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1
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27844600267
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note
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Strictly speaking, the emittance of a crystalline beam is finite because of quantum effects. The possible lowest limit of projected emittances should be around ℏ/mc where ℏ is the Planck constant and c is the speed of light.
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5
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27844576739
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note
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The only exception is a one-dimensionally ordered coasting beam (string crystalline beam) in which all particles are aligned along the design beam orbit.
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-
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10
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27844500257
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Knoxville, Tennessee (to be published)
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An extensive study of phonon modes in various crystalline states has been performed by X.-P. Li et al. See: in Proceedings of the Particle Accelerator Conference, Knoxville, Tennessee, 2005 (to be published).
-
(2005)
Proceedings of the Particle Accelerator Conference
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Li, X.-P.1
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23
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0000943576
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Steck and co-workers reported an anomaly of Schottky signals from electron-cooled heavy-ion beams [M. Steck et al., Phys. Rev. Lett. 77, 3803 (1996)],
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(1996)
Phys. Rev. Lett.
, vol.77
, pp. 3803
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Steck, M.1
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24
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0037193029
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which was reconfirmed later by Danared et al [H. Danared et al., Phys. Rev. Lett. 88, 174801 (2002)].
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(2002)
Phys. Rev. Lett.
, vol.88
, pp. 174801
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Danared, H.1
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25
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0000807185
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Although this curious event can be interpreted as a longitudinal ordering of stored ions [R.W. Hasse, Phys. Rev. Lett. 83, 3430 (1999)],
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(1999)
Phys. Rev. Lett.
, vol.83
, pp. 3430
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Hasse, R.W.1
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26
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42749103733
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it is believed to be substantially different from the formation of a string crystalline beam [H. Okamoto et al., Phys. Rev. E 69, 066504 (2004)]
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(2004)
Phys. Rev. E
, vol.69
, pp. 066504
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Okamoto, H.1
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28
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27844468762
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note
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As first discussed in Ref. [9] and theoretically formulated in Ref. [24], a longitudinal tapered force simultaneously cools the transverse dimension, provided that the cooling section has finite dispersion. Therefore, this type of frictional force is useful not only for beam crystallization but also for general 3D cooling of a charged-particle beam.
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31
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27844461207
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note
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The spatial configurations of Coulomb crystals in an ordinary ion trap are similar to "bunched" crystalline beams rather than "coasting" crystalline beams.
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34
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27844512537
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private communication
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A. M. Sessler (private communication).
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Sessler, A.M.1
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35
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4644312007
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U. Schramm, M. Bussmann, and D. Habs, Nucl. Instrum. Methods Phys. Res., Sect. A 532, 348 (2004).
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(2004)
Nucl. Instrum. Methods Phys. Res., Sect. A
, vol.532
, pp. 348
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Schramm, U.1
Bussmann, M.2
Habs, D.3
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36
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11744270024
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IOP, Bristol
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J. Wei and A.M. Sessler, in Proceedings of the 1996 European Particle Accelerator Conference, Sitges, Spain, 1996 (IOP, Bristol, 1996), p. 1179.
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(1996)
Proceedings of the 1996 European Particle Accelerator Conference, Sitges, Spain, 1996
, pp. 1179
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Wei, J.1
Sessler, A.M.2
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37
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27844484002
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note
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Since the tapered force cannot directly cool the vertical betatron motion, we have added weak transverse dissipation in these simulations. Similarly, the crystalline beams in Figs. 1 and 3 have been obtained with a combination of the ideal tapered force and transverse linear friction.
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41
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27844435262
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note
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Only when the beam is initially well conditioned, we observe some "sympathetic" transverse cooling due to Coulomb collisions.
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42
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27844549481
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note
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The vertical periodic oscillations are driven by the vertical dispersion created through the solenoid coupling.
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44
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27844454489
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note
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The authors of Ref. [40] call this scheme "dispersive cooling" instead of "tapered cooling."
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46
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27844606035
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T. Kihara, report, 1999 (unpublished)
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T. Kihara, report, 1999 (unpublished).
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-
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47
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27844504117
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note
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Essentially the same procedure was taken in the cooling experiment reported in Ref. [40].
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