VERY LOW OUTPUT-IMPEDANCE RF SYSTEM
FOR A PROTON SYNCHROTRONT. Oki1, Y. Irie, S. Takano, KEK, 1-1 Oho, Tsukuba-shi, Ibaraki, 305-0801, Japan

Abstract
The very low output-impedance RF system is required
for a high intensity proton synchrotron in order to cancel
the beam loading. A grounded cathode scheme, having
dual resonant circuits, can provide such system. The one
resonant circuit is formed between grid and cathode, andthe other comprises a feedback loop between plate andgrid. The model system has been tested using the Eimac
3CW40,000H3 triode as a final tube. By choosing theappropriate resonant frequencies, the output-impedance isobtained as 30-80 ohms and the voltage gain 6-10 overthe frequency range of 2.5-8.5 MHz. Stability of thesystem is also discussed.

1 INTRODUCTION
In a high intensity proton synchrotron, the wall current
induced by the beam in an RF cavity can not be ignored
any more against the drive current which is supplied by
RF power supply and the instability occurs without propercompensation. The contribution of this beam is called abeam loading, many analyses are investigated to avoid it.
As that example, the stability of the RF system including
the beam was evaluated by using the relative beamloading Y which is the ratio of the beam current tounloaded generator current [1]. Fig. 1 shows the typicalstability analysis which is distinguished by Y, and φz is thephase of impedance of the RF system which consists ofcavity and power supply. As the result, stability is realisedby the small value of Y, and the very low outputimpedance RF system is required for that value of Y. Asthe system, following two methods are applied. The one isthe feed-forward beam compensation [2]. In this method,
the signal of the beam is fed back with one-turn delay tomake up for the beam current, in which a complex
procedure should be necessary. The other is the low
output-impedance RF system by the cathode-follower
scheme (CF) [3]. In this method, because of that low
output-impedance characteristic, the beam loading can becompensated for without a complex procedure. However
there is the disadvantage that a voltage gain is smaller
than unity in this method, and it causes huge power
consumption in the driver stage.

1also RCNP, Osaka University, Osaka, 567-0047, JapanFig. 1 Stability analysis. Synchrotron angular frequency is2kHz, and the bandwidth of the RF system is 19 MHz.
There are the automatic voltage control loop and thephase loop. These bandwidths are 10 kHz and 200 kHz,respectively.
Against these compensations, the grounded cathodescheme, having dual resonant circuits, is able to realise ahigh voltage gain and the low output-impedancecomparable to the CF. The one resonant circuit comprisesa parallel tuned circuit between grid and cathode, and theother a feedback loop between plate and grid. Fig. 2
shows this scheme.

Fig. 2 Grounded cathode scheme having dual resonant
circuits and the equivalent circuit.
The output-impedance (Zo) in the grounded cathodescheme can be expressed by−11
1 + µβ 1 ,++Zo = 
z +z
rzpg
gkpk



(1)

with

β=z gkz pg + z gk.

Where µ is the amplification factor, rp the plate resistanceof the tube, zk the load impedance, zpg the grid-plate
impedance and zgk the grid-cathode impedance. The main

term in the bracket of Eq. (1) is the second one, and thenthe output-impedance is approximated byZo ≈rp1 + µβ.

It should be noted that the output-impedance of the CF is
also expressed in Eq. (1). Then, by choosing theappropriate value of β, the proposed system can provide
an output-impedance as low as that of the CF while thevoltage gain is much higher than unity.

Fig. 3 Model RF system for the grounded cathode scheme, which has dual resonant circuits.
Table 1 Parameters of the model RF system.

2 SYSTEM SETUP

µrp

18310

cgk

(Ω)
(pF)

75.7

cpg

(pF)

50.8

lzg

(µH)

41.3

czg

(pF)

27.5

rdrv

(Ω)

50

lspg

(µH)

50.7

rsh

(Ω)

428

cst

(pF)

28.5

ck

(nF)

120

lk

(µH)

0.3

lin

(µH)

0.5

cavity gap capacitance cgap

(pF)

273

cavity inductance lcav(µH)

1.3-15

cavity shunt resistance rcav

(Ω)

500

Fig. 3 shows the schematic views of the model RFsystem for the grounded cathode scheme, which has dual
resonant circuits. The Eimac triode (3CW40,000H3) isused as the final tube. The dc-bias power supply feeds abias current to keep the ferrite-loaded cavity at resonance.
The relation of the resonant frequency versus bias current
was measured over the frequency range of 2.5-8.5 MHz.
The maximum frequency is restricted by the current
limitation of the bias power-supply. The plate voltage forthe tube is 6.3 KV and the quiescent current is 5.4 A. A
Pearson model 150 monitors the cavity input current. Thezpg comprises a parallel resonant circuit with lspg, rsh, aplate-grid capacitance (cpg) and stray capacitance (cst) oflspg, and the zgk with lzg, rdrv, a grid-cathode capacitance(cgk) and stray capacitance (czg) of lzg. The resonant
frequencies of zpg and zgk are set near to the lowest
frequency of the frequency range. The parameters are
summarised in Table 1.

