JAERI-Conf 95-021

PB03
The Effect of the Aberration on the Emittance Growth Revealedin Design Study of LEBT using Magnetic Lenses for the JHP RFQ
Satoshi Fujimura, Akira Ueno and Yoshishige Yamazaki
National Laboratory for High Energy Physics, KEK
Graduate University for Advanced Studies
Abstract
1-1 Oho, Tsukuba-shi, 1baraki-ken, 305, Japan
if this is the reason for the emittance growth. At first, of course,
The growth of effective emittances in a low energy beam
we have to find the reason for the emittance growth in the magnetic
lenses. For this purpose we performed beam-simulation studies
transport (LEBT) is one of the most important problems to besolved for the high-energy, high-intensity proton linacs, in theon magnetic-lens LEBTs in the realistic magnetic field calculated
by using the computer program POISSON or MAFIA [5,6].
high-energy part ofwhich the beam loss should be extremely
reduced. Although a variety of LEBTs using electrostatic lenses
Design Beam Parameters and Preliminary Design Study
were examined at Superconducting Super Collider Laboratory,large effective emittance growth due to lens aberrations was
The design beam parameters at the entrance and exit ofobserved in almost of them. Therefore, we performed design
the LEBT are respectively listed in Table 1. These parametersstudies on LEBTs with magnetic lenses in order to inject a proton
were estimated or assumed, based upon the beam-simulation
beam into a 432-MHz radio frequency quadrupole linac developed
results in the RFQ and the measured beam parameters extracted
for the Japanese Hadron Project. The smallest effective emittancefrom a volume production H- ion source at KEK [7]. It is assumed
growth (no growth in RMS emittance and small growth of lessthan 15% in 100% emittance) was obtained in the LEBT withthat the particles are distributed with the KV -distribution at thetwo short, strong solenoid magnets (SMs). The LEBT with two
entrance of the LEBT (the particle distribution at the exit of thetriplet quadrupole magnets gave rise to the larger effective
ion source (IS) is not well-known). It is thus possible to study theemittance growth than that with two SMs, even in the case that
effect of the lens aberrations on the emittance growth, separately
the beam optics was simulated in the ideal quadrupole field withoutfrom the non-linear space charge effect, since the particles withhigher-order components under the linear space charge force.
the KV -distribution (uniform distribution in real space) exert only
the linear space-charge defocusing force. If the particles are nonIntroduction
uniformly distributed, the stronger focusing force than that for
the KV -distribution is required (almost the same focusing force
required for a 40 rnA beam with the KV-distribution is necessary
A 432-MHz, radio-frequency quadrupole (RFQ) linac was·developed as a pre-injector for the high-intensity proton linac ofin order to focus a 20 rnA beam with the Gaussian-distribution).
Therefore, the: design peak beam intensity of the LEBT is chosen
the Japanese Hadron Project (JHP) [1]. A variety of low-energy
beam transports (LEBTs) for RFQs with resonant frequencies
to be twice as high as the required value of the JHP linac.
around 400 MHz have been studied extensively at
As the first step, three LEBTs were preliminarily designed
Superconducting Super Collider Laboratory (SSCL) and Los
by using the computer program TRACE [8]. (With TRACE using
Alamos National Laboratory (LANL) [2,3,4]. LEBTs withlinear transfer matrices, we cannot obtain any information on theelectrostatic lenses were studied at SSCL, while those withlens aberration.) The design parameters of each magnet aremagnetic lenses at LANL. However, the results of theirsummarized in Table 2. The LEBT is schematically shown indevelopments are not satisfactory for our purpose, since theFig. 1. Two solenoid magnets are used in each of the first two
measured "effective emittances" at the exit of their LEBTs were
LEBTs, respectively referred to as BT-SM 1 and BT -SM2. Twoabout twice as high as that measured just after the ion sources.
triplet quadrupole magnets (TQMs) are used in the third LEBT,
It is perhaps necessary to present the definition ofreferred to as BT-TQM. The following four technical restrictions"effective emittance" and the reason why we introduce this. How
were imposed on these designs; ( 1) a distance of 90 mm between
to eliminate the loss of the high-intensity, high-energy beam isthe exit of the ion source (IS) and the first magnet is required forone of the most important issues for the design of the high-energy,
sufficient vacuum pumping speed just after the IS, (2) a distancehigh-intensity proton linacs, since the beam loss gives rise to theof 215 mm between the two magnets is necessary for the space ofradioactivity, eventually making the maintenance impossible.·
Table 2
From this point of view the mathematically defined emittance orParameters of magnets determined by using TRACE
even the root-mean-square (rms) emittance is not an appropriate
BT-SMlBT-SM2 BT-TQM
measure of the beam quality. In order to represent the quality of aMagnet length L (em)1020
20
LEBT we use the phase-space area surrounding the positions and
5.0
2.5
Magnet bore radius r ~x~r(em) 2.5
gradients of all the particles with the designed TWISS parameters
Field strength of 1st magnet 1.02 T
0.533 T
-10.2 T/mof the RFQ linac. We here refer to thus defined emittance as an
15.9T/meffective emittance. Of course the parameters of the LEBT are-10.2T/mhere adjusted to obtain the lowest effective emittance.
Field strength of 2nd magnet 1.15 T
0.573T
10.8T/m
Critically inspecting the experimental results at SSCL we-16.9T/mconcluded that the effective emittance grew in the LEBT with
10.8T/melectrostatic lenses mostly through their lens aberrations. Since it
54
Total length (em)7474
is difficult to reduce the aberration of electrostatic lens, we had to
2.5
Max. beam radius rbmx (em) 1.2
1.7
give up the use of the electrostatic lenses. On the other hand,
0.34
1.0
ratio of radii r bmx/r~x~r
0.48
although the effective emittance in the LEBT with magnetic lenses
at LANL was also increased (the reason is not clear from theirpapers), there is a hope of the improvement in this case, since one
may find the way to improve the aberration of the magnetic lenses,
TabellDesign beam parameters in the LEBT
Proton or H- beam energy
50 keY
Beam intensity
40 rnA
Particle distribution in transeverse emittance KV
4 times of normalized RMS emittance
1.5 1t mm•mrad
a. . =a. .=0.00
TWISS parameters at the entrance~XI =~y~=0.043

