1. LNF Laboratory Report
S. Guiducci

2. A solution for the present DR design has been worked out at LNF.
Damping Ring Kickers
An injection extraction scheme for TESLA based on RF deflectors has been suggested by P. Raimondi.
A solution for the present DR design has been worked out at LNF.
The possibility of obtaining a much shorter bunch distance in the DR is envisaged.
This opens the possibility of having an unified DR design for any LC project independent on the Linac technology (warm/SC)

3. APDG Working Group TESLA Damping Ring: Injection/Extraction Schemes with RF Deflectors D. Alesini, F.Marcellini TESLA Damping Ring: RF Deflectors Design F.Marcellini, D. Alesini

4. INTRODUCTION: CTF3 INJECTION SCHEME

5. Two frequencies f2=4f1 F=16 Recombination factor F=16
CTF3 Recombination factor F=5

6. CTF3-LIKE INJECTION/EXTRACTION SCHEME
-Number of bunches in the Linac = NB
-Bunch time spacing in the Linac = TL
(Bunch spacing LL= TL*c)
-Total length of the bunch train = LB
-Number of RF deflectors = 2 (1 inj. + 1 extr.)
-fRF= n*1/ TL (in the Figs. n=1)
-Recombination Factor (F)
-Total length of the damping ring (LDR) = LB/F LL/F
-Bunch time spacing in the Damp. Ring TDR = TL/F
-(Bunch spacing LDR= LL/F)
Injection
Extraction

7. (first evaluations made by J.P. Delahaye)
If the filling time (F) of the deflectors is less than TDR it is possible to inject or extract the bunches without any gap of the filling pattern in the DR;
 should be  * (depending on the ring optics)
(considering a single RF frequency  /MAX=1-cos(2/F))
IN THE TESLA CASE
(first evaluations made by J.P. Delahaye)
-NB = 2820
-TL= 337 ns
(LL=101 m)
-LB 285 km
-fRF 1.3 GHz (= 438*1/ TL)
-F=20
-*=0.6 mrad
-LDR  14 km
-TDR = ns
TESLA klystrons
inj./extr. with more RF frequencies near 1.3 GHz
/MAX  5%  MAX  12 mrad!!
TW RF Deflectors
GAP
F  ns !!

8. RF Deflectors Recombination factor F=20
Gap to turn on and off the deflectors:
1 empty bucket over 141
Two (or Three) Frequencies near 1.3 GHz
(Linac Klystron)
Effect of bunch length
Error sensitivity
Design of the deflectors

9. 3 Km Damping Ring? How critical?
F=100 is feasible for a very short bunch length sl ~ 2mm.
How critical?
An exercise:
A parameter list for a 3Km long DR

10. Space charge tune shift
TDR: DQ = .23
Short DR: DQ = .23 · .18 / .33 = .13
C Km Km
sl mm mm

11. Damping time  gC/U0 ; U0 = g2 B2 dl
U0 = U0,arc + U0,wig = U0,arc (1 + Fw)
To get the same damping time:
U0 = 21 · 3/17  3.7 MeV
and
B2 dl = 605 · 3/17  107 T2m

12. ex = ea/(1+Fw) + ew Fw/(1+Fw) = 8 10-6 m
Emittance
ex = ea/(1+Fw) + ew Fw/(1+Fw) = m
TDR: ea/(1+Fw) = m
ew Fw/(1+Fw) = m
Bw = 1.6 T Fw = 17.5
Short DR: ea/(1+Fw) = m
ew Fw/(1+Fw) ~ ew  Bwig3 l2<b> ~ m
Bw = .8 T
Fw  smaller or ea  larger

13. e+ Parameters @5GeV TDR Short DR Circumference Km 17 3
Inj. emittance rms (m)
.01
Norm. emitt. hor/ver (m)
8/2 10-6
Damping time (ms) 28
Bunch num/space (ns)
2820/ 20
2820/ 3.5
Particles/bunch
2 1010
B2 dl (T2m)
605
107
Wiggler l (m) / B0 (T)
.4 / 1.6
.4/ 0.8
Energy loss/turn(MeV) 21
3.7
Rel. Energy spread sp
Bunch length (mm) 6 2
Space charge DQ
.23
.13

14. Conclusions
RF deflectors for the Damping Ring with a recombination factor F=20 are proposed.
The possibility of a larger recombination (F=100) is interesting in order to shorten the Damping Ring and make it less demanding.

15. RF DEFLECTORS AND RECOMBINATION
1st turn - 1st bunch train from linac
2nd turn
3rd turn
4th turn

16. TW RF DEFLECTORS GAP
nB=1 1 bunch over 141  TG=337 ns