• A. Noda
  
• H. Fadil, M. Grieser
  MPI-K, Heidelberg
• M. Ikegami, T. Ishikawa, M. Nakao, T. Shirai, H. Souda, M. Tanabe, H. Tongu
  Kyoto ICR, Uji, Kyoto
• I. N. Meshkov, A. V. Smirnov
  JINR, Dubna, Moscow Region
• K. Noda
  NIRS, Chiba-shi

S-LSR is a storage and cooler ring with the circumference of 22.56 m applied for an electron beam cooling of 7 MeV proton beam and laser cooling of 24Mg+ beam with 35 keV. From the measurement with the use of Schottky pich-up of the momentum spread of 7 MeV proton beam reducing the particle number to suppress the effect of intra-beam scattering,abrupt jump in fractional momentum spread and Schottky power has been observed, which is considered the 1 dimensional phase transition to the ordered state*. The situation has also been expected from numerical simulation**. Laser cooling with much stronger cooling force is expected to realize 2Dand 3D crystalline states if the maintenance condition can be satisfied. Experimental approaches to realize such a condition at S-LSR as dispersion free lattice and "tapered cooling" are also decribed in the present paper.

* A Noda, et al., , New Journal of Physics, 8 (2006)288.** A. Smirnov et al., Beam Science and Technology, 10 (2006) 6*** J. Wei, X-P, Li and A. M. Sessler, , Phys. Rev. Lett. 73 (1994) 3089.