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. 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.

© Optical Society of America

1. Non-Neutral Plasma Physics II, eds. J. Fajans and D. H. E. Dubin (AIP, New York, 1995).
2. J. H. Malmberg and T. M. O'Neil, ``Pure electron plasma, liquid, and crystal," Phys. Rev. Lett. 39, 1333-1336 (1977). [CrossRef]
3. C. F. Driscoll, J. H. Malmberg, and K. S. Fine, ``Observation of transport to thermal equilibrium in pure electron plasmas," Phys. Rev. Lett. 60, 1290-1293 (1988). [CrossRef] [PubMed]
4. L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, ``Static properties of a non-neutral 9 Be + ion plasma," Phys. Rev. A 38, 859-873 (1988). [CrossRef] [PubMed]
5. J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, ``Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks," Phys. Plasmas 1, 1403-1414 (1994). [CrossRef]
6. D. H. E. Dubin,``Theory of electrostatic uid modes in a cold spheroidal non-neutral plasma," Phys. Rev. Lett. 66, 2076-2079 (1991). [CrossRef] [PubMed]
7. J. J. Bollinger, D. J. Heinzen, F. L. Moore, W. M. Itano, D. J. Wineland, and D. H. E. Dubin, ``Electrostatic modes of ion-trap plasmas," Phys. Rev. A 48, 525-545 (1993). [CrossRef] [PubMed]
8. R. G. Greaves and C. M. Surko, ``Antimatter plasmas and antihydrogen," Phys. Plasmas 4, 1528-1543 (1997). [CrossRef]
9. G. Gabrielse, X. Fei, L. A. Orozco, R. L. Tjoelker, J. Haas, H. Kalinowsky, T. A. Trainor, and W. Kells, ``Cooling and slowing of trapped antiprotons below 100 meV," Phys. Rev. Lett. 63, 1360 (1989). [CrossRef] [PubMed]
10. M.H. Holzscheiter, X. Feng, T. Goldman, N.S.P. King, R. A. Lewis, M. M. Nieto, and G.A. Smith, ``Are antiprotons forever?," Phys. Lett. A 214, 279 (1996). [CrossRef]
11. D. J. Heinzen, J. J. Bollinger, F. L. Moore, W. M. Itano, and D. J. Wineland, ``Rotational equilibria and low-order modes of a non-neutral ion plasma," Phys. Rev. Lett. 66, 2080-2083 (1991). [CrossRef] [PubMed]
12. 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). [CrossRef]
13. D. H. E. Dubin and J. P. Schiffer, ``Normal modes of cold confined one-component plasmas," Phys. Rev. E 53, 5249-5267 (1996). [CrossRef]
14. D. H. E. Dubin, ``Effects of correlations on the thermal equilibrium and normal modes of a non-neutral plasma," Phys. Rev. E 53, 5268-5290 (1996). [CrossRef]
15. C. S. Weimer, J. J. Bollinger, F. L. Moore, and D. J. Wineland, ``Electrostatic modes as a diagnostic in Penning trap experiments," Phys. Rev. A 49, 3842-3853 (1994). [CrossRef] [PubMed]
16. M. D. Tinkle, R. G. Greaves, and C. M. Surko, ``Low-order longitudinal modes of single-component plasmas," Phys. Plasmas 2, 2880-2894 (1995). [CrossRef]
17. R. G. Greaves, M. D. Tinkle, and C. M. Surko, ``Modes of a pure ion plasma at the Brillouin limit," Phys. Rev. Lett. 74, 90-93 (1995). [CrossRef] [PubMed]
18. C. F. Driscoll, ``Observation of an unstable m = 1 diocotron mode on a hollow electron column," Phys. Rev. Lett. 64, 1528-1543 (1990). [CrossRef]
19. J. N. Tan, J. J. Bollinger, B. Jelenkovic, and D. J. Wineland, ``Long-range order in laser-cooled, atomic-ion Wigner crystals observed by Bragg scattering," Phys. Rev. Lett. 75, 4198-4201 (1995). [CrossRef] [PubMed]
20. W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenkovic, X.-P. Huang, and D. J. Wineland, ``Bragg diffraction from crystallized ion plasmas," Science 279, 686-689 (1998). [CrossRef] [PubMed]
21. Here ! lm is the mode frequency in a frame rotating with the plasma. For the m = 0 modes discussed here this distinction is not necessary because their frequency is the same in either the laboratory or rotating frame.
22. Information on the mode eigenfunction can be obtained from the side-view images even when there is a change in the phase-averaged ion uorescence. However, the images may no longer provide a linear measure of the mode axial velocity.
23. R. C. Thompson, K. Dholakia, J-L. Hernandez-Pozos, G. Zs. K. Horvath, J. Rink, and D. M. Segal, ``Spectroscopy and quantum optics with ion traps," Phys. Scr. T72, 24-33 (1997). [CrossRef]

