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Compressing Single-component Plasmas Using Rotating Electric Fields – the “Rotating Wall Technique”
Single-component plasmas (SCP) in Penning-Malmberg (PM) traps have found many uses, including the accumulation, storage and delivery of antiparticles (both positrons and antiprotons). Applications include the creation and study of antihydrogen , beams to study the interaction of positrons with ordinary matter and to create dense gases of positronium (Ps) atoms   , and the creation of Ps-atom beams.

The “rotating wall (RW) technique” uses rotating electric fields to compress SCP in PM traps radially to increase the plasma density and/or to counteract the tendency of plasma to diffuse radially out of the trap. It has proven crucial to tailor trapped plasmas for many applications.

Principles of operation
The PM trap uses a uniform magnetic field and an axial electrostatic potential to confine single-component plasmas. A confinement theorem due to O’Neil states that the canonical angular momentum of a single component plasma in a PM trap can expressed as

"$L\approx -\frac{ \mathrm{{\mu\omega }_{c}}}{ \mathrm{2} }\Sigma {x}_{j}r^{2}_{j}$, (1)"

where is the cyclotron frequency, m is the particle mass, and  is the radial position of the jth particle. If there are no torques on the plasma, the second radial moment of the particle distribution is constant, and hence the plasma cannot expand. Conversely, if a torque is applied to the plasma in such a way as to spin it faster, this acts to increase the inward directed Lorentz force and compresses the plasma.



Cold, single-component plasmas in PM traps can come to thermal equilibrium and rotate as a rigid body at frequency

"$f_{E} =\frac{ \mathrm{e} n}{ \mathrm{4\pi \varepsilon _{0}} B}$,(2) |undefined"

where n is the plasma density and B is the magnetic field. As illustrated in Fig. 1, the RW technique uses an azimuthally segmented cylindrical electrode covering a portion of a plasma and phased rf voltages applied to the segments. The result is a rotating electric field perpendicular to the axis of symmetry of the plasma. This field induces an electric dipole moment in the plasma and hence a torque. As shown in Fig. 2, rotation of the field in the direction of, and faster than the natural rotation of the plasma, produces plasma compression.



An important requirement for plasma compression is good coupling between the plasma and the rotating field to overcome asymmetry-induced transport which acts as a drag on the plasma and tends to oppose the RW torque. For high quality PM traps with little asymmetry induced transport, one can access a so-called “strong drive regime”,. In this case, application of a rotating electric field at frequency results in the plasma spinning up to the applied frequency, namely   (cf. Fig. 3). This has proven enormously useful as a way to fix plasma density by tuning the RW frequency.



History
The RW technique was first developed by Huang et al., to compress a magnetized Mg+ plasma. They used a segmented electrode such as that described above to couple to waves (Trivelpiece-Gould modes) in the plasma. This technique was soon thereafter applied to electron plasmas. It was also used to phase-lock the rotation frequency of laser cooled single-component ion crystals. The first use of the RW technique for antimatter was done using small positron plasmas without coupling to modes. The strong drive regime, which was discovered somewhat later using electron plasmas, has proven to be more useful in that tuning to (and tracking) plasma modes is unnecessary. A related technique has been developed to compress single-component charged gases in PM traps (i.e., charge clouds not in the plasma regime),.

Uses
The RW technique has found extensive use in manipulating antiparticles in Penning-Malmberg traps. One important application is the creation of specially tailored antiparticle beams for atomic physics experiments. Frequently one would like a beam with a large current density. In this case, one compresses the plasma with the RW technique before delivery. This has been crucial in experiments to study dense gases of positronium (Ps) atoms and formation of the Ps2 molecule (e+e-e+e-) [5-7]. It has also been important in the creation of high-quality Ps-atom beams.

The RW technique is used in three ways in the creation of low-energy antihydrogen atoms. Antiprotons are compressed radially by sympathetic compression with electrons co-loaded in the trap. The technique has also been used to fix the positron density before the positrons and antiprotons are combined. Recently it was discovered that one could set all of the important parameters of the electron and positron plasmas for antihydrogen production using the RW to fix the plasma density and evaporative cooling to cool the plasma and fix the on-axis space charge potential. The result was greatly increased reproducibility for antihydrogen production. In particular, this technique, dubbed SDREVC (strong drive regime evaporative cooling), was successful to the extent that it increased the number of trappable antihydrogen by an order of magnitude. This is particularly important in that, while copious amounts of antihydrogen can be produced, the vast majority are at high temperature and cannot be trapped in the small well depth of the minimum-magnetic field atom traps.