Coulomb crystals

Thus, the interaction of streamers in DBD can lead to the formation of an organized structure of microdischarges (similar to Coulomb crystals see Fridman Kennedy, 2004), which plays a significant (sometimes positive, sometimes negative) role in plasma-chemical applications. From this perspective it is important to analyze how highly organized the... 

Homecker, L. Drewsen, M. Formation process of large ion Coulomb crystals in linear Paul traps. Phys. Rev. A 2002, 66, 013412-12. 

Strong cooling results in a transition from a gaseous to a fluid and then to a crystalline state (Coulomb crystal) see Figure 18.6 later. The precise meaning of crystalline will be explained in Section 18.4. The shape of these ensembles is spheroidal if the quasipotential has axial symmetry. Equation 18.1. 

FIGURE 18.7 Ion diffusion in Coulomb crystals, (a) Trajectories of several individual Be" " ions in a cold (10 mK) Be -HD ion crystal (time-averaged trap potential assumed duration 1 msec). Because of diffusion, except for special sites, individual spots in a (simulated) CCD image are not the positions where a particular single ion is confined, but where the probabihty to find any ion is high, (b) Axial view of a section of the crystal in (a). 

A particular processes of interest is radio-frequency heating, the transfer of energy from the trap field to the ion ensemble. In an important early study [51], it was shown that for a crystallized ensemble, even containing many particles, radio-frequency heating is very small. This was confirmed in experiments on Mg ions in a ring trap [57], where the Coulomb crystals did not melt even if the cooling light was intermpted for seconds. 

Homekaer, L., Kjaergaard, N., Thommesen, A.M., and Drewsen, M., Structural properties of two-component coulomb crystals in Unear Paul traps, Phys. Rev. Lett., 86, 1994,2001. 

Frdhlich, U., Roth, B., and Schiller, S., Ellipsoidal Coulomb crystals in a Unear radiofrequency trap Phys. Plasmas, 12, 073506, 2005. 

Besides sensitive and spectrally resolved detection of the light emitted from trapped ions, progress in the development of imaging devices (e.g. intensified CCD cameras) made it possible to record pictures of the trapped ensemble with high spatial resolution. This has allowed many tests to be performed on so-called Coulomb crystals. Trapped ions that are cooled with laser light below a translational temperature T, arrange themselves in spatial structures. A detailed analysis of regular arrays of a few laser-cooled Hg+ ions which have been observed in an rf quadrupole trap has... 

By storing and cooling a cloud of many particles of the same sign of charge in a trap, large ion Coulomb crystals are formed and are the basis of many interesting experiments. Such an one-component plasma has been... 

A few selected properties of Coulomb crystals are illustrated in Fig. 6.3. The left part shows a photo from the pioneering experiment performed by Wuerker et al An ensemble of 32 charged aluminum particles having a diameter of a few jim was stored in the effective potential of a three dimensional quadrupole trap operated with an ac voltage of some hundred Hz. Cooling of the translational motion was achieved by collisions with room temperature buffer gas. In this example the ions were confined in the plane of the ring electrode of the Paul trap leading to a radial oscillation with an amplitude that increases with the distance from the center. The other two panels of Fig. 6.3 show results from numerical simulations of a 1000-ion... 

Fig. 6.3. Motions and crystalline arrangements of trapped charged particles. The left figure is a photo of a cluster of 32 charged micro-particles stored in a Paul trap. The two other figures are results from a numerical simulation of a 1000-ion Coulomb crystal confined in a linear quadrupole trap. In the left and the center panel the micro-motion of the particles in the oscillatory electric field can be seen. The amplitude increases proportionally to the distance from the center. The time-averaged positions plotted in the right part for a selected sample shows that the ions remain well-localized. This is the basis for defining an effective translational temperature of the ion cluster by subtracting the periodic oscillation from the overall motion.

Coulomb crystal confined in a linear quadrupole trap published by Schiffer et al As in the picture on the left, the lines in the middle image indicate the micro-motion. Other than in the left picture, here the ions are stored in a linear quadrupole and the image shows the motion in a plane orthogonal to the axis of the rod system. As a consequence the direction of the rf held induced micro-motion is radial in front of the rods and tangential in between them. More details on the micro-motion can be foimd in Chapter 3 (see for example Fig. 3.1). The time-averaged positions plotted in the right part for a selected sample of ions shows that they remain weU-localized. As discussed already in Chapter 3 and in more detail below, this observation is the basis for dehning an effective translational temperature of the ion cluster. 

Of special interest for the present chapter is the possibility that complex ions can be integrated into Coulomb crystals. The first detection of charged molecules in a laser-cooled Mg+ ensemble has been reported by Baba and Waki. Subsequent applications of forming and confining translationally cold molecular ions include MgH" /MgD, CaO+, BeH" ", HD" ", and others. For a recent summary see the publications by Roth et These... 

The problem of the real kinetic energy of the ultra-cold ions has been discussed already in Chapter 3 and is illustrated in Fig. 6.3. Briefly, the effective temperature is just a practical parameter which describes surprisingly well the ordering process in a Coulomb crystal. Its definition... 

Cold, trapped HD+-ions are ideal objects for direct spectroscopic tests of quantum-electrodynamics, relativistic corrections in molecules, or for determining fundamental constants such as the electron-proton mass ratio. It is also of interest for many applications since it has a dipole moment. The potential of localizing trapped ions in Coulomb crystals has been demonstrated recently with spectroscopic studies on HD+ ions with sub-MHz accuracy. The experiment has been performed with 150 HD+ ions which have been stored in a linear rf quadrupole trap and sympathetically cooled by 2000 laser-cooled Be+ ions. IR excitation of several rovibrational infrared transitions has been detected via selective photodissociation of the vibra-tionally excited ions. The resonant absorption of a 1.4/itm photon induces an overtone transition into the vibrational state v = A. The population of the V = A state so formed is probed via dissociation of the ion with a 266 nm photon leading to a loss of the ions from the trap. Due to different Franck-Condon factors, the absorption of the UV photon from the v = A level is orders of magnitude larger than that from v = 0. 

Drewsen M, Jensen I, Lindballe J, Nissen N, Martinussen R, Mortensen A, Staanum P, Voigt D. (2003) Ion Coulomb crystals A tool for studying ion processes. Int. J. Mass. Spec. 229 83-91. 

Vogelius IS, Madsen LB, Drewsen M. (2006) Rotational cooling of molecular ions through laser-induced coupling to the collective modes of a two-ion Coulomb crystal. J. Phys. B At. Mol. Opt. 39 1267-1280. 

Roth B, Blythe P, Schiller S. (2007) Motional resonance coupling in cold multispecies Coulomb crystals. Phys. Rev. A. 75 023402-1-023402-8. 

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