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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

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Simulation of touschek effects for dafne with strong rf focusing

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


Simulation of touschek effects for dafne with strong rf focusing

Introduction Focusing

  • Azimuth-dependent Beam Length

  • Touschek effects in 2D collision approach

  • Energy Aperture

  • Results for DAFNE SRFF experiment (A)

  • Conclusions


Introduction
INTRODUCTION Focusing

  • 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


Simulation of touschek effects for dafne with strong rf focusing

  • Origin of IBS Code used: Focusing

    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).



1 azimuth dependent beam length
1. AZIMUTH-DEPENDENT BEAM LENGTH Focusing*

  • Beam length as function of the azimuth with taking into account the RF focusing is

  • On the contrary, the energy spread does not vary alongthe ringbut 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

2.TOUSCHEK EFFECTS IN 2D COLLISION APPROACH

the transverse momentum spread

the coupling parameter in velocity space

at

(flat beam)

at

(“round” beam)


Distribution function plot in 2d collision approach
Distribution function plot in 2D collision approach Focusing

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.


Simulation of touschek effects for dafne with strong rf focusing

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 c m p m s p 2
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”


Simulation of touschek effects for dafne with strong rf focusing

loss rate=inverse beam life-time

the Loss Function

flat beam

limit

=Energy Aperture

 1/(Ap2 sL)


Modified loss function
Modified Loss Function the parameter

“Flat Beam”

“Round Beam”


3 energy aperture calculation
3. ENERGY APERTURE CALCULATION the parameter

  • 6D Particle Tracking for nonlinear dynamics simulation

    (AcceleraticumCode*, 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).


Simulation of touschek effects for dafne with strong rf focusing

4. RESULTS FOR DAFNE SRFF EXPERIMENT (A) the parameter

  • 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.




Gain in energy spread due to ibs in srff expr a vs bunch current
Gain in Energy Spread due to IBS in SRFF Expr A the parameter 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 bunch current
Gain in Horizontal Emittance due to IBS in SRFF Expr A the parameter 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
Beam Life Time vs. Coupling in RF SRFF Expr A the parameter 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
Loss Rate due to IBS in SRFF Expr A the parameter vs. Bunch Current at Coupling=0.01

Urf=0 MV _____

Urf =1 MV _____

Urf =4 MV ____

Urf =8 MV ____


5 conclusions
5. CONCLUSIONS the parameter

  • 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%).