• A. Afanasev, R.P. Johnson
  Muons, Inc, Batavia
• Y.S. Derbenev
  JLAB, Newport News, Virginia
• V.S. Morozov
  ODU, Norfolk, Virginia

Parametric-resonance Ionization Cooling (PIC) is envisioned as the final 6D cooling stage of a high-luminosity muon collider. Implementing PIC imposes stringent constraints on the cooling channel's magnetic optics design. This paper presents a linear optics solution compatible with PIC. Our solution consists of a superposition of two opposite-helicity equal-period and equal-strength helical dipole harmonics and a straight normal quadrupole. We demonstrate that such a system can be adjusted to meet all of the PIC linear optics requirements while retaining large acceptance.

• T. Katayama
  GSI, Darmstadt
• T. Kikuchi
  Nagaoka University of Technology, Nagaoka, Niigata
• R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• I.N. Meshkov
  JINR, Dubna, Moscow Region

The stochastic cooling is employed to reduce the momentum spread of accelerated 2 GeV proton beam at COSY. In addition the barrier voltages are successfully used to compensate the mean energy loss of the beam due to the thick internal target such as pellet target. To analyze the experimental results at COSY, we have developed the particle tracking code which simulate the particle behavior under the influences of stochastic cooling force, Schottky diffusion, thermal diffusion and IBS effects. The synchrotron motion due to the RF fields are included with 4th order symplectic way. The simulation results are well in agreement with the observed cooling process for the case of barrier voltage as well as RF field of harmonic number=1. In the present paper, the systematic analysis of the experimental results with use of the developed tracking codes are described. In addition the process of short bunch formation at the heavy ion collider at NICA project is investigated with use of the stochastic cooling. In that case the strong IBS effects are main limiting factor of making and keeping the short bunch as well as the space charge effects. Details of the simulation study will be presented.

• T. Katayama, M. Steck
  GSI, Darmstadt
• T. Kikuchi
  Nagaoka University of Technology, Nagaoka, Niigata
• R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• I.N. Meshkov
  JINR, Dubna, Moscow Region

Anti-proton beam accumulation at CERN and FNAL has been performed with use of stochastic stacking in the momentum space. Thus accumulated beam has a large momentum spread and resultantly large radial beam size with large dispersion ring. In the present proposed scenario, beams from the pre-cooling ring are injected into the longitudinal empty space prepared by the barrier voltages and subsequently the stochastic cooling is applied. After the well cooling, barrier voltages will prepare again the empty space for the next beam injection. We have simulated the stacking process up to 100 stacking with use of the bunched beam tracking code including the stochastic cooling force and the diffusion force such as Schottky diffusion term, thermal diffusion, IBS effects. The synchrotron motion by barrier voltages are included with 4th order symplectic method. Examples of the application to 3 GeV anti-proton beam for the HESR ring in FAIR project are presented as well as the accumulation of heavy ion beam 3.5 GeV/u Au, at the NICA collider at JINR project.

• M. Steck, C. Brandau, C. Dimopoulou, C. Kozhuharov, F. Nolden
  GSI, Darmstadt

The ESR storage ring at GSI is operated with a wide range of heavy ions. In addition to stable heavy ions also rare isotope beams are studied in various experiments. A novel method to provide one- or few-component cooled fragment beams has been demonstrated experimentally. This technique uses a primary high energy heavy ion beam (several hundred MeV/u) bombarding a thick target in front of the storage ring. The reaction products are first separated by the magnetic structure of the storage ring. After storage of isotopes in a rigidity window of typically ± 2 per mille the isotopes are cooled to the same velocity by electron cooling. The cooled ions are circulating on different orbits according to their mass and charge. The momentum spread of the individual components is on the order 0.01 per mille or smaller depending on the intensity. The different components are radially well separated in regions with large dispersion. By the use of mechanical scrapers beam components in a certain radial region, corresponding to a range in masses and charges, can be selected, This way the stored rare isotope beam is curtailed to the components of choice.

• J. Dietrich, V. Kamerdzhiev
  FZJ, Jülich
• M.I. Bryzgunov, A.D. Goncharov, V.M. Panasyuk, V.V. Parkhomchuk, V.B. Reva, D.N. Skorobogatov
  BINP SB RAS, Novosibirsk

The 2 MeV electron cooling system for COSY-Jülich was proposed to further boost the luminosity even in presence of strong heating effects of high-density internal targets. The project is funded since mid 2009. Manufacturing of the cooler components has already begun. The space required for the 2 MeV cooler is being made available in the COSY ring. The design and construction of the cooler is accomplished in cooperation with the Budker Institute of Nuclear Physics in Novosibirsk, Russia. The 2 MeV cooler is also well suited in the start up phase of the High Energy Storage Ring (HESR) at FAIR in Darmstadt. It can be used for beam cooling at injection energy and is intended to test new features of the high energy electron cooler for HESR. Two new prototypes of the modular high voltage system were developed, one consisting of gas turbines the other based on inductance-coupled cascade generators. The new 2 MeV electron cooler is described in detail and tests of components are reported.

