Design of Multi-Beam Klystron in X-Band
A. Larionov*, V. Teryaev*, S. Matsumoto, Y.H. Chin,KEK, High Energy Accelerator Research Organization,
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

Abstract
Design study of an X-band multi-beam klystron wasstarted to pursuit its feasibility as the power sources ofJLC (Japan Linear Collider) main linacs. The gundesign together with PPM (Periodic Permanent Magnets)
focusing system (which is common for all beamlets) has
been done. The RF design and klystron simulation basedon annular cavities operating with HOM (Higher OrderMode) has also been done. Discussion on the possibilityof 150MW klystron is made.

1 WHY MULTIPLE BEAM?
Japan Linear Collider (JLC) Project [1] is planed to use
X-band (11.42GHz) 75MW pulsed klystrons (pulselength 1.5µs) as the power source of its main linacs.
The required parameters for a JLC klystron are shown in
Table 1 below. Recent R&D work on JLC klystron has
been devoted to the design and building a PPM (Periodic
Permanent Magnets) focused klystron. Its prototypes
have shown very good performance [2].
The combination of high cathode voltage (480kV) andlow perveance (0.8µΚ) has been chosen for the JLC
klystron specification, where the klystron is supposed touse a single beam carrying whole beam power (130MW).
One of the issues of JLC klystron is its high cathodevoltage. The high voltage may have an impact on thelifetime of the system and may degrade its reliability.
Another is the high energy density of the klystron beam
(radius 3mm). A rather strong focusing system isnecessary to stabilize the beam. The output RF circuit is amulti-cell cavity to handle large RF power from the beam
as well as to make the surface field practical.
Table 1: JLC klystron specifications
Frequency
11.424 GHzPower75 MWPulse width
1. 5 µ s
Repetition
150 HzCathode Voltage
480 kVPerveance
0. 8 µ K
Efficiency
55%
A multi-beam klystron (MBK) [3] can be anothersolution to JLC klystron. MBK uses a bundle of small
perveance beamlets. Although each beamlet carries small
amount of current, the total current can be large. As aresult, we can choose moderate cathode voltage for MBK.
The power density of beamlet can be low due to small
current and low voltage.
An MBK has these advantages to a conventional(single beam) klystron. We have looked for a realistic
design of MBK operable in X-band to meet with JLC
klystron specifications.

2 DESIGN OUTLINE
A pilot design study was started first to see thefeasibility of 75MW MBK operable in X-band, which iscompletely compatible to the prototype klystrons. We
found that this kind of device was possible to design.
Some detail design of the focusing system and cavity
design were done in this study. Right after the study, webegan to consider the possibility of double-powered
150MW MBK by an extrapolation.
The design parameters of the 150MW MBK and of theJLC prototype klystrons are compared in Table 2 below.
Six (identical) beamlets are used in the MBK. The
perveance of each beamlet and the cathode voltage arechosen to be 0.6µK and 340kV. The power of theindividual beamlet is 43MW. If the efficiency is 60%,
which is reasonable for 0.6µK beam, each beamlet
produces the RF power of 25MW and the total output
power will be 150MW.
Table 2: klystron parameters
MBKCathode Voltage (kV)Beam(let) cuurent (A)Perveance (µK)
Number of beam(lets)
Output Power (MW)
Efficiency (%)

340
750 (125)
3.6 (0.6)
6150
>50

JLC
prototype
480
266
0.8
17555

Fig 1: schematic view of the device (diode).

The schematic view of the MBK is given in Fig.1. Eachbeamlet runs in its own drift tube. The drift tubes are inparallel to each other and distributed in hexagonal way(separated by 75mm with each other) around the deviceaxis.

3 GUN AND FOCUSING SYSTEMDESIGNThe parameter of beamlet gun is given in Table 3.
The criterion on the maximum surface field on electrodeis that it should be smaller than that of prototype JLCklystron. No trouble has been found in the guns ofprototype klystrons during their operation.
Table 3: Gun parameters
Cathode Current
Cathode Diameter
Cathode Load
Surface E max
Cathode Voltage
Cathode B Field(Beam Radius)

125A @ 340kV
38mm< 12 A/cm^2260 kV/cm
480 kV
10 – 30 Gs(2 – 2.5 mm)

3 RF DESIGN
Let us discuss the cavity structure of the MBK driven
by all the beamlets. Note that the wavelength of theoperation frequency is 26mm (in free space) while thetrajectories of the beamlets are separated by 75mm, which
is much larger than the wavelength. Therefore the cavities
installed in the MBK cannot be a simple pill-box cavity
operated in its fundamental mode, found in most of theklystrons.
We employ an annular cavity structure instead, which isschematically shown in Fig. 2. The E field of TMmn0
mode in the cavity (without the beam holes) is
Ez(r,φ ,t)=e j ω t cos(mφ ) [ Jm (kc r)+Nm (kc r) ](1)

where Jm and Nm are the Bessel function of order m. The
radial wave number kc is determined by the boundary
condition on the cavity wall. We use m=12, n=1 mode
since the neighbors (m=11 and m=13) locate far away(±350MHz). The cavity should be free from mode
contamination form them.

The focusing system consists of both permanent andelectric magnets as shown in Fig.1. Here is a list of theirrole:••••

The main focusing is provided by PPM (PeriodicPermanent Magnet). The PPM focusing systemcommon for all beamlets.
The cathode coils produce a uniform magnetic
field on the whole cathodes. The cathode field
controls the beamlet size (cross-sectional) in thedrift tube (see Table 3 above).
The matching coil is installed for the good beamtransportation from the gun to the PPM focusedregion.
The corrector coil produces a local transverse B
field there to compensate the magnetic interaction
between the beamlets occurred in the gun region.
The magnetic flux around one beamlet can exert on
the others in the gun region.

