Single crystals of a one-component plasma were observed by optical Bragg diffraction. The plasmas contained 10(5) to 10(6) single-positive beryllium-9 ions (9Be+) at particle densities of 10(8) to 10(9) per cubic centimeter. In approximately spherical plasmas, single body-centered cubic (bcc) crystals or, in some cases, two or more bcc crystals having fixed orientations with respect to each other were observed. In some oblate plasmas, a mixture of bcc and face-centered cubic ordering was seen. Knowledge of the properties of one-component plasma crystals is required for models of white dwarfs and neutron stars, which are believed to contain matter in that form.
We apply "rotating wall" electric fields to spin up a non-neutral plasma in a Penning-Malmberg trap, resulting in steady-state confinement (weeks) of up to 10 9 Mg 1 ions. The resulting ion columns can be near global thermal equilibrium, with near-uniform temperature and rotation frequency. The equilibrated plasma E 3 B rotation rate f E is observed to be somewhat less than the drive frequency f w , with slip Df ϵ f w 2 f E depending on temperature as Df~T 1͞2 for 0.05 & T & 5 eV. Dynamic measurements of applied torque versus slip frequency show plasma spin up and compression for Df. 0 and plasma slowing and expansion for Df , 0. By gradually increasing f w , density compression up to 20% of the Brillouin density limit has been achieved. Heating resonances and hysteresis in plasma parameters are also observed.
Laser-cooled 9 Be ϩ ions confined in two-dimensionally extended lattice planes were directly observed, and the images were used to characterize the structural phases of the ions. Five different stable crystalline phases were observed, and the energetically favored structure could be sensitively tuned by changing the areal density of the confined ions. The experimental results are in good agreement with theoretical predictions for the planar (infinite in two dimensions) one-component plasma. Qualitatively similar structural phase transitions occur, or are predicted to occur, in other experimentally realizable planar systems.The one-component plasma (OCP) has been a model of condensed matter in statistical physics for over 30 years, and it is used to describe such diverse systems as dense astrophysical matter (1) and electrons on the surface of liquid helium (2). Laser-cooled trapped ions (3) are an excellent experimental realization of the OCP. The phase structures of spatially homogeneous (infinite) (4) and cylindrical (infinite in one dimension only) (5) OCPs have been explored previously. Here, images of individual ions that were confined in twodimensionally extended lattice planes are presented and used to characterize the structural phases; the observed structures agree well with the predictions of an analytic theory for the planar OCP.The OCP model consists of a single charged species embedded in a uniform, neutralizing background charge. In Paul (6) or Penning (6, 7) traps, which are used to confine charged particles, a (fictitious) neutralizing background is provided by the confining potentials. The thermodynamic properties of the infinite classical OCP are determined by its Coulomb coupling parameter, ⌫ ϵ, which is the ratio of the Coulomb potential energy of neighboring ions to the kinetic energy per ion; ⑀ 0 is the permittivity of the vacuum, e is the charge of an ion, k B is Boltzmann's constant, T is the temperature, and a WS is the Wigner-Seitz radius [defined by 4(a WS ) 3 /3 ϭ 1/n 0 , where n 0 is the ion density]. The onset of shortrange order for the infinite OCP is predicted (8) at ⌫ Ϸ 2, and a phase transition to a body-centered cubic (bcc) lattice is predicted (8, 9) at ⌫ Ϸ 170. With an OCP in a planar geometry (infinite in only two dimensions), boundary effects are predicted to cause the formation of a variety of additional structural phases, such as the hexagonal close-packed (hcp) and face-centered cubic (fcc) phases (10, 11). Qualitatively similar structural phase transitions occur, or are predicted to occur, in other planar systems with varied interparticle interactions, such as plasma dust crystals (12), colloidal suspensions (13), semiconductor electron bilayer systems (14), and hard spheres (15).The crystallization of small numbers (total number N Ͻ 50) of laser-cooled ions into Coulomb clusters (16) was first observed in Paul traps (17). With larger numbers of trapped ions, concentric shells (18) were directly observed in Penning (19) and Paul traps (5,20). Recently, Bragg diffractio...
We report the precise control of the rotation frequency of strongly coupled non-neutral plasmas by rotating electric fields. These plasmas of up to 10 6 9 Be 1 ions are trapped in a Penning trap and laser cooled into crystallized structures which undergo a rigid-body rotation. Bragg diffraction shows that the crystalline lattice can be stable for longer than 30 min (ϳ10 8 rotations), and that the plasma rotation can be phase locked to the applied field without any slip. These corotating plasmas are in a novel global thermal equilibrium whose asymmetric surface shape (triaxial ellipsoid) has been measured.
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