RESONANT MULTI-GAP FUNNELING AND DE-FUNNELING SYSTEMSYu. Senichev and W. Braeutigam, FZJ, Juelich, D-52425, Germany
1 INTRODUCTION
At present the ESS super-conducting option is underconsideration, where the linear accelerator is divided into
two main parts: the low energy part up to 100 MeV andthe high energy super-conducting part from 100 MeV to1333 MeV. The only change of frequency just after thefunnelling allows filling each separatrix in the accelerator,
which results in the smaller number of particles in eachbunch and makes easier to fulfill the particles losses
requirements. Simultaneously the funneling helps to reachthe required beam intensity for ESS of 107 mA in peak
per micro pulse. Two identically bunched beams have tobe merged into a single beam with double intensity.
We propose the resonant method of the beams funnellingbased on the multi-gap deflector /1/. The new idea differsfrom another ones /2,3/ by the possibility to organize theπ -mode standing wave deviation system. It is different
from another method by the higher efficiency. We haveanalyzed, designed and compared two types of different
H-cavities with the quadrupole TE211 mode and thedipole TE111 mode. They both can provide the effective
resonant merging of beams. Additionally, instead of thepulse dividing method into two rings (or more for multipurposes facilities) this device can be used to split thebeam after acceleration into two or three beams and todeliver them to different facilities simultaneously.

2 ELECTRODYNAMICS OF FUNNELDEVICE
2.1 Dipole or quadrupole mode?
To provide the transverse electrical field we should
install the electrodes inside the cavity.

Figure 1: TE211 mode structure
The figure 1 shows the deflector based on the fourchambers H resonator excited on the quadrupole mode
TE211. The resonator consists of the pipe and four wanes.

The wanes divide the pipe on four equal sectors. The
deflecting plates are kept to the edge of wane by “legs”.
Each pair of wanes forms the sequence of one-polarity
capacitors and it interleaves to another pair of wanes withthe opposite polarity. Thus, the total sequence of thecapacitors forms the lattice with the required change ofpolarity.
Figure 2 shows schematically the main idea of funnel
device based on TE111 mode.

Figure2: One period of TE111 mode structure
The pairs of electrodes are alternately changed byposition along the cavity. The magnetic field has one
variation in all directions. The magnetic flux rounds theelectrodes from above to bellow. The electrical field isperpendicular to the magnetic field and it is directed fromleft to right. The quasi-electrical field arises in the gap
between them, and it is directed top-down. For the next
pair the electrodes are changed by position and the quasielectrical component flips top. Since the longitudinal
distance between the neighboring pairs equals to βλ / 2 , itis exactly the π -mode standing wave deviation system
for the beam.
The figure 3 shows the transverse electrical field along
the funnel device for both modes.

Figure 3: The transverse electrical field in the TE211 andTE111 mode structures
In the empty cylindrical cavity without any electrodes
inside (unloaded cavity) the critical wavelength of TE211
and TE111 modes is connected with the radius of cavity

bytheratio
andR = λ / 2.06
R = λ / 3.41
correspondingly. In result of the electrode’s capacity thecavity radius decreases for both modes, but the radius ofcavity based on TE211 mode remains to be bigger incomparison with the cavity based on TE111 mode.
In case of 352.2 MHz the ratio between the gap andcavity sizes is quite reasonable, and it is another situation
for the lower frequency 176.1 MHz. Since the gap size isdetermined by the beam parameters as before, but thecavity sizes increase almost by factor of 2, this ratio looks
not so optimised. Therefore the dipole mode funnel
device is more preferable.
2.2 Cylindrical or rectangular cavity?
Due to similarity (see fig.2) with “OPEL” emblem wecalled this structure by “OPEL”-structure. The insertionof electrodes in the “OPEL” cavity breaks the axial
symmetry, and later it initiated us to pass to therectangular option. The sizes of cavity for this mode takesomething average between TE211 and TE111 modes.
But due to another magnetic field distribution this cavity
has the more convenient construction for the tuning andthe cooling systems. Figure 4 shows the segment of therectangular structure from MAFIA simulation.

it is desirable to have the homogeneous electrical field
distribution in the transverse plane for all gaps. For thispurpose we use the one-dimensional shimming. Figure 5
shows the profile of the electrodes. After shimming thefield in the beam region has the deviation ± 0.05% ,what is quite satisfactory from the beam dynamics pointof view.

3 BEAM DYNAMICS IN FUNNEL DEVICE
3.1 Space and angle deviation
Let us represent the transverse electrical field
distribution through the series:
2πE x ( z) =E k sinz.
(1)βλkΣ

For the even field (without slope along cavity) the angle
and space deviations are determined by:βλdx
eE1 cos ϕ⋅ n(∆( ) =)222dz
2m0 c γβ(2)2eE1 cos ϕ2 βλ∆x =⋅n ()24m0 c 2γβ 2where E1 is the amplitude of the first harmonic, ϕ is thephase of particle relatively of the RF field and n is thenumber of gaps. In reality (see fig.3) the field has the[ δEE − 2 EEδ⋅ Lz],slope described by formula E1 = E 0 1+0

where L = nβλ20, the angle and the space deviations are:(dzdx)= 2eEm ccosγβϕ ⋅ L and ∆x = 4eEm ccosγβϕ ⋅ L (1 + 13 δEE ) .

