LNF Laboratory Report S. Guiducci

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)

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

INTRODUCTION: CTF3 INJECTION SCHEME

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

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

(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 = 16.85 ns TESLA klystrons inj./extr. with more RF frequencies near 1.3 GHz /MAX  5%  MAX  12 mrad!! TW RF Deflectors GAP F  16.85 ns !!

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

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

Space charge tune shift TDR: DQ = .23 Short DR: DQ = .23 · .18 / .33 = .13 C 17Km 3Km .18 sl 6 mm 2 mm .33

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

ex = ea/(1+Fw) + ew Fw/(1+Fw) = 8 10-6 m Emittance ex = ea/(1+Fw) + ew Fw/(1+Fw) = 8 10-6 m TDR: ea/(1+Fw) = 2 10-6m ew Fw/(1+Fw) = 6 10-6 m Bw = 1.6 T Fw = 17.5 Short DR: ea/(1+Fw) = 7 10-6 m ew Fw/(1+Fw) ~ ew  Bwig3 l2<b> ~ 1 10-6 m Bw = .8 T Fw  smaller or ea  larger

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 1.3 10-3 .65 10-3 Bunch length (mm) 6 2 Space charge DQ .23 .13

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.

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

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