The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

TRANSIENT BEAM LOADING EFFECTS CAUSED BY
BACK-STREAMING ELECTRONS ONTO A
THERMIONIC CATHODE IN AN RF GUN
T. Horii, K. Masuda, S. Amazaki, T. Kii, H.Toku, H. Ohgaki,T. Yamazaki, and K. Yoshikawa
Institute of Advanced Energy, Kyoto University
Gokasho, Uji, Kyoto 611-00ll, Japan

Abstract
Adverse effect of back-streaming electrons onto athermionic cathode in an S-hand 4.5-cell rf gun wasstudied. A numerical model is presented based on anequivalent circuit of the rf gun, taking beam-loading
effectinto
account
through2-dimensional
particle-in-cell simulations. Experimentally observed
time evolutions of rf power reflected from the rf gun,and of output beam energy were both well reproducedby the present numerical model, on an assumption ofcathode temperature rise during the rf macro-pulse.
Conclusively, observed undesirable decrease of beamenergy during the macro -pulse is found caused by aconsiderable increase of the cathode temperature due
to back-streaming electrons hitting on the cathode.

1. INTRODUCTIONRf guns have advantages against widely usedelectrostatic electron guns, such as compactness andhigh brightness of the output beam, exclusively
because they can provide much higher accelerating
fields. For long macro-pulse electron beam productions,however, they suffer from a serious problem, thatback-streaming electrons tend to hit cathodes resulting
in cathode temperature rises [1 ], which finally makeboth beam currents and energies unstable during
macro-pulses longer than several f.tSec
For compensating the beam energy decrease due tothe cathode temperature rise during the beammacro-pulse, transient control of pulsed rf power
supply to thermionic rf guns would be efficient. As afirst stage to the final goal of the optimum control of
the rf power supply, we developed a numerical model
to reproduce experimentally observed transient beamloading effects in a thermionic rf gun. Presented in thispaper are the numerical model, and comparisons withexperimental results for verification in terms of time
evolutions of output beam energy and reflected rf
power from the rf gun.

2. EXPERIMENTAL SETUP
AND RESULTS
The present rf gun (AET Associates, MG-500) has
4.5 cells, with a resonant frequency fo = 2857.60
MHz at 30 "C body temperature. A 6 rom-diameter
tungsten impregnated thermionic cathode (Heat Wave,411M) is mounted in the first half cell. The cathodesurface temperature can be measured by use of an
infrared (IR) fiber thermometer through a view-port
mounted on the half cell. The sampling interval ofmeasuring the temperature is 25 f..tSec, and the distancefrom cathode surface to IR fiber thermometer is200mm. Beam measurement system is also equipped
for measuring time evolutions of beam current by useof a current monitor (CT1 in Figure 1), and of energy
spectrum by use of a bending magnet (BM), a beam slit,
and a current monitor (CT2).
Fig. 2 shows measured time evolutions of beam
current Ib and reflected rf power P,.1 together withthe pulsed rf input Pin of 4.0 Mw, 2.1 f..tSec. The rf
frequency was set as f = 2857.77 MHz so as tominimize Pref at t = 2.1 f..tSec, which is slightly
different from f = 2857.60 MHz due to the beamloading. Averaged cathode surface temperature wasmeasured as 1115 °C, which was found higher than thatwithout rf input of 1109 °C. Although time evolution of
the temperature through the 2.1 f..tSec duration
macro-pulse could hardly be observed, of course,
owning to the poor time resolution of the IR
thermometer, there must be a considerable temperaturerise within the macro-pulse [1,2], which seems to resultin an increase of /b in Fig. 2, and, accordingly, adecrease of Prer after the rf filling time of around 1
f..tSeC.
By measuring beam current waveforms by use of
CT2 for various BM coil currents, i.e. for various beamenergies, the time evolution of beam energy spectrum
shown in Fig. 3 can be obtained, which shows adecrease of peak energy Eb, peak after the rf fillingtime, t > 1 f..tSec, implying, again, the increasing beamloading.

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The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October2001

the resonant angular frequency w 0 , the unloaded
quality factor Q0 , and the R/0 factor (R/ Q). The
constant f3 denotes the coupling coefficient of the input
waveguide to the cavity. The constants L, C, G, and f3
are, thus, all given. The current supplyI g (t) = Re [ I g (t} jmt ] corresponds to the pulsed rf
power supply to the rf gun, where w !2:rr = f denotes
the rf frequency, and I g (t) is given by the pulsed rf
power Pin (t) shown in Fig. 2, as follows [3].

CCDcamera

Q2IIllFC1
RF gun ·tllat~~gltfo,.P.fro+"-lt!IIJ"'""""'""""'""'"'of.