None of the beamlets is on the device axis. Therefore,
there should be the transverse field along the axis(trajectory) of beamlets unless we eliminate it explicitly.
Generally speaking, the transverse field affects the beamtransmission and/or gives potential danger for a parasiticoscillation.
The magnet screens are necessary at various places tosuppress the transverse field near the beamlet trajectory to
restore the local cylindrical symmetry of the field. This
work has been done. This is a trade-off for the use ofcommon focusing system for all multiple beam.

Fig 2: schematic view of the annular cavity.
For TM12, 1, 0 of 11.42GHz, R_outer and R_inner in
Fig.2 are found to be 84 and 66mm. The width of thecavity is thus 18mm, which is large enough compared tothe diameter of the beam hole, 8mm. The local Ez fieldnear the beamlet trajectory has good cylindrical symmetryaround the beam axis.
For a 8mm-gap cavity, the shunt impedance is 60kOhms
and Q=8500. The R/Q value for a single beamlet is a few
Ohms, which is much lower than that in the prototype
klystrons (installs pill-box cavities, typically 100 Ohms).
The degenerated mode, which represented by a simple
replacement of the cosine function into sine in Eq. (1), ispotentially dangerous since it has its B max at the locationof the beam holes and it deflects the beam. However, themode frequency is naturally detuned by the introductionof the beam holes. A 3D calculation shows the detuning isa few hundreds MHz. The detuning should be enough themode not to be excited.

4 KLYSTRON SIMULATION
We design the MBK with all the cavities being annular.
1D simulation of each beamlet motion is eligible if we areallowed to assume (1) All the beamlet are identical and (2)The local field near the beamlet inside the annular cavity
looks like the field in an ordinary klystron cavity. 1Dsimulation of each beamlet is possible by a proper
modelling of Ez field on the beam axis and a redefinitionof the cavity parameters in the code.
We found that we needed at least 7 cavities to getenough gain in our 1D simulation study. This is due tolow R/Q of the annular cavity, which indicates theinteraction between the cavity and the beamlet is weak.
By the same reason, we found that a single annular cavity
does not work efficiently as the output cavity. However,
if we use a double gap output cavity structure as shown inFig. 3, we found that we could improve the efficiency (aswell as to reduce the maximum surface field in thecavity).

There remains some important problems: One of themis that the effects induced by an unbalance in the beamlets(their current or phase). This is really a 3D problem. We
have no answer yet. The other issue is the way to extract
the power from the tube. We did not design the output
port connected to the waveguide(s).
Table 4: Simulation results
Cathode voltage
Beamlet current
Input RF power / Gain
BandwidthEfficiency
Emax_surface (kV/cm)
Beamlet tube diameter
Tube diameter @ outputcavity
Upstream / Downstream
Length from Input toOutput cavity

Single gap
Double gap
340 kV
125 A
134 W/ 60 dB
40 MHz
50 %
55 %
910
7208mm
10 mm / 12.8mm

459 mm

4 CONCLUSION

Fig 3: A double-gap output cavity.

(1/12 segment.)

In order to simulate the single beamlet motion by 2D
code, we introduce an equivalent cavity to model theinteraction between the beamlet and the annular cavity
structure. The equivalent cavity is a pill-box cavity andhas the same gap field as the actual field in the annularcavity. The resonant frequency, R/Q and Q values of theequivalent cavity are matched to those of the annularcavity. The actual focusing magnetic field has good axial
symmetry with respect to the beamlet axis. The field isrecalculated and reproduced by a 2D magnetic code.
In 2D simulation, we found that the aperture of thebeam pipe at output region has to be large. The results are
summarized in Table 4. The single-gap and double-gap
output cavity are compared in the table.
The equivalent cavity works correctly for the operating
mode. However, it does not for the other modes in theannular cavity. Their resonant frequencies are known(even analytically known for the cavity without beamholes). In fact, the frequencies are well detuned and we
conclude that they will not give rise to a problem
immediately.

Our design study thus far shows that the key parameters,such as the maximum field strength, can be moderate andlook realistic. The designed performance is fairly good.
We have got 55% efficiency, which means we get
150MW at 360kV cathode voltage. We conclude that an
MBK of 150MW in X-Band is a realizable device.
If 150MW MBK is realized, we can reduce the numberof klystrons by half in JLC main linacs. Even a 75MW
MBK has a merit, since this MBK requires the lowest
cathode voltage (260kV) among the klystrons that we
considered here. Although the MBK itself is a rather
complicate device (multiple cathodes, multiple beamtubes, multiple collectors, a complicated focusing system,
so on), we believe that the low voltage is good for thereliablility and/or the lifetime of the system and can makethe system compact.

Acknowledgement
The authors are grateful to A. Lunin for discussions.

REFERENCES* Permanent Address: BINP, Branch of the Institute of
Nuclear Physics, Protovino, 142284 Moscow Region,Russia.
[1] JLC Group, JLC Design study, KEK Report 97-1.
[2] S. Matsumoto, et al., “Development of PPM-focused
X-band Pulse Klystron” in Proc. of the 13th
Symposium on Accelerator Science and Technology(SAST 01), Osaka, Japan, 2001.
[3] Some articles on MBK are found in “High Energy
Density Microwaves”, Editor R.M. Philips, AIP Conf.
Proc. 474 (1999).