Other

• Non-Neutral Plasma Physics II, eds. J. Fajans and D. H. E. Dubin (AIP, New York, 1995).
• J. H. Malmberg and T. M. O'Neil, ``Pure electron plasma, liquid, and crystal," Phys. Rev. Lett. 39, 1333-1336 (1977). [CrossRef]
• C. F. Driscoll, J. H. Malmberg, and K. S. Fine, ``Observation of transport to thermal equilibrium in pure electron plasmas," Phys. Rev. Lett. 60, 1290-1293 (1988). [CrossRef] [PubMed]
• L. R. Brewer, J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, ``Static properties of a non-neutral 9 Be + ion plasma," Phys. Rev. A 38, 859-873 (1988). [CrossRef] [PubMed]
• J. J. Bollinger, D. J. Wineland, and D. H. E. Dubin, ``Non-neutral ion plasmas and crystals, laser cooling, and atomic clocks," Phys. Plasmas 1, 1403-1414 (1994). [CrossRef]
• D. H. E. Dubin,``Theory of electrostatic uid modes in a cold spheroidal non-neutral plasma," Phys. Rev. Lett. 66, 2076-2079 (1991). [CrossRef] [PubMed]
• J. J. Bollinger, D. J. Heinzen, F. L. Moore, W. M. Itano, D. J. Wineland, and D. H. E. Dubin, ``Electrostatic modes of ion-trap plasmas," Phys. Rev. A 48, 525-545 (1993). [CrossRef] [PubMed]
• R. G. Greaves and C. M. Surko, ``Antimatter plasmas and antihydrogen," Phys. Plasmas 4, 1528-1543 (1997). [CrossRef]
• G. Gabrielse, X. Fei, L. A. Orozco, R. L. Tjoelker, J. Haas, H. Kalinowsky, T. A. Trainor, and W. Kells, ``Cooling and slowing of trapped antiprotons below 100 meV," Phys. Rev. Lett. 63, 1360 (1989). [CrossRef] [PubMed]
• M.H. Holzscheiter, X. Feng, T. Goldman, N.S.P. King, R. A. Lewis, M. M. Nieto, and G.A. Smith, ``Are antiprotons forever?," Phys. Lett. A 214, 279 (1996). [CrossRef]
• D. J. Heinzen, J. J. Bollinger, F. L. Moore, W. M. Itano, and D. J. Wineland, ``Rotational equilibria and low-order modes of a non-neutral ion plasma," Phys. Rev. Lett. 66, 2080-2083 (1991). [CrossRef] [PubMed]
• 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). [CrossRef]
• D. H. E. Dubin and J. P. Schiffer, ``Normal modes of cold confined one-component plasmas," Phys. Rev. E 53, 5249-5267 (1996). [CrossRef]
• D. H. E. Dubin, ``Effects of correlations on the thermal equilibrium and normal modes of a non-neutral plasma," Phys. Rev. E 53, 5268-5290 (1996). [CrossRef]
• C. S. Weimer, J. J. Bollinger, F. L. Moore, and D. J. Wineland, ``Electrostatic modes as a diagnostic in Penning trap experiments," Phys. Rev. A 49, 3842-3853 (1994). [CrossRef] [PubMed]
• M. D. Tinkle, R. G. Greaves, and C. M. Surko, ``Low-order longitudinal modes of single-component plasmas," Phys. Plasmas 2, 2880-2894 (1995). [CrossRef]
• R. G. Greaves, M. D. Tinkle, and C. M. Surko, ``Modes of a pure ion plasma at the Brillouin limit," Phys. Rev. Lett. 74, 90-93 (1995). [CrossRef] [PubMed]
• C. F. Driscoll, ``Observation of an unstable m = 1 diocotron mode on a hollow electron column," Phys. Rev. Lett. 64, 1528-1543 (1990). [CrossRef]
• J. N. Tan, J. J. Bollinger, B. Jelenkovic, and D. J. Wineland, ``Long-range order in laser-cooled, atomic-ion Wigner crystals observed by Bragg scattering," Phys. Rev. Lett. 75, 4198-4201 (1995). [CrossRef] [PubMed]
• W. M. Itano, J. J. Bollinger, J. N. Tan, B. Jelenkovic, X.-P. Huang, and D. J. Wineland, ``Bragg diffraction from crystallized ion plasmas," Science 279, 686-689 (1998). [CrossRef] [PubMed]
• Here ! lm is the mode frequency in a frame rotating with the plasma. For the m = 0 modes discussed here this distinction is not necessary because their frequency is the same in either the laboratory or rotating frame.
• Information on the mode eigenfunction can be obtained from the side-view images even when there is a change in the phase-averaged ion uorescence. However, the images may no longer provide a linear measure of the mode axial velocity.
• R. C. Thompson, K. Dholakia, J-L. Hernandez-Pozos, G. Zs. K. Horvath, J. Rink, and D. M. Segal, ``Spectroscopy and quantum optics with ion traps," Phys. Scr. T72, 24-33 (1997). [CrossRef]

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