IEEE Transactions on Nuclear Science, Vol. NS-30, No. 2, April 1983

I3UiuIiifiG ChIARACTo.KISTPICS OF A BULiPJiG'h USING; fsiLICAL RECCi.tNATI'ORS

Chen Chia-erh, Guo Zhi-yu, Zliao KuiDepartment of Technical Physic.sPeking UJniversity, Beijing, China

Abstract

A hF Burnclier consistirng of two coupled Helicestuned to 28.4 MiPZ was tested on the beam line of a400 KV DC injector. Bunched waveforms versus RFpower input were measured and analysed. With 8.4 Wpower input the proton beam was compressed to 1 ns(QWIPHM) bursts. The beam pulse splitted into doublepeaks at a higher power level depending on the ini-tial energy dispersion. Both peak separation andthe pulse height changed remarkably with increasingpower input, arid the overlapping of peaks in rneigh-bouring cycles occured alternately. By making useof phase diagram in time-energy space a simple for-malism is presented for the analyBis of the bunchingcharacteristics. Results obtained are well consi-striet with the experiment. The effect of the quadru-pole lens on bunched waveform was also observed anddiscussed.

Introduc tioIn

Interest in bean bunching technique has beenincreased considerably with the development of thetime-of-flight method in heavy ion experiments andthe iinstallation of post accelerators in many la-boratories. Sine wave bunchers have been used andstudied extensively for various purposes for a longtimne 1-4. Since discrepancies existed between onedimnensional theory and the experimental waveforms,the dynamics of bunching process remained to bestudied further, so as to get better performance.During the design studies of our 4.5 MV heavy ionelectrostatic accelerator project and its RF booster,a itF buncher consisting of Helices was developed andtested on the beam line of a 400 KV DC injector.Waveforms of the bunched beam were measured versusincreasing RF power input under different beam en-ergies and different bunching lengths. Beam burstsof 1 ns was obtained with comparative'ly low powerconswnption. In order to get better understandingof the buncher performance, efforts have been madeto anialyse the experiment in time-energy space5.It turned out that the results calculated in thisway were well consistent with the reality.

It is the purpose of this paper to examine care-fully the bunching characteristics by systematicmpasuremermts and to present a simple formalism de-veloped in the time-energy space for the analysis ofthe perfoimance of a single sine wave buncher. Ef-fect of tije niatching between the quadrupole and thecavi ty on the bunched waveform was also observed anddiscussed. In the following sections the experiment-al layout aind the bunched waveforms obtained will bedescribed first and then an analysis will be pre-sented.

Experimental layout

The vertical beam from the 400 KV injector wasbended irnto horizontal direction by a 90 cegreebending ma,net and then focused by a quadrupoledoublet to a waist at about 3.5 m downstream closeto the ceniter of the cavity. With an errmittance of30 inmm-rad., the size of the waist in both X and Ydirections was less then 1 cm. After being modu-lated by the RP field of the bunching cavity, thebeam was focussed againi by a pair of QD doublets andthen drifted downwards to a fast response target,whtich was set 4.129 m and 1.904 m away from the cen-ter of the cavity in two cases. A 90 degree doublefocusing analyzing magnet with a radius of curvatureof 250 mm was set before the target to caliberate theamplitude of energy modulation by the buncher or tomeasure the energy distribution of the CW incidentbeam when the buncher was off. The energy dispersionof the irncident beam depended upon the performance ofthe ion source, typically about 2x1053. The layoutof the experiment is shown in fig. 1.

