Magnetic trapping

The magnetic trapping of cold atoms is especially effective in combination with optical fields that allow one to control the motion of the atoms (to cool and reflect them, and so on). But let us consider first the purely magnetic trapping of atoms and molecules. 

All static magnetic traps for atoms use nonuniform stationary magnetic fields. In a nonuniform magnetic field B = B(r), an atom with a permanent magnetic moment /LX has a magnetic dipole interaction energy 

Since the Maxwell equations do not allow a maximum of a static magnetic field in free space, the force in eqn (6.9) can be used to trap atoms only in a minimum of a static magnetic field. The force in eqn (6.9) can hold an atom near a minimum of a static magnetic field if the direction of the magnetic moment /lx is opposite to that of the magnetic field, that is, 0. 

One direct way to close the chaimel whereby atoms escape from the central region of a quadrupole magnetic trap is to displace the potential (Fig. 6.9(a)) in the symmetry 

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Recent research (1995-) has produced at very low temperatures (nanokelvins) a Bose-Einstein condensation of magnetically trapped alkali metal atoms. Measurements [41] of the fraction of molecules in the ground... 

Pure magnetic traps have also been used to study cold collisions and tliey are critical for tire study of dilute gas-phase Bose-Einstein condensates (BECs) in which collisions figure importantly. We anticipate, tlierefore, tliat magnetic traps will play an increasingly important role in future collision studies in and near BEC conditions. 

This explosion could have been prevented with a tramp metal collector, for example, a magnetic trap or a screen. An additional safeguard would be the addition of an inerting gas. 

The ion motion in the cell is complex because of the presence of electrostatic and magnetic trapping fields it consists of three different modes of oscillation. However, the primary mode of interest is the cyclotron motion, whose frequency, v., is directly proportional to the strength of the magnetic field B end inversely proportional to the mass-to-charge ratio m z of the ion v. = kzB/m). 

By using two traps, it is possible to maintain a constant force [91]. This is also possible with magnetic tweezers. However, because of the low stiffness of the magnetic trap, the spatial resolution due to thermal flucmations is limited to a few tens of nanometers. 

Magnetic Separator Classification. Whereas a wide variety of magnetic equipment has evolved over the years, much of this equipment is specialized and has limited usage. A fundamental equipment classification can be made on the basis of feed condition. A wet condition involves the treatment of a slurry or slip a dry condition involves treatment where the particles are essentially free to move as independent particles. Both conditions depend on liberation of the magnetic particles. If liberation does not occur, the magnet traps the middling particles and reduces the concentration of... 

The measurements of 2s — Is transitions in magnetically trapped hydrogen have achieved a relative accuracy of one part in 1012 [21] by means of two-photon spectroscopy which eliminates the first-order Doppler broadening. It is hoped that this technique will allow the measurement of the Is — 2s transition with the accuracy limited only by the shape of the transition line dictated by quantum electrodynamics, i.e. to a few parts in 1015. Further, if the center of the Is — 2s line could be determined with the accuracy of a few parts in 103 of its width, the relative accuracy for this transition would increase to a few parts in 1018. 

Hess, H.F., Kochanski, G.P., Doyle, J.M., Masuhara, N., Kleppner, D. and Greytak, T.J. (1987). Magnetic trapping of spin-polarized atomic hydrogen. Phys. Rev. Lett. 59 672-675. 

Figure 13. Magnetic trapping of ions in a magnetic bottle as a function of mass.

As a consequence, the electrons which are accelerated in the cathode sheath are forced onto a closed loop drift path parallel to the target surface because of the Lorentz Force. This magnetic trapping of the electrons and the corresponding ambipolar diffusion of the ions raises the plasma density in front of the target. A much higher ion current and therefore deposition rate is possible. Furthermore, the pressure can be decreased, which improves... 

Continuous wave coherent Lyman-a radiation has recently become available [85] so that laser cooling or sensitive shelving spectroscopy of magnetically trapped hydrogen atoms is coming within reach. The ability to work with a small number of atoms is of particular interest for laser spectroscopy of antihydrogen, a goal pursued by the ATRAP and ATHENA collaborations at CERN [8]. 

The major advantage of ultracold trapped hydrogen is that one may be able to achieve a coherence time comparable with the natural lifetime, 122 ms. As described in H-l, [16], The magnetic trapping fields can be reduced to a level where the residual Zeeman shift of the transition is on the order of the natural linewidth of 1.3 Hz. The light-induced shift and the photoionization rate can be reduced to the same level. 

The second phase will be designed and constructed based on the results of Phase 1. While the focus is on 2-photon laser spectroscopy of magnetically trapped antihydrogen atoms, other measurements (e.g. a measurement of the hyperfine structure using an atomic antihydrogen beam) are being explored for this program. 

Shelving spectroscopy thus involves many decisions whether the antihydrogen atom has been excited to the metastable 2 2S /2 state or not. These decisions have to be made somewhat quicker than the natural lifetime of the metastable state and are based on the observation or the non-observation of fluorescent light at Lyman-a. The detection efficiency for fluorescent light from an antihydrogen sample in a magnetic trap with superconducting coils is probably rather... 

Fig. 4. Hydrogen atomic beam apparatus and scheme for laser cooling and magnetic trapping of hydrogen atoms.

The temperature for Bose-Einstein condensation varies with density as n20. Because density is limited by three-body recombination, the search for the transition leads naturally to lower temperatures. Unfortunately, at temperatures below 0.1 K, adsorption rapidly becomes prohibitive. To avoid this problem, Hess [4] suggested confinirig the atoms in a magnetic trap without any surfaces. The states confined are the "low-field seeking" states, (HT, electron spin "up"). These are the hyperfine states (F-l,m-l) and (F=l,m=0). 

The ideal conditions for studying an atom is to have it at rest in free space, or in free fall as in a "fountain" experiment. Any process which confines an atom perturbs it However, as has been shown, at ultra low temperatures the perturbations of hydrogen due to a magnetic trap are small. Furthermore, the trap provides an enormous advantage in density compared to atomic beams or fountains density of 10u - 1012cm-3 is readily available. Thus, the trap is particularly attractive from the point of view of signal to noise ratio. 

Weinstein JD, de Carvalho R, Guillet T, Friedrich B, Doyle JM (1998) Magnetic trapping of calcium monohydride molecules at milliKelvin temperatures. Nature 395 148-150... 

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