SC :Steering CoilQ :Q-magnet
BM :Bending Magnet
FC :Faraday cup
BPM:Beam profile monitor
CT :Current Transformer

Figure 1 Experimental setup.

(1)

The remaining ~~ in Fig. 4, the beam loading current,represents the beam loading effect on the cavity field.
For the equivalent circuit in Fig. 4, the following
equations are obtained,

1000750

1500 ~-..t'250

L d!L =V - 'wLJL•}
Cdt0

(3)

3t [llsec]

Figure 2 Measured time evolution of I b, Prejand Pin.

6

where ~ is the beam admittance, which will be given
as a function of Vc and the cathode surface
temperature Tcathode in the following section.

~ =~(Vc,Tcathode).

(4)
By numerically solving eqs. (2),(3) and (4) time
evolution of Vc can be obtained. Time evolutions ofP..r and Eb,peak are, then, given in terms of Vc asfollows,(5)
Eb,peak =Eb,peak(Vc,Tcathode),

v;

(6)

represents the conjugate complex of Vc ,whereand Eb,peak as a function of Vc is, again, given in
the following section.
>----=l~:L~-__,--~ :;-]fbi
I,r;~~6--~~us~~--7~.0~--~~~~

Eb

Figure 3 Measured time evolution of beam energyspectrum.

3. NUMERICAL MODEL
3.1 Equivalent circuit modelInteraction between an rf resonant cavity and anelectron beam can be represented by an equivalentcircuit shown in Fig. 4, where the equivalent voltage Vc
represents the rf cavity voltage, the circuit constants L,
C, and G correspond to the cavity parameters such as

4~ {Vci L1 cf G{](Vc,rf power supplyT-)

IrfgunFigure 4 Equivalent circuit model.

3.2 Evaluation of beam admittance by PICsimulation
To give ~ and Eb, peak as functions of Vc and2-dimensinal time-domain particle-in-cellsimulations were carried out by use of a numericalcode KUBLAI [3].
Tcathode ,- 35-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

With a constant Vc and a constant current density
J cathode on the cathode surface as input parameters, theKUBLAI code simulates electron dynamics in the rf
gun, and gives output beam characteristics and ~ (orI bi ) as well, while Jcathode [ Ncm2 ] is given as a functionof Tcathode [K] as
Jcathode =1.12x10 exp -1.89x10 Tcathode).

7 (4/~-explliment
I· · -calruation

0.6'[0.4c..,'ll.

4. COMPARISON BETWEENNUMERICAL AND
EXPERIMENTAL RESULTS

t (f.loS"C)Firstly, for verification of the circuit model, time
evolutions of f>.er were calculated without an electron
beam, i.e. J cathode = 0. As seen in Fig. 5 the results
are found to agree with the experimental ones
without heating the cathode, for both cases off = fo and f ¢ fo ·Secondly, it was applied to the case with anelectron beam to reproduce the experimentallyobserved Prer shown in Fig. 2. The rf frequency fwas
fixed at f = 2857.77 MHz. Neither of the numericalresults is found to agree with the experimental one.
Then, by assuming a linear dependence of Tcathode on tduring the macro-pulse, the experimental one could bereproduced well, as seen in Fig. 6 with trials and errors
for a temperature rise from Tcathode = 1000 "C at t = 0 toTcathode = 1150 °C at t = 2.1 f.A.Sec.
Finally, on the above assumption of the cathodetemperature rise, calculated! evolution of Eb,peak wascompared with the experimental one shown in Fig. 3.
They are found in good agreement as seen in Fig. 7.

Figure 6 Calculated time evolution of P,ef with anincrease of cathode temperature.
10

80~

60000

.....1 4

0.5

1.0

1.5

2.0

25

3.0t [f.loS"C)

Figure 7 Time evolution of peak beam energy
Eb, comparing experiments and calculation.

5. CONCLUSION·\_________} · · ...

.

40-1.

:·-JA.

_j'·.~0The observed time evolutions of the reflected rf
power and the beam energy were well reproduced by
the present numerical model. The observed energy
decrease through the macro-pulse is supposed to becaused by a considerable cathode temperature rise due
to back-streaming electrons onto the thermioniccathode.

1

2

3

4

REFERENCES..

[1].
5t f f.A.Sec][2].

Figure 5
Time evolution of Pref comparing
experiment and calculation, without electron beam for f= 2857.60 MHz at resonance.

[3].

- 36-T. Kii, et al., "Experiment and analysis on
back-bombardment effect in thermionic rf gun",Nucl. Instr. Meth. A, in press.
T. Kii, et al., "Evaluation of thermal effects due
to back-streaming electrons in iae rf gun ", inthese proceedings.
K. Masuda, "Development of Numerical
Simulation Codes and Application to Klystron
Efficiency Enhancement", Ph.D. thesis, Kyoto
University (1998).