The bunching cavity consists of two stronglycoupled Helices tuned to 28.4 MHZ, each has a radiugof 40 mrn, a pitch of 5.65 mm and a length of 170 mmWith a resonably high bare impedenk e of 22 Meg-Ohm/m,the cavity can be run in a wide ran,ge of field levelsat a comparatively low power conswuiption. The ampli-tude of the energy modulation is m asured in terms ofC., the fractional enrergy change,,E/hEi=6e*SinTc

4o0KVInjec-tor

_ QD(QuadrupoleLDoublet)

_I- SI Steeringa}naet

Bending SMagnet

QDI _+ Fast

Fluorescent lTargetScreen S --

_ FaradyCup7T a

Fig. 1 . The layout of the experiment

001 8-9499/83/0400-1524$01.00O@ 1983 IEEE

1524

1525

(Ei mean energy of the incident beam,95c the RFphase seen by the particle at the centre of thecavity.) As the operating frequency of the cavitywas rather low, the diopersion in modulation causedby the radial inhemogeneity of the Ez component wouldbe less than 2x10-4 for a beam having a diameter lessthan 1 cm. .

The structure of a fast response target7 isshown schematically in fig.2. A biased tungsten gridis set infront of the collector to schield off thedisplacement current induced by the ions beforeentering the target. With a positive bias of 250 V,secondary electrons emitted at the collector are col-lected by the grid and results in amplified signalsof the ion pulse current. An effective 2-3 fold in-crease in primary beam current of protons is obtain-ed under such condition. The rise time of the tar-get-cable assembly measured by a TDR is 0.2 ns andthe output impedence of it is 50 Ohm. The outputsignals were displayed on a Tektronix 485 oscillo-scope with a rise time of 1 ns.

Bunched Waveforms

A family of bunched waveform photos illustrat-ing the change of the beam pulse shape with succes-sive increase in RF power input P to the Helicesloaded cavity is given in fig. 3. The experimentwas carried out with a 250 Kev proton beam having amean target current of approximately 50)ua. Thepower input to the cavity was indicated by a signalfrom a probe. It was caliberated by the temperaturerise of the cavity cooling water. The bunchinglength in first case was 4.129 m.

In order to estimate the change of the bunchedwaveforms with the power input, half width (FWHM)and pulse height are plotted against the longitudi-nal focusing power L/F in Fig. 4, where the timefocus F (see next section) is inversely proportionalto the amplitude of modulation Em, and L the fixedbunching length. It is shown that the half widthdrops first with L/F to a broad minimum of 1.4 ns atL/FW1-1.22 (P=5.6-8.4 W). Taking the effect-offinite rise time of the measuring system tr=1.02 nsin-to account, it is estimated that the incidentbeam was compressed to bursts having a half width of1 ns. The maximum of the pulse height ip appearsnear L/F-=1.26, and the maximum peak to incident DCcurrent ratio is about 14.5:1. The beam appears tobe over bunched immediate-ly after the maximum andthe peak starts splitting into double peak forms,which refer to dashed lines on the figure. The se-paration of peaks increses with L/F, while the hei-ght of the peaks drops with it. On the other hand,the valley to peak ratio R increases with L/F firstand then tends to saturation. It is very interest-ing to notice that at L/F=4.73 (P=126 W) the peakseparation equals to the period of the RF field, and

