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Beam self-excited oscillation in linac buncher section
Nuclear Instruments and Methods in Physics Research A 349 (1994) 614-617 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A
Beam self-excited oscillation in linac buncher section A.V. Smirnov *, V.N. Smirnov Russian Research Center "Kurchatov Institute", Moscow, 123182, Russian Federation Received 25 February 1993; revised form received 21 March 1994
The effect of self-excited RF-oscillation by a continuous low voltage beam in a waveguide linac section is observed experimentally. The common features and differences compared with a conventional backward-wave tube are analysed. Application of this effect is proposed for the purpose of impedance and group velocity measurements in slow-wave periodic structures.
1. Introduction Stable RF-generation at the same operating frequency was observed in the first section of a multisection RF travelling wave linac when the klystron was turned off. This effect has a number of features different from a conventional BWO tube. The first one is a relatively high efficiency. The experimental layout is shown in Fig. 1. The injector with thermionic gun can deliver the electron beam with the following maximum parameters of current, voltage and pulse duration: I b = 7 A, Vb = 120 kV, t b = 7 p.s. The structure consists of a circular disk loaded tapered waveguide (DLWG structure) with internal RF ohmic load and symmetrized RF-coupler. Focusing is provided by a set of three solenoid coils with variable field profile. Magnetic field maximum is about 0.13 T. Another elements are intended for measuring the amplitude, frequency and time parameters of generated signal and for tuning the phase and absolute value of the reflection coefficient F 1 seen by the section in the regime of self-excited oscillation. In the accelerating mode this section gives about 5.5 MeV, 1 A accelerated beam at 15 MW RF-power.The main parameters are plotted along the section in Fig. 2. The relative amplitude parameter DA, = E , A / xfff = / R s , 2 W A / ( Q / 3 g , ) and wave phase velocity related to the speed of light are presented in the Fig. 2 for both fundamental harmonic (n = 0) and backward space harmonic (n = - 1 ) . Here P and /3grc are the power and group velocity of the travelling wave, A = 2~rc/f, Q is the waveguide quality factor, E , is the electric field amplitude and Rs, is the shunt impedance for the n-th space harmonic. The section consists of three main parts: L a is the prebunching subsection at /3o = const = / 3 b = Ub/C (-rr/2 accelerating mode); L 2 is the bunching and acceler* Corresponding author.
ating subsection at /3o = var ( r r / 2 mode) and supplied by phase shifting cells; L 3 is the accelerating subsection with /3o = 1 ( 2 ~ / 3 accelerating mode), which is separated from L 2 by matching cell and supplied by the end cells covered by absorbing layer. The last L 3 subsection has the following geometry: loading parameter a / A = 0.11, disk thickness t / h = 0.0365, internal radii ratio a / b = 0.26.
2. Experimental results Since the injected beam with fib = 0.5--0.6 is close to the synchronism with - 1 space harmonic in the L 3 subsection we can expect beam-backward wave interaction of BWO type. Fig. 3 shows the plots of measured peak power Pg and generated pulse length tg v e r s u s the beam current at beam voltage Vb = 100 kV, t b = 5.5 la.s. The measured width of the dominant frequency component is about 1 MHz and the optimum value of reflection coefficient I F1 I is about 0.17. It is interesting to note, that the generated RF peak power can be comparable with the pulse beam power due to generated pulse length reduction (compression effect). Pulse length increasing took place while the leading edge of the RF-envelope was moving in the left direction (see Fig. 4). In the Fig. 4 we see that the trailing edge of the generated pulse (top curve) arrives before that of the beam current pulse (down curve). The maximum electronic efficiency of the oscillation was calculated as a ratio of energies and has reached the value of 65%. This value depends very strong on the quality of the adjustment of the following parameters: - t h e voltage standing wave ratio of the section ( " c o l d " measurements) close to 1.25 ( f = 1817_+0.2 MHz) by means of disk curving and subsections matching; - phase and absolute value of the coefficient of reflections from the external load; - focusing solenoidal field profile along the section.
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-9002(94)00462-G
A.V. Smirnov, V.N. Smirnov /Nucl. Instr. and Meth. in Phys. Res. A 349 (1994) 614-617
i Oscilloscope
peak power, kW
and ~requency spectrum analyse ~]
Poiseduration tcj, microseconds
Pulse
15Oloo
615
~~
22'5335
15
Peak power 50
1 O5
0
~ 02
0
04
~ 08
06
1
12
~ 1.4
16
18
0
2
Beam current I, A Fig. 1. Experimental layout for measurement of the parameters of the self-excited oscillation in DLWG tapered section.
