Paper  Title  Page 

TPAT086  Enhanced Optical Cooling of Particle Beams in Storage Rings  4179 


In this scheme undulators are installed in straight sections of a storage ring at distances determined by a phase advance 2pπ+π between first and second undulators and 2π between next undulators, where p=1,2,3.. . UR emitted in the first undulator pass through an optical system with movable screens 1,2 in the image plane of the particle beam. If screens let pass the UR then the past UR is amplified and pass through the second and next undulators together with the particle. Every particle loses its energy in the overlapped fields of the amplified UR and these undulators. Motion of screens in the optical system leads to particle energy losses in second and following undulators similar to losses in moving targets T1,2 in the schemes of enhanced ion cooling.* Energy losses are accompanied by a decrease of both energy spread and amplitudes of betatron oscillations that is enhanced cooling if, at first, the moving screen 2 will produce conditions of the energy loss for higher energy particles. When the screen 2 will open image of all particles the system must be closed and then the cooling process can be repeated*.
*physics/0404142. 

TPAT087  The Effect of Magnetic Field Errors on Dynamical Friction in Electron Coolers  4206 


Funding: Work supported by US DOE grants DEFG0301ER83313 and DEFG0395ER40926.
A proposed luminosity upgrade to the Relativistic Heavy Ion Collider (RHIC) includes a novel electron cooling section,* which would use ~55 MeV electrons to cool fullyionized 100 GeV/nucleon gold ions. A strong (15 T) solenoidal field will be used to magnetize the electrons and thus enhance the dynamical friction force on the ions. The physics of magnetized friction is being simulated for RHIC parameters, using the VORPAL code.** Most theoretical treatments for magnetized dynamical friction do not consider the effect of magnetic field errors, except in a parametric fashion.*** However, field errors can in some cases dramatically reduce the velocity drag and corresponding cooling rate. We present a simple analytical model for the magnetic field errors, which must be Lorentz transformed into the beam frame for use in our simulations. The simulated dynamical friction for the case of a perfect solenoidal field will be compared with results from this new model, for parameters relevant to RHIC.
*Fedotov et al., Proc. 33rd ICFA Adv. Beam Dynamics Workshop (2004). **Nieter & Cary, J. Comp. Phys. 196 (2004). ***Parkhomchuk, Nucl. Instr. Meth. Phys. Res. A 441 (2000). 

TPAT088  Consideration of Relativistic Dynamics in HighEnergy Electron Coolers  


Funding: Work supported by U.S. DOE grant DEFG0204ER84094.
A proposed electron cooler for RHIC would use ~55 MeV electrons to cool fullyionized 100 GeV/nucleon gold ions.* At two locations in the collider ring, the electrons and ions will copropagate for ~13 m, with velocities close to c and gamma>100. To lowestorder, one can Lorentz transform all physical quantities into the beam frame and calculate the dynamical friction forces assuming a nonrelativisitc, electrostatic plasma. However, we show that nonlinear space charge forces of the bunched electron beam on the ions must be calculated relativistically, because an electrostatic beamframe calculation is not valid for such short interaction times. The validity of nonrelativistic friction force calculations must also be considered. Further, the transverse thermal velocities of the highcharge (~20 nC) electron bunch are large enough that some electrons have marginally relativistic velocities, even in the beam frame. Hence, we consider relativistic binary collisions – treating the model problem of two charged particles on a line, comparing nonrelativistic dynamics, marginally relativistic (in the Darwin approximation) and fully relativistic, with retarded potentials.
*A.V. Fedotov et al., Proc. 33rd ICFA Advanced Beam Dynamics Workshop (2004), in press. 

TPAT089  Cooling Dynamics Studies and Scenarios for the RHIC Cooler  4236 


Funding: Work supported by the U.S. Department of Energy under contract No. DEAC0298CH10886 In this paper, we discuss various cooling dynamics studies for RHIC, such as an equilibrium process between intrabeam scattering within ion bunch and electron cooling, critical number of electrons needed, magnetized cooling logarithm and resulting requirements on parameters of electron beam, effects of solenoid errors, etc. We also present simulations of various possibilities of using electron cooling at RHIC, which includes cooling at the top energy, precooling at low energy, aspects of transverse and longitudinal cooling and their impact on the luminosity. Electron cooling at various collision energies both for heavy ions and protons is also discussed. 

TPAT090  Simulations of HighEnergy Electron Cooling  4251 


Funding: Work supported by the U.S. Department of Energy under contract No. DEAC0298CH10886. Highenergy electron cooling of RHIC presents many unique features and challenges. An accurate estimate of the cooling times requires a detailed calculation of the cooling process, which takes place simultaneously with various diffusive mechanisms in RHIC. In addition, many unexplored effects of highenergy cooling in a collider complicate the task of getting very accurate estimates of cooling times. To address these highenergy cooling issues, a detailed study of cooling dynamics based on computer codes is underway at Brookhaven National Laboratory. In this paper, we present an update on code development and its application to the highenergy cooling dynamics studies for RHIC. 

TPAT091  IBS for Ion Distribution Under Electron Cooling  4263 


Funding: Work supported by the U.S. Department of Energy under contract No. DEAC0298CH10886.
Standard models of the intrabeam scattering (IBS) are based on the growth of the rms beam parameters for a Gaussian beam distribution. As a result of electron cooling, the core of beam distribution is cooled much faster than the tails, producing a denser core. Formation of such a core is an important feature since it plays dominant role in the luminosity increase. A simple use of standard rmsbased IBS approach may significantly underestimate IBS for the beam core. A detailed treatment of IBS, which depends on individual particle amplitudes, was recently proposed by Burov,* with an analytic formulation done for a Gaussian distribution. However, during the cooling process the beam distribution quickly deviates from a Gaussian profile. To understand the extent of the dense core formation in the ion distribution, the "coretail" model for IBS, based on the diffusion coefficients for biGaussian distributions, was employed in cooling studies for RHIC. In addition, the standard IBS theory was recently reformulated for rms parameters growth of a biGaussian distribution by Parzen.** In this paper, we compare various approaches to IBS treatment for such distribution. Its impact on the luminosity is also discussed.
*A. Burov, FERMILABTM2213 (2003). **G. Parzen, Tech Note CAD/AP/150 (2004). 

TPAT092  Numerical Studies of the Friction Force for the RHIC Electron Cooler  4278 


Funding: Work performed under the auspices of the U.S. Department of Energy.
Accurate calculation of electron cooling times requires an accurate description of the dynamical friction force. The proposed RHIC cooler will require ~55 MeV electrons, which must be obtained from an RF linac, leading to very high transverse electron temperatures. A strong solenoid will be used to magnetize the electrons and suppress the transverse temperature, but the achievable magnetized cooling logarithm will not be large. Available formulas for magnetized dynamical friction are derived in the logarithmic approximation, which is questionable in this regime. In this paper, we explore the magnetized friction force for parameters of the RHIC cooler, using the VORPAL code.* VORPAL can simulate dynamical friction and diffusion coefficients directly from first principles.** Various aspects of the friction force, such as dependence on magnetic field, scaling with ion charge number and others, are addressed for the problem of highenergy electron cooling in the RHIC regime.
*C. Nieter & J.R. Cary, J. Comp. Phys. 196 (2004), p. 448. **D.L. Bruhwiler et al., Proc. 33rd ICFA Advanced Beam Dynamics Workshop (2004). 