Proceedings of the 25th Linear Accelerator Meeting in Japan (July 12-14, 2000, Himeji, Japan)[12P-30]

Investigation of Spurious Oscillation in Klystron Due to BackBack-goingElectrons from Collector
Z. Fang, *S. Fukuda, *S. Yamaguchi, and *S. Anami
The graduate university for advanced studies*High energy accelerator research organization (KEK)
1-1, Oho, Tsukuba-shi, Ibaraki, 305-0801, Japan
Abstract
Back-going electrons from a collector to a drift tube are one of the possibilities causing spurious
oscillations in a klystron. This kind of instability occurred in the 324MHz klystrons being developed atKEK. In this paper, the oscillation phenomena and mechanism are described. And simulations ofback-going electrons using EGS4 have been performed. The back-going electron coefficients and energy
distributions were obtained under different beam voltages and collector shapes. The simulation results
are the basis of the oscillation condition study and the collector design.
1. Introduction
In a klystron, electrons are emitted from anelectron gun, pass through a drift tube, andfinally enter and spread in a collector underspace-charge forces. After the electrons
bombard the collector surface, back-scatteredelectrons are produced, and some of them
return to the drift tube of the klystron. Theseback-going electrons are modulated by the gap
voltage of the output cavity, and induce a gap
voltage in the input cavity. Thus the back-going
electrons and the main beam of the klystronform a feedback system and it’s possible tocause spurious oscillations in the klystron. Thiskind of instability occurred in the 324MHz
klystrons(3MW output power, 650µs pulse
width, and 110kV beam voltage) being
developed at KEK. During the high voltage
processing of the klystrons, spurious
oscillations were observed without any driving
input power.
In order to suppress the oscillations,back-going electron simulations using EGS4
have been performed. The back-going electron
coefficients and energy distributions have been
investigated under different beam voltages andcollector shapes.
2. Oscillation phenomena
During the high voltage processing of thetube #1 of 324MHz klystron, unexpectedoscillations were observed from both the output
and input cavities without any driving input
power. The oscillation frequency is near to324MHz, and the oscillations occurred when
the beam voltage is 63~71kV and larger than

90kV.
When a bending magnetic field was appliedat the collector region to deflect the electron
beam, the oscillations stopped. It showed thatthe collector region was the source of theoscillations. And there is no resonance in thecollector since the operating frequency of324MHz is very low. So, the oscillations were
not caused by collector resonance. Therefore
the oscillations were concluded to be caused by
the back-going electrons. When the back-going
electrons going into the drift tube weredeflected by the applied magnetic field, theoscillation stopped.
We could decrease the amount of back-going
electrons by enlarging the collector size. In thetube #1A, a collector with a larger radius andlength was used. And the experiment results
showed that the oscillations disappeared in the
low beam voltage region and the oscillations
started from 95kV. The collector length wasincreased further in the tube #2, and the beam
voltage threshold of the oscillations became
higher again. The collector shapes and theoscillation regions of these 3 tubes are
summarized in Table 1.
Table 1. Collector shapes and beam voltage
regions of oscillations

−216−

Tube

Collector
radius(cm)Collector
length(cm)

#1
#1A
#2

6.5
11.5
11.5

62.4
92.4
122.4

Beam voltage
regions ofoscillation (kV)
63<V<71,V>90
V>95
V>102

3. Oscillation mechanism
After the electrons bombard the collector
surface, due to an inelastic process with atomic
electrons,
back-scatteredelectrons
areproduced. And some of the back-scatteredelectrons in the collector return to the drift
tube of the klystron and form a feedback
system to cause spurious oscillations when thefollowing condition is satisfied:A•β >1
A is the voltage gain induced by the main beamof the klystron. A = Vo / Vi, where Vi and Vo are
the input and output cavity gap voltages
respectively. β is the voltage gain induced by
the back-going electron current. The back-going
electrons are modulated by the output cavity
gap voltage Vo′, and induce a voltage Vi′ in theinput cavity gap. β = Vi′/ Vo′. And β is
proportional to the back-going electron current
since the beginning of the oscillations is in thesmall-signal linear region. So, in order tosuppress the oscillations, we must decrease theamount of back-going electrons.
4. Simulation of backback-going electrons
We applied the EGS4(Electron GammaShower) Monte Carlo method[1] to theback-scattered electron simulation in thecomplicated case of a klystron collector with an
external magnetic field. Before this complicatedsimulation, we had applied EGS4 to some
simple cases, such as an electron beam isincident on a copper plate(thicker than 1mm),and compared the simulation results withexperiment results. We found that thesimulation results of back-scattered electron
coefficients and energy distributions agree withexperiment results very well.
In order to perform the EGS4 simulation of
the back-scattered electron in the klystroncollector, the trajectories of the incident
electron beam were calculated at first. The
cathode radius is 4.5cm with a magnetic field of
130Gauss on it. The beam radius is 3.5cm at
the entrance of collector and the focusing
magnetic field on axis Z in the collector regionis shown in Fig.1. The trajectories of theincident electron beam are shown in Fig.2.
Then the calculation results(incident electronpositions, velocities and energies when theybombard the collector surface) are used as
initial conditions to start the EGS4 Monte

