• E. Bagli
  INFN-Ferrara, Ferrara
• V. Guidi
  UNIFE, Ferrara
• V.A. Maisheev
  IHEP Protvino, Protvino, Moscow Region

We present an analytical model to calculate the physical quantities of interest experienced by relativistic particles in their motion aligned with periodic complex atomic structures. Classical physics equations and the expansion of periodic functions as a Fourier series have been used for the calculation. This method allows calculating the contribution from all the planes and axes inside the crystal, in contrast to other simulation codes for which the motion is evaluated only on nearest neighbors atomic strings. Based on the calculation technique we have developed the "ECHARM" program, which allows calculating one- and two- dimensional averaged physical quantities of interest. The calculation holds for the main axes of any orthorhombic and tetragonal structures and for any orientation in the cubic structure. To underline the capability of the program, complex structures such as zeolites have been worked out. Based on the "ECHARM" code, simulation of the relativistic particle motion within complex structures has been developed. With this code it is possible to simulate the motion in bent crystal to study planar and axial channeling volume reflection.

• V. Guidi, E. Bagli, A. Mazzolari
  INFN-Ferrara, Ferrara
• A.G. Afonin, Y.A. Chesnokov, V.A. Maisheev, I.A. Yazynin
  IHEP Protvino, Protvino, Moscow Region
• S. Baricordi, P. Dalpiaz, M. Fiorini, D. Vincenzi
  UNIFE, Ferrara
• D. Bolognini, S. Hasan, M. Prest
  Università dell'Insubria & INFN Milano Bicocca, Como
• G. Della Mea, R. Milan
  INFN/LNL, Legnaro (PD)
• A.S. Denisov, Yu.A. Gavrikov, Yu.M. Ivanov, L.P. Lapina, L.G. Malyarenko, V. Skorobogatov, V.M. Suvorov, S.A. Vavilov
  PNPI, Gatchina, Leningrad District
• S. Golovatyuk, A.D. Kovalenko, A.M. Taratin
  JINR, Dubna, Moscow Region
• A. Mattera
  INFN MIB, MILANO
• W. Scandale
  CERN, Geneva
• S. Shiraishi
  Enrico Fermi Institute, University of Chicago, Chicago, Illinois
• E. Vallazza
  INFN-Trieste, Trieste
• A. V. Vomiero
  INFM-CNR, Istituto Nazionale di Fisica della Materia - Consiglio Nazionale delle Ricerche, Brescia

New results in coherent interaction of negatively-charged particles with bent crystals showed unprecedentedly and significantly high efficiency to manipulate such beams, in the same way as for positively charged particles. Key feature under experimental attainment was the usage of high-quality suitably thin silicon crystals. We experimentally tested crystals Vs. 150 GeV negative pions at external lines of CERN SPS. We observed planar channeling at full deflection angle 30% high single-pass efficiency and large acceptance (about 20μrad). Moreover in the axial case, we reached more than 90% deflection efficiency and larger acceptance (about 60μrad). We also observed volume reflection in a bent crystal, at more than 70% single-pass efficiency with such a wide acceptance as the bending angle. At last, volume reflection by several planes in a single bent crystal was successfully tested with very high efficiency (about 80%). In summary both channeling and volume reflection modes appear to be useful technique for the manipulation of negatively charged beams, e.g. for collimation in the new generation of high intensity accelerators.

The UA9 collaboration