New approach toward optimized resonant slow-extraction

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Nuclear Instruments and Methods in Physics Research A 515 (2003) 853–861

*Corresp

Sciences, D

4-9-1 Anag

+81-43-251

E-mail a

0168-9002/$

doi:10.1016

New approach toward optimized resonant slow-extraction

T. Furukawaa,*, K. Nodab, M. Muramatsub, T. Uesugib, S. Shibuyab,H. Kawaia, E. Takadab, S. Yamadab

aGraduate School of Science and Technology, Chiba University, Yayoi-cho, Inage-ku, Chiba 263-8522, JapanbNational Institute of Radiological Sciences, Anagawa, Inage-ku, Chiba 263-8555, Japan

Received 19 June 2003; accepted 17 July 2003

Abstract

A resonant slow-extraction method from synchrotron rings has been successfully developed in order to deliver a

beam for a period of over several seconds. In the resonant slow-extraction method, an optimization of the parameters is

necessary in order to keep the beam size and position constant during the extraction for sufficient use of the extracted

beam. For this purpose, a simple method to measure the outgoing separatrix was proposed and verified at the HIMAC

synchrotron. In this method, two tantalum rods each with diameter of 1mm are used as internal probes located near the

extraction channel. By observing the extracted beam under the rods inserted into the ring, the outgoing separatrix can

be measured. This technique will significantly contribute to the operation of a synchrotron employing resonant slow-

extraction.

r 2003 Elsevier B.V. All rights reserved.

PACS: 29.20.Lq

Keywords: Resonant slow-extraction; Synchrotron; Separatrix; RF-knockout

1. Introduction

The resonant slow-extraction from a synchro-tron ring [1,2] has been developed in order todeliver a beam for a period of over several secondsfor physics experiments or other applications. Inresonant slow-extraction from a synchrotron, ithas usually been required to keep the beamposition and size constant during extraction. An

onding author. National Institute of Radiological

epartment of Accelerator Physics and Engineering,

awa, Inage-ku, Chiba-shi 263-8555, Japan. Tel.:

-2111; fax: +81-43-251-1480.

ddress: t [email protected] (T. Furukawa).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.07.036

extraction efficiency as high as possible is alsonecessary to suppress the radiation at the extrac-tion channel. For these purposes, it is necessary tocontrol the separatrix by adjusting the latticeparameters. However, there are some difficultiesto optimize all of the lattice parameters, whichinclude a nonlinearity created by unwanted multi-pole fields. Thus, a quick and easy method tomeasure the actual separatrix in phase space willmake it much easier to optimize the parameters forresonant slow-extraction. Further, such a techni-que will significantly contribute to the operation ofa multipurpose synchrotron, like the Heavy IonMedical Accelerator in Chiba (HIMAC) [3,4],because they should supply beams with various

d.

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Rod 1 Rod 2

Synchrotron ring

S1

X' X'

XX

S2

Fig. 1. Schematic diagram of the method with two rods. Rod1

produces ‘‘blanks’’ for each outgoing separatrix in the phase

space at s1 and s2.

T. Furukawa et al. / Nuclear Instruments and Methods in Physics Research A 515 (2003) 853–861854

conditions. In the case of HIMAC, it has beenrequired to supply ion beams, not only for iontherapy, but also for a wide-range of fields, such asbiological and physics experiments, using variousion species from H to Xe. Thus, two kinds ofslow-extraction methods have been developedand utilized at the HIMAC synchrotron [5]:third-order resonant slow-extraction (ordinaryslow-extraction) and that with RF-knockout(RF-knockout extraction) [6,7].It is well-known that turn-by-turn measure-

ments of the beam position by using a couple ofelectrostatic pickups and a fast kicker magnet candiagnose the particle motion in phase space, whichis a strong tool to investigate any nonlinearity inthe ring [8,9]. In this method, the beam size shouldbe much smaller compared with the separatrix size.Thus, additional devices, such as an electroncooler, will be necessary to reduce the beam size,because the beam size after acceleration is usuallycomparable to the size of the separatrix under thecondition of extraction in the ring.In order to measure the outgoing separatrix

under such a situation, an easier method using twothin rods has been proposed and verified at theHIMAC synchrotron. In this method, since it isnecessary to extract the beam from the constantseparatrix, RF-knockout extraction was adopted.This method can measure only one of the outgoingseparatrix for extraction. However, it bringssufficient information to optimize the latticeparameters for extraction.We describe the details of the experimental and

simulation results in this paper.

