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

3. 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

4. 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

5. 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

6. Touschek Equation

7. 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

8. Results – Comparison to CLEO-c Yellow Book

9. 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

10. 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

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

12. 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

13. citations
[1] “Lifetime and Beam Size in a Storage Ring”, B. Touschek, et.al. Physical Review Letters. Volume 10, Number 9. May
[2] “The Touschek Effect in Strong Focusing Storage Rings”, A. Piwinski. Available at arxiv:physics/ v1 22 Mar 1999
[3] “Recommendations for the ILC Damping Rings Baseline Configuration”, A. Wolski, et. al. Soon to be published. Available at:
[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.
[6] “Numerical Recipes in Fortran 90”,
[7] “Particle Accelerator Physics II: Nonlinear & Higher-Order Beam Dynamics”, Wiedemann, Helmut. Springer-Verlag Berlin and Heidelberg GmbH & Co. K October
[8] “Experimental, Simulation, and Design Studies for Linear Collider Damping Rings”, Sagan, D. Progress report submitted to DOE.