T B. Mitchell

Phase-Locked Rotation of Crystallized Non-neutral Plasmas by Rotating Electric Fields

Large numbers of particles with a single sign ofcharge can be trapped and cooled in Penning traps [1,2],which use a combination of static electric and magneticfields for particle confinement. The global rotation ofthese non-neutral plasmas about the magnetic field axisis necessary for the radial confinement [3]. Activecontrol of this rotation prevents plasmas from spinningdown under the ambient drag from static field errorsand background neutrals, and is important for a numberof experiments including Coulomb crystal studies [4,5],precision spectroscopy [6–8], measurements of particleand energy transport [9], trapping of antimatter plasmas[10,11], and storage of highly stripped ions [12]. As anexample, the second-order Doppler (time dilation) shiftdue to rotational velocity in a Penning trap atomic clockcan be minimized by stabilizing the rotation at a particularfrequency [7]. Radiation pressure from laser beams hasbeen used to vary the plasma rotation frequency [13,14].However, this method is limited to the few ion specieswhose atomic transitions are accessible by a laser, and isnot precise due to laser power, frequency, and pointingfluctuations. Recently, rotating azimuthally asymmetric(“rotating wall”) electric fields have been used to applya torque on Mg

Precise control of the global rotation of strongly coupled ion plasmas in a Penning trap

Rotating asymmetric electric fields have been applied to control the rotation frequency (and hence the density) of non-neutral plasmas, which are confined in Penning-type traps and have relaxed close to thermal equilibrium characterized by a global rigid-body rotation. “Infinite” confinement times and density compression were first reported for uncorrelated plasmas of ∼108 Mg+ ions with temperatures ranging from 1 K to 5×104 K (4 eV) [Huang et al., Phys. Rev. Lett. 78, 875 (1997)]. In this paper, the rotating field technique has been applied to control strongly coupled plasmas of ∼105 9Be+ ions which are laser-cooled to millikelvin temperatures so that the plasma freezes into a solid with a crystalline lattice. Here, Bragg diffraction peaks from crystals provide an accurate way of measuring the rotation frequency, and it is observed that the plasma rotation can be phase locked to the applied rotating field without any slip. In essence, these corotating plasmas have reached thermal equilibrium with the rot...

Direct observations of the structural phases of crystallized ion plasmas

Laser-cooled 9Be+ ions confined in a Penning trap were directly observed, and the images were used to characterize the structural phases of the ions. With the ions in two-dimensionally extended lattice planes, 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. Qualitatively similar structural phase transitions occur or are predicted to occur in other planar single-component systems with a variety of interparticle interactions. Closed-shell structures were observed with small ion clouds that were spherical or prolate, and crystals with long-range order were observed in the centers of clouds with large numbers of ions. These experimental results are in good agreement with theoretical predictions for the strongly coupled one-component plasma. Laser-cooled 9Be+ ions confined in a Penning trap were directly observed, and the images were used to characterize the structural phases of the ions. With the ions in two-dimensionally extended lattice planes, 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. Qualitatively similar structural phase transitions occur or are predicted to occur in other planar single-component systems with a variety of interparticle interactions. Closed-shell structures were observed with small ion clouds that were spherical or prolate, and crystals with long-range order were observed in the centers of clouds with large numbers of ions. These experimental results are in good agreement with theoretical predictions for the strongly coupled one-component plasma.

Doppler imaging of plasma modes in a Penning trap.

We describe a technique and present results for imaging the modes of a laser-cooled plasma of 9 Be + ions in a Penning trap. The modes are excited by sinusoidally time-varying potentials applied to the trap electrodes. They are imaged by changes in the ion resonance fluorescence produced by Doppler shifts from the coherent ion velocities of the mode. For the geometry and conditions of this experiment, the mode frequencies and eigenfunctions have been calculated analytically. A comparison between theory and experiment for some of the azimuthally symmetric modes shows good agreement.

A Laser-cooled Positron Plasma

We present results on trapping and cooling of positrons in a Penning trap. Positrons from a 2 mCi 22 Na source travel along the axis of a 6 T magnet and through the trap after which they strike a Cu reflection moderator crystal. Up to a few thousand positrons are trapped and lose energy through Coulomb collisions (sympathetic cooling) with laser-cooled 9 Be +. By imaging the 9 Be + laser-induced fluorescence, we observe centrifugal separation of the 9 Be+ ions and positrons, with the positrons coalescing into a column along the trap axis. This indicates the positrons have the same rotation frequency and comparable density (4 × 10 9 cm−3) as the 9 Be + ions, and places an upper limit of approximately 5 K on the positron temperature of motion parallel to the magnetic field. We estimate the number of trapped positrons from the volume of this column and from the annihilation radiation when the positrons are ejected from the trap. The measured positron lifetime is > 8 days in our room temperature vacuum of 10 −8 Pa.

