Simulation of Touschek Effects for DAFNE with Strong RF Focusing E. Levichev, S. Nikitin & P. Piminov Budker Institute of Nuclear Physics SB RAS ICFA mini-workshop on "Frontiers of Short Bunches in Storage Rings“ Frascati National Laboratories 7-8 November 2005

Introduction Azimuth-dependent Beam Length Touschek effects in 2D collision approach Energy Aperture Results for DAFNE SRFF experiment (A) Conclusions

INTRODUCTION Aim: Determine the steady-state emittance and energy spread as well as the beam life-time for the designs of e+e- collider based on SRFF concept proposed and developed in Frascati Peculiarities: Take into account conjointly the single and multiple IBS (Intra-Beam Scattering otherwise Touschek) processes Consider variability of the beam length and DA with the machine azimuth Make calculations for sufficiently wide changes in the betatron coupling parameter and the beam current per bunch Tools: 6D Particle Tracking Code to calculate Energy Aperture Code to calculate IBS influence taking into account two-dimensional character of particle collisions inside beam

Origin of IBS Code used: Based on the well-known IBS theory (see G. Brook, 1970) Developed with modification of 1D approach to 2D one in BINP (1999)* Regardless of considerations by other authors (in particular, A. Piwinski) Tested in comparison with experimental data at VEPP-4M and CESR** *D. Golubenko and S. Nikitin. PAC’01, v.4(5), p. 2845; BINP Preprint 99-110 (1999). * * S. Nikitin and A. Temnykh. BINP Preprint 2004-56 (2004).

Hierarchy of Calculation Stages

1. AZIMUTH-DEPENDENT BEAM LENGTH* Beam length as function of the azimuth with taking into account the RF focusing is On the contrary, the energy spread does not vary along the ring but it is modified in its value due to RF focusing: SRFF “OFF” * A.Gallo, P.Raimondi, M.Zobov. DAΦNE Techical Note G-60 (2003).

2. TOUSCHEK EFFECTS IN 2D COLLISION APPROACH Modified function of distribution over momentum (p) in CMS the transverse momentum spread the coupling parameter in velocity space at (flat beam) at (“round” beam)

Distribution function plot in 2D collision approach x=p/p  cm relative velocity Conversion due to Coupling growth Møller differential cross section Maximum of distribution function shifts to region of greater relative momentums due to coupling that affects the IBS processes.

Co-Kinetics of Quantum (Q ) and multiple Touschek (T ) processes the relative energy dispersion the radial phase volume Touschek Diffusion coefficients averaged over azimuth  1/L…  in our case the system of transcendental equations to determine the steady-state values of u and v (the quantities uQ and vQ from SR contribution are used as input values in solving)

Function describing the dependence of IBS diffusion rate on the parameter cm=(pm/sp)2 pm=mc(r0/bmax)1/2, the classical lower limit of momentum transfer “Flat Beam” “Round Beam”

 1/(Ap2 sL) Loss Rate due to single Touschek processes loss rate=inverse beam life-time the Loss Function flat beam limit =Energy Aperture  1/(Ap2 sL)

Modified Loss Function “Flat Beam” “Round Beam”

3. ENERGY APERTURE CALCULATION 6D Particle Tracking for nonlinear dynamics simulation (Acceleraticum Code*, in Talk by E. Levichev) At a given azimuth, a particle starts with Dp/p≠0 and “infinitesimal” seed deviations from the equilibrium orbit Find max(Dp/p) that does not yet result in particle loss Thus, the Energy Aperture Ap =Min (ARF, ADA) is automatically determined between ARF, RF separatrix size, and ADA, the Dynamic Aperture limit As a result, we obtain the azimuth-dependent Energy Aperture which determines the IBS particle loss rate * P.Piminov. Master’s thesis, BINP, Novosibirsk, 2000 (in Russian).

4. RESULTS FOR DAFNE SRFF EXPERIMENT (A) Proof-of-principle experiment is planned now in the existing DAFNE storage ring* Tesla type SC RF cavity at 1.3 GHz, with a maximum voltage of 10 MV, can provide the necessary voltage derivative But SRFF regime produces strong coupling of the transverse and longitudinal incoherent oscillations of particle and may deteriorate a stable motion area (DA) Simulation of Touschek effects allows to make an reasonability check of the given DAFNE version in the view point of beam life time *D.Alesini et al., “Proposal of a bunch length modulation experiment in DAΦNE”, LNF-05/04(IR), 22-Feb-2005.

Beam Length versus Azimuth in DAFNE SRFF Expr A

Dynamic Aperture versus Azimuth in DAFNE SRFF Expr A

Gain in Energy Spread due to IBS in SRFF Expr A vs. Bunch Current Urf=0 MV _____ Urf =1 MV _____ Urf =4 MV ____ Urf =8 MV ____ Coupling =V-Emittance/H-Emittance=0.01

Gain in Horizontal Emittance due to IBS in SRFF Expr A vs Gain in Horizontal Emittance due to IBS in SRFF Expr A vs. Bunch Current Urf=0 MV _____ Urf =1 MV _____ Urf =4 MV ____ Urf =8 MV ____ Coupling =V-Emittance/H-Emittance=0.01

Beam Life Time vs. Coupling in RF SRFF Expr A at 1mA Bunch Current Urf=0 MV _____ Urf =1 MV _____ Urf =4 MV ____ Urf =8 MV ____

Loss Rate due to IBS in SRFF Expr A vs. Bunch Current at Coupling=0.01 Urf=0 MV _____ Urf =1 MV _____ Urf =4 MV ____ Urf =8 MV ____

5. CONCLUSIONS At Urf=8 MV (Max{beam length}/Min{beam length} ≈2), N≈1010 particles, Ev/Eh=0.01, the Beam Life Time is about 10 minutes that opens opportunity for SRFF experiment from this side. Taking into account the azimuthal dependence of Energy Aperture and Beam Length plays a crucial role. At Urf=10 MV Max{EA}/Min{EA} ≈3. Loss Rate varies as squared EA. Influence of IBS on the gains in Beam Emittance and Energy Spread is negligible (≤ 1%).