∆20Figure 4: TE101 rectangular structure
2.3 Electrical field correction
The number of electrodes pairs depends on the required
angle deviation of the beam and the maximum possible
field in the gap. In the same time the RF power heating is
proportional to the squared amplitude and it could be
restricted by the water-cooling system.

Figures 5: Transverse profile of electrodes
The initial gaps have to be wider, since the beams
deviation from axis is bigger at entrance. Simultaneously,

21120220Thus, the angle deviation does not depend on the slope
value, but the space deviation is bigger for the positiveslope.
Unfortunately, in order to increase the geometricalacceptance of the funnel device we have to have the firstgap as biggest one and then gradually we decrease the gap
width with the number. But it is known that in the H
structure cavity the quasi-potential is constant and,
consequently, the electrical field has just exactly thepositive slope. In reality it is not significant effect, sinceeven at the ratio 1 : 3 between the first and last gap sizes
the space deviation is changed on 50/3 % only.
3.2 Coupling between longitudinal and transverse
motions
You can see from (2) the particle deviation depends on
the RF phase ϕ . It is the most important factor causing
the emittance growth. We have calculated the trajectories
for the case, when the coasting bunch with the length of
2π is launched on the entrance of the funnel device, andwe observed the beam on the exit. Obviously, theparticles are grouped around “0” and π phases, and theemittance growth is proportional to the average value ofdeviation:(∆xcos Φ) ≈( 1 −) . For the beam with the∆x ′2length of 20 degrees the emittance grows by ≈ 10% , andthis value almost does not depend on the number of gaps.

4 EFFICIENCY OF DEFLECTOR
Three factors having an influence on the funnel
construction are the necessary deviation angle, themaximum field and the maximum RF power absorbed by
the cooling system. The multi-gap funnel device has a bigadvantage over the one-gap device, since the angledeviation is proportional to the squared length of device(number of gaps), and we can get the necessary deviation
angle by the appropriate choice of the length. However,simultaneously with the angle deviation the spacedeviation grows with the length. Therefore the initial gaps
have to be more open and the efficiency of funnel device
goes down with the transverse field E ∝U
as well. Tod

characterize the efficiency we introduce the value
Eff =α 2 Lcavity
PRFlosses

measuredinthedimensionofdegree**2/(MW/m). Figure 6 shows the efficiency of thefunnel device versus the gaps number for two frequencies
352.2 MHz and 176.1 MHz.
Eff= α2Lcavity

PRF loss

α - a ngle o f devia tion, degre ePRf loss

-RF losse s in d eflector, MW

L - le ngth o f deflecto r cavity, m100. 00

Eff, d e g re e **2/( MW/ m )352. 2 M Hz

80. 00176. 1 M Hz

60. 0040. 00In principle, just only the one-gap device for 352.2 MHz
is restricted by the field maximum, if to deviate the beam
by more than one degree. For all another options the main
parameter is the power limit absorbed by the coolingsystem. From this point of view we suggest the six-gap
device for the frequency 352.2 MHz and the four-gap
device for 176.1 MHz. Both options can work in the highduty cycle regime.

5 DE-FUNNELING SYSTEM
In principle, if we know how to merge the beams, thenthe inverted system has to split the beams. This idea has achance to be used on the exit of the accelerator to deliver
the accelerated particles to many different facilities
simultaneously. The bunches, following with thefrequency 704.2 MHz and passing through the defunneling system with the operating frequency 352.2
MHz, are split into two beams with equal intensity. In
spite of the angle deviation decreases with the energy theresonator with 10 plates can split the beams by ± 1 .
Such a resonator has the length of 3.9m and at 7.5MV/m
requires the power 160 kW.
06 CONCLUSION
We have developed the constructions of the funnel
device based on the quadrupole mode TE211, the dipole
mode TE111in the cylindrical cavity and TE101 in therectangular cavity. They meet to all requirements of thehigh duty cycle accelerator facility. The efficiency of themulti-gap RF deflector is by an order of magnitude
greater in comparison with the single gap deflector. For
both frequencies 352.2 MHz and 176.1 MHz therectangular construction is more optimal from the tuning
and cooling point of view. At present the real constructionof funnel device is fabricated in Institute of High Energy
Physics in Protvino, which will be tested on the RF test
bench.
We would like to thank IKP and ESS scientists for lot offruitful and stimulating discussions of this device.

7 REFERENCES

20. 001.
Number of electrodes pairs f o r 176.1 MHz funneling
12

3456

0. 00
0. 00

4.00

8. 00

12. 00Nu m b e r o f el ec t rod e s p ai rs fo r 3 52. 2 M Hz funne lin gFigure 6: Efficiency of Funnel device
You can see the significant gain of the 5-6 gaps (3-4 gapsfor 176.1 MHz) over the one-gap device. But then theefficiency is almost constant. It is because the growth ofthe gap size is compensating the advantages of the multigap device. From this data you can see that in the one-gap
device deviating the beam by 2 degrees the RF power
1MW has to be absorbed in CW regime, what is notrealistic even for 6 % duty cycle machine like for ESS
project.

2.

3.

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Yu.Senichev, The resonant multi-gap funnelingand de-funneling system, preprint ESS 103-00A, ISSN 1433-559X, ESS, June 2000.
A.Schempp et al. RFQ-, Chopping- andFunneling-studies for the ESS-Injector-Linac.
Proc.18 LINAC Conf., 1996.
F.L.Kravczyk, S.Kurennoy, Funnel cavities for 4
MW upgrade of Spallation Neutron Source,
Proceeding of PAC, New York, 1999.