TESLA Damping Ring: Injection/Extraction Schemes with RF Deflectors D. Alesini, F. Marcellini

Summary CTF3-like Injection/Extraction scheme for TESLA DR NO Bunch Length 2 (or 3) freq. in 4 (or 6) RF Defl. [2 (or 3) inj. + 2 (or 3) extr.] 2 (or 3) freq. in 2 RF Defl. [1 inj. + 1 extr.] WITH Bunch Length Effects of Errors in DR parameters (phase advance between RF Deflectors, RF Amplitudes and Phase,...)

Injection scheme in the CR CTF3 INJECTION SCHEME The long bunch train with an intra-bunch distance of 20 cm is converted into a series of short bunch trains, with an intra-bunch distance of 2 cm. This is done in 2 steps: by a factor of 2 in the DL, then by a factor of 5 in the CR. DL Beam axis 2nd Deflector 1st Deflector Injection scheme in the CR

What we have done in Frascati - BEAM DYNAMICS STUDY: BEAM LOADING IN THE RF DEFLECTORS - RF DEFLECTORS DESIGN What we have done in Frascati 1st turn - 1st bunch train from linac Recomb. in the CTF3 Prelim. phase 2nd turn 3rd turn 4th turn

CTF3-LIKE INJECTION/EXTRACTION SCHEME (simple scheme) LINAC TRAIN Extraction Injection If the filling time (F) of the deflectors is less than TDR it is possible to inject or extract the bunches without any gap in the DR filling pattern.  should be  * depending on the ring optics and septum position. Considering a single RF frequency   /MAX=1-cos(2/F) Rec. factor

(first evaluations made by J.P. Delahaye) IN THE TESLA CASE (first evaluations made by J.P. Delahaye) QUANTITY SYMBOL VALUE LINAC Number of bunches in the Linac NB 2820 Bunch time spacing in the Linac TL 337 ns Bunch spacing LL= TL*c 101 m Total length of the bunch train LB= NB* LL 285 km DR Recombination factor F 20 Total length of the DR LDR = LB/F LL/F 14 km Bunch spacing in the DR LDR= LL/F 5 m Bunch time spacing in the DR TDR = TL/F 16.85 ns RF DEFL. Number of RF deflectors ND 2 (1 inj. + 1 extr.) Freq. of the RF deflectors fRF= n*1/ TL 1.3 GHz (= 438*1/ TL) Delta deflection between the extr./inj. bunches and the stored ones * 0.6 mrad Deflection of the extr./inj. Bunches MAX (= / (1-cos(2/F))) 12 mrad!! /MAX  5% 1 F  16.85 ns !! TW RF Deflectors GAP TESLA klystrons 2 inj./extr. with more RF frequencies near 1.3 GHz

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

2 = INJ./EXTR. WITH MORE RF FREQUENCIES NEAR 1.3 GHz (F=20)  maximization of MAX in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  no bunch length 2 distant freq. case (every possible freq. in the considered range) = 2 close freq. case (frequencies differ for 1/ TL) Extracted bunches DEFLECTOR PARAMETERS (Mode /2) 4 Deflectors (2 inj. + 2 extr.) Cell dimensions a = 41.80 [mm] b = 133.00 [mm] D = 58.06 [mm] t = 11.53 [mm] Defl 1  fRF1 = 432*1/ TL = 1281.90 [MHz] Defl 2  fRF2 = 431*1/ TL = 1278.93 [MHz] Total beam deflection = 1.36 [mrad] Deflection defl.1 = 0.68 [mrad] Deflection defl.2 = 0.68 [mrad] MAX = 44 % P = 9 [MW] L = 1.51 [m] F = 112 [nsec] n. Cells/defl = 26 P = 5 [MW] L = 2.03 [m] F = 150 [nsec] n. Cells/defl = 35