Ii

~~~.--. ~ " - ...----

_ _ _ _ . TL _(a) P=EB.4 W

(c) P=25 W (d) P50 W

. ....t _..

(e) P=100 W (f) P-126 W

Fig. 3- Photos of bunched waveforms

overlapping of peaks between neighbouring periodstakes place, consequently instead of double peak a

combined single peak appears. As the power in--put increases further this kind of combined peak ap-

pears periodically.Families of bunched waveforms similar to above

were obtained for three other cases, i.e. Ei=25OKev,L=1.904 m; Ej=35OKev, L=4.129 m; Ei=35OKev,I=1.9O4 m.

In each case a curve similar to that of figure 4 was

obtained. Shortest half width of tm=1.06 ns was re-

corded at P=66.8 W in the last case. This means we

might have got bursts having a half width less than0.5 ns, unfortunately we were not able to confirmthis without a wider bandwidth oscilloscope at thattime.

The effect of the quadrupole on the bunchedwaveform was observed during the experiment. Fbr an

over bunched beam, the height of one peak could be

altered with respect to the other by adjusting the

Fig. 4. Waveform parameters versus L/F

A

.. N4.N._'

Fig. 2. The fast taxget assembly

1526

focusing power of the matching quadrupole (Fig. 5).In an extreme case of high power input, it was evenpossible to cut off one of the peaks by deliberatelymismatching the quadrupole lens. Actually, due tothe coupling be tween transverse and longi tudinalmotions inside the cavity, the transverse entittanceof the beam becomes phase dependent after bunching,and this might explain the phenomena described above.It might be possible to make use of this effect tolimit the phase range in a bunched beam. This wouldbe similar to the function of a Dee gap and associat-ed vertical phase selective slits assembly in thecentral region of a Cyclotron.

Analysis of Waveforms

An ideal linear buncr,ing system, characterizedby the time focus F=Vi/7rwmfo (vi is the mean velo-city of the incident beam,fo is the operating fre-quency), compresses a CW beam to a longitidinalwaist at its focal point, where the bunched pulse isin a rectengular form having a full width of

, = eom - F/v;V(1f)&om in above is the initial efier,;y dispersion of thebeam.

Ebr a pratical bunching system using sine wave,however, the nonlinear effect must be taken intoaccount. It is for this purpose a theory, whichdeduces the bunched waveform directly from the phaseplot in the ti,.e-energy space, has been developed.

In case of weak modulation, the bunching cavitycall be taken effectively as a single gap buncher atthe center of the cavity8. Those particles whichsee a RF phase of g;c at the gap will arrive at thetarget at a relative phase of Sp(with respect tothose with 9c=o) after drifting a distance of L.

where g is the fractional energy modulation, 6=6o+£fmSin5Pc (eo=O.Ei/Ei initial deviation to the meanenergy).

The area occupied by the bunched particles isbounded by two curves e1 ( 9 ).E2 (99 ), which can bewritten as following if considering 641, FO=±m:

e~ ~ ~ C(?~mils+ L-- r.5) 0oEs(e)~Emsn (;P+F Em (3)m=

Suppose the ions distribute uniformly in the(TC,&) space with a constant density jp then thenumber of those ions lying in (9, 9'+dq' is propor-tinal to the differential area occupied. HencedN=.p-df EA,(CP), where TAr(9) is the sum of theheight ofiall area elements along g direction (re-fer to figure 6), and thus the instaneous intensityof the beam will be:

(9P)= e d N = ecpwy , (97)For an incident beam with an intensity of io. obvi-osly Zt6;(g;)=2Fom, so

1-_

L(a) KL1=0-457;YKL2=0.185

. ...

,

.~

I

(b) KLi=0.457;KL2=0.355Fig. 5. The effect of OD on bunched waveforms

Fig. 6. Phase plot il. ( 1,E) space

(SO)(v')(4)) 2 &;OnrTheoretical bunched waveforms versus L/F were

calculated on a computer according to (2)-(4). Theresults are presented in a graphical form in fig.7a. The waveforms thus calculated are well consis-tent with the experiment though they are quite dif-ferent from those calculated from the existing onedimensional theory, which predicts a infinite peakof zero width at L=F and infinite double peaks forany L>F(see fig. 7b). There are three more pointsworth mentioning:

