The Touschek Lifetime Equation and its Implementation in BMAD Michael Ehrlichman School of Physics and Astronomy University of Minnesota

Particle Loss maximum momentum deviation δp_m In Touschek effect, 2 particles are lost one with δp > δp_m, one with δp < δp_m Intra-beam scattering causes beam blow-up Touschek effect causes particle loss

Discovery of Effect First observation at ADA in 1963 [1] First e+e- collider, single ring Lifetime shorter than predicted from residual air pressure, independent of presense of opposing beam Dependant on beam energy Effect described qualitatively, determined empirically Lifetime defined such that after that, half of particles are lost

A. Piwinski Derivation Most recent, first to include horizontal and vertical betatron oscillations [2] Two particles in momentum space in lab frame Characterized by angle X1,2 between p1, p2 and p1+p2 Lorentz transformation parallel to p1+p2 applied X2 now assumed to be small, X1 ~= X2 p1 and p2 assumed perpendicular to j-axis, abs(p1) ~= abs(p2) Obtains delta p1 = -p2 = f(p,gamma,X,j-axis) Moller scattering cross section used to find probability that two particles collide such that delta p > p_m Gaussian distribution of momentum assumed, characterized by beam parameters Integration over all particle positions and angles resulting in delta p > p_m gives loss rate Lifetime defined as time at which half of original number of particles are lost

Touschek Equation

Implementation in BMAD Fortran 90 with Numerical Recipes Beam parameters extracted from BMAD [6] Modified version of NR bessi_0 used to evaluate modified bessel function Integration done with NR qromb using tan version of Touschek equation Romberg’s method

Results – Comparison to CLEO-c Yellow Book

Results – Comparison to Damping Ring Configuration Document [3] ILC DR Touschek (min) DR Est. Lattice Energy (GeV) at 1% pz aprature BRU 3.74 14 18 PPA 5 17 16 OTW OCS_v2 5.07 34 33 DAS 52 44 dog642 62 50 MCH 93 68

CESR Test Facility Touschek effect not an issue for CLEO or ILC Damping ring Is an issue for CESR Test Facility [8] Touschek Lifetime 8 sigma: 3.3 minutes Touschek Lifetime 10 sigma: 6.4 minutes Touschek Lifetime 12 sigma: 11.3 minutes

Further Analysis Ring segmenting Yellow Book and DRCR calculations use equation from Wiedemann [7] that neglects vertical betatron function, dispersions, and derivative of dispersions

Conclusion Touschek module in CVS and to be included in next distribution Results will go into CesrTF design Results may be included in Damping Ring Configuration Recommendation document

citations [1] “Lifetime and Beam Size in a Storage Ring”, B. Touschek, et.al. Physical Review Letters. Volume 10, Number 9. May 1 1963 [2] “The Touschek Effect in Strong Focusing Storage Rings”, A. Piwinski. Available at arxiv:physics/9903034v1 22 Mar 1999 [3] “Recommendations for the ILC Damping Rings Baseline Configuration”, A. Wolski, et. al. Soon to be published. Available at: http://www.desy.de/~awolski/ILCDR/DRConfigurationStudy_files/DRConfigRecommend.pdf [4] “CLEO-c and CESR-c: A New Frontier of Weak and Strong Interactions”, CLEO-c collaboration. October 12, 2001 [5] “The BMAD Reference Manual”, Sagan, D. http://www.lepp.cornell.edu/~dcs/bmad/ [6] “Numerical Recipes in Fortran 90”, http://www.library.cornell.edu/nr/cbookf90pdf.html [7] “Particle Accelerator Physics II: Nonlinear & Higher-Order Beam Dynamics”, Wiedemann, Helmut. Springer-Verlag Berlin and Heidelberg GmbH & Co. K October 30 1998 [8] “Experimental, Simulation, and Design Studies for Linear Collider Damping Rings”, Sagan, D. Progress report submitted to DOE.