Penning trap

A Penning trap electrically charged particles can be caught and stored by means of a constant magnetic field and an electrostatic quadrupole field. By the storage of the charged particles, it is possible to examine the physical properties with high precision. Hans Georg Dehmelt succeeded in 1987, a very precise determination of the Landé factor of the electron and the positron in the Penning trap. He received the 1989 Nobel Prize in Physics for his development of the Penning trap.

The Penning trap is named after the Dutch physicist Frans Michel Penning, since the principle of the storage of charged particles based on his proposal of 1936 to extend by adding a magnetic field, the storage time of charged particles in vacuum gauges.

Areas of application

This case is particularly suitable for the precise measurement of the properties of ionic and stable sub-atomic particles. One of its main applications is the Penning trap in mass spectrometry. In chemistry Penning traps are used for identification of molecules in FT -ICR mass spectrometers. In nuclear physics, nuclear binding energies are determined by mass measurements of stable and short-lived radioactive nuclei. Furthermore, it is possible to determine the G factor of the stored particles and thus to check the quantum electrodynamics. Furthermore, this case is used for the physical realization of quantum computers and quantum information processing. At CERN Penning traps are used to store antiprotons and are part of the Penning trap mass spectrometer ISOLTRAP at the facility for the production of radioactive ion beams ISOLDE.

Principle

In the homogeneous magnetic field of the Penning trap the charged particles on circular orbits are forced. It thus limits the radial motion of the particles. Prevents the quadrupole electric field that the particle wriggle along magnetic field lines from the trap. It restricts the movement in the axial direction by means of electrostatic repulsion.

Typically a Penning trap of three electrodes: a ring electrode and two end caps, wherein the two end caps are at the same potential. This results in a saddle point, the charged particles in captures the axial direction.

Particle motion in the trap

In a magnetic field with the magnetic flux density B for a charged particle to oscillate due to the Lorentz force on the mass m and charge q along a circular path about the magnetic field lines of the cyclotron frequency:

Due to the electric quadrupole field, however, this movement is modified. Penning trap in the motion of the particle can be described by the superposition of three harmonic oscillators. The vibration caused by the electric field between the end caps is called axial movement. The axial frequency is:

Where U is the potential difference between the end caps and the ring electrode, and d is a geometrical parameter of the trap. In a trap with hyperbolic electrodes d can be determined from the distance between the case middle and the end caps and the case radius:

The movement in the radial plane is defined by two frequencies: the modified cyclotron and magnetron frequency. The modified cyclotron as the free cyclotron a circular movement around the magnetic field lines, however, the frequency of the movement is reduced by the quadrupole electric field:

The magnetron is a slow drift motion around the trap center with the frequency:

The cyclotron frequency can be calculated from the above frequencies either via the relation

Or decide on the so-called Invarianztheorem that even for a less than ideal setup a Penning trap is valid:

The cyclotron frequency can be measured very accurately by absorption of injected electromagnetic waves, making it possible to the ratio of the masses of different particles can be determined very precisely to their charge. Many of the most accurate mass determinations are from Penning traps that can achieve a relative accuracy of. Among the most precise known masses are the masses of electron, proton, deuteron, 16O, 20Ne, 23Na, 28Si, 40Ar.

Differences to the Paul trap

Penning traps have some advantages over Paul traps. First, the Penning trap used only static electric and magnetic fields. Therefore, there is no micro-motion and associated heating due to the dynamic fields. Nevertheless, laser cooling is difficult in Penning traps, as a degree of freedom ( the magnetron ) can not be cooled directly.

Second, a Penning trap with the same case thickness to be built larger. Thereby, the ion can be kept further away from the surfaces of the electrodes. Interaction with surface potentials, which leads to heating operations and decoherence falls rapidly with increasing distance from the surface.

Sources and References

• Atomic physics