Penning traps

As an example of the preceding analysis, we examine the rotation of the single particle wave function of a trapped charged particle around the z-axis. We consider a particle with charge q and mass m in a Penning trap... 

In a commercially available device based on Penning traps - the Fourier transform ion cyclotron... 

The radius of ion trajectory in the Penning trap is then determined by ... 

Figure 3.14 Schematic representation of an ion cyclotron resonance cell (Penning trap) for high resolution mass spectrometry. The magnetic field is oriented and the ions are injected along the z axis. The ions are trapped along this axis by a trapping voltage (e.g., I V applied to the front and back plates 3 and 4). (Modified from C. Brunnee, Int. j. Mass Spectrom. 76, 125 (1987). Reproduced by permission from Elsevier.)...

Storage has mainly been achieved in four types of traps (11 the radio frequency or Paul trap (2) the Penning trap (3) the Kingdon electrostatic trap and (4) the magnetostatic (magnetic bottle) trap. The principles, advanlages, and disadvantages of these traps are detailed by DJ. Wineland (Science, 226, 395-400, Oct. 26, 1984). 

As outlined by Wolf (1993) and Holzscheiter et al. (1996), similar considerations to those described above also apply to recombination in traps, and in particular the nested Penning-trap scheme (see below), again with appropriate assumptions regarding the speed distributions of the trapped positrons and antiprotons and their degree of spatial overlap. As an example, Holzscheiter et al. (1996) argued that the recombination rates are of the order of one per second (though dependent upon Ee) for 106 positrons and 105 antiprotons trapped in a volume of 1 cm3. 

Fig. 8.11. Illustration of the principle of nested Penning traps for holding antiprotons and positrons in close proximity, in order to promote antihydrogen formation.

Gabrielse, G., Haarsma, L. and Rolston, S.L. (1989). Open-endcaps Penning traps for precision experiments. Int. J. Mass. Spec. Ion Processes 88 319-332. 

Hall, D.S. and Gabrielse, G. (1996). Electron cooling of protons in a nested Penning trap. Phys. Rev. Lett. 77 1962-1965. 

PENNING TRAP A different approach to mass measurements was developed at Mainz. Thermal ions can be confined in a static homogenous magnetic field and a superimposed electrostatic quadrupole field. A measurement of the cyclotron frequency enables the measurement of the mass of the stored ion. A resolving 6 8 -7 -8... 

PENNING TRAP 2 deceleration and trapping induction of cyclotron frequency u>c increase of radial energy pulsed ejection... 

Fig. 3 Principle (right) and experimental set-up (left) for mass measurements in a Penning trap.

A recent effort of this laboratory has resulted in the introduction of a hyperbolic Penning trap (3 p. The cell consists of two end caps and one ring electrode similar to the design of Byrne and Farago (51.) (see Figure 8). 

Elemental mass spectrometry has undergone a major expansion in the past 15-20 years. Many new a, elopments in sample introduction systems, ionization sources, and mass analyzers have been realized. A vast array of hybrid combinations of these has resulted from specific analytical needs such as improved detection limits, precision, accuracy, elemental coverage, ease of use, throughput, and sample size. As can be seen from most of the other chapters in this volume, however, the mass analyzers used to date have primarily been magnetic sector and quadrupole mass spectrometers. Ion trapping devices, be they quadrupole ion (Paul) [1] traps or Fourier transform ion cyclotron resonance (Penning) traps, have been used quite sparingly and most work to date has concentrated on proof of principal experiments rather that actual applications. 

In this section the use of commercially available devices based on Penning traps, namely, Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometers, is presented. Since its introduction in 1974 [60], the FT-ICR technique has been applied to a plethora of problems in organic, inorganic, and physical chemistry and... 

In a Penning trap, ions are constrained spatially by a combination of electric and magnetic fields. In the presence of a homogeneous magnetic field (B) ions that have a component of velocity perpendicular to B are subjected to the Lorentz force and subsequently follow a circular trajectory [70]. The rotational frequency of this trajectory is proportional to B and to the ion charge (q) and inversely proportional to the ion mass (m). When expressed in radians, this rotational frequency is known as the cyclotron frequency, coc, where... 

Figure 16 Depiction of two important types of ion motion in Penning traps cyclotron and harmonic oscillation in the field produced by the trapping potential.

In addition to the Rydberg constant a number of different quantities, all based on intrinsically accurate frequency measurements, are needed. Experiments are under way in Stanford in S. Chu s group to measure the photon recoil shift free = fmh/2mcs( of the cesium Di line [48]. Together with the proton-electron mass ratio mp/me, that is known to 2 x 10-9 [49] and even more precise measurements of the cesium to proton mass ratio mcs/mp in Penning traps, that have been reported recently [50], our measurement has already yielded a new value of a [45]. 

This was the beginning of a long series of measurements and theoretical calculations over 40 years in which the precision has been improved from 10-3 to 10-12. The latest results for the electron and positron anomalies obtained in Penning trap experiments are [1]... 

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