Carlo simulation. The trajectories of theback-scattered and back-going electrons areshown in Fig.3.

B z (G)
250
200
150
100
5002865

2965

3065
3165
Z(mm)

32653365

Fig.1. Magnetic field on axis Z in the collector
region.

Fig.2. Trajectories of the incident electron beamin the collector.

Fig.3. Trajectories of the back-scattered andback-going electrons in the collector.
The back-going electron coefficients andenergy distributions have been investigatedunder different beam voltages(Fig.4). We foundthat the back-going coefficients are almost
same and the peak energy (E/Eo) of the energy
distributions always locates at 0.7~0.8.

well.

Fraction(%)

Energy distribution of back-going electrons
110kV
0.07
100kV
90kV
0.06
80kV
70kV
0.05
65kV
55kV
0.04
0.03
0.02
0.01

6. Summary
The back-going electrons might cause
spurious oscillations. By the simulation using
EGS4, the back-going electron coefficients andenergy distributions as function of beam
voltage and collector shape were obtained.
Oscillation conditions are always complex, andwe will go on with the study of the oscillation
conditions by using the EGS4 simulation
results.

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
E/E0

Fig.4. Energy distribution of the back-going
electrons under different beam voltages.

B a c k-going c oe ffic ie nt (% )R (6.5c m )R (11.5c m )R (15c m )R (20c m )0.7
0.6
0.50.4

5. Collector shape and backback-going electrons
Simulations of back-going electrons havebeen performed for different collector shapes(Fig.5). For a certain collector radius, when thecollector length becomes larger, the back-going
coefficient decreases rapidly at first, thenslowly, and finally tends to a constant. Thismeans that the contribution to the back-going
coefficient from the cone surface of the collector
becomes smaller and smaller, and finally thecontribution to the back-going coefficient
mainly comes from the part of thebeam-sinking cylinder surface which is nearer
to the collector entrance. Also for a certain
collector length, when the collector radius
becomes larger, the back-going coefficientdecreases in the same way. In short, thebeam-sinking collector surface which is nearer
to the collector entrance will gives the main
contribution to the back-going coefficient. So,
when we design a collector, we should let all of
the parts of the beam-sinking collector surface
far away from the collector entrance. Also we
could decrease the back-going coefficient byusing a small the drift tube radius(Fig.6).
For the collector of the tube #1, #1A, and #2,
the back-going coefficients are 0.66%, 0.17%,
and 0.14% respectively. From the recent study
results of the oscillation conditions[2], weexpected that the spurious oscillations would
start from 103±1kV in the tube #2. And thelatest experiment results showed that theoscillations started from 102kV. They agreed

0.3
0.2
0.1
0050

100

150
L (c m )

200

250

300

Fig.5. Back-going coefficient as function ofcollector shape. (drift tube radius : 5.0cm, R:
collector radius, L: collector length.)
B a c k-going c oe ffic ie nt(% )
0.15
0.1
0.05
02

2.5

33.5
4
D rift tube ra dius (c m )4.5

5Fig.6. Back-going coefficient as function of drift
tube radius.(collector radius: 11.5cm,collector length: 122.4cm)
References[1]. W. R. Nelson, H. Rirayama and D. W. O.
Rogers, SLAC-report-265, 1985.
[2]. Z. Fang, S. Fukuda, S. Yamaguchi, and S.
Anami, to be presented in Proc. of the 20thinternational linac conference, California,USA, August, 2000.