2. Measurement method of an outgoing separatrix

2.1. Principle of the method

This method can measure the outgoing separa-trix in phase space by using two thin rods that arelocated separately in the ring, as shown in Fig. 1.In order to measure the outgoing separatrix, it isnecessary to extract the beam from the constantseparatrix during the measurement. Therefore, theRF-knockout extraction method is employed. Onecould produce a ‘‘blank’’ in the outgoing separa-

trix by inserting a rod into the ring, if the particlehits the rod, it is to be lost from the ring. Byinserting the rod, further, some blanks would beproduced where the particles hit the rod, whichwould go along with the outgoing separatrix.Utilizing these blanks that originate with the rod, ameasurement of the outgoing separatrix is carriedout as follows:Firstly, rod1 at s1, as shown in Fig. 1, should be

inserted and fixed at x ¼ x1: Secondly, it ispossible to search for a shadow of rod1 at s2 bychanging the horizontal position of the second rod(rod2 in Fig. 1) at every operation cycle of thesynchrotron. This search is carried out by measur-ing the extracted beam intensity, because thedecrease of the extracted intensity is to beminimized when rod2 is just in the blank ofthe outgoing separatrix. In the case of Fig. 1, theextracted intensity will have three peaks fordifferent positions of rod2, because of threeblanks. We can estimate that the shadow of rod1at s2 is the inside most peak of the intensity. Withthe transfer matrix between two positions of eachrod, we can estimate the angle of the particles onthe outgoing separatrix at s1. As a result, we canmeasure one point on the outgoing separatrix inphase space. After repeating the above measure-ment for each position of rod1, we can finallyobtain the outgoing separatrix in phase space. Foroptimization of ordinary slow-extraction, the out-going separatrix should be measured for differentT1 (delay time of the measurement) by keeping theseparatrix constant, as shown in Fig. 2.

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BM

QF

SXFr,SXDr

BumpMag.

ESD

RF-kicker

Measurement

T1 T2

Fig. 2. Operation pattern during a single flattop. From the

upper, the bending magnet (BM), the quadrupole magnet (QF),

the separatrix exciters (SXFr, SXDr), the bump magnets

(Bump. Mag), the electrostatic deflector (ESD), the transverse

RF field (RF-Kicker). The dashed line shows the normal

operation of the extraction. The solid line shows the operation

for the measurement.

100806040200

0

1

2

3

4

5

x [mm]

s[m

]

ES

D2

ESD

1Q

D

rod2

rod1

Septum Magnet

Fig. 3. Extraction configuration of the HIMAC synchrotron

including two rods with both the trajectories of the extracted

beam and circulating beam.

T. Furukawa et al. / Nuclear Instruments and Methods in Physics Research A 515 (2003) 853–861 855

2.2. Simulation of the measurement

In order to verify the feasibility of the proposedmethod, a simulation of the measurement wascarried out using the particle-tracking code [10]. Inthe simulation, an individual sample particle istraced to the end, just as it proceeds in a realconfiguration of the ring. Further, two thin rodsare installed for the simulation of the measure-ment. The configurations of the extraction includ-ing two rods are shown in Fig. 3. The HIMACsynchrotron has two successive electrostatic de-flectors (ESD) as an extraction channel, ESD1 and

ESD2. In order to easily obtain the outgoingseparatrix at the entrance of the extractionchannel, the first rod (rod1) and the second rod(rod2) are set at the entrance of ESD1 and at theexit of ESD2, respectively, because there is onlythe drift space of 2.9m between s1 and s2 alongwith the reference orbit of the ring. The horizontalphase advance between s1 and s2 is estimated to be0.41 rad (=23.4 deg) under the condition ofextraction. The rod size is 1.0mm in diameterand 45mm in height to cover the vertical beamsize. When a particle hits the rod, this particle isassumed to be lost from the ring. The particles areextracted from the constant separatrix by thehorizontal RF-field under the monochromaticcoasting beam. The main parameters for thesimulation are summarized in Table 1. Fig. 4(a)and (b) show the separatrix at s1 and s2,respectively, under this condition without therods.The outgoing separatrix at s2 is shown in

Fig. 5(a), when rod1 is fixed at x1 ¼ 71:0mm.Under the same initial conditions, the extractedintensity and the loss at rod2 are calculated as afunction of the horizontal position of rod2. Theresult is shown in Fig. 5(b). We can estimatethe shadow of rod1 at s2 from Fig. 5(b), because

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(b)

(a)

]mx [

]adr

x' [

080.040.04.00-

010.

50.00

0

05.0-0

10.-0

x [m]

]darx'

[

080.040.04.00-

010.

50.00

0

05.0-0

10.-0

Fig. 4. Simulation results of the separatrix: (a) at s1, (b) at s2.

