the electrodes (as in the Paul trap) and it also has a static magnetic field (as in the Penning trap). The advantage of the combined trap is that it has a wider range of parameters that give stable trapping than either the Penning trap or the Paul trap, and it can also be used to study charged particles of widely differing mass and different charge at the same time.