The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Impedance Measurement Utilizing Bunch Lengthening Effectin ATF Damping RingToshiyuki OKUGI, Yoshinori HASHIMOTO*, Hitoshi HAYANO*, Eunsan KIM*,
Masayuki MUTO*, Takashi N AlTO* and J unji URAKAWA *Department of Physics, Facility of Science, Tokyo Metropolitan University,Hachioji, Tokyo, 192-03 JAPAN*High Energy Accelerator Research Organization,
Tsukuba, Ibaraki, 305 JAPAN
Abstract
The inductive component of the longitudinal
impedance in the ATF damping ring was measured using
the bunch lengthening effect with streak camera. The
amount of inductance was evaluated to L = 52.8nH. It
was consistent of the simulated value with TBCI andABCI codes.
1 Introduction
The vacuum chamber in the ATF damping ringis designed to keep low impedance for avoiding a single bunch instability[l, 2]. The threshold of the single
bunch instability is correlated to the absolute value ofimpedance IZu/nj. It was reported that the purely resistive impedance generated a new type of longitudinal
single bunch instability extremely[3], and the thresholdof single bunch instability for the vacuum chamber ofthe inductive impedance was higher than the purely resistive one. On the other hand, the induced voltage bya single bunch passing through an inductive componentof z 11
has the slope of the opposite sign of RF field,
and it generates significant bunch lengthening. For intence, it was measured that the rms bunch length wasincreased by 60% at 3 x 10 10 for old inductive vacuum
chamber in SLC damping ring[4].

;nwakefields. By taking the derivate of both side ofEq.(l),jt\lindJaw

VRFO"w- = --2- + --.--2-(3)is derived as another formation of it.
2.2 Purely Inductive Impedance ModelIn the ATF design[!], the amount of resisteive partis v.ery small, so it can be ignored for the bunch lengthening. When the impedance of the ring is assumed topurely inductive one, namely the induced voltage is given
bydiVind = -L dt(4)with a constant inductance L, Eq. (3) can be written as
dydx

xy

--1 +y(5)with the variables of x = tfaw , y = LI /VRpaf0 • Here,it is possible to define the normalized charger, the complete integral of y, as follows(6)

2 Inductive Impedance
2.1 Vlasov equation
The beam current distribution below the turbulent
threshold, calculated with Vlasov equation[5], is given
by1t

t2- + . 1I(t) = K exp ( - dt' Vind(t')
222aw
VRFO"w o)(I)

The numerical solution of Eq. (5) is shown inFig. l(a) for several values of r. The charge distribution for a perfect inductor is symmetric about x = 0and it is almost the same as Gaussian distribution atlow intensity regions. On the other hand, it is apparent
that the solution of Eq. (5) is rather parabolic distribution than Gaussian distribution whenever y » 1. Thea X values of Gaussian function for various r values is,where aw and VRF are the natural bunch length andthe slope of the rf voltage at the position of the bunch.
Furthermore, Vind, the transient induced voltage witht = 0 the synchronous position for the low current beam,is given byVind(t) =-1(b) 2.0

1.8
1.6

o" 1.4"'·00

dt' W(t') I(t- t')

1.2(2)

1.0

with W(t) a Green function of the longitudinal wakefield.
The value bf the normalized constant K in Eq.(l) isdefined as the complete integral of I(t) is equal to thetotal charge in bunch Q. If we know the Green functionof the wakefield, Eq.(l) can be solved numerically togive the current distribution of the bunch in the present0.8-6-4-2

4X

0101520r

Fig. 1 (a) The bunch shape for several values of bunchcharge, and (b) The bunch length variation asa function of bunch charge-476-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Table 1Main Parameter of Streak Camera
Vertical Sweep Unit
streak time range
resolution
repetition rate
Horizontal Sweep Unit
sweep range
Sensitive Wavelength
MCP gain