• H. Stockhorst, R. Maier, D. Prasuhn, R. Stassen
  FZJ, Jülich
• T. Katayama
  GSI, Darmstadt

Numerical studies of longitudinal filter and time-of-flight (TOF) cooling suggest that the strong mean energy loss due to an internal Pellet target in the High Energy Storage Ring (HESR) at the FAIR facility can be compensated by cooling and operation of a barrier bucket (BB) cavity. In this contribution detailed experiments at COSY to compensate the mean energy loss are presented. The internal Pellet target was similar to that being used by the PANDA experiment at the HESR. A BB cavity was operated and either TOF or filter stochastic momentum cooling was applied to cool a proton beam. Experimental comparisons between the filter and TOF cooling method are discussed. Measurements to determine the mean energy loss which is used in the simulation codes are outlined. The experiments proved that the mean energy loss can be compensated with a BB cavity. Results are compared with numerical tracking simulations which include the synchrotron motion in a barrier bucket as well as in an h = 1 cavity and stochastic momentum cooling. A detailed discussion of the tracking simulation code will be outlined in a separate contribution to this conference.

• E. Benedetto
  National Technical University of Athens, Zografou

A compact ring with an internal target for the production of Li-8 or B-8 as neutrino or antineutrino emitters has been proposed*, to enhance the flux of radioactive isotopes for a beta-beam facility. The circulating beam is expected to survive for thousands of turns and, according to this scheme, the ionization cooling provided by the target itself and a suitable RF system will be enough to keep the beam transverse and longitudinal emittances under control. The ionization cooling potential for a preliminary ring design is here investigated by means of tracking simulations and analytical considerations, keeping in mind that a correct modeling of the beam-target interactions is fundamental for these studies. Technological issues for such a ring and possible show-stoppers are also briefly discussed.

* C.Rubbia et al, NIM-A 2006..

• T. Kikuchi, N. Harada, T. Sasaki, H. Tamukai
  Nagaoka University of Technology, Nagaoka, Niigata
• J. Dietrich, R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• T. Katayama
  GSI, Darmstadt

A small momentum spread of proton beam has to be realized and kept in a storage ring during an experiment with a dense internal target such as a pellet target. A stochastic cooling alone does not compensate the mean energy loss by the internal target. Barrier bucket operation will cooperate effectively the energy loss. In addition, the further small momentum spread can be realized with use of an electron cooling. In the present study, the simulation results on the simultaneous use of stochastic cooling and electron cooling at COSY are presented.

• T. Hiromasa, M. Nakao, A. Noda, H. Souda, H. Tongu
  Kyoto ICR, Uji, Kyoto
• K. Jimbo
  Kyoto IAE, Kyoto
• T. Shirai
  NIRS, Chiba-shi

In order to achieve three dimensional crystal beam, laser cooling forces are required not only in the longitudinal direction, but also in the transverse directions. With the resonance coupling method*, transverse temperature is transmitted into longitudinal direction, and we have already demonstrated horizontal laser cooling experimentally **. In the present paper, we describe an approach to extend this result to three dimensional cooling. The vertical cooling requires that the horizontal oscillation couples with the vertical oscillation. For achieving horizontal-vertical coupling, a solenoid in electron beam cooling apparatus is utilized with an experiment (Qx=2.07,Qy=1.07). For various solenoidal magnetic fields from 0 to 40Gauss, horizontal and vertical betatron tunes are measured by beam transfer function. For a certain region of the solenoidal magnetic field, these tunes are mixed up each other. By optimization of such a coupling, we aim to proceed to three dimensional laser cooling.

* H. Okamoto Phys. Rev. E 50, 4982 (1994)
** H. Souda et.al.,contribution to this conference

• M. Nakao, T. Hiromasa, A. Noda, H. Souda, H. Tongu
  Kyoto ICR, Uji, Kyoto
• M. Grieser
  MPI-K, Heidelberg
• K. Jimbo
  Kyoto IAE, Kyoto
• H. Okamoto
  HU/AdSM, Higashi-Hiroshima
• T. Shirai
  NIRS, Chiba-shi
• A.V. Smirnov
  JINR, Dubna, Moscow Region

Experiments of transverse laser cooling for 24Mg+ beam have been performed at the small ion storage and cooler ring, S-LSR. It is predicted that the longitudinal cooling force is transmitted to the horizontal direction with synchro-betatron coupling at the resonant condition*. The laser system consists of a 532nm pumping laser, a ring dye laser with variable wavelength around 560nm, and a frequency doubler. The horizontal beam size and the longitudinal momentum spread were optically measured by a CCD and a PAT (Post Acceleration Tube) respectively**, ***. The CCD measures the beam size by observing spontaneous emission from the beam and records in sequence of 100ms time windows the development of the beam profile. The time variation of the beam size after beam injection indicates the transverse cooling time. The initial horizontal beam size, which was about 1mm, was decreased by 0.13mm in 1.5s. The longitudinal momentum spread measured by PAT is increased at the resonant condition. This suggests transverse temperature was transferred to longitudinal direction by synchro-betatron coupling. Both measurements denote the horizontal cooling occurred only in the resonant condition ****.

