Three-dimensional laser cooling method based on resonant linear coupling

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 3, 1999, Pages 3594-3604

  Kihara, T ^a   Okamoto, H ^a   Iwashita, Y ^a   Oide, K ^b   Lamanna, G ^c   Wei, J ^d  

^a KYOTO UNIVERSITY   (Japan)

^b HIGH ENERGY ACCELERATOR RESEARCH ORGANIZATION KEK   (Japan)

^c UNIVERSITY OF BARI   (Italy)

^d BROOKHAVEN NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000642270     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.3594     Document Type: Article

References (38)

1. S. van der Meer, Report No. CERN/TSR-PO/72-31 (1972).
2. G. I. Budker, At. Energ. 22, 345 (1967).
3. D. J. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975)
4. T. Hänsch and A. Schawlow, Opt. Commun. 13, 68 (1975).
5. A. Rahman and J. P. Schiffer, Phys. Rev. Lett. 57, 1133 (1986)
6. R. W. Hasse and J. P. Schiffer, Ann. Phys. (N.Y.) 203, 419 (1990)
7. J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993)
8. J. Wei, and A. M. Sessler, X-P. Li, Report No. BNL-52381 (1993)
9. Phys. Rev. Lett. 73, 3089 (1994).
10. S. Schröder, R. Klein, N. Boos, M. Gerhard, R. Grieser, G. Huber, A. Karafillidis, M. Kieg, N. Schmidt, T. Kühl, R. Neumann, V. Balykin, M. Grieser, D. Habs, E. Jaeschke, D. Krämer, M. Kristensen, M. Music, W. Petrich, D. Schwalm, P. Sigray, M. Steck, B. Wanner, and A. Wolf, Phys. Rev. Lett. 64, 2901 (1990).
11. J. S. Hangst, M. Kristensen, J. S. Nielsen, O. Poulsen, J. P. Schiffer, and P. Shi, Phys. Rev. Lett. 67, 1238 (1991).
12. H-J. Miesner, R. Grimm, M. Grieser, D. Habs, D. Schwalm, B. Wanner, and A. Wolf, Phys. Rev. Lett. 77, 623 (1996).
13. H. Okamoto, A. M. Sessler, and D. Möhl, Phys. Rev. Lett. 72, 3977 (1994).
14. H. Okamoto, Phys. Rev. E 50, 4982 (1994).
15. I. Lauer, U. Eisenbarth, M. Grieser, R. Grimm, P. Lenisa, V. Luger, T. Schätz, U. Schramm, D. Schwalm, and M. Weidemüller, Phys. Rev. Lett. 81, 2052 (1998). In the laser-cooling experiment reported in Ref. 10, a transverse linear coupling resonance (Formula presented) was actually employed to improve the vertical cooling efficiency. As clearly seen in Fig. 33 in this reference paper, the vertical cooling rate becomes equal to the horizontal rate with the resonance condition satisfied. This experimental observation indicates that the idea of indirect resonant cooling studied in Refs. 8 and 9 is basically correct. Since there is no substantial difference between the horizontal-vertical and longitudinal-horizontal coupling, as is shown in Ref. 9, the transverse dissipative force can be enhanced only by driving the ring operating point onto a synchrobetatron resonance. (In both TSR and ASTRID, a rf cavity is already located at a dispersive position. Thus, a linear synchrobetatron coupling potential required for our resonant coupling scheme in Sec. II A is always available in bunched-beam laser cooling.)
16. For the details of the SAD code, see http://www-acc-theory.kek.jp/SAD/sad.html
17. The three sets of the canonical variables, (Formula presented) and (Formula presented) describe the horizontal, vertical, and longitudinal motion, respectively. The detailed derivation of Eq. (2) is available in Ref. 9.
18. H. Okamoto, S. Machida, and A. M. Sessler, in Crystalline Beams and Related Issues, edited by D. M. Maletic and A. G. Ruggiero (World Scientific, Singapore, 1996), p. 173.
19. To excite a synchrobetatron coupling resonance, the longitudinal tune must be nonzero.
20. There may be a solution utilizing the nonlinear coupling in order to raise the transverse cooling efficiency. In such a case, one may choose (Formula presented) greater than (Formula presented) to increase the strength of the nonlinear contributions. This is a future issue to study.
21. J. S. Hangst, J. S. Nielsen, O. Poulsen, P. Shi, and J. P. Schiffer, Phys. Rev. Lett. 74, 4432 (1995). Theoretically speaking, one can apply much higher voltage with no problem. However, in practice, the application of too high a voltage is dangerous, since it may heat up the cold beams, e.g., due to the inevitable noises of the rf system. It is thus better to use as low a rf voltage as possible.
