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Compressing Single-component Plasmas Using Rotating Electric Fields – the “Rotating Wall Technique”

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Single-component plasmas (SCP) in Penning-Malmberg (PM) traps [1] have found many uses, including the accumulation, storage and delivery of antiparticles (both positrons and antiprotons). Applications include the creation and study of antihydrogen [2][3][4], beams to study the interaction of positrons with ordinary matter and to create dense gases of positronium (Ps) atoms [5][6][7], and the creation of Ps-atom beams [8][9].

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

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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 [10] states that the canonical angular momentum of a single component plasma in a PM trap can expressed as

, (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.

Fig. 1. Apparatus used to radially compress electron plasmas using the RW technique

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

,(2)


where n is the plasma density and B is the magnetic field [10]. 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. [11]

Fig. 2. Radial compression of an electron plasma vs time with the RW fields turned on at t = 0. Note the log scale for density and the flat density profiles, before and after compression, that are characteristic of rigid plasma rotation
Fig. 2. Radial compression of an electron plasma vs time with the RW fields turned on at t = 0. Note the log scale for density and the flat density profiles, before and after compression, that are characteristic of rigid plasma rotation

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” [11], [12]. 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.

Fig. 3. Density of a positron plasma as a function of applied RW frequency. The solid line corresponds to ballz, characteristic of the strong drive regime. For this experiment, B = 0.04 T, and the maximum density achieved is 17% of the Brillouin density limit , which is the maximum possible density for a SCP confined in a field of strength B.
Fig. 3. Density of a positron plasma as a function of applied RW frequency. The solid line corresponds to , characteristic of the strong drive regime. For this experiment, B = 0.04 T, and the maximum density achieved is 17% of the Brillouin density limit [5], which is the maximum possible density for a SCP confined in a field of strength B.



History

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The RW technique was first developed by Huang et al., to compress a magnetized Mg+ plasma [7]. 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 [13]. It was also used to phase-lock the rotation frequency of laser cooled single-component ion crystals [14]. The first use of the RW technique for antimatter was done using small positron plasmas without coupling to modes [15]. The strong drive regime, which was discovered somewhat later using electron plasmas [16], 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) [17], [18].

Uses

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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 [5]. 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 [8][9].

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 [2][3]. 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 [4]. In particular, this technique, dubbed SDREVC (strong drive regime evaporative cooling) [19], 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 [20].



See also

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Positron

Antiproton

Penning trap

Nonneutral plasmas

Positron annihilation

Positronium

Antihydrogen


References

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  1. ^ D. H. E. Dubin and T. M. O'Neil, Trapped Nonneutral Plasmas, Liquids, and Crystals (the Thermal Equilibrium States), Rev. Mod. Phys. 71, 87-172 (1999).
  2. ^ a b M. Amoretti, C. Amsler, G. Bonomi, A. Bouchta, P. Bowe, C. Carraro, et al., Production and Detection of Cold Antihydrogen Atoms, Nature 419, 456-459 (2002).
  3. ^ a b G. Gabrielse, N. Bowden, P. Oxley, A. Speck, C. Storry, J. Tan, et al., Background-Free Observation of Cold Antihydrogen with Field-Ionization Analysis of Its States, Phys. Rev. Lett. 89, 213401-213404 (2002).
  4. ^ a b M. Ahmadi, B. X. R. Alves, C. J. Baker, W. Bertsche, A. Capra, C. Carruth, et al., Characterization of the 1s-2s Transition in Antihydrogen, Nature Letters 557, 71 (2018).
  5. ^ a b c J. R. Danielson, D. H. E. Dubin, R. G. Greaves, and C. M. Surko, Plasma and Trap-Based Techniques for Science with Positrons, Rev. Mod. Phys. 87, 247 (2015).
  6. ^ D. B. Cassidy and A. P. Mills, The Production of Molecular Positronium, Nature 449, 195-197 (2007).
  7. ^ a b D. B. Cassidy, T. H. Hisakado, H. W. K. Tom, and A. P. J. Mills, Optical Spectroscopy of Molecular Positronium, Phys. Rev. Lett. 108, 133402-133405 (2012).
  8. ^ a b A. C. L. Jones, J. Moxom, H. J. Rutbeck-Goldman, K. A. Osorno, G. G. Cecchini, M. Fuentes-Garcia, et al., Focusing of a Rydberg Positronium Beam with an Ellipsoidal Electrostatic Mirror, Phys. Rev. Lett. 119, 053201 (2017).
  9. ^ a b K. Michishio, L. Chiari, F. Tanaka, N. Oshima, and Nagashima, A High-Quality and Energy-Tunable Positronium Beam System Employing a Trap-Based Positron Beam, Rev. Sci. Instrum. 90, (2019).
  10. ^ a b T. M. O'Neil and C. F. Driscoll, Transport to Thermal Equilibrium of a Pure Electron Plasma, Physics of Fluids 22, 266-277 (1979).
  11. ^ a b J. R. Danielson and C. M. Surko, Torque-Balanced High-Density Steady States of Single Component Plasmas, Phys. Rev. Lett. 94, 035001-035004 (2005).
  12. ^ J. R. Danielson, C. M. Surko, and T. M. O'Neil, High-Density Fixed Point for Radially Compressed Single-Component Plasmas, Phys. Rev. Lett. 99, 135005 (2007).
  13. ^ F. Anderegg, E. M. Hollmann, and C. F. Driscoll, Rotating Field Confinement of Pure Electron Plasmas Using Trivelpiece-Gould Modes, Phys. Rev. Lett. 81, 4875-4878 (1998).
  14. ^ X. P. Huang, J. J. Bollinger, T. B. Mitchell, and W. M. Itano, Phase-Locked Rotation of Crystallized Non-Neutral Plasmas by Rotating Electric Fields, Phys. Rev. Lett. 80, 73-76 (1998).
  15. ^ R. G. Greaves and C. M. Surko, Radial Compression and Inward Transport of Positron Plasmas Using a Rotating Electric Field, Phys. Plasmas 8, 1879-1885 (2001).
  16. ^ J. R. Danielson and C. M. Surko, Radial Compression and Torque-Balanced Steady States of Single-Component Plasmas in Penning-Malmberg Traps, Phys. Plasmas 13, 055706-055710 (2006).
  17. ^ R. G. Greaves and J. M. Moxom, Compression of Trapped Positrons in a Single Particle Regime by a Rotating Electric Field, Phys. Plasmas 15, 072304 (2008).
  18. ^ C. A. Isaac, C. J. Baker, T. Mortensen, D. P. v. d. Werf, and M. Charlton, Compression of Positron Clouds in the Independent Particle Regime Phys. Rev. Lett. 107, 033201-033204 (2011).
  19. ^ M. Ahmadi, B. X. R. Alves, C. J. Baker, W. Bertsche, A. Capra, C. Carruth, et al., Enhanced Control and Reproducibility of Non-Neutral Plasmas, Phys. Rev. Lett. 120, 025001 (2018).
  20. ^ C. Amole, M. D. Ashkezari, M. Baquero-Ruiz, W. Bertsche, P. D. Bowe, E. Butler, et al., Resonant Quantum Transitions in Trapped Antihydrogen Atoms, Nature 483, 439-444 (2012).
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