* H. Okamoto, Phys. Rev. {E50}, 4982 (1994)
** M. Tanabe et. al, Appl. Phys. Express 1 (2008) 028001
*** T. Ishikawa Master Thesis, Kyoto Univ.(2008)
**** H. Souda et. al., contribution to IPAC10.

• H. Souda, T. Hiromasa, M. Nakao, A. Noda, H. Tongu
  Kyoto ICR, Uji, Kyoto
• M. Grieser
  MPI-K, Heidelberg
• K. Jimbo
  Kyoto IAE, Kyoto
• H. Okamoto
  HU/AdSM, Higashi-Hiroshima
• T. Shirai
  NIRS, Chiba-shi
• A.V. Smirnov
  JINR, Dubna, Moscow Region

Transverse laser cooling with the use of a synchro-betatron coupling is experimentally demonstrated at the ion storage/cooler ring S-LSR. Bunched 40keV ²⁴Mg⁺ beams are cooled by a co-propagating laser with a wavelength of 280nm. Synchrotron oscillation and horizontal betatron oscillation are coupled by an RF drifttube at a finite dispersive section (D = 1.1m) in order to transmit longitudinal cooling force to the horizontal degree of freedom*. Time evolution of horizontal beam size during laser cooling was measured by a CCD camera**. Horizontal beam sizes were reduced by 0.13mm within 1.5s after injection when the tune values satisfy a difference resonance condition, ν_s - ν_h = integer, at the operating tunes of (ν_h, ν_v, ν_s)=(2.067, 1.104, 0.067) and (2.058, 1.101, 0.058). Without resonance condition, the size reduction was negligibly small. The momentum spread was 1.7x10^-4 on the resonance otherwise 1.2x10^-4. These results show that the horizontal heats are transferred to the longitudinal direction through the synchro-betatron coupling with the resonance condition and are cooled down by a usual longitudinal bunched beam laser cooling.

* H. Okamoto, Phys. Rev. E 50, 4982 (1994).
** M. Nakao et. al., contribution to this conference.

• H. Tongu, T. Hiromasa, M. Nakao, A. Noda, H. Souda
  Kyoto ICR, Uji, Kyoto
• T. Shirai
  NIRS, Chiba-shi

S-LSR is a compact ion storage and cooler ring to inject beam of the 7MeV proton and the 40MeV Mg+. The average vacuum pressure measured by the vacuum gauges without beam was achieved up to about 4x10^-9 Pa in 2007. Many experiments have been carried out using the proton and Mg beam, for example the one-dimensional beam ordering of protons utilizing the electron cooler, the extraction tests of the short bunched beam and the laser cooling for the Mg beam had been performed. The beam lifetime can be estimated with the vacuum pressure or the loss-rate of the beam energy. The values of the estimated lifetime are nearly equal to the measured lifetime values. The present status of the proton beam lifetime and the vacuum pressure is reported.

• A.V. Shemyakin, L.R. Prost, G.W. Saewert
  Fermilab, Batavia

AAntiprotons in Fermilab's Recycler ring are cooled by a 4.3 MeV, 0.1 ' 0.5 A DC electron beam (as well as by a stochastic cooling system). The unique combination of the relativistic energy (γ = 9.49), an Ampere - range DC beam, and a relatively weak focusing makes the cooling efficiency particularly sensitive to ion neutralization. A capability to clear ions was recently implemented by way of interrupting the electron beam for 1-30 μs with a repetition rate of up to 40 Hz. The cooling properties of the electron beam were analyzed with drag rate measurements and showed that accumulated ions significantly affect the beam optics. For a beam current of 0.3 A, the longitudinal cooling rate was increased by factor of ~2 when ions were removed.

• K. Yonehara
  Fermilab, Batavia
• Y.S. Derbenev
  JLAB, Newport News, Virginia
• R.P. Johnson, M.L. Neubauer
  Muons, Inc, Batavia

Fast muon beam six dimensional (6D) phase space cooling is essential for muon colliders. The Helical Cooling Channel (HCC) uses hydrogen-pressurized RF cavities imbedded in a magnet system with solenoid, helical dipole, and helical quadrupole components that provide the continuous dispersion needed for emittance exchange and effective 6d beam cooling. A series of HCC segments, each with sequentially smaller aperture, higher magnetic field, and higher RF frequency to match the beam size as it is cooled, has been optimized by numerical simulation to achieve a factor of 10⁵ emittance reduction in a 300 m long channel with only a 40% loss of beam. Conceptual designs of the hardware required for this HCC system and the status of the RF studies and HTS helical solenoid magnet prototypes are described.

• G. Wang, M. Blaskiewicz, V. Litvinenko
  BNL, Upton, Long Island, New York

We report recent progresses on analytical studies of Coherent Electron Cooling. The phase space electron beam distribution obtained from the 1D FEL amplifier is applied to an infinite electron plasma model and the electron density evolution inside the kicker is derived. We also investigate the velocity modulation in the modulator and obtain a closed form solution for the current density evolution for infinite homogeneous electron plasma.