0.040 0.044 0.048 0.052

-0.007

-0.008

-0.009

-0.010

x [m]

x[r

ad]

200

150

100

50

0ex

trac

ted

inte

nsit

y(a

rb.u

nit)

200

150

100

50

00.044 0.046 0.048 0.050 0.052

position of rod2 [m]

intensity loss at rod2

(a)

(b)

loss

at

rod2

(ar

b.un

it)

Fig. 5. Simulation result for the case of the rod1 at 76mm: (a)

separatrix at s2, (b) intensity spectrum for different position of

rod2.

Table 1

Main parameters of the simulation

Energy of C6+ 400.0MeV/u

Tune (Qx/Qy) 3.684/3.130

Revolution frequency 1.653MHz

Frequency of RF kicker 1.126MHz

Full bandwidth of FM 14kHz

Repetition frequency of FM 977.5Hz

Max Kick angle of RF kicker 2.0 mrad

Field strength of sextupole field

K2 (SXFr1/2) 1.644m�3

K2 (SXDr1/2) 1.978m�3

K2 ¼ B00=ðBrÞ:


the extracted intensity is to be decreased whenrod2 is not located just inside the shadow of rod1.A certain position of rod2, where the extractedintensity has a peak pointed by the arrow inFig. 5(b), corresponds to the shadow of rod1

at s2. This value is estimated to be x2 ¼ 45:9mm.It should be noted that the beam loss at rod2is not to be zero, even when rod2 is just insidethe shadow of rod1, because the separatrix isslightly rotated between s1 and s2, as shown inFig. 4. Using this value, we can estimate thephase-space position on the outgoing separatrixas (71.0mm, �8.67mrad) at s1. Further, theresults are calculated in a similar way for bothcases of rod1 at x1 ¼ 73:0 and 76.0mm, respec-tively. We can estimate two points on the out-going separatrix additionally as (73.0mm,�8.88mrad) and (76.0mm, �9.12mrad) at s1.Consequently, it is clearly observed from Fig. 6that the outgoing separatrix at s1 could be wellreproduced.As shown in Fig. 6, on the other hand, it should

be noted that the measured point near the unstablefixed-point slightly deviates upwards from theoutgoing separatrix. The reason can be clearlyexplained by the difference of the turn-separationcaused by the difference of the initial position inphase space. The spiral step in the normalizedphase space after three turns at the rod can be

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-0.01

-0.008

-0.006

0.05 0.06 0.07 0.08

x' [

rad]

x [mm]

Fig. 6. Simulation result of the measurement. The measured

points in the simulation (squares) are almost onto the outgoing

separatrix.0.015 0.016 0.017 0.018

0.005

0.006

0.007

0.008

(c)(b)

X'

X

(a)

Fig. 7. Difference of the spiral step for each trajectory outside

of the separatrix obtained by analytical formulae.


written as

dX3 turn ¼ eX 00 þ

34

SfðX 20 � X 02

0 Þ sinð3DmÞ

þ 2X0X00 cosð3DmÞg

dX 03 turn ¼ � eX0 þ 3

4SfðX 2

0 � X 020 Þ cosð3DmÞ

� 2X0X00 cosð3DmÞg

where Dm is the phase advance from the separatrixexciter to the rod and S the normalized sextupolestrength for the separatrix excitation. From theseequations, we can estimate the turn-separation atthe rod, as shown in Fig. 7. For five particles withthe same X0 and different X 0

0; their positions afterthree turns are plotted with the trajectory of theoutgoing separatrix. The turn-separation ðdX3 turnÞincreases with increasing initial angle ðX 0

0Þ: Whenthe rod (hatched area in Fig. 7) is set near the fixedpoint, some of the particles, having a relativelysmaller dX3 turn; cannot jump across the rod in thephase space because of their small turn-separation.For example, if the rod is set as shown in Fig. 7, allthe particles on the phase-space trajectory (c)would hit the rod, but not for trajectories (a) and(b). As a result, it can be estimated that themeasured point near the unstable fixed-pointslightly deviates upwards from the outgoingseparatrix. As a result of a simulation, as shownin Fig. 6, however, the deviation of the point isestimated to be 0.14mrad at maximum. Therefore,this might not disturb the measured outgoingseparatrix so much, but should be noted concern-ing the above results.