TWISS parameters at the exit

UXI=rl' =-1.05~xo =~Y0=0.0473
xo

yo

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Fig. l. Schematic view of the LEBTJAERI-Conf 95-021

the gate valve, beam diagnostics and vacuum pumping, (3) adistance of 35 mm between the second magnet and the entranceof the RFQ vane was already occupied by the end plate of the
RFQ, (4) the field strength should be smaller than the value
obtainable without significant saturation in iron yoke of SM or
TQM.
The BT -SM 1 was designed in such a way that the
maximum beam radius rbmx was minimized by using almost thestrongest magnetic field obtainable with normal-conducting
solenoid magnet. The BT -SM2 was studied in order to find out
the reason for the emittance growth observed at LANL. The total
length of BT -SM2 and the dimensions of the SMs in BT -SM2 aresimilar to those used in the LEBT developed at LANL. As seenfrom Table 2, the significant differences between BT-SMl and
BT -SM2 are in rbmx (1.2 em in BT-SMl and 1.7 em in BT-SM2)
and in the ratio of rbmx with the bore radius r 00, (rbmx/r00,=0.48 in
BT -SMl and 0.34 in BT -SM2). In the later section, we will
investigate which parameter of rbmx or rbmx/r00, has more effect on
the lens aberrations.
In general, quadrupole magnets are considered to havesmaller aberrations than SMs. This is the reason for studying the
BT-TQM. Since the convergence angle of the beam injected into
the RFQ is very large (about 80 mrad), the shorter quadrupole
magnets is preferable in order to reduce the beam radius. On theother hand, the thin quadrupole magnet has large higher-ordercomponents due to the fringing field. In order to compromise thesetwo conflicting requirements we set the two additional restrictions
upon TQM: ( 1) the minimum pole length of the quadrupole magnet
is equal to the bore diameter, (2) the minimum space between thetwo quadrupole magnets is equal to the bore radius.
Beam Optics Simulation in LEBTs
As described in the previous section, we expected thatthe lens aberrations play an important role in the growth of theeffective emittance. In order to study the effect of the lensaberrations, we have to simulate the trajectories of particles in therealistic field, for example the solenoid magnetic field calculatedwith POISSON. However, it takes very long time to optimize the
LEBT design by using the simulation program such as
BEAMPATH [9]. Therefore, we developed the program, referred
to as SHU in order to simulate the effect of the lens aberrations

