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Okamoto, H.

Paper Title Page
TPAT082 Phonon Modes and the Maintenance Condition of a Crystalline Beam 4111
 
  • J. Wei
    BNL, Upton, Long Island, New York
  • H. Enokizono, H. Okamoto, Y. Yuri
    HU/AdSM, Higashi-Hiroshima
  • X.-P. Li
    Skyworks Solutions, Inc., Newbury Park. California
  • A. Sessler
    LBNL, Berkeley, California
  
  Funding: * Work performed under the auspices of the U.S. Department of Energy.

Previously it has been shown that the maintenance condition for a crystalline beam requires that there not be a resonance between the crystal phonon frequencies and the frequency associated with a beam moving through a lattice of N periods. This resonance can be avoided provided the phonon frequencies are all below half of the lattice frequency. Here we make a detailed study of the phonon modes of a crystalline beam. Analytic results obtained in a “smooth approximation” using the ground-state crystalline beam structure is compared with numerical evaluation employing Fourier transform of Molecular Dynamic (MD) modes. The MD also determines when a crystalline beam is stable. The maintenance condition, when combined with either the simple analytic theory or the numerical evaluation of phonon modes, is shown to be in excellent agreement with the MD calculations of crystal stability.

[1] X-P. Li, A. M. Sessler, J. Wei, EPAC (1994) p. 1379 - 1381. ‘Necessary Conditions for Attaining a Crystalline Beam''}[2] J. Wei, H. Okamoto, A.M. Sessler, Phys. Rev. Lett., Vol. 80, p. 2606-2609 (1998).

 
FOAD001 Frozen Beams 4
 
  • H. Okamoto
    HU/AdSM, Higashi-Hiroshima
  
  In general, the temperature of a charged particle beam traveling in an accelerator is very high. Seen from the rest frame of the beam, individual particles randomly oscillate about the reference orbit at high speed. This internal kinetic energy can, however, be removed by introducing dissipative interactions into the system. As a dissipative process advances, the beam becomes denser in phase space or, in other words, the emittance is more diminished. Ideally, it is possible to reach a "zero-emittance" state where the beam is Coulomb crystallized. The space-charge repulsion of a crystalline beam just balances the external restoring force provided by artificial electromagnetic elements. In this talk, general discussion is made of coasting and bunched crystalline beams circulating in a storage ring. Results of molecular dynamics simulations are presented to demonstrate the dynamic nature of various crystalline states. A possible method to approach such an ultimate state of matter is also discussed.