2 Deflectors (1 inj. + 1 extr.) 1 RF Deflector powered with 2 (or 3 frequencies) DEFLECTOR PARAMETERS (Mode /2) 2 Deflectors (1 inj. + 1 extr.) Defl 1  fRF1 = 432*1/TL = 1281.90 [MHz]  fRF2 = 431*1/ TL = 1278.93 [MHz] Total beam deflection = 1.36 [mrad] Deflection fRF1 = 0.68 [mrad] Deflection fRF2 = 0.68 [mrad] P = 9 @fRF1 + 9 @fRF2 [MW] 1/*=95% (fRF1 = f*+1/2 TL) 2/* =95% (fRF2 = f*-1/2 TL) L = 1.59 [m] F = 118 [nsec] n. Cells/defl = 28 P = 5 @fRF1 + 5 @fRF2 [MW] 1/*=90% (fRF1 = f*+1/2 TL) 2/* =90% (fRF2 = f*-1/2 TL) L = 2.25 [m] F = 167 [nsec] n. Cells/defl = 39

DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) 3 Frequencies maximization of MAX in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  no bunch length 3 distant freq. case  3 close freq. case MAX = 69 % DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) Defl 1  fRF1 = 433*1/ TL = 1284.87 [MHz] Defl 2  fRF2 = 438*1/ TL = 1299.70 [MHz] Defl 3  fRF3 = 443*1/ TL = 1314.54 [MHz] Total beam deflection = 0.87 [mrad] Deflection defl.1 = 0.29 [mrad] Deflection defl.2 = 0.29 [mrad] Deflection defl.3 = 0.29 [mrad] P = 9 [MW] L = 0.64 [m] F = 48 [nsec] n. Cells/defl = 11 P = 5.00 [MW] L = 0.86 [m] F = 64 [nsec] n. Cells/defl = 15

DEFLECTOR PARAMETERS (/2) 2 Deflectors (1 inj. + 1 extr.) maximization of MAX in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  no bunch length 3 distant freq. case  3 close freq. case IDEAL CASE MAX = 67 % DEFLECTOR PARAMETERS (/2) 2 Deflectors (1 inj. + 1 extr.) Defl 1  fRF1 = 436*1/ TL = 1293.77 [MHz]  fRF2 = 437*1/ TL = 1296.74 [MHz]  fRF3 = 435*1/ TL = 1290.80 [MHz] P = 9 @ fRF1 + 9 @ fRF2 + 9 @ fRF3 [MW] Total beam deflection = 0.91 [mrad] Deflection @ fRF1= 0.31 [mrad] Deflection @ fRF2= 0.3 [mrad] Deflection @ fRF3= 0.3 [mrad] MAX = 66 % L = 0.69 [m] F = 51 [nsec] n. Cells/defl = 12 P = 5 @ fRF1 + 5 @ fRF2 + 5 @ fRF3 [MW] Total beam deflection = 0.92 [mrad] Deflection @ fRF1 = 0.32 [mrad] Deflection @ fRF2 = 0.3 [mrad] Deflection @ fRF3 = 0.3 [mrad] MAX = 65 % L = 0.96 [m] F = 71 [nsec] n. Cells/defl = 17 REAL CASE: w.p. with vphc   no perfect synchronism

 different recombination factors F  2 or 3 freq. optimization in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  no bunch length  different recombination factors F 2 distant freq. 2 close freq. 3 distant freq. 3 close freq.

FINITE BUNCH LENGTH z=6 mm, the same 2 freq. optimized in the previous case give: Extracted bunch 1 = 9 % New optimization procedure: to increase 1 (if possible) to reduce the RF slope over the bunch length How to avoid the effect of the RF curvature on the extr. bunches

DEFLECTOR PARAMETERS (/2) 4 Deflectors (2 inj. + 2 extr.) 2 Frequencies  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 2 distant freq. case  2 close freq. case DEFLECTOR PARAMETERS (/2) 4 Deflectors (2 inj. + 2 extr.) Defl 1  fRF1 = 447*1/ TL = 1326.41 [MHz] Defl 2  fRF2 = 432*1/ TL = 1281.90 [MHz] Total beam deflection = 2.66 [mrad] Deflection defl.1 = 1.33 [mrad] Deflection defl.2 = 1.33 [mrad] 1 = 22.5 % P = 9.00 [MW] L = 2.9 [m] F = 215 [nsec] n. Cells/defl = 50 P = 5.00 [MW] L = 3.97 [m] F = 294 [nsec] n. Cells/defl = 68

2 Deflectors (1 inj. + 1 extr.)  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 2 distant freq. case  2 close freq. case 1 = 14 % NO SOLUTION WITH 2 Deflectors (1 inj. + 1 extr.)

DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) 3 Frequencies  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 3 distant freq. case  3 close freq. case DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) Defl 1  fRF1 = 444*1/ TL = 1317.51 [MHz] Defl 2  fRF2 = 437*1/ TL = 1296.74 [MHz] Defl 3  fRF3 = 435*1/ TL = 1290.80 [MHz] Total beam deflection = 1.05 [mrad] Deflection defl.1 = 0.35 [mrad] Deflection defl.2 = 0.35 [mrad] Deflection defl.3 = 0.35 [mrad] 1 = 57 % P = 9 [MW] L = 0.78 [m] F = 58 [nsec] n. Cells/defl = 13 P = 5.00 [MW] L = 1.04 [m] F = 77 [nsec] n. Cells/defl = 18

DEFLECTOR PARAMETERS (/2) 2 Deflectors (1 inj. + 1 extr.)  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 3 distant freq. case  3 close freq. case IDEAL CASE DEFLECTOR PARAMETERS (/2) 2 Deflectors (1 inj. + 1 extr.) Defl 1  fRF1 = 435*1/ TL = 1290.80 [MHz]  fRF2 = 436*1/ TL = 1293.77 [MHz]  fRF3 = 434*1/ TL = 1287.83 [MHz] 1 = 40 % P=9+9+9 [MW] Total beam defl. = 1.57 [mrad] Defl. @ fRF1= 0.57 [mrad] Defl. @ fRF2= 0.5 [mrad] Defl. @ fRF3= 0.5 [mrad] MAX = 38 % L = 1.26 [m] F = 93 [nsec] n. Cells/defl = 22 P=6+6+6 [MW] Total beam defl. = 1.68 [mrad] Defl. @ fRF1 = 0.67 [mrad] Defl. @ fRF2 = 0.51 [mrad] Defl. @ fRF3 = 0.51 [mrad] MAX = 35 % L = 1.83 [m] F = 135 [nsec] n. Cells/defl = 32 REAL CASE: w.p. with vphc   no perfect synchronism

6 Deflectors (3 inj. + 3 extr.)  minimization of the bunch slope (with 1  30%) in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 3 “distant” freq. DEFLECTOR PARAMETERS (Mode /2) 6 Deflectors (3 inj. + 3 extr.) Defl 1  fRF1 = 442*1/ TL = 1311.57 [MHz] Defl 2  fRF2 = 438*1/ TL = 1299.70 [MHz] Defl 3  fRF3 = 435*1/ TL = 1290.80 [MHz] Total beam deflection = 1.96 [mrad] Deflection defl.1 = 0.65 [mrad] Deflection defl.2 = 0.65 [mrad] Deflection defl.3 = 0.65 [mrad] 1 = 31 % P = 9 [MW] L = 1.45 [m] F = 108 [nsec] n. Cells/defl = 25 P = 5.00 [MW] L = 1.94 [m] F = 144 [nsec] n. Cells/defl = 34

HOW TO COMPENSATE THE DISTORTION DUE TO THE FINITE BUNCH LENGTH IN THE EXTRACTION PROCESS

DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) F=45  LDR6.3 Km  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=6 mm 3 distant freq. 1 = 30 % DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) Defl 1  fRF1 = 447*1/ TL = 1326.41 [MHz] Defl 2  fRF2 = 440*1/ TL = 1305.64 [MHz] Defl 3  fRF3 = 438*1/ TL = 1299.70 [MHz] Total beam deflection = 2.02 [mrad] Deflection defl.1 = 0.67 [mrad] Deflection defl.2 = 0.67 [mrad] Deflection defl.3 = 0.67 [mrad] P = 9 [MW] L = 1.5 [m] F = 111 [nsec] n. Cells/defl = 26 P = 5.00 [MW] L = 2.00 [m] F = 149 [nsec] n. Cells/defl = 35

DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) F=100  LDR2.85 Km  maximization of 1 in the range [430*1/ TL 450*1/ TL] =1.276  1.335 GHz  bunch length z=2 mm 3 distant freq. 1 = 28 % DEFLECTOR PARAMETERS (/2) 6 Deflectors (3 inj. + 3 extr.) Defl 1  fRF1 = 447*1/ TL = 1326.41 [MHz] Defl 2  fRF2 = 440*1/ TL = 1305.64 [MHz] Defl 3  fRF3 = 436*1/ TL = 1293.77 [MHz] Total beam deflection = 2.16 [mrad] Deflection defl.1 = 0.72 [mrad] Deflection defl.2 = 0.72 [mrad] Deflection defl.3 = 0.72 [mrad] P = 9 [MW] L = 1.6 [m] F = 119 [nsec] n. Cells/defl = 28 P = 5.00 [MW] L = 2.15 [m] F = 160 [nsec] n. Cells/defl = 37

EFFECT OF ERRORS Possible Error sources in the Injection/Extraction process Errors in the Injection process can be damped after some turns in the DR

First extracted bunches EFFECT OF ERRORS IN THE EXTRACTION PROCESS ERROR IN THE PHASE ADVANCE 2-1 (nominal value 180 deg) Example: -2 distant freq. case -F=20 -Ph. Adv. 1-2 = 150 and 200 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Ph. Adv. 2-1 = 179 deg; First extracted bunches In each particular case it is possible to define this two quantities. The position (or angle) of the bunches at the extraction point are between xMAX and xMIN (or MAX and MIN)

CASE 1 -2 dist. freq. case compared with 3 dist. freq. case -F=20 -Ph. Adv. 1-2 = 0-360 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Ph. Adv. 2-1 = 179 deg;

CASE 2 -2 dist. freq. case compared with 3 dist. freq. case -F=20 -Ph. Adv. 1-2 = 200 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Ph. Adv. 2-1 = 160-200 deg;

RF AMPLITUDE (Deflector 1) CASE 3 -2 dist. freq. case compared with 3 dist. freq. Case (F=20) -Ph. Adv. 1-2 = 200 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Amplitude variation VRF1 ERROR IN THE RF AMPLITUDE (Deflector 1) 2 dist. freq. 3 dist. freq.

ERROR IN THE RF PHASE (Deflector 1) CASE 4 -2 dist. freq. case compared with 3 dist. freq. Case (F=20) -Ph. Adv. 1-2 = 200 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Phase variation VRF1 ERROR IN THE RF PHASE (Deflector 1) 2 dist. freq. 3 dist. freq.

2 dist. freq. 3 dist. freq. CASE 5 -2 dist. freq. case compared with 3 dist. freq. Case (F=20) -Ph. Adv. 1-2 = 0-360 deg; -RF1=  RF2 =50 m;  RF1= RF2 =0 -Amplitude VRF1=99% of the nominal value (each single freq.) 2 dist. freq. 3 dist. freq.

Conclusions Further analysis The Injection/Extraction process in the DR with RF deflectors is feasible. In particular the cases of 2-3 RF frequencies and different recombination factors have been illustrated and discussed; The problem of the finite bunch length has been discussed; Best results have been obtained using 3 RF frequencies (eventually powering the same RF deflector); TW RF Defl. working @ 1.3 GHz reach the required performances in term of F and deflection; The effects induced by errors in the DR parameters or RF Amplitude/Phase have been discussed. The study allows determining the tolerances in the power supply of the magnets or in the RF jitter in Amplitude and Phase. Further analysis -Effects of the RF Deflectors in the S.B./M.B. Beam dynamics of the DR; (...)