Experimental Setup

The Penning trap, along with the positron source and positron moderator are shown in Fig. 1. The stack of cylindrical electrodes (60 mm long) forms two Penning traps. The top (load) trap was used to create 9Be+ plasmas by ionizing neutral Be atoms sublimated from a heated

Be filament and directed through a small hole on the ring electrode. The 9Be+ ions are transferred to the lower (experimental) trap for experimentation. In a single load-transfer cycle we can store over one million ions. By repeating this procedure we can further increase the number of ions. The inner diameter of the trap electrodes is 10 mm, and the traps are enclosed in a glass cylinder that, after baking at -350 °C, maintains a vacuum better then 10-8 Pa. The magnetic field is Bo = 6 T, which produces a cyclotron frequency for ions of The magnetic field is aligned to the trap symmetry axes to within 0.01°. An axisymmetric, nearly quadratic trapping potential is generated by biasing the ring of the experimental trap to a negative voltage Vr and adjacent compensation electrodes to Vc = 0.9xV/j. For Vr= -100 V, and for the endcap voltage Vec = 0 the single particle axial frequency is and the magnetron frequency is

In Penning traps, the ion plasma undergoes an ExB drift and rotates about the trap axis. This rotation through the magnetic field produces, through the Lorentz force, the radial binding force and radial plasma confinement. When a plasma reaches thermal equilibrium the whole ion plasma rotates at a uniform rotation frequency uT. A two-fold az-imuthally segmented electrode located between the ring and the lower compensation electrode (not shown on Fig. 1), was used to generate an oscillating electric-field perturbation by applying out-of-phase sinusoidal potentials on its two segments. The oscillating field is the superposition of components that rotate with and against the plasma rotation. The co-rotating component was used to control the plasma rotation frequency (the "rotating wall") [21, 22].

The ions were cooled by a laser beam tuned -10 MHz lower than a hyperfine-Zeeman component of the 2s2S\/2 2p2P3/2 resonance at 313 nm. The laser beam was directed through the trap, intersecting the ion plasma on the side receding from the laser beam due to the plasma rotation. As shown in Fig. 1 the beam entered the trap between the upper compensation and ring electrodes, passed through the trap center, and exited through the gap between the ring and lower compensation electrode, making an 11° angle with the horizontal (x-y) plane. Based on measurements performed in previous experiments [23, 24, 25] we expect Tj_ < T|| < 100 mK, where T± and 7]| describe the velocity distributions in the direction perpendicular and parallel to the trap axis (z axis).

An ion plasma in thermal equilibrium at these cryogenic temperatures is a uniform-density plasma with a rigid-body rotation frequency ojt in the range wm < wr < fi - wm. The ion density is constant within the plasma and is given by no = 2eomuv (fi — wr)/g2, where q and m are the charge and mass of an ion, and eo is the permittivity of the vacuum. With

Figure 1. Schematic diagram of the cylindrical Penning traps showing the load trap used to load 9Be+ ions and experimental trap for experimentation with positrons and ions. Vfl, Vc and Vec are respectively the voltages applied to the ring, compensation and end cap electrodes of the experimental trap. The laser light at ~313 nin is directed through the ion plasma which is located at the center of the experimental trap.

Figure 1. Schematic diagram of the cylindrical Penning traps showing the load trap used to load 9Be+ ions and experimental trap for experimentation with positrons and ions. Vfl, Vc and Vec are respectively the voltages applied to the ring, compensation and end cap electrodes of the experimental trap. The laser light at ~313 nin is directed through the ion plasma which is located at the center of the experimental trap.

the quadratic trapping potential near trap center, the plasma has the shape of a spheroid whose aspect ratio, a = zo/ro, depends on uir. Here 2zo and 2ro are the axial and radial extents of the plasma. Low rotation (uiT ~ u>m) results in an oblate spheroid of large radius. Increasing ur increases the Lorentz force due to the plasma rotation through the magnetic field, which in turn increases a and n<j. At ojt — i2/2 (Brillouin limit) the ion plasma attains its maximum aspect ratio and density. For 9Be+ ions at 6 T the maximum ion density is 1.1 xlO10 cm-3. High density can be reached by using torques produced by a cooling laser beam [26] or by a rotating electric field perturbation [21, 22] to control the plasma's angular momentum. Typically, the ions were first Doppler laser-cooled and oy was approximately set by the laser torque. The "rotating wall" was then turned on at a frequency near the rotation frequency of the 9Be+ plasma. Resonantly scattered 313 rail photons were collected by an f/5 imaging system in a direction 11° above the z = 0 plane of the trap and imaged onto the photocathode of a photon-counting imaging detector. Such an optical system produces an approximate side-view image of the 9Be+ plasma.

The source for the positrons is a 2 mCi 22Na source with an active diameter of ~1 mm. The source is placed just above the vacuum envelope, and positrons enter the trap through a Ti foil of ~ 7/zm thickness. Positrons travel along the axis of the Penning traps until they hit the moderator crystal placed below the lower end-cap of the experimental Penning trap. The positron current reaching the crystal was measured by an electrometer. At the beginning of our experiment the measured current was ~2 pA, in accordance with the expected positron losses in the Ti foil and the fringing fields of the magnet at the position of the source. A thin chopper wheel is placed between the source and the Ti foil for lock-in detection of the positron current (if needed) and to temporary block the positrons from entering the trap without removing the source.

For the method of trapping positrons discussed in [2], a room temperature kinetic-energy distribution of moderated positrons is important. Room-temperature distributions of moderated positrons have been reported in the literature for a number of single-crystal metallic moderators. We chose a Cu(111) moderator crystal because of the expected narrow distribution of positrons [27, 28], and because it can be annealed and cleaned at a lower temperature (~900 °C). The experimental results discussed here were obtained with the moderator crystal heated to 350 °C during the vacuum bakeout.

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