22. See, e.g., User’s Guide for the POISSON/SUPERFISH Group of Codes, LA-UR-87-115 (Los Alamos National Laboratory, Los Alamos, 1987).
23. For the information about SOLID, see, e.g., J. Wei, X.-P. Li, and A. M. Sessler, BNL-52387 (1993).
24. P. P. Ewald, Ann. Phys. (Leipzig) 64, 253 (1921).
25. See, e.g., J. Wei, A. Draeseke, A. M. Sessler, and X.-P. Li, in Crystalline Beams and Related Issues (Ref. 13), p. 229.
26. T. Katayama, A. Andou, K. Chida, T. Hattori, T. Honnma, K. Kanazawa, A. Mizobuchi, H. Mutou, N. Nakai, S. Ninomiya, A. Noda, K. Noda, M. Sekiguchi, F. Soga, T. Tanabe, N. Ueda, S. Watanabe, T. Watanabe, and M. Yoshizawa, in Proceedings of the 2nd European Particle Accelerator Conference, edited by P. Martin and P. Mandrillon (Editions Frontières, Gif-sur-Yvette, 1990), p. 577.
27. The value of (Formula presented) at which the temperature jump takes place is roughly independent of the nature of the cooling force. For example, even in the tapered cooling scheme 29, the achievable beam temperature suddenly changes at (Formula presented)
28. Note, however, that the beam density must be high enough in order for the longitudinal cooling force to be sympathetically effective in transverse directions. The sympathetic transverse cooling is thus generally inefficient for common beams in storage rings. By contrast, the coupling method studied here works even for low-density initial beams, since it has nothing to do with the Coulomb interactions.
29. S. Y. Lee and H. Okamoto, Phys. Rev. Lett. 80, 5133 (1998).
30. The maintenance condition is, therefore, not limited to crystalline beams. At the high-temperature limit, Eq. (14) is changed to (Formula presented) [or, equivalently, (Formula presented) where (Formula presented) and (Formula presented) denote, respectively, horizontal and vertical betatron phase advances per lattice period. This condition is identical to the well-known design criterion for high-intensity linear transport systems.]
31. T. Kihara, H. Okamoto, Y. Iwashita, K. Oide, G. Lamanna, and J. Wei, in Proceedings of the 6th European Particle Accelerator Conference, edited by S. Myers, L. Liljeby, Ch. Petit-Jean-Genaz, J. Poole, and K.-G. Rensfelt (Institute of Physics Publishing, Bristol, 1998), p. 1040.
32. N. Madsen, P. Bowe, M. Drewsen, L. Hornekaer, N. Kjaergaard, A. Labrador, P. Shi, J. S. Hangst, J. S. Nielsen, and J. P. Schiffer, in Proceedings of the 6th European Particle Accelerator Conference (Ref. 26), pp. 1043 and 1046; In this reference, researchers from Aarhus University have reported on an interesting experimental observation which suggests that the transverse beam quality in the ASTRID ring may be limited by some resonance mechanism. Although further investigation is necessary, we speculate that the result may be explained by the Mathieu instability discussed here.
33. It has been experimentally verified that ions confined in a rf trap system are immediately lost unless the design parameters of the system, such as the rf voltage, the operating frequency, etc., are properly chosen to avoid the Mathieu instability.
34. J. Wei, H. Okamoto, and A. M. Sessler, Phys. Rev. Lett. 80, 2606 (1998)
35. H. Okamoto and J. Wei, Phys. Rev. E 58, 3817 (1998)
36. J. P. Schiffer, in Crystalline Beams and Related Issues (Ref. 13), p. 217.
37. See, e.g., J. Wei, A. Draeske, A.M. Sessler, and Xi Pi Li, in Crystalline Beams and Related Issues (Ref. 20)
38. Since the 1D string structure has no transverse extent, it is free from the Mathieu instability. It may thus be possible to create string crystals even in ASTRID and TSR. However, considering that sympathetic cooling is extremely slow, or simply negligible for such a low-density beam, the resonant coupling method must be applied.