6C,07JA, C~lm1/'2 soo4oc,rl : soo i i I
Re ative phase & grou9('~O) velocities //
/~ / -=
,///
"
[}~, \x\
s
J
/
~hase velocity ,:in=-':) o |
f
s/ " ~,oo ~L" ~ i
e "1E-4 Relative frequency deviation (f fo)/fo
//
,/
0
>base ve!osit y (r'=O)
The frequency sensitivity is plotted in Fig. 5 for the beam currents in the range of 0.25-0.6 A. Averaged electronic tuning rate ( S ) = A f / A V b measured is 72 Hz/V.
/
200
0
12
Fig. 3. Generated peak power and pulse duration as a function of the beam current.
"\
• Greuo velocitv*lC, 02 L3, , "l
L2
,
2
O4
4 .
.
.
.
.
6 2-
.
.
.
.
~Sig MHZ fo ~
~
l
-4
i
3
4
5
6
1,
8
9
10
z/waveler'gth Fig. 2. The parameters of the experimental section. Relative amplitude, dimensionless phase velocity for the fundamental and backward - 1 space harmonic, group velocity are plotted along the section.
6 -8 10
62
I
67
72
77 82 87 Beam vo:tage, kV
92
97
102
Fig. 5. The frequency sensitivity plot for the generated RF-pulse.
Fig. 4. Traces of the oscilloscope RF-envelope (top curve) and input current pulse (bottom curve) shapes.
616
A. IA Smirnou, V.N. Smirnov / Nucl. Instr. and Meth. in Phys. R es. A 349 (1994) 614-617
Under some conditions (focusing field profile and F 1 readjustment) we have observed ripples in RF-envelope with period = 0.7 tzs (that is about twice of the filling time tf for the section) and relative amplitude variation up to 30% at tg = 6 ~ s and t b = 5.1 Izs. As the beam current was increasing I b > 2.5 A the ripples were converting into chaotic pulsations.
3. The analysis of the experimental results The experimental value of the threshold current I s = 0.25 A at Vb = 8 0 kV is very close to that the value calculated according to BWO theory [1] for the L 3 subsection in assumption of weak space charge effect: I S = V b / ( 8 . 2 N 3 R c ) , where N is the number of slow waves per interaction length L 3 with the exception of cells with high RF-losses, R c is the coupling impedance. In our case the dimensionless space charge parameter value C = 0.05 << 1, the coupling impedance for - 1 space harmonic calculated with the help of handbook [2] is equal to R c = 150 ~ . The group velocity J~gr¢ for the L 3 subsection can be defined from the experimental data with taking into account relativistic effects from the following expression: e
S
f
1
me2l~b,y3 Relative
1-
(1)
j~b//~gr "
amol rude A
Bunching
factor
F io4
0/-!i8A
a) 1o3
03
02
0
C,
04,
i
~elative
Calculated /~gr v a l u e is - 0.011 at Vb = 88 kV and S = 170 H z / V , while for the average value ( S ) = 72 H z / V / 3 g r = - 0 . 0 0 4 7 . Note, the precise value of I/3g r I is 0.011 at f = 1818.5 MHz. We suppose the nonlinearity of Fig. 4 plot is due to reflected waves neglected in Eq. (1). We have assumed also that the enormously high efficiency of RF generation with respect to a conventional BWO is provided by the e-beam prebunching resulted from interaction with partially reflected wave from the RF coupler and transformed into forward wave in subsection L 1. A qualitative verifying of this assumption can give simulation results presented below. Time-dependent code used and described in the refs. [3,4] was modified to take into account non-fundamental space harmonics. We can compare dimensionless RF-field amplitude eEA/mo c2 and beam bunching factor plots along the section for the cases of nonzero reflections (Fig. 6a [ F 1 J = 0.25, I b = 1.15 A) and zero reflections (Fig. 6b F 1 = 0, I b = 2.5 A). Beam voltage was taken 95 kV, pulse length is equal to tf. We see more stronger and enhanced bunching in L 1 and L 2 subsections in the first case. Thus beam prebunching takes place in the first subsection and results in improved efficiency.