0.2ns to 50ns
1.5ps for 0.2ns range
max. 10kHz
lOOns to lOOms
400 to 900mm
max. 3000

shown in Fig. l(b). Fig. l(b) shows that ax varieslike
as linear for small current regions and roughly as r! forlarge current regions.
·3. Bunch Lengthening in ATF Damping Ringwith O'meas. the measured bunch lengthand O'spot the·contribution from the beam spot size at the streak tube.
Furthermore, it is known that the effect of the measured pulse length increases with high intensity of incident light pulse, especially for short pulses[8]. It iscalled space charge effect inside the streak tube. For t]lepreparation of the bunch length measurement, the effect was measured by inserting the ND filters of severaltransmission ratios at the entrance of the streak camera
for the same bunch population of the beam(5 x 109 ). theresults is shown in Fig.3. We chose the 15% ND filter,
which enhansed the bunch_ length by 5% at the bunchcharge of 5 X 109 , for the bunch length measurement
and we carried out the correction of the contribution
for space charge enhancement with linear function. The
correction factor is evaluated as follows:
fs.C. = (8.72 ± 0.81) X 10-ll [mmjparticles] ,(8)3.1 Experimental Apparatus
DC Current Transformer (DCCT)The beam current was measured with DCCT locatedat straight section in the ATF damping ring. The characteristic of DCCT is not perfectly linear, but has someof deformation come from readout electronics. Thereby,
we used the 3 dimensional polynominal calibration curve
shown in Fig.2(a). It is found from Fig.2(b) that the displacement from calibration curve is 0.044% rms at thebunch population of 5 x 109 and the displacement ismuch smaller than the contribution of the thermal noisefrom readout electronics. The thermal is the main error
source of this DCCT current monitor system, however
the contribution, which is about 0.3% rms for 5 x 109
beam, is also small fraction of the error component inthis measurement.
(a)Calibration for Space Cbarge Effectin tbe Streak Camera
at 5 x 109 electrons I bunch

M13000Sd.

a~~~~~~~~~~~~'b 10R

Y-MO+M1xx+M2xx 1+M3>ot3.cwith Nbunch the bunch population.

(b)

4000

-From Eq.(7),(8), _the bunch length is evaluated withstreak camera and 15% ND filter by"~"'M3R

u=0

.§

uti:~ 1000.g

5!

I

8

10

1240

50

60

-5

.§ -10 o!.--~~.......s~""a~10~12·a~30

Fig. 3 The measured bunch length with streak camera by inserting the ND filters of several transmittion ratios.

E

Bunch Population I X I o"J I20Filter[%)'l'l'l,l,
jil~'~''''''I••§0 2000

10Bunch Population I X 109 I

Fig. 2 The characteristic for DCCT : (a) Beam Current vs. ADC counts, and (b) The displacement from calibration curve
Streak Camera [6, 7]
The bunch length was observed by streak camera(Hamamatsu, C5680). Main parameter of the streak
camera are given in Table 1. Horizontal and verticalranges of lOOms and Ins are adopted in this measurement, respectively. The resolution for this range is about
1.5mm caused by beam spot size at the streak tube. The.
contribution is subtracted from the longitudinal profile,then the bunch length is calculated as follows:

3.2 Bunch Lengthening Measurement
The parameter of the ATF damping ring is listed
in Table 2. The result of correlation plot for the bunch
population and the bunch length is shown in Fig.4. The
bunch lengths in Fig.4 are already made the correction
by Eq,(9). Here, the normalized charge of r in Eq.(6)Table 2
ATF Damping Ring Parameter at This Measurement

(7)

-477-

Beam Energy
Bunch Population
RF Frequency
RF Voltage
Harmonic Number
Momentum Compaction
Synchrotron Frequency

1.299 GeV
up to 5.5 x 109
714 MHz220.6 kV330
1.96 x w- 3
8.95 kHzThe 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997
1.10

can be evaluated by applying the curve of Fig.l (b), thatis(10)r I Nbunch = (1.39 ± 0.07) X 109 'az = 6.83 ± 0.05 [mm] .

1.08
1.06c(11)

01.04

0'

From Eq.(6),(10),(11) and Table 2, the inductive component of the longitudinal impedance for the ATF damping
ring can be evaluated as follows.

