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

LOW OUTPUT-IMPEDANCE RF SYSTEM
FOR HEAVY BEAM LOADING IN PROTON SYNCHROTRONT. Oki\ Y. Irie, S. Takano, KEK, 1-1 Oho, Tsukuba-shi, Ibaraki, 305-0801, JapanThe output-impedance (Zo) in the grounded cathodescheme can be expressed byAbstract
The instability, which is caused by beam induced
current, occurs without effective compensation in a highintensity proton synchrotron. The very low outputimpedance RF system is required for this compensation.
A grounded cathode scheme, having a feedback loop
between plate and grid, can provide such system. 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.

1 INTRODUCTION
In a high intensity proton synchrotron, the wall current
induced by the beam in an RF cavity can not be ignored
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, and many analyses are investigated toavoid it. The stability of the RF system including thebeam was evaluated by using the relative beam loading Y,
which is the ratio of the beam current to the unloaded
generator current [1]. It is implied that the small value of
Y is required for stability, and the very low outputimpedance RF system realises that value of Y.
HVz =(o1+ 1+ pf3 +_!_J-1
zpg +zgkrPzk(1)withz,.kzpg +zgk

/3 =--"-"'Where 11 is the amplification factor, rp the plate resistanceof the tube, zk the load impedance, Zpg the grid-plateimpedance which is composed of rsh, lspg and Cpg, and Zgk
the grid-cathode impedance which is composed of rdrv, lzg
and cgk. The main term in the bracket of Eq. (1) is thesecond one, and then the output-impedance isapproximated byr<::$p(2)z0

1+ J.L/3

Here, the lead inductance (lk) in the cathode circuit infollowing is neglected.
h in Fig. 2 gives a significant contribution to theoutput-impedance. Eq. (1) or Eq. (2) is then modified toinclude the impedance between cathode and ground (zt)that comprises lk and the bypass capacitor (ck) at thefilament power in Fig. 2. The output-impedance including
the contribution of Zt is approximately given by_r..!..P-+zt·(zpg +zggJ .
1+ J.L/3
zgg(3)

Where, zgg is the impedance between grid and groundwhich is composed of r drv, l;n, lzg and Czg. Comparing to Eq.
(2), the zt multiplied by (zpg + zgg) I Zgg increases theoutput-impedance.
Fig. 1 Grounded cathode scheme having dual resonant
circuits and the equivalent circuit.

2 SYSTEM SETUP

As the system, the grounded cathode scheme, having
dual resonant circuits, is able to realise a high voltage
gain and the low output-impedance comparable to thecathode-follower scheme, which is well known by the
low output-impedance characteristic. The one resonant
circuit comprises a parallel tuned circuit between grid andcathode, and the other a feedback loop between plate andgrid. Fig. 1 shows this scheme.

Fig. 2 shows the schematic views of the model RF
system for the grounded cathode scheme, which has dual
resonant circuits. The Eimac triode (3CW40,000H3) isused as the final tube. The de-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

1 also RCNP, Osaka University, Osaka, 567-0047, Japan-220-

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

frequencies of zpg and Zgk are set near to the lowest
frequency of the frequency range. The parameters are
summarised in Table 1.

Pearson model 150 monitors the cavity input current. The
aplate-grid capacitance (cpg) and stray capacitance (c,,) oflspg• and the zgk with lzg, r drv• a grid-cathode capacitance(cgk) and stray capacitance (czg) of lzg. The resonant

Zpg comprises a parallel resonant circuit with lspg• r,h,6.3KV, 5.4A
r----------~~---------,

I1

solid-statewide-band
amplifierr----1/pk Clpk

1I

ferrite cavity

Pearson 1
model150 1

II
IIII
IIII
III
I

I

filament
powerI
1drive----voltageII-4!------- ~avity- cavi; j.

-195V

Eimac
voltage current
3CW40,000H3

programmablearbitrary/functio
generator

bias
power supply

Fig. 2 Model RF system for the grounded cathode scheme, which has dual resonant circuits.
Table 1 Parameters of the model RF system.

cavity gap capacitance Cgap

(pF)

273

18

cavity inductance lcav

(IJ.H)

1.3-15(0)310

cavity shunt resistance rcav

(0)

500

Cgk

(pF)

75.7

Cpg

(pF)

50.8

lzg

(IJ.H)

41.3

3.1 Output-impedanceCzg

(pF)

27.5

(0)

50(IJ.H)

50.7(0)

428

(pF)

28.5

A Hewlett Packard 4195A network/spectrum analyser
is used to measure the output-impedance. The probe isconnected to the output terminal of RF system. As theoutput-impedance is dependent on the P in Eq. (1),various measurements for the shunt resistor (rtirv) of 50,150, and 300 0 are performed. The measurements andcalculations at the resonant cavity frequency arecompared in Fig. 3.

(nF)

120

(IJ.H)

0.3(IJ.H)

0.5

3 EXPERIMENTAL RESULTS-221-The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

100 .------.----.------,------,----.----,-----,---(a)10~~~-r--r--+--+--+--+-~.••c .••.•....•••

....
8~1~
_ _T~==~~~=~~o~··.J.-j--J-~r--

I--;.:··-o ..

6~-~~~~--~---+~~~~-~~-.+~----~
20~~-~--+--+--r-,r-1--

4~

(b)

4~-~--~--~--+---+---+---+-~
2~--~--1----I-----1----+--+--+-----J

10

6frequency[MHz],------,--,------,------,--,--,-,---,
440~~--4--+--+--+--r-,r~l,......,;!

20 ~-.....--- - - --- 0

c r---:.:o·· ···o··· ·o····* ··to'''!> "'"o'''~--20c

910Fig. 4 Voltage gain of the driver to the cavity gap.
Square shows the measurements under the gap voltage of530-820 V. The solid and dotted lines show thecalculations at 500 and 1500 Q ofrcav, respectively.

.

----40 ~~--4--+--+--+--r--t-~4

6
fi-equency[MHz]10frequency[MHz]Fig. 3 Output-impedance of the grounded cathode schemeat the shunt resistor (rdrv) of 50 (square), ISO (lozenge),and 300 (triangle) Q; (a) magnitude and (b) phase.
Measurements are compared to calculations denoted bysolid, dotted and dashed lines, respectively.
For rdrv of 300 Q, Absolute value of the first term in Eq.
(3) and (zpg + Zgg) I zgg, which is the coefficient of z1, are36.8-34.7 Q and 2.53-1.53 over the frequency range of 210 MHz, respectively. Therefor, the second term in Eq.
(3) occupies 20-60 percent of output-impedance.

3.2 Voltage gain
Fig. 4 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 l;nthat is the lead inductance of input terminal of RF system
in Fig. 2.
In the calculations, a peaking structure can be seen. Itis explained mainly in terms of the series resonance,
which is composed of the lin + lk and the plate-grid
capacitance, where the capacitance becomes (1 +,u)-times
larger by the Miller effect. Because it is surmised that thecavity shunt resistance (rcav) decreases with frequency
gradually, there is no peaking structure in themeasurement.

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.
We have studies with much higher power tube for
future applications. The triode whose maximum plate
dissipation is 240 kW is used as a final amplifier. As theexpectation, the output-impedance is 21-27 ohms and thevoltage gain is 25-60 over the frequency range of2.7-6.2
MHz. Regarding output-impedance, it is comparable withthat obtained by cathode-follower beam buncher in theProton Storage Ring [2].

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

REFERENCES[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] G. Lawrence, private communication (Accelerator
Technology Division semi-annual report, LosAlamos National Laboratory, 1985)-222-