Mode and transport studies of laser-cooled ion plasmas in a Penning trap

We describe a technique and present results for imaging the modes of a laser-cooled plasma of 9Be+ ions in a Penning trap. The modes are excited by sinusoidally time-varying potentials applied to the trap electrodes, or by static field errors. They are imaged by changes in the ion resonance fluorescence produced by Doppler shifts from the coherent ion velocities of the mode. For the geometry and conditions of this experiment, the mode frequencies and eigenfunctions have been calculated analytically. A comparison between theory and experiment for some of the azimuthally symmetric modes shows good agreement. Enhanced radial transport is observed where modes are resonant with static external perturbations, such as those caused by misaligning the trap with respect to the magnetic field. Similarly, the plasma angular momentum can be changed through the deliberate excitation of azimuthally asymmetric modes. The resultant torque can be much greater than that from the “rotating wall” perturbation, which is not mo...

Crystalline order in strongly coupled plasmas

Laser-cooled trapped ions can be strongly coupled and form crystalline states. This manuscript reviews experimental studies which measure the spatial correlations of Be+ ion crystals formed in Penning traps. Both Bragg scattering of the cooling-laser light and spatial imaging of the laser-induced ion fluorescence are used to measure these correlations. In spherical plasmas with more than 2×105 ions, body-centered-cubic (bcc) crystals, the predicted bulk structure, are the only type of crystals observed. The orientation of the ion crystals can be phase-locked to a rotating electric-field perturbation. With this “rotating wall” technique and stroboscopic detection, images of individual ions in a Penning trap are obtained. The rotating wall technique also provides a precise control of the time-dilation shift due to the plasma rotation, which is important for Penning trap frequency standards.

Structure and Control of Coulomb Crystals in a Penning Trap

We apply rotating electric fields to ion plasmas in a Penning trap to obtain phase-locked rotation about the magnetic field axis. These plasmas, containing up to 1069Be+ ions, are laser-cooled to millikelvin temperatures so that they freeze into solids. Single body-centered cubic (bcc) crystals have been observed by Bragg scattering in nearly spherical plasmas with ≳ 2 × 105 ions. The detection of the Bragg patterns is synchronized with the plasma rotation, so individual peaks are observed. With phase-locked rotation, the crystal lattice and its orientation can be stable for longer than 30 min or ∼108 rotations.

FORMATION AND CONTROL OF COULOMB CRYSTALS IN TRAPPED ION PLASMAS

Trapped non-neutral plasmas consisting of one charged particle species provide an experimental realization of a classical one-component plasma (OCP). I In Penning traps, which use static electric and magnetic fields for confinement, trapped plasmas can relax to a global thermal equilibrium which undergoes a rigid-body rotation about the magnetic field axis2 In a frame rotating with the plasma, there arises an induced electric field which takes the place of the field from the uniform neutralizing background in the OCP model. Active control of the rotation frequency prevents plasmas from spinning down under the ambient drag from static field errors and background neutral molecules, and allows variation of the plasma density and With Doppler laser cooling, pure ion plasmas with density no greater than 1 O8 cmP3 and temperature T less than 5 mK can be routinely obtained,2 resulting in a Coulomb coupling parameter r z ( e 2 / 4 ~ ~ o u w s ) ( k ~ T ) 1 greater than 200. Here, e is the ion charge and uws is the Wigner-Seitz radius defined by 47ru&/3 I/no. A classical, infinite OCP freezes into a bcc lattice at x 172.4 However, this result does not strictly apply to the trapped plasmas because of the surface effects associated with their finite size. Both simulations and experiments6 show that a structure of concentric shells forms for nearly spherical plasmas with lo3 to lo4 ions. For plasmas with 2 2 x lo5 ions or 2 30 shells, time-averaged Bragg scattering patterns are consistent with bcc crystals (presumably located near the plasma enter),^ in agreement with a theoretical estimate. But this measurement can not determine whether the Bragg pattems come from single crystals or polycrystals. In this report, we demonstrate that azimuthally asymmetric electric fields rotating in the same sense as the plasma can phase-lock the rotation of crystallized plasmas without slip, therefore precisely controlling the plasma rotation frequency, density, and surface shape. We synchronize the detection of Bragg-scattered light either with this active rotation control or using the time dependence of the scattered light itself measured by a fast photomultiplier tube. Time-resolved (stroboscopic) Bragg diffraction pattems are obtained, effectively removing

A laser-cooled, high density positron plasma

We present results on trapping and cooling of positrons in a Penning trap. Up to a few thousand positrons are trapped and sympathetically cooled through Coulomb collisions (sympathetic cooling) with laser-cooled 9Be+ ions. By imaging the 9Be+ laser-induced fluorescence, we observe centrifugal separation of the 9Be+ ions and the positrons, with the positrons coalescing into a column along the trap axis. This indicates the positrons have the same rotation frequency and comparable density (∼4×109u2009cm−3) as the 9Be+ ions, and places an upper limit of approximately 5 K on the positron temperature of motion parallel to the magnetic field. The measured positron lifetime is >8 days in our room temperature vacuum of 10−8u2009Pa.