Penning trap

In a Penning trap , electrically charged particles can be caught and stored with the help of a constant magnetic field and an electrostatic quadrupole field . By storing the charged particles, it is possible to examine their physical properties with high precision. In 1987, Hans Georg Dehmelt succeeded in determining the Landé factor of the electron and the positron in the Penning trap very precisely . In 1989 he received the Nobel Prize in Physics for his developments at the Penning trap.

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

application areas

This trap is particularly suitable for the precise measurement of the properties of ions and stable subatomic particles . The Penning trap is used in mass spectrometry . In chemistry , Penning traps are used to identify molecules in FT-ICR mass spectrometers . In nuclear physics , nuclear binding energies are determined by mass measurements of both 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 trap is used for the physical realization of quantum computers and quantum information processing . Penning traps are used at CERN to store antiprotons or are part of the Penning trap mass spectrometer ISOLTRAP at the facility for generating radioactive ion beams ISOLDE .

principle

Scheme of a Penning trap with a positively charged particle (center) on its orbit. The electric field (blue) is generated by a quadrupole consisting of end caps (a) and ring electrode (b), the magnetic field (red) by the solenoid C.

In the homogeneous magnetic field of the Penning trap, the charged particles are forced onto circular paths. This limits the radial freedom of movement of the particles. The electric quadrupole field prevents the particles from twisting out of the trap along the magnetic field lines. It restricts movement in the axial direction through electrostatic repulsion .

Typically, a Penning trap consists of three electrodes : a ring electrode and two end caps, the two end caps being at the same potential . This creates a saddle point that catches the charged particles in the axial direction.

Particle movement in the trap

In a magnetic field with the magnetic flux density , a charged particle oscillates due to the Lorentz force with the mass and the charge on a circular path around the magnetic field lines with the cyclotron frequency : ${\displaystyle B}$ ${\displaystyle m}$ ${\displaystyle q}$

${\displaystyle \omega _{c}={\frac {q}{m}}B}$

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

${\displaystyle \omega _{z}={\sqrt {{\frac {q}{m}}{\frac {U}{d^{2}}}}}}$,

where the potential difference between the end caps and the ring electrode, and is a geometric parameter of the trap. In a trap with hyperbolic electrodes, the distance between the center of the trap and the end caps and the trap radius can be used to determine: ${\displaystyle U}$ ${\displaystyle d}$ ${\displaystyle d}$ ${\displaystyle z_{0}}$ ${\displaystyle r_{0}}$

${\displaystyle d^{2}={\frac {1}{2}}\left(z_{0}^{2}+{\frac {r_{0}^{2}}{2}}\right).}$

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

${\displaystyle \omega _{+}={\frac {\omega _{c}}{2}}+{\sqrt {{\frac {\omega _{c}^{2}}{4}}-{\frac {\omega _{z}^{2}}{2}}}}\approx \omega _{c}-{\frac {U}{2d^{2}B}}}$.

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

${\displaystyle \omega _{-}={\frac {\omega _{c}}{2}}-{\sqrt {{\frac {\omega _{c}^{2}}{4}}-{\frac {\omega _{z}^{2}}{2}}}}\approx {\frac {U}{2d^{2}B}}}$.

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

${\displaystyle \!\ \omega _{c}=\omega _{+}+\omega _{-}}$,

or use the so-called invariance theorem to determine that a Penning trap is also valid for a less than ideal structure:

${\displaystyle \omega _{c}={\sqrt {\omega _{+}^{2}+\omega _{-}^{2}+\omega _{z}^{2}}}}$

The cyclotron frequency can be measured very precisely through the absorption of radiated electromagnetic waves, so that the ratio of the masses of different particles to their charge can be determined very precisely. Many of the most accurate mass determinations come from Penning traps, which can achieve a relative accuracy of . Among the most precise known masses are the masses of electron , proton , deuteron , ¹⁶ O , ²⁰ Ne , ²³ Na , ²⁸ Si , ⁴⁰ Ar . ${\displaystyle \delta m/m<10^{-10}}$

Differences to the Paul trap

Penning traps have several advantages over Paul traps . First, the Penning trap only uses static electric and magnetic fields. Therefore there is no micro-movement and the associated heating up due to the dynamic fields. Even so, laser cooling in Penning traps is difficult because one degree of freedom (the magnetron movement) cannot be cooled directly.

Second, a Penning trap can be made larger with the same trap strength. This allows the ion to be kept further away from the surfaces of the electrodes. The interaction with surface potentials, which leads to heating and decoherence , decreases rapidly with increasing distance from the surface.

Sources and references

1. ↑ Frans Michel Penning: The glow discharge at low pressure between coaxial cylinders in an axial magnetic field . In: Physica . tape 3 , 1936, pp. 873 , doi : 10.1016 / S0031-8914 (36) 80313-9 .
2. ↑ Klaus Blaum , Frank Herfurth, Alban Kellerbauer: A balance for exotic nuclei: Determining the mass of atomic nuclei with Isoltrap. In: Physics in Our Time . 36th year, no. 5 , 2005, p. 222–228 , doi : 10.1002 / piuz.200501074 ( PDF; 688 kB ).
3. ^ Lowell S. Brown, Gerald Gabrielse : Geonium theory: Physics of a single electron or ion on a Penning trap . In: Review of Modern Physics . tape 58 , 1986, pp. 233 , doi : 10.1103 / RevModPhys.58.233 .
4. ↑ Frank Difilippo, Vasant Natarajan, Kevin R. Boyce and David E. Pritchard : Accurate Atomic Masses for Fundamental Metrology . In: Phys. Rev. Lett. tape 73 , 1994, pp. 1481 , doi : 10.1103 / PhysRevLett.73.1481 .
5. ^ G. Audi, AH Wapstra, C. Thibault: The AME2003 atomic mass evaluation . In: Nucl. Phys. A . tape 729 , 2003, p. 337 , doi : 10.1016 / j.nuclphysa.2003.11.003 .