Since the width of the outgoing separatrixdepends on the amplitude of the horizontal RF-field, we can obtain a relatively smaller deviationof the point by reducing the RF-knockoutamplitude. In the measurement, however, all ofthe particles should be spilled out from theseparatrices during the flattop by the transverseRF-field in order to equalize the momentumdistribution of the extracted beam and that ofthe beam in the ring. This procedure is necessary inorder not to misestimate the actual outgoingseparatrix, because the momentum distributionand the center of the extracted beam depend on thehorizontal chromaticity in the RF-knockout ex-traction [11]. Thus, the amplitude of the transverseRF-field cannot be reduced by less than thethreshold of the amplitude to extract all theparticles from the separatrix. In this simulation,the amplitude is larger than the threshold, becauseall of the particles have been finally lost from thering.In this method, particular attention should be

given to the particles, which hit the rod. The designof the rod should be carried out for these particlesto be lost from the ring. Using a tantalum rod witha diameter of 1mm, the momentum loss and theangle of the multiple scattering were calculated fortypical ion species and energies at HIMAC, as

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Table 2

Effect of a tantalum rod 1mm for the typical beam at the

HIMAC synchrotron

Ion

species

Kinetic energy

(MeV/u)

Energy lossa

(%)

Scattering

angle at s(mrad)

He2+ 230 �0.9 6.25

C6+ 140 �5.7 7.55

290 �1.9 5.77

400 �1.3 5.23

Ne10+ 600 �1.2 4.70

Ar18+ 650 �1.8 4.16

Fe24+ 500 �3.1 4.21

aEnergy loss is presented as momentum deviation, Dp/p.


summarized in Table 2, by the analytical formulae[12]. From this result, the thickness of the rod issufficient to induce a loss of the particles foralmost all ion species and energies at the HIMACsynchrotron. In order to verify whether theparticles, which hit the rod, can be lost from thering or not, the process of the beam loss in the ringwas simulated in respect of the energy loss andmultiple scattering by the tantalum rod with adiameter of 1mm. For the case of fully strippedcarbon ions with an energy of 400MeV/u at theHIMAC synchrotron, it was verified that almostall of the particles (more than 90%) were lost fromthe ring after hitting the rod. Thus, an experimentfor fully stripped carbon ions with an energy of400MeV/u are carried out.

3. Experimental results and discussion

3.1. Experimental setup

The experimental condition is similar to thesimulation as summarized in Table 1. In order tomeasure the outgoing separatrix, two tantalumrods are set at the extraction channel of theHIMAC synchrotron just as the simulation shownin Fig. 3. These rods can move horizontally with aprecision of 0.1mm. The intensity and profile of

the extracted beam were measured by the existingbeam-monitoring system [13] at the high-energybeam transport (HEBT) line. These monitorscould be gated only for measuring time T2 (inFig. 2) during the flattop. The extracted beamintensity was measured by averaging over 10pulses in the measurement. At the HIMACsynchrotron, the flattop duration is kept at around2 s under an operation period of 3.3 s to providecarbon ions with an energy of 400MeV/u. Theoperation pattern of the measurement during asingle flattop is schematically shown in Fig. 2. Thetransverse RF field is applied along with the beamgate signal. In the measurement, the beam wasdebunched after the acceleration, so as to have atime-independent separatrix [10,11] in the RF-knockout extraction. When we measured theoutgoing separatrix for different momentum, wechanged the RF frequency for acceleration whileall magnetic parameters were fixed.Using a DC Current Transformer (DCCT), it

was verified for each measurement that all of theaccelerated particles were lost from the ring duringa single flattop. Since all of the particles wereextracted from the ring, or lost in the ring afterhitting the rod, it can be estimated that theextracted beam has the same momentum distribu-tion in the ring. Further, in the ring themomentum distribution was measured to bearound 0.04% at s by observing the Schottkyspectrum.

3.2. Measurement of the outgoing separatrix

Using the proposed method, the outgoingseparatrix for each momentum of 0.3%, 0.0%and �0.3%, were measured, respectively, at theHIMAC synchrotron. The experimental results areshown in Fig. 8. In this measurement, the delaytime of the measurement T1 (in Fig. 2) was setto be 0 s. The error of the measured angle, whichis shown in Fig. 8, was estimated to be 70.1mradat s originated with the position error of therod (sx ¼ 70:1mm) and the length error betweentwo rods (sL ¼ 70:3mm). The dependence ofqthe extracted intensity on the horizontal positionof rod2 is typically shown in Fig. 9 for threedifferent positions of rod1 as 71, 73 and 76mm. As

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46 48 50 52 540.00E+000

2.00E+008

4.00E+008

6.00E+008

8.00E+008

1.00E+009

extr

acte

d in

ten

sity

[p

pp

]

positionof rod2 [mm]

76mm 73mm 71mm

Fig. 9. Dependency of the extracted intensity on the horizontal

position of rod2 for 3 different positions of rod1 as 71

(triangles), 73 (circles) and 76mm (squares). Each arrow points

the shadow of rod1 at s2.