2
3
,I
ampiitude
5 6 7 z/wavelength
8
A
9
10
Bunching
11
12
factor
F
~04 i
b)
4. Conclusions 1) The measurement of the threshold current and frequency sensitivity of the self-excited RF oscillation which is induced by the low voltage beam is a simple way of experimental determining coupling impedance and group velocity for accelerating (slow wave) structures. 2) The high efficiency of the RF-generation observed is due to the action of the second delayed feedback loop when the reflected wave causes the initial beam prebunching in the first subsection. In the first two subsections we have basically klystron type of bunching, the second subsection plays a role of a drift space. 3) RF pulse shortening and compression observed in experiment is concerned with the action of the delayed feedback loop and requires further consideration. 4) The considered interaction of beam with two harmonics can be classified as an oscillator of BWO-TWT type. On the other hand, it has common features with a twystron amplifier with a feedback loop. It may be used in a special two-purpose accelerating/oscillating structures.
Acknowledgements 0
2
3
4
5 6 7 z/wavelength
8
9
~0
11
12
Fig. 6. Calculated plot of the dimensionless field amplitude A and bunching factor F along the section with taking into account reflected wave (a) and without taking into account reflected wave (b).
The authors wish to express their sincere appreciation to Prof. V.V. Petrenko for the experimental work organisation and helpful discussions, K.E. Sokolov for the skilful RF-measurements and all staff of the linac lab for the comprehensive assistance during the experimental work.
A. V. Smirnov, V.N. Smirnov / NucL Instr. and Meth. in Phys. Res. A 349 (1994) 614-617
The authors would like to acknowledge very useful discussions with Profs. V.I. Mostovoy, E.S. Masunov, N.P. Sobenin and C. Pellegrini.
References [1] I.V. Lebedev, RF-Technique and Devices. Part 2, Vushya shcola, Moscow, USSR, 1972 (in Russian).
617
[2] O.A. Valdner, N.P. Sobenin, B.V. Zverev, I.S. Schedrin, The Handbook on Circular Disk Loaded Waveguides (Atomizdat, Moskow, 1977) (in Russian) [3] V.V. Kalashnikov et al., Proc. 13th Int. Conf. on High Energy Accelerators, Novosibirsk, USSR, ed. A.N. Skrinski (Nauka, 1987) vol. 1, p. 304-307. [4] A.V. Smimov, Proc. l l t h All-Union Conf. on Charged Particles Accelerators, Dubna, JINR, 1989, vol. 1, pp. 488-490 (in Russian).
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A
Beam self-excited oscillation in linac buncher section A.V. Smirnov *, V.N. Smirnov Russian Research Center "Kurchatov Institute", Moscow, 123182, Russian Federation Received 25 February 1993; revised form received 21 March 1994
The effect of self-excited RF-oscillation by a continuous low voltage beam in a waveguide linac section is observed experimentally. The common features and differences compared with a conventional backward-wave tube are analysed. Application of this effect is proposed for the purpose of impedance and group velocity measurements in slow-wave periodic structures.
1. Introduction Stable RF-generation at the same operating frequency was observed in the first section of a multisection RF travelling wave linac when the klystron was turned off. This effect has a number of features different from a conventional BWO tube. The first one is a relatively high efficiency. The experimental layout is shown in Fig. 1. The injector with thermionic gun can deliver the electron beam with the following maximum parameters of current, voltage and pulse duration: I b = 7 A, Vb = 120 kV, t b = 7 p.s. The structure consists of a circular disk loaded tapered waveguide (DLWG structure) with internal RF ohmic load and symmetrized RF-coupler. Focusing is provided by a set of three solenoid coils with variable field profile. Magnetic field maximum is about 0.13 T. Another elements are intended for measuring the amplitude, frequency and time parameters of generated signal and for tuning the phase and absolute value of the reflection coefficient F 1 seen by the section in the regime of self-excited oscillation. In the accelerating mode this section gives about 5.5 MeV, 1 A accelerated beam at 15 MW RF-power.The main parameters are plotted along the section in Fig. 2. The relative amplitude parameter DA, = E , A / xfff = / R s , 2 W A / ( Q / 3 g , ) and wave phase velocity related to the speed of light are presented in the Fig. 2 for both fundamental harmonic (n = 0) and backward space harmonic (n = - 1 ) . Here P and /3grc are the power and group velocity of the travelling wave, A = 2~rc/f, Q is the waveguide quality factor, E , is the electric field amplitude and Rs, is the shunt impedance for the n-th space harmonic. The section consists of three main parts: L a is the prebunching subsection at /3o = const = / 3 b = Ub/C (-rr/2 accelerating mode); L 2 is the bunching and acceler* Corresponding author.
ating subsection at /3o = var ( r r / 2 mode) and supplied by phase shifting cells; L 3 is the accelerating subsection with /3o = 1 ( 2 ~ / 3 accelerating mode), which is separated from L 2 by matching cell and supplied by the end cells covered by absorbing layer. The last L 3 subsection has the following geometry: loading parameter a / A = 0.11, disk thickness t / h = 0.0365, internal radii ratio a / b = 0.26.