more easily. With SHU, we trace the trajectories of particles, thepositions of which in the x-x' phase space are shown in Fig. 2 (noemittance in the y-y' phase space : y=y'=O for every particle),undergoing the realistic magnetic field. In SHU, the particles also
undergo the linear space charge force estimated only from theintensity and diameter of the beam (the axially symmetric beamwith the uniform particle distribution in the real space is assumed).
In order to justify the validity of the calculation using SHU, thesimulated results will be compared with those using BEAMP ATH.
The emittance profiles calculated with SHU at the exitsof BT-SMl, BT-SM2 and BT-TQM are shown in Fig. 3a), 3b)
and 3c), respectively. In these figures, the design emittance profiles
injected into the RFQ and the areas of the 100% emittances arealso shown with dotted lines. The 100% emittance surrounding
the simulated emittance profile has the same TWISS parameters
as those designed. The magnetic field distributions calculated with
POISSON were used in the simulations for BT-SMl and BTSM2. Since the current version of BEAMP ATH supports thesimulation only for the ideal quadrupole field (not for the arbitrary
3-dimensional field), the ideal quadrupole magnetic fields wereused in the simulations for BT-TQM in order to make possible
the comparison with the BEAMPATH results. The calculated
emittance profiles were matched with the design profile by slightly
tuning the field strength. The beam envelopes, calculated at thesame time with Figs. 3, are shown in Fig. 4. In this figure, we also
show the beam envelopes when the beam intensities are 0 rnA.
In order to compare the simulation results using SHU withthose using BEAMP ATH, we performed the simulations in BTSMl, BT-SM2 and BT-TQM under the same conditions as before.
In these simulations, we traced the trajectories of 10000 particles.
The simulated emittance profiles at the exits of BT -SM 1, BTSM2 and BT-TQM are shown in Fig. 5a), 5b) and 5c), respectively.
In these figures, the design emittance profiles injected into the
RFQ and the 100% emittance profiles are also shown with dottedlines. As can be seen from Figs. 3 and Figs. 5, the simulation
results using SHU are ih good agreement with those using
BE AMP ATH. In this sense the use of SHU is justified in order tostudy the lens aberration effects. The. calculated RMS and 100%
normalized .emittances of each LEBT are summarized in Table 3.
The results of the present simulation studies are
summarized as fol)ows;( 1) Almost no growth of the effective emittance was observed inalpha ,; 0.00
0.043.
100%=1.50•

100~beta =

EE .