3 EXPERIMENTAL RESULTS
3.1 Output-impedance
A Hewlett Packard 4195A network/spectrum analyser
is used to measure the output-impedance. The probe isconnected to the output terminal of RF system. As theoutput-impedance is dependent on the β in Eq. (1),various measurements for the shunt resistor (rdrv) of 50,150, and 300 Ω are performed. The measurements andcalculations at the resonant cavity frequency arecompared in Fig. 4.

Fig. 4 Output-impedance of the grounded cathode scheme.
Measurements with shunt resistor (rdrv) at 50 (square), 150(lozenge), and 300 (triangle) Ω are compared tocalculations denoted by solid, dotted and dashed lines,respectively.

3.2 Voltage gain
Fig. 5 shows the voltage gain of the driver to the cavity
gap under the gap voltage of 530-820 V. At a higher
frequency, the gain decreases with frequency due to linthat is the lead inductance of input terminal of RF system.

measurements are higher than calculations at low
frequency range.

4 DISCUSSION AND CONCLUSIONS
Low impedance RF system with high voltage gain wastested in the frequency range of 2.5-8.5 MHz. The model
system comprises a 1 KW solid-state amplifier and a 40
KW triode as a final amplifier. The grounded cathodescheme, having dual resonant circuits, can provide thevery low output-impedance RF system. Consequently, theoutput-impedance is obtained as 30-80 ohms and thevoltage gain 6-10.
At the Rutherford Appleton Laboratory’s neutron
spoliation source ISIS, the upgrade plan has been studied
that is to increase the extracted beam current from 200 to
300 µA as an average by using 2nd harmonic RF cavity[3]. And the beam current in the ring reaches 3.9-9.3A
from injection to extraction of the beam. For thisapplication, We have studied with much higher power
tube. The triode whose maximum plate dissipation is 240
kW is used as a final amplifier. As the calculations, theoutput-impedance of 21-27 ohms and the voltage gain of25-60 are expected over the frequency range of 2.7-6.2
MHz. Because an output voltage of 1-10kV leads theunloaded generator current to 33-333A, Y becomes 0.120.03 and decides to belong to stable region fully be seenin Fig. 1.
Regarding output-impedance, it is comparable with thatobtained by cathode-follower beam buncher in the Proton
Storage Ring [4].

ACKNOWLEDGMENTS
Discussions with Prof. K. Sato and Prof. S. Ninomiya
are appreciated. The authors would also like to thank Prof.
I. Yamane for continuous encouragement.

REFERENCES
Fig. 5 Voltage gain of the driver to the cavity gap.
Square shows the measurements under the gap voltage of
530-820 V. The solid and dotted lines show thecalculations at 500 and 1500 Ω of rcav, respectively.
In the calculations, a peaking structure can be seen. It isexplained mainly in terms of the series resonance, whichis composed of the lin + lk, that is the lead inductance of
cathode circuit, and the plate-grid capacitance, where thecapacitance becomes (1+µ)-times larger by the Millereffect. Because it is surmised that the cavity shunt
resistance (rcav) decreases with frequency gradually, there
is no peaking structure in the measurement, and the[1] F. Pedersen, “BEAM LOADING EFFECTS IN THE
CERN PS BOOSTER,” IEEE Trans. Nucl. Sci., vol.
NS-22, No. 3, pp. 1906-1909, June 1975.
[2] P. Barratt, “The ISIS Synchrotron RF System at HighIntensity,” Proc. ICANS XII, Oxfordshire, U.K., May
1993, pp. 109-114.
[3] M. R. Harold et al., “A POSSIBLE UPGRADE FOR
ISIS,” Proc. PAC 97, Vancouver, Canada, May 1997,
pp. 1021-1023.
[4] G. Lawrence, private communication (Accelerator
Technology Division semi-annual report, Los Alamos
National Laboratory, 1985)