2. Experimental results Since the injected beam with fib = 0.5--0.6 is close to the synchronism with - 1 space harmonic in the L 3 subsection we can expect beam-backward wave interaction of BWO type. Fig. 3 shows the plots of measured peak power Pg and generated pulse length tg v e r s u s the beam current at beam voltage Vb = 100 kV, t b = 5.5 la.s. The measured width of the dominant frequency component is about 1 MHz and the optimum value of reflection coefficient I F1 I is about 0.17. It is interesting to note, that the generated RF peak power can be comparable with the pulse beam power due to generated pulse length reduction (compression effect). Pulse length increasing took place while the leading edge of the RF-envelope was moving in the left direction (see Fig. 4). In the Fig. 4 we see that the trailing edge of the generated pulse (top curve) arrives before that of the beam current pulse (down curve). The maximum electronic efficiency of the oscillation was calculated as a ratio of energies and has reached the value of 65%. This value depends very strong on the quality of the adjustment of the following parameters: - t h e voltage standing wave ratio of the section ( " c o l d " measurements) close to 1.25 ( f = 1817_+0.2 MHz) by means of disk curving and subsections matching; - phase and absolute value of the coefficient of reflections from the external load; - focusing solenoidal field profile along the section.
0168-9002/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-9002(94)00462-G
A.V. Smirnov, V.N. Smirnov /Nucl. Instr. and Meth. in Phys. Res. A 349 (1994) 614-617
i Oscilloscope
peak power, kW
and ~requency spectrum analyse ~]
Poiseduration tcj, microseconds
Pulse
15Oloo
615
~~
22'5335
15
Peak power 50
1 O5
0
~ 02
0
04
~ 08
06
1
12
~ 1.4
16
18
0
2
Beam current I, A Fig. 1. Experimental layout for measurement of the parameters of the self-excited oscillation in DLWG tapered section.
6C,07JA, C~lm1/'2 soo4oc,rl : soo i i I
Re ative phase & grou9('~O) velocities //
/~ / -=
,///
"
[}~, \x\
s
J
/
~hase velocity ,:in=-':) o |
f
s/ " ~,oo ~L" ~ i
e "1E-4 Relative frequency deviation (f fo)/fo
//
,/
0
>base ve!osit y (r'=O)
The frequency sensitivity is plotted in Fig. 5 for the beam currents in the range of 0.25-0.6 A. Averaged electronic tuning rate ( S ) = A f / A V b measured is 72 Hz/V.
/
200
0
12
Fig. 3. Generated peak power and pulse duration as a function of the beam current.
"\
• Greuo velocitv*lC, 02 L3, , "l
L2
,
2
O4
4 .
.
.
.
.
6 2-
.
.
.
.
~Sig MHZ fo ~
~
l
-4
i
3
4
5
6
1,
8
9
10
z/waveler'gth Fig. 2. The parameters of the experimental section. Relative amplitude, dimensionless phase velocity for the fundamental and backward - 1 space harmonic, group velocity are plotted along the section.
6 -8 10
62
I
67
72
77 82 87 Beam vo:tage, kV
92
97
102
Fig. 5. The frequency sensitivity plot for the generated RF-pulse.
Fig. 4. Traces of the oscilloscope RF-envelope (top curve) and input current pulse (bottom curve) shapes.
616
A. IA Smirnou, V.N. Smirnov / Nucl. Instr. and Meth. in Phys. R es. A 349 (1994) 614-617
Under some conditions (focusing field profile and F 1 readjustment) we have observed ripples in RF-envelope with period = 0.7 tzs (that is about twice of the filling time tf for the section) and relative amplitude variation up to 30% at tg = 6 ~ s and t b = 5.1 Izs. As the beam current was increasing I b > 2.5 A the ripples were converting into chaotic pulsations.
