• P.-CH. Yu, J. Wei
  TUB, Beijing
• Z.Q. He
  Tsinghua University, Beijing
• H. Okamoto
  HU/AdSM, Higashi-Hiroshima
• A. Sessler
  LBNL, Berkeley, California
• Y. Yuri
  JAEA/TARRI, Gunma-ken

During the beam crystallization process, the main heating source is Intra-beam scattering (IBS), in which the Coulomb collisions among particles lead to a growth in the 6D phase space volume of the beam. The results of molecular dynamics (MD) simulation have shown an increase of heating rate as the temperature is increased from absolute zero, but then a peak in the heating rate, and subsequent decrease with ever increasing temperature*. This phenomenon has been carefully studied by Y. Yuri, H. Okamoto, and H. Sugimoto**. On the other hand, in the traditional IBS theory valid at high temperatures, heating rate is monotonically increasing as the temperature becomes lower***. In this paper we attempt to understand the "matching" at low temperatures between the MD results and traditional IBS theory, by including many body effects in the traditional IBS theory. In particular the Debye shielding is included. We shall present how the traditional theory is modified by shielding, and show how this effect improves the "matching" with the results from MD.

* J. Wei, H. Okamoto, and A. Sessler, Phys. Rev. Lett. 80, 2606
** Y.Yuri, H. Okamoto, and H. Sugimoto, J. Phys. Soc. Jpn. 78, 124501
***A. Piwinski, Lect. Notes Phys. 296, 297 (1988)