50

-50

~~~~···~~~········; ~~~

-100

i

-4

•2

0

-2

0

-2

x (mm)x (mm)x(a) BT-SMl, (b) BT-SM2, and (c) BT-TQM, respectively.

-BT-SM1, 0 rnA,..-...,-----,-..........,-------j=:i~~!: ~om~A·····BT-SM2. 40 rnA

25

-20

E

§_
"'15

"
15

e1a

~

Fig. 3. The emittance profile at the exit ofLEBTs estimated with SHU.

the entrance of LEBTs.
30

x (mm)~

00

Fig. 2. The emittance profile at

(mm)

..,
r~-

100

100

-··BT-TQM, 0 rnA-··BT-TQM, 40 rnA-,fbi~\~

50

50

'0

'0

~

"'
go

§_0

-,.

x

-50

-50

-100
a~~-~~~~~~~~·~·
100 200 300 400 500 600 700
0z (mm)

Fig. 4. beam envelopes
calculated with SHU.

-4

-2

0

~

2

-2

0

0

x (mm)x (mm)x (mm)

(a)

(b)

(c)

Fig. 5. Simulated emittance profile at the exit of LEBTs with BEAMPATH.
(a) BT-SMl, (b) BT-SM2, and (c) BT-TQM, respectively.

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JAERI-Conf 95-021

Table3
Normalized emittances
240 --T• .. _____ T. ________ f'l ........ ; ........ ..,. .. jsimulated with BEAMPATH. 160 ....................... , ......... , ........., ... ,(1t mm•mrad)
4xRMS 100% :c 80
!!!
1.50
1.74
BT-SM1
.§. 0
1.52
1.83
BT-SM2---·------------------2.10
1.53
BT-TQM_]11!~..~-~..~,~~ .. ,...

100

·r+·

50

::J'""'"!''"""'

-160
-240

··---------··-r··

r. . . .,. . . .
r. . .

100

..

~5o

..

i

--·:.

0

... ...

) 01l.~..y--':.~ ~

!

';(

-50

-60

-100

-320 L.,_j••:-------"........,_2,..--'---:-0~--:-~~._]

-100
-4

x (mm)

-2

0

2

4

-4

x (mm)

Fig. 7. Calculated emittanceprofile at the exit ofBTTQM with the practicalquadrupole magietic
field.

-2

0

2

4

x (mm)

Fig. 6. Calculated emittance profile of the focused particles
extracted from a point source with the ideal focusing
quadrupole field.
any LEBT, when the beam intensity was 0 rnA.
(2) It can be seen from Table 3 that the effect of the lens aberration
was revealed on the growth of the effective emittance for the 40mA beam, while almost no effect on the RMS emittance.
(3) The growth in BT-SM1 with two short; strong SMs was thesmallest among the three LEBTs.
(4) The largest growth of the effective emittance was observed in
BT-TQM in contrast to the naive prediction from its ideal
quadrupole magnetic fields.
The sources of these emittance growths are discussed in
the next section.

Fig. 8. Calculated emittanceprofile at the exit of BTSMl with the first ordermagietic field
distribution.
is magnified in proportion to the beam radius. This is the reason
why the aberration of BT-SM2 becomes larger than that of BTSML On the other hand, the difference of the ratio r-/r'oor in BTSM 1 and BT-SM2 has not so large effect on the aberration. (Thesimulated emittance growth in BT-SM2 is smaller than thatmeasured at LANL, perhaps due to the lower beam energy (35kev) in the LEBT at LANL.)

Sources of Aberrations

Three types of LEBTs with magnetic lenses were
investigated. In BT-SM 1 with two short, strong solenoid magnets,
the smallest effective emittance growth was obtained (no growthin RMS emittance and a small growth of less than 15% in 100%
emittance). We will-construct BT -SM 1 in near future for thisreason. BT-SM1 is suitable for precise experiment on the nonlinear:space charge:effect, since there is only small emittance
growth when the linear space charge force is assumed.
Two important mechanisms. of the emittance growth inthe (i}Uadrupole magnets were also comprehended. One is theaberration due to partieles with large divergence angles of morethan ±120 mrad. The other is large aberration due to the fringing
field of a thin quadrupole magnet. We should also pay attention
to these aberrations in the medium energy beam transport (MEBT)
located just after thl' RFQ, since a number of thin quadrupole
magnets are used there.

(1) Source of Aberration in TQM
In order to find the source of the aberration occurring in
BT-TQM, we simulated the trajectories of the particles extracted
from a point source in the ideal focusing quadrupole field by using
SHU. In this simulation, the beam intensity was 0 rnA and theparticles with initial divergences of up to ±300 mrad were traced.
Since the focal length of the quadrupole niagnet is 7 em, theparticles were traced until 14 cril, where the particles will befocused again at one point if there is no aberration. The simulated
emittance is shown in Fig. 6. It can be seen that the linear
oscillation in the ideal quadrupole filed is satisfied only for theparticle with initial divergence angle of within around ±120 mrad.
In the BT-TQM, the simulated maximum value of the divergenceangles for the beam intensities ofO rnA and 40 rnA are 140 mradand 270 mrad, respectively. The latter value is significantly higher
than 120 mrad. This is the reason for the remarkable filamentationin the simulated emittance at the exit of BT-TQM.
In order to study the effect of the fringing field in BTTQM we used the SHU together with the realistic quadrupole
magnetic field calculated with MAFIA. The simulated emittanceat the exit is shown in Fig. 7. The extremely large filamentation
was generated due to the fringing field. The filamentation shownin this figure is very similar to that observed in the LEBT withseveral electrostatic quadrupoles developed at SSCL. It is thus
concluded that any short quadrupole lens has large aberration due
to the fringing field, when it is necessary to inject the beam withlarge convergence angle into the RFQ with a resonant frequency
of around 400 MHz.
(2) Source of Aberration in SM
If the divergence angle of the particles exceeded ±120
mrad, the aberration described above should also occur in the
SM. Fortunately, this is not the case for SM, since there is no
defocusing force in the field of SM and the divergence angle isnot so enlarged as above.
In order to reveal the source of the aberration observed in
BT-SM1, we simulated the beam optics inBT-SM1 with the firstorder magnetic field distribution (Br=-r/2*(dBz/dz)) by using
SHU. The simulated emittance at the exit is shown in Fig, 8.
Almost no filamentation can be seen in this emittance profile.
Therefore, the effect of the aberration seen in Fig. 3a) and Sa)
arises from the higher-order components of the field which are
generated by the edge of the iron yoke and the fringing field. It isnoted that this kind of geometrical aberrations in BT-SMl issignificantly smaller than that due to the fringing field in therealistic TQMs. The aberration in BT-SM2 also arises from thehigher-order components of the field. It is seen that filamentation

Conclusion

Acknowledgment
The authors wish to express their sincere thanks to Dr. Y.
Batygin (Institute of Physical and Chemical Research in RIKEN)
for his offer of the computer program BEAMPATH and several
useful advices. They also appreciate Mr. K. Yoshino for his help
in calculation of the 3-dimensional magnetic field in the triplet
quadrupole magnet.
References[1] A.Ueno et. al.,Proc. 1994 International Linac Conf., Vol. 1,(1994) 166.
[2] K.F.Johnson et. al., Proc. Lin. Accel. Conf, AECL-10728;
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[3] F.W.Guy et. al., Proc. 1993 IEEE Part. Accel. Conf.,
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[4] S.K. Guharay et. al, Nucl.Inst. and Meth. in Phys. Rev., A339
(1994) 429.
[5] User's Guide for POISSON/SUPERFlSH group of codes, LAUR-87-115, LANL (1987)[6] MAFIA, The Universal Software-System for Electromagnetic
CAD.
[7] Y. Mori, T. Okuyama, A. Takagi and D. Yuan, Nucl. Inst. andMeth. A30 1 (1991) 1.
[8] K.R.Crandall, TRACE 3D documentation, LA-11054 MS.
[9] Y. Batygin, "BEAMPATH: A Program Library for Beam
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Berlin, Vol. 1, (1992) 822.

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