1.02
1.00
0.98

L = 52.8 ± 1.3(S.C.) ± 2.7(Jit.) [nH](12)

The fraction of error for "~pace charge" in Eq.(12) areevaluated by the slope error in Eq.(8) and the ratio of
the slope for the bunch length enhancement of the spacecharge to the potential well distortion, "fitting" error
comes from the contribution of the error in Eq.(10),(11 ).
The inductance in Eq.l2 corresponds to the longitudinal
impedance of J!m(ZIIIn)J ;::;:; 0.114Q.

5.§.. 8.5..c00" 8.0~..cuco""

7.5
7.0
6.5 L.....~..L.o_~..J.......~....c...~......_~.......J..~._._,
654203Bunch Population [ x I 09 ]Fig. 4 The correlation plot for bunch population andthe bunch length.

.

3.3 Effect of Intra Beam Scattering
There is another possibility for the bunch lengthening with increasing the beam current. It is called theintra beam scattering and the bunch length caused by
the intra beam scattering is depends upon the volume ofthe bunch. The bunch lengthening calculated with SAD
codes[9] for intra beam scattering is shown in Fig.5 forthe various ratios of vertical emittance to horizontal one.
Furthermore, it is reported that the dispersion ratio ofvertical to horizontal is about 30%, which generates thevertical emittance of 30% for horizontal one, by the previous experiment in the ATF damping ring[lO]. Hence,the vertical emittance of the beam in the ATF damping
ring is evaluated larger than 30% compared to horizontal one. From Fig.5, it is estimated that the effect of theintra beam scattering for the longitudinal inductance isless than 6. 7nH. The value of 6. 7nH is, however, a little
bit overestimated for the reason why the SAD calculation in Fig.5 is not included the effect of the bunch
lengthening for potential well distortion.
4 Consideration
The measurement has good agreement with the simulation results for the designed impedance[!]. The inductive impedance sources are, however, not evaluatedwith actual geometories, but evaluated with approximate 2 dimensional geometories using TBCI and ABCI
codes. Furthermore, the recent impedance of the ATF

02

345Bunch Population [ x I 09 ]Fig. 5 The bunch lengthen caused the intra beam
scattering for various emittance ratios of vertical to horizontal.
damping ring is small compared to the design for thereason why 2 RF cavities are only located in the ring,the cavities are, however, capacitive rather than inductive. The more precise calculation of the impedance for
the ATF damping ring is in progress.
5 Summary
The inductive component of the longitudinal
impedance in the ATF damping ring was measured using
the bunch lengthening effect with streak camera. The
amount of inductance was evaluated to L = 52.8nH. It
was consistent of the simulated value with TBCI andABCI codes. We plan to make certain of the inductive
component of the longitudinal impedance and to measure the synchrotron phase shift, the spectral analysisof BPM electrodes and the phase shift to estimate theabsoulte value of the longitudinal impedance Iz 11 I nl andto investigete the single bunch instability.
Acknowledgement
The authers would like to express our thanksProf. K. Takata and Prof. T. Hirose for for his encouragement and K. Kubo, K. Oide and N. Terunuma for
their useful discussion and C. Montag for his help thecalibration of DCCT. We also wish to thank the ATF
operation group for their support.
References[1] F. Hinode et al., "ATF Design and Study Report",
KEK Internal 95-4(1995)[2] M. Takao et al., Proc. of the 1991 IEEE Particle Ace.
Con£., San Francisco ,p.506(1991)[3] K. Oide, KEK Preprint 94-138(1994)[4] L. Revken et al., Proc. of 1st European Particle Ace.
Con£., Roma, p.637(1988)[5] K. L. F. Bane et al., Proc. of the 1989 IEEE Particle
Ace. Conf., Chicago, p.789(1989)[6] T. Naito et al.,"SR MONITOR FOR THE ATF
DAMPING RING", Proc. of the 1997 PAC(1997)[7] Y. Hashimoto et al.," SR Monitor System for the ATF
Damping Ring", in this conference[8] D. B. Bradley, Rev. Sci. Instrum.,51, 824,(1980)[9] K. Hirata, Proc. 2nd ICFA Beam Dynamics Workshop, Lugano (1988)[10] K. Kubo et al., "Dispersion measurement in ATF
DR", ATF-97-19-478-