1) The calculated half widthCb(FWHM) depends onboth time focusing power and initial energy disper-sion. It gets down to a minimum at L/F6=1, where itcan be expressed effectively byrb= e, -L/v . Itappears that a great number of particlles concentrat-ed in a small interval of it'il&0ie,,1, in the linearregion, so that the effect of nonlinearity on b ismuch less than that estimated by9

2) The existence of initial dispersion makes themaximum of the pulse height occur at a higher powerlevel than that need for obtaining a minimum halfwidth, and meanwhile it makes the maximum peak afinite height pulse. The maximum peak to initialDC current ratio can be estimated by:

bpm - COS[( t +0.85 T LL0 4m LAn-)m ,,J'' 7Y (tbF4 ( 5

where the term (L/F)m satisfies

[(tF)m - I )J - Cos~(T') = XT (6)which means two boundary curves are symmetricallytangential to the e axis in the ( 9', & ) space.

3) The double peak form occurs immediately afterthe peak maximum, and the separation of the peaksalso depends upon both L/F and 6oi. Actually it canbe given by:

ITF)121 - Cos'(F)_ .L J>O ('7)'Ld increases with L/F, and any time if 'Cd=nT holds(n integer, T period of the RF field), overlappingof peaks across n periods takes place.

To compare the theoretical waveforms with theexperimental results, the frequency response of themeasuring system was taken into account. Accordingto 3 the frequency response G may be written as:

CT=Sin(H1 gr f,- r)/(H 7r fo-tr,-) (8)where .fo-.tr=0.09 for our system, and H is the har-monic nuwmber. Actually harmonics up to H=30 wereincluded in the calculation. The interesting pointgot from the response calculation is that the effectof the finite rise time on the half wicth can readilybe estimated approximately by the e-.ression:

'I I I I

....'AI A

...

M.... 7E,

i....I....I ....

I II .1 II

..- 10AWi 114.ti+jE=_

(a) by Two dimensional theory

(b) One dimensional theory

1?ig. 7. Calculated waveforms

(ZTb2 + C.2 )1/2where 'm is the measured value of 'Cb.

A set of parameters of the bunched waveformswere calculated according to the foregoing analysis.A part of them are listed in table 1 and 2. The ini-tial dispersion used in the calculation was derivedfrom the measured value of tb according to (1) and(9). As Tb is insensitive to slow change of the meanenergy, the value derived in all cases are slightlyless than that measured by the analyzing magnet.

Conc lusions

It has been shown that short bursts of 1 ns(FWiM) can be produced cornveniently by Helices load-ed cavity. The characteristics of bunched waveformsversus RF field level of the cavity have been pre-sented with beam ener,y and bunching length as varia-bles. In comparing with the experimental waveforms,the theory developed in (9', 6) space seems to givemuch better results than that given by one dimension-al theory.

1527Tab le 1

ii=250kev, L,4.129m, £om=1.64x10 5

P(W) L/F T Tb,d(ns) n

8.4 1.22 1 .40 1.41 1.00 1.0015 1.64 3.40 3.31 0.58 0.54 0.30 0.3625 2.11 7.80 7.81 0.42 0.43 0.56 0.5649 2.96 16.5 16.5 0.5 2 0.33 0.65 0.68

100 4.22 30.7 30.1 0.25 0.24 0.74 0o73126 4.74 35.2 35o7

Table 2ij-350Ke'v_l1.904,9_ ,=1 .4x1O3

P(W) L/F bd(s)p b

____ ~~a b a b

66.8 1.10 1.06 1.07 1.00 1.00178.9 1.80 5.20 5.10 0.417 0.46285.7 2.27 10.0 10.0 0.40 0.38417.5 2.75 15.0 14.5 0.35 0.32a-measuredl dataq, b-calculated data.

The authors wish to thank Professor F. C. Yufor his erncourangement and advice. Thanks are alsodue to Professor J.M. Hu for his valuable sugges-tions. We are also indebted to Mr. X. J. Zhang, Mr.Z.Z. Ban, and Mr. P. L. he for their help during theexperiment.

Re ferences

1. F. E. Whiteway, A.W.R.E. Report No. 0-12/61(1961).

2. J. H. Anderson, N.I.M., 41 (1966) 30.3. L. h. Evans, D1. J. Warner, Proc. Proton Linear

Accelerators conference (1972) 349.4. L. M. Bollinger et. al., IEEE. Trans. NS-22,

3 (1975) 114.5. Chen Chia-erh, Proc. of the Particle Accelerators

Conference, May 1979, Chengdu, China, (1980) 75.6. Chen Chia-erh et al, "Status Report of a Helix

Booster" Paper submitted to the 1980 NationalParticle Accelerators Conference, Shanghai,China,October 20 1980.

7. Guo Zhi-yu, M. A. Thesis of Peking Univ., October1981.

8. Chen Chia-erh, Internal Memo, June 1976.9. S. J. Skorka, Proc. of the 3ed International

Conference on Electrostatic Accelerator Techno-logy, (1981) 130.