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

Simulation of Touschek Effects for DAFNE with Strong RF

Focusing

Introduction1. Azimuth-dependent Beam Length2. Touschek effects in 2D collision approach3. Energy Aperture 4. Results for DAFNE SRFF experiment (A)5. 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 azimuthMake calculations for sufficiently wide changes in the betatron coupling parameter and the beam current per bunch

•Tools: 6D Particle Tracking Code to calculate Energy ApertureCode 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

LifeTime

Total effect of SR and IBSin beam sizes

and energy spread

DA as function of azimuthBeam parameters due to SR

Twiss parameters

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:

.)(

1)(

212

)( 5656/

E

eV

L

sRsR

eV

ELs RF

RFRF

RFEEL

s

sdsshsR0

56 ,)()()(

E

eVL RF

RFEEEE

1cos ,)cos1(

)cos2(

3

20//

L

LR )(56

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 coupling parameter in velocity space

at

at

(flat beam)

(“round” beam)

the transverse momentum spread

•Distribution function plot in 2D collision approach

Møller differential cross section

Conversion due to Coupling growth

x=p/p cm relative velocity

Maximum of distribution function shifts to region of greater relativemomentums 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 m=(pm/p)2

pm=mc(r0/bmax)1/2, the classical

lower limit of momentum transfer

“Flat Beam”

“Round Beam”

• Loss Rate due to single Touschek processes

=Energy Aperture

flat beamlimit

loss rate=inverse beam life-time

the Loss Function

Ap2L)

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 p/p≠0 and “infinitesimal” seed deviations from the equilibrium orbit

•Find max(p/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 RFcavity 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

Coupling =V-Emittance/H-Emittance=0.01

Urf=0 MV _____Urf =1 MV _____Urf =4 MV ____ Urf =8 MV ____

Gain in Horizontal Emittance due to IBS in SRFF Expr A

vs. Bunch Current

Coupling =V-Emittance/H-Emittance=0.01

Urf=0 MV _____Urf =1 MV _____Urf =4 MV ____ Urf =8 MV ____

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%).