-10

-9

-8

-7

-6

-5

50 55 60 65 70 75 80

x' [

mra

d]

x [mm]

Fig. 8. Outgoing separatrix for each momentum of �0.3%,0.0% and 0.3% from the bottom, as a result of the experiment.

-30 -20 -10 0 10 20 30-20

-10

0

10

20

-30 -20 -10 0 10 20 300

10

20

30

Cou

nts

(arb

. uni

t)

x [mm]

-30 -20 -10 0 10 20 300

10

20

30

(c)

(b)

Cou

nts

(arb

. uni

t)

x [mm]

(a)

20

30

Cou

nts

rb. u

nit)

x' [m

rad]

x [mm]


rod1 was inserted into the ring, the extractedintensity relatively decreased, because the spiralstep decreased as the rod became close to theunstable fixed point. In Fig. 9, each arrow pointsto the shadow of the rod1 at s2, where theextracted intensity has a peak, for 3 differentpositions of rod1. These results are consistent with

(d)-30 -20 -10 0 10 20 30

0

10(a

x [mm]

Fig. 10. Extracted beam at the HEBT profile monitor: (a)

phase-space distribution obtained by the simulation, (b)

measured profile without both the rods, (c) measured profile

with rod1 at 73mm and rod2 set outside the ring, (d) measured

profile with rod1 set at 73mm and rod2 at 47.4mm.

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the simulation results, as typically shown in Fig. 5.In order to optimize the ordinary slow extraction,the delay time of measurement T1 (in Fig. 2) waschanged to 0.5 and 1.0 s. From the result, it can beestimated that the extracted beam position in thephase space at the entrance of the ESD s1 isslightly different compared with the case ofT1 ¼ 0 s (shown in Fig. 8). After the parametersof the dynamic bump for the extraction wereoptimized in order to equalize the measuredoutgoing separatrix between T1 ¼ 0; 0.5 and1.0 s, it was verified that the optimized slowextraction could supply a beam with a constantsize and position during a single flattop.Further, measuring the horizontal profile of

the extracted beam, information was obtainedabout the blank in the extracted beam (part ofthe outgoing separatrix) made by the rod. Inthe measurement, we chose a profile monitor witha horizontal phase advance of 136+720 deg atHEBT. Since the extracted beam was almostparallel to the x-axis in phase space at thisprofile-monitor position, we could easily observethe blank in the extracted beam. The phase-space distribution at the profile monitor wasestimated by simulation, as shown in Fig. 10(a).The measured profile without both rods isshown in Fig. 10(b). Fig. 10(c) shows the profilewith rod1 at 73.0mm without rod2. Additionally,Fig. 10(d) shows the profile after inserting rod2at 47.4mm. Comparing between Fig. 10(c) and(d), it seems, there is a small difference. Whenthe position of the rod was changed by only0.2mm, however, it was clearly observed thatthe profile shape was different in each measure-ment. Therefore, we can verify the shadow ofrod1 at s2 not only by the extracted intensitymeasurement, but also by the horizontal profilemeasurement.On the other hand, it should be noted that this

method could not measure an outgoing separatrixperfectly under the situation, as mentioned below.When the maximum turn-separation was largerthan the gap of the ESD at the entrance of theESD, there was frequently no change in theextracted beam, even while inserting the rod,because the rod could not produce a ‘‘blank’’ inthe extracted beam.

4. Conclusion

A simple method to measure the outgoingseparatrix using two tantalum rods was proposedand verified at the HIMAC synchrotron. Theseparatrix was kept constant with constant latticeparameters during the measurement. Further, thetechnique of RF-knockout extraction was requiredto extract the beam from the constant separatrix.By measuring the extracted beam intensity byinserting two rods into the ring, the intensityspectrum for different positions of rod2 could beobserved for each position of rod1. As a result,finally, one of the outgoing separatrix for theextraction could be estimated. This provided suf-ficient information to optimize the lattice para-meters for the extraction. Therefore, this techniquewill much contribute to the operation of synchro-trons employing resonant slow-extraction.

Acknowledgements

The authors would like to express their thanks tothe members of Accelerator Engineering Corpora-tion for their skilful operation of the HIMACaccelerator complex. They are also grateful to theother members of the Department of AcceleratorPhysics and Engineering at NIRS for warm support.This work was carried out as part of the ResearchProject with Heavy Ions at NIRS-HIMAC.

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New approach toward optimized resonant slow-extraction