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Title |
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| TUA1C03 |
Necessary Condition for Beam Ordering
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87 |
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- A. V. Smirnov, I. N. Meshkov, A. O. Sidorin
JINR, Dubna, Moscow Region
- J. Dietrich
FZJ, Jülich
- A. Noda, T. Shirai, H. Souda, H. Tongu
Kyoto ICR, Uji, Kyoto
- K. Noda
NIRS, Chiba-shi
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The very low momentum spread for small number of particle was reached on different storage rings. When the sudden reduction of the momentum spread ("phase transition") was observed during decreasing of the particle number it was interpreted as ordered state of ion beams. The most extensive study of ordered ion beams was done on storage rings ESR (GSI, Darmstadt) and CRYRING (MSL, Stockholm). Recently, for the first time, the ordered proton beam has been observed on S-LSR (Kyoto University). From analysis of the ESR experimental results we assumed that the ordered state can be observed if the dependence of momentum spread on the particle number can be approximated as ∆P/P ~ Nk for k < 0.3. In pioneering experiments at NAP-M (INP, Novosibirsk) and, in recent years, at COSY (FZJ, Juelich) the phase transition was not observed and the coefficient was found equal k > 0.5. This report presents the experimental investigations of low intensity proton beams on COSY and S-LSR which have the aim to formulate the necessary conditions for the achievement of the ordered state. The experimental studies on S-LSR and numerical simulations with the BETACOOL code were done for the dependence of the momentum spread and transverse emittances on particle number with different misalignments of the magnetic field at the cooler section. As result of both experimental and numerical studies one can conclude that the necessary condition for the phase transition appearance is k < 0.3.
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Slides
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| TUA1I04 |
High-Energy Colliding Crystals – A Theoretical Study
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91 |
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- J. Wei
BNL, Upton, Long Island, New York
- H. Okamoto
Hiroshima University, Higashi-Hiroshima
- A. Sessler
LBNL, Berkeley, California
- H. Sugimoto, Y. Yuri
HU/AdSM, Higashi-Hiroshima
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Funding: * Work performed under the auspices of the U. S. Department of Energy.
Recent theoretical investigations of beam crystallization mainly use computer modeling based on the method of molecular dynamics (MD) and analytical study based on phonon theory [1]. Topics of investigation include crystal stability in various accelerator lattices under different beam conditions, colliding crystalline beams [2], and crystalline beam formation in shear-free ring lattices with both magnets and electrodes [3]. In this paper, we review the above mentioned theoretical studies and, in particular, discuss the development of the phonon theory in a time-dependent Hamiltonian system representing a storage ring of AG focusing. Analytical study of crystalline beam stability in an AG-focusing ring was previously limited to the smooth approximation. In a typical ring, analytical results obtained under such approximation largely agrees with the results obtained with the molecular dynamics (MD) simulation method. However, as we explore ring lattices appropriate for beam crystallization at high energies (Lorentz factor gamma much higher than the betatron tunes) [2,4], this approximation fails. Here, we present a newly developed formalism to exactly predict the stability of a 1-dimensional crystalline beam in an AG focusing ring lattice.
[1] X.-P. Li, et al, PR ST-AB, 9, 034201 (2006). [2] J. Wei, A. M. Sessler, EPAC, 862 (1998)[3] M. Ikegami, et al, PR ST-AB 7, 120101 (2004).[4] J. Wei, H. Okamoto, et al, EPAC 2006.
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Slides
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| THM1I02 |
Electron Cooling Experiments at S-LSR
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139 |
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- T. Shirai, S. Fujimoto, M. Ikegami, A. Noda, H. Souda, M. Tanabe, H. Tongu
Kyoto ICR, Uji, Kyoto
- H. Fadil, M. Grieser
MPI-K, Heidelberg
- T. Fujimoto, S. I. Iwata, S. Shibuya
AEC, Chiba
- I. N. Meshkov, A. V. Smirnov, E. Syresin
JINR, Dubna, Moscow Region
- K. Noda
NIRS, Chiba-shi
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Funding: The present work has been supported from Advanced Compact Accelerator Development Project by MEXT of Japan and 21 COE at Kyoto University-Center for Diversity and Universality in Physics.
The ion storage ring, S-LSR in Kyoto University has an electron beam cooler and a laser cooling system. The electron cooler for S-LSR was designed to maximize the cooling length in the limited drift space of the ring. The effective cooling length is 0.44 m, while the total length of the cooler is 1.8 m. The commissioning of the electron cooling was started from October 2005. The 7 MeV proton beam from the linac was used and the first cooling was observed on October 31. The momentum spread became 2×10-4 and the beam diameter was 1.2 mm with the particle number of 2×108 and the electron current of 60 mA. The various experiments have been carried out using the electron cooling at S-LSR. The one-dimensional ordering of protons is one of the important subjects. The momentum spread and the beam size were observed while reducing the particle number. They were measured by the Schottky noise spectrum and the scraper. The particle number was measured by the ionization residual gas monitor. Abrupt jumps in the momentum spread and the Schottky noise power were observed for protons at a particle number of around 2000. The beam temperature was 0.17 meV and 1 meV in the longitudinal and transverse directions at the transition particle number, respectively. The normalized transition temperature of protons is close to those of heavy ions at ESR. The lowest momentum spread below the transition was 1.4×10-6, which corresponded to the longitudinal beam temperature of 0.026 meV (0.3 K). It is close to the longitudinal electron temperature. The transverse temperature of the proton beam was much below that of electrons (34 meV). It is the effect of the magnetized electron.
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| THAP21 |
Longitudinal Schottky Signals of Cold Systems with Low Number of Particles
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213 |
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- R. W. Hasse
GSI, Darmstadt
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Very cold systems of ions with sufficiently low number of particles arrange in an ordered string-like fashion. The determination of the longitudinal momentum spread and of the transverse temperature then is no longer possible by normal Schottky diagnosis. In this paper we simulate such systems in an infinitely long beam pipe with periodic boundary conditions under the influence of all long-range Coulomb interactions by Ewald summation. Then we derive the behaviour of the longitudinal Schottky signals for cold string-like systems as well as for the transition to warmer systems when the strings break, up to hot gas-like systems. Here effects from the finite number of particles, of higher harmonics and of temperature agree with those derived analytically in the limits of very low and very high temperatures.
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Poster
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| THAP22 |
Limitations of the Observation of Beam Ordering
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217 |
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- M. Steck, K. Beckert, P. Beller, C. Dimopoulou, F. Nolden
GSI, Darmstadt
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One dimensional beam ordering of electron cooled low intensity heavy ion beams has been evidenced at the ESR storage ring as a discontinuous reduction of the momentum spread. Depending on the beam parameters, technical imperfections or any sources of heating can hamper or even prevent the observation of the momentum spread reduction. Limitations for the detection of the ordered beam will be described and illustrated by experimental results.
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