Plasmas of Mg 1 ions, containing more than 10 5 ions, have been observed to reach well-ordered (crystalline) states by applying laser cooling. The crystals are highly elongated with up to ten concentric cylindrical shells surrounding a central string. Such large structures have not previously been observed in a Paul trap. The amplitude of the micromotion of the ions can be larger than the shell spacings. As the diameter changes along the crystals, sharp transitions are observed when new shells form, in good agreement with molecular dynamics simulations. The predictions from simulations of how ordering develops with decreasing temperature are also confirmed. [S0031-9007(98)07188-9] PACS numbers: 32.80. Pj, 42.50.Vk, 52.25.Wz Clouds of laser-cooled, trapped ions have previously been observed to condense and to exhibit quasicrystalline spatial order in Penning [1,2] and Paul (radiofrequency or rf) traps [3][4][5]. A classical, infinite, one-component plasma undergoes a transition from liquidlike behavior to a body-centered-cubic (bcc) lattice when the ratio G of the Coulomb energy between adjacent particles to the random thermal kinetic energy exceeds 175 [6]. In contrast, for finite plasmas molecular dynamics (MD) simulations predict formation of concentric shells with near-hexagonal ordering within the shell [7,8]. (Though these structures have no long-range periodic order, they are often referred to as crystals, a usage we follow here.)In Paul traps the rf field drives micromotion, which is a modulation (at the rf frequency) of the secular harmonic motion in the effective trapping potential. The magnitude of the micromotion increases with an ion's distance from the trap central axis, and such motion can couple energy from the rf drive into the random motion of the ions through their mutual Coulomb interaction. This so-called rf heating (see, e.g., [9,10]) is widely assumed to limit attainable crystal sizes. The kinetic energy associated with the micromotion can be several orders of magnitude higher than the thermal energy at which spatial ordering occurs in static potentials, so the coupling of micromotion into thermal motion can be expected to be critical for crystal formation. The noninertial constraints and the continually changing shape of the cloud in the rf field can affect the ordering process and the resultant structure of the crystals in interesting ways that at present are poorly understood.Crystals consisting of at most five shells have been attained earlier [5] in a ring rf trap, and simulations with up to 512 ions in a standard Paul trap, with the emphasis on the averaged position of ions in the crystal [11] have been reported previously. By contrast, the largest ordered systems so far were seen in Penning traps, where more than 10 5 ions have been crystallized and show evidence of central bcc structures [2].In this Letter, we present evidence for Coulomb crystals of the largest transverse size observed in a linear Paul trap [12], as well as evidence on how the ordering develops gradually as the r...

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We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than 50% were cooled only sympathetically through the Coulomb interaction with laser-cooled Mg 1 ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions. [S0031-9007(99)08637-8] PACS numbers: 32.80.Pj, 42.50.Vk, 52.25.Wz Trapped ions, when cooled sufficiently, form spatially ordered structures (Coulomb crystals). For smaller crystals (typically #10 5 ions), where surface effects play a dominant role, shell and stringlike structures are the equilibrium states [1-3]. Molecular dynamics (MD) simulations of infinite one component plasmas predict a body centered cubic (bcc) structure [4] as the lowest energy state. By applying laser cooling, string and shell structures have been observed in both Paul and Penning traps by imaging the fluorescence from the ions [5][6][7][8][9][10][11], and recently bcc structures at the center of very large ion crystals in a Penning trap have been revealed by Bragg scattering techniques [12,13]. Since only ions with simple level schemes accessible to lasers can easily be laser cooled, most atomic ion species, and all molecular ions, due to their complex vibrational and rotational structure, are excluded from this type of cooling. Hence, to date only very few singly charged ion species have been laser cooled and crystallized. The equations of motion in both Penning and Paul traps allow, however, ions within a certain chargeto-mass ratio to be trapped simultaneously, which makes sympathetic cooling [14] through the Coulomb interaction possible.Several authors have previously investigated sympathetic cooling, where directly laser cooled ions were used to cool ions of a different species through mutual Coulomb interaction [9,[14][15][16][17]. In most of these experiments, the typically achieved temperatures of the sympathetically cooled ions were several hundred mK, which were too high for ordering of the whole plasma. In a ring-shaped [18] and a linear Paul trap [19] a few nonfluorescing sites in crystals consisting of laser cooled 24 Mg 1 were attributed to indirectly cooled impurity ions. Recently, a crystal consisting entirely of Ca 1 was observed to stay crystallized when some of the constituent ions were decoupled from the cooling laser by being optically pumped into a metastable dark state [9].In this Letter we report on formation of Coulomb crystals consisting of up to a few hundred ions in a linear Paul trap where the fraction of indirectly (sympathetically) cooled ions is greater than 50%. In one case particularly interesting for spectroscopy, 14 sympathetically cooled ions were maintained in...

The detection of electrostatic nonneutral plasma modes in the ATHENA (ApparaTus for High precision Experiment on Neutral Antimatter) experiment [M. Amoretti, C. Amsler, G. Bonomi et al., Nature (London) 419, 456 (2002)] is described. A complete nondestructive diagnostic of the plasma based on a fit to the line shape of the function describing the power transmitted through the plasma around the frequency of the fundamental mode is developed and the experimental results are presented and discussed.