3. The analysis of the experimental results The experimental value of the threshold current I s = 0.25 A at Vb = 8 0 kV is very close to that the value calculated according to BWO theory [1] for the L 3 subsection in assumption of weak space charge effect: I S = V b / ( 8 . 2 N 3 R c ) , where N is the number of slow waves per interaction length L 3 with the exception of cells with high RF-losses, R c is the coupling impedance. In our case the dimensionless space charge parameter value C = 0.05 << 1, the coupling impedance for - 1 space harmonic calculated with the help of handbook [2] is equal to R c = 150 ~ . The group velocity J~gr¢ for the L 3 subsection can be defined from the experimental data with taking into account relativistic effects from the following expression: e
S
f
1
me2l~b,y3 Relative
1-
(1)
j~b//~gr "
amol rude A
Bunching
factor
F io4
0/-!i8A
a) 1o3
03
02
0
C,
04,
i
~elative
Calculated /~gr v a l u e is - 0.011 at Vb = 88 kV and S = 170 H z / V , while for the average value ( S ) = 72 H z / V / 3 g r = - 0 . 0 0 4 7 . Note, the precise value of I/3g r I is 0.011 at f = 1818.5 MHz. We suppose the nonlinearity of Fig. 4 plot is due to reflected waves neglected in Eq. (1). We have assumed also that the enormously high efficiency of RF generation with respect to a conventional BWO is provided by the e-beam prebunching resulted from interaction with partially reflected wave from the RF coupler and transformed into forward wave in subsection L 1. A qualitative verifying of this assumption can give simulation results presented below. Time-dependent code used and described in the refs. [3,4] was modified to take into account non-fundamental space harmonics. We can compare dimensionless RF-field amplitude eEA/mo c2 and beam bunching factor plots along the section for the cases of nonzero reflections (Fig. 6a [ F 1 J = 0.25, I b = 1.15 A) and zero reflections (Fig. 6b F 1 = 0, I b = 2.5 A). Beam voltage was taken 95 kV, pulse length is equal to tf. We see more stronger and enhanced bunching in L 1 and L 2 subsections in the first case. Thus beam prebunching takes place in the first subsection and results in improved efficiency.
2
3
,I
ampiitude
5 6 7 z/wavelength
8
A
9
10
Bunching
11
12
factor
F
~04 i
b)
4. Conclusions 1) The measurement of the threshold current and frequency sensitivity of the self-excited RF oscillation which is induced by the low voltage beam is a simple way of experimental determining coupling impedance and group velocity for accelerating (slow wave) structures. 2) The high efficiency of the RF-generation observed is due to the action of the second delayed feedback loop when the reflected wave causes the initial beam prebunching in the first subsection. In the first two subsections we have basically klystron type of bunching, the second subsection plays a role of a drift space. 3) RF pulse shortening and compression observed in experiment is concerned with the action of the delayed feedback loop and requires further consideration. 4) The considered interaction of beam with two harmonics can be classified as an oscillator of BWO-TWT type. On the other hand, it has common features with a twystron amplifier with a feedback loop. It may be used in a special two-purpose accelerating/oscillating structures.
Acknowledgements 0
2
3
4
5 6 7 z/wavelength
8
9
~0
11
12
Fig. 6. Calculated plot of the dimensionless field amplitude A and bunching factor F along the section with taking into account reflected wave (a) and without taking into account reflected wave (b).
The authors wish to express their sincere appreciation to Prof. V.V. Petrenko for the experimental work organisation and helpful discussions, K.E. Sokolov for the skilful RF-measurements and all staff of the linac lab for the comprehensive assistance during the experimental work.
A. V. Smirnov, V.N. Smirnov / NucL Instr. and Meth. in Phys. Res. A 349 (1994) 614-617
The authors would like to acknowledge very useful discussions with Profs. V.I. Mostovoy, E.S. Masunov, N.P. Sobenin and C. Pellegrini.
References [1] I.V. Lebedev, RF-Technique and Devices. Part 2, Vushya shcola, Moscow, USSR, 1972 (in Russian).
617
[2] O.A. Valdner, N.P. Sobenin, B.V. Zverev, I.S. Schedrin, The Handbook on Circular Disk Loaded Waveguides (Atomizdat, Moskow, 1977) (in Russian) [3] V.V. Kalashnikov et al., Proc. 13th Int. Conf. on High Energy Accelerators, Novosibirsk, USSR, ed. A.N. Skrinski (Nauka, 1987) vol. 1, p. 304-307. [4] A.V. Smimov, Proc. l l t h All-Union Conf. on Charged Particles Accelerators, Dubna, JINR, 1989, vol. 1, pp. 488-490 (in Russian).