Contrib. Plasma Phys. 47, No. 4-5, 281 – 290 (2007) / DOI 10.1002/ctpp.200710038 Shell Structure of Yukawa Balls H. Baumgartner ∗1 , H. K¨ ahlert 1,2 , V. Golobnychiy 1 , C. Henning 1 , S. K¨ ading 3 , A. Melzer 3 , and M. Bonitz 1 1 Institut f¨ ur Theoretische Physik und Astrophysik, Christian-Albrechts-Universit¨ at, Leibnizstr. 15, 24118 Kiel 2 University of Kansas, Department of Physics and Astronomy, Lawrence, KS 66045 3 Institut f¨ ur Physik, Ernst-Moritz-Arndt-Universit¨ at Greifswald, 17489 Greifswald Received 13 December 2006, accepted 14 December 2006 Published online 6 June 2007 Key words Coulomb balls, Yukawa balls, Coulomb crystals, dusty plasmas. PACS 52.27.Lw, 52.27.Gr, 52.35.Fp, 82.70.Dd Spherical crystals continue to attract increasing interest in many ﬁelds, including trapped ions and dusty plas- mas. These strongly coupled systems are excellent objects to study fundamental interactions and interesting correlation phenomena while they are relatively easy to realize and observe. Experiments and simulations show a spherical arrangement in nested shells. This work discusses new experimental and simulation results for small systems (N ≤ 54) as well as the inﬂuence of temperature and charge ﬂuctuations on the shell popula- tions. Finally, the cluster conﬁgurations are compared with an analytical shell model which is able to predict shell populations and energies for larger clusters. c  2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction Coulomb crystal formation is among the most exciting cooperative phenomena in charged particle systems and has been observed in a variety of ﬁelds, including ultracold ions [1, 2] and dusty plasmas [3, 5]. Furthermore, computer simulations predict electron crystallization in quantum dots, e.g. [6, 7], crystallization of holes [8,9] and excitons [10,11] in semiconductors and ion crystallization in expanding neutral plasmas [12] showing the universality of this phenomenon. Particular recent attention has been devoted to three-dimensional spherical crystals (so-called “Coulomb balls” or “Yukawa balls”) after their experimental observation in dusty plasmas [4]. These clusters consist of tens to thousands of micrometer sized plastic particles in a rf-discharge. Due to the higher mobility of electrons the dust particles are charged with q ≈ 10 3 e. The conﬁnement in experiments is realized by thermoforetic force, electric ﬁeld force of the rf-discharge, gravity and ion winds. A closer analysis of such a conﬁnement can be found in [13] which concludes that the conﬁnement potential is nearly parabolic and spherically symmetric. The simplest theoretical model of these ﬁnite systems is given by the hamiltonian H (r i , v i )= N  i m 2 v 2 i + N  i α 2 r 2 i + N  ij q 2 r ij · exp(-κr ij ). (1) It consists of kinetic energy, a conﬁnement potential and the interaction potential, where m is the mass of the par- ticles, α the constant of the parabolic trap, r i and v i the positions and velocities of the particles and r ij = |r i - r j | the distance of the particles i and j . The particles interact via a Yukawa potential, the screening parameter κ re- ﬂects the inﬂuence of the surrounding plasma. In Ref. [5] it was shown that ground state conﬁgurations computed from this model reproduce the structure of the experimentally observed Yukawa balls very well, including their radius and shell populations. A comparsion between the Kiel experiment of the group of A. Piel [4] and simulations showed that a screening parameter of ∗ Corresponding author: e-mail: baum@theo-physik.uni-kiel.de, Phone: +00 49 431 880 4063, Fax: +00 49 431 880 111 c  2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim