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Observation of chirping in a traveling-wave cyclotron maser experiment
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH
Nuclear Instruments and Methods in Physics Research A 341 (1994) 115-118 North-Holland
Section A
Observation of chirping in a traveling-wave cyclotron maser experiment a E . Jerby a, *, G . Bekefi b , A . Shahadi
° Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel 6 Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Following the recent traveling-wave cyclotron (TWC) amplifier experiment at MIT, we report in this paper on a frequency modulation (FM) effect observed in the TWC oscillator experiment conducted at Tel Aviv University . The TWC oscillator operates in the microwave regime (9.4 GHz) . It consists of a low-energy (8 keV) low-current (0 .2 A) electron beam spiraling m a metallic periodic waveguide. The TWC oscillator produces an RF pulse of - 400 W power. Frequency modulation (chirping) is observed during the TWC pulse by an heterodyne technique. This effect is related to the electron energy variation during the pulse. 1. Introduction The traveling wave cyclotron (TWO free-electron maser is a cyclotron-type device in which a nonrelativistic electron beam interacts with traveling waves in a metallic periodic waveguide. In the first TWC amplifier experiment conducted recently at MIT [1,21 a low-energy electron beam (- 10 keV, - 1.0 A) spiraling in an axial magnetic field of 3.1 kG, amplified a 8.2 GHz signal in a periodic waveguide. The interaction region consisted of an array of metal posts in a rectangular waveguide as shown in Fig. 1 . Electronic gain of - 10 dB was measured in this experiment near the cyclotron resonance [1,2]. A theoretical analysis of the TWC interaction in the linear regime [1,3] shows that the tuning relation of the TWC interaction with the fundamental spatial harmonic of the periodic waveguide is given by to = co y + Uo(-) " ( 1)
where to and to y are the electromagnetic wave and the electron cyclotron frequencies, respectively, Ve is the electron axial velocity, and 6 t,(to) is the wavenumber of the fundamental spatial harmonic in the periodic waveguide determined by its dispersion relation . The cyclotron frequency is given by : e o, Bo, Wo - -B (2) where e, m, and y are the electron charge, mass, and relativistic factor, respectively, and B o is the axial magnetic field. The TWC interaction incorporates different opposing effects including cyclotron resonance maser and Weibel effects. The theory shows that the TWC interaction has different properties for V1 ,, = 0 * Corresponding author .
and V1 p *- 0, where V1 o is the electron initial transverse velocity. The TWC gain scales in general as Vi o . Near cutoff of the inductive periodic waveguide, stimulated emission of radiation is feasible even with V1 0 = 0, as observed in refs . [1,2]. Following the TWC amplifier experiment at MIT, we constructed an oscillator experiment at Tel Aviv University . The oscillator apparatus is based on the traveling-wave FEM experimental setup [4]. In this paper we present frequency modulation (chirping) observed in the TWC oscillator experiment at Tel Aviv University . 2. The oscillator experiment The TWC oscillator employs a Pierce type electron gun. A low-energy electron beam (8 keV) is injected on-axis into the periodic waveguide. The electrons acquire initial transverse velocity by a small kicker coil at the entrance to the interaction region . The oscillator experiment employs the same inductive periodic waveguide used at MIT [1,2]. It consists of an array of metal posts in a rectangular waveguide (WR90) as shown in Fig. 1 . The beam is contained by a uniform axial magnetic field (4 .2 kG) produced by a solenoid . The electron beam is collected at the exit of the interaction region by a collector which measures the current. The parameters of the oscillator experiment at Tel Aviv University are listed in Table 1 . In comparison with the parameters of the amplifier experiment at MIT, the main differences between the two setups are: (a) the TWC oscillator, unlike the TWC amplifier, requires a strong kicker magnet as a means to spin-up the electron beam in order to acquire an initial transverse velocity component V 1 o # 0; (b) with the same waveguide and electron beam energy,
0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V . All rights reserved SSDI 0168-9002(93)E1101-3
11 . EXPERIMENTAL RESULTS
E. Jerby et at. /Nucl. Instr. and Meth . i n Phys. Res A 341 (1994) 115-118 TO OSCILLOSCOPE
Fig. 1 . A principal scheme of the traveling-wave cyclotron (TWC) free-electron maser.
ATTENUATOR LOW-PASS FILTER
~~
MIXER
TO OSCILLOSCOPE
LO
00
the oscillator tends to operate at higher frequency, and in a stronger axial magnetic field than the amplifier (9.4 GHz at 4.2 kG vs . 8.2 GHz at 3 .1 kG); (c) the oscillator interaction region is much shorter than the amplifier interaction region (54 cm vs . 170 em); and (d) a theoretical analysis indicates the possibility that the two experiments operate in different TWC regimes; the amplifier interacts with a forward wave near cutoff with F/_,,,= 0, whereas the oscillator operates with V10 =A 0 and interacts with a backward wave near the , IT mode (where ßo a -Tr/p where p is the waveguide period). The RF power produced in the TWC oscillator is detected by means of the apparatus shown in Fig. 2. The TWC output signal is sampled by a 20 dB crosscoupler and attenuated by a 30 dB attenuator in each arm. One arm measures the total RF power of the order of - 400 W inside the cavity . The other arm is used to analyze the frequency characteristics of the TWC oscillator . In this arm, the TWC signal is mixed with a fixed frequency signal from a local oscillator (LO). The output of this arm is the intermediate frequency (IF) signal . Its frequency is given by
pendent TWC oscillator frequency with the fixed 9 .41 GHz local oscillator frequency. Fig. 3c shows the IF local frequency (3) evaluated by measuring 1/T where T is the nth period of the IF signal in Fig. 3a. The IF frequency follows the e beam energy trace in Fig. 3b . This indicates that the frequency chirp is a consequence of the electron energy sweep near the peak of its Gaussian pulse. The slow time dependence of the electron velocity Ve(t) results in a corresponding sweep of the TWC resonance frequency &a(t) in accordance with the transcendental tuning equation am(t) = ca e + Ve(t)t30(w(t)) derived from Eq . (1).
(3) where ca LO is the LO frequency. In the experiment, 0LO is tuned to 9.41 GHz. The IF signal is filtered by the internal 20 MHz low-pass filter of a Tektronix TDS 540 digital oscilloscope .
Table 1 Parameters of the TWC oscillator experiment e beam
3. The FM effect
energy current pulse width
8 keV 0.2 A 1 ms
Magnet
solenoid cyclotron frequency kicker
4.2 kG 11 .4 GHz
Waveguide
rectangular metal post array periodicity length
0.9 X 0.4 in .z
em wave
frequency in cavity power
9 .41 GHz
WIF = 0-J - wLO>
A typical result of the mixed TWC oscillator output (the IF signal) is shown in Fig. 3a. The frequency sweep during the TWC pulse is clearly observed . The electron beam energy trace is shown in Fig. 3b . Two local zeros are observed in the IF signal at approximately the same level of electron energy in the leading and the trailing edges of the electron voltage pulse. These zeros represent the intersection of the time-de-
LOCAL OSCILLATOR
Fig. 2. The microwave diagnostic setup of the TWC oscillator experiment .
4. Discussion In this experiment we demonstrate a frequency modulation effect in the TWC oscillator output which
5 kA turns see Fig. 1 20 mm 54 cm 400 W
E. Jerby et al. I Nucl. Instr. and Meth . to Phys. Res A 341 (1994) 115-118 7 80 7 73 % 76 7,
76S~ I,` _ 6E Cd
7
t
I
60 Sl5
1
I
1
1
1
400
425
450
475
500
t
[us]
t
[us]
[us]
Fig. 3. Experimental results. (a) The IF signal output . (b) The electron gun voltage trace. (c) The IF signal temporal frequency (the dots represent the reciprocal of the period of the IF signal in (a). The solid line is their 2nd order regression curve) .
results from the variation of the electron gun voltage. In a future practical device, this modulation could be achieved by a separate low-current control electrode in the electron gun. Frequency modulation might be a useful feature of TWC devices in many applications including radar, electronic warfare, communication, and cyclotron resonance heating. This feature is added to the other useful TWC properties, such as the low-voltage highefficiency operation, and low sensitivity to electron spread . Hence, the TWC is expected to be a practical free-electron maser device for useful applications .
Further experimental and theoretical studies are being conducted in order to evaluate the TWC features and to develop new TWC devices in various frequency bands and power level regimes.
Acknowledgements This work is supported by the Israeli Ministry of Energy and by the Belfer Center for Energy Research . II . EXPERIMENTAL RESULTS
E. Jerby et al. I Nucl. Instr. and Meth. t o Phys . Res . A 341 (1994) 115-118
References [1] E . Jerby and G. Bekefy Proc . SPIE, Vol . 1872 (1993) p . 276. [2] E . Jerby and G . Bekefi, Cyclotron maser experiments in a
periodic waveguide and references therein, Phys . Rev . E (Dec . 1993) . [3] E . Jerby et al., Linear model of periodic waveguide cyclotron maser, submitted for publication in Phys . Rev . E. [4] E . Agmon, H . Golombek and E . Jerby, Nucl . Instr . and Meth . A 331 (1993) 156 .
Nuclear Instruments and Methods in Physics Research A 341 (1994) 115-118 North-Holland
Section A
Observation of chirping in a traveling-wave cyclotron maser experiment a E . Jerby a, *, G . Bekefi b , A . Shahadi
° Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel 6 Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Following the recent traveling-wave cyclotron (TWC) amplifier experiment at MIT, we report in this paper on a frequency modulation (FM) effect observed in the TWC oscillator experiment conducted at Tel Aviv University . The TWC oscillator operates in the microwave regime (9.4 GHz) . It consists of a low-energy (8 keV) low-current (0 .2 A) electron beam spiraling m a metallic periodic waveguide. The TWC oscillator produces an RF pulse of - 400 W power. Frequency modulation (chirping) is observed during the TWC pulse by an heterodyne technique. This effect is related to the electron energy variation during the pulse. 1. Introduction The traveling wave cyclotron (TWO free-electron maser is a cyclotron-type device in which a nonrelativistic electron beam interacts with traveling waves in a metallic periodic waveguide. In the first TWC amplifier experiment conducted recently at MIT [1,21 a low-energy electron beam (- 10 keV, - 1.0 A) spiraling in an axial magnetic field of 3.1 kG, amplified a 8.2 GHz signal in a periodic waveguide. The interaction region consisted of an array of metal posts in a rectangular waveguide as shown in Fig. 1 . Electronic gain of - 10 dB was measured in this experiment near the cyclotron resonance [1,2]. A theoretical analysis of the TWC interaction in the linear regime [1,3] shows that the tuning relation of the TWC interaction with the fundamental spatial harmonic of the periodic waveguide is given by to = co y + Uo(-) " ( 1)
where to and to y are the electromagnetic wave and the electron cyclotron frequencies, respectively, Ve is the electron axial velocity, and 6 t,(to) is the wavenumber of the fundamental spatial harmonic in the periodic waveguide determined by its dispersion relation . The cyclotron frequency is given by : e o, Bo, Wo - -B (2) where e, m, and y are the electron charge, mass, and relativistic factor, respectively, and B o is the axial magnetic field. The TWC interaction incorporates different opposing effects including cyclotron resonance maser and Weibel effects. The theory shows that the TWC interaction has different properties for V1 ,, = 0 * Corresponding author .
and V1 p *- 0, where V1 o is the electron initial transverse velocity. The TWC gain scales in general as Vi o . Near cutoff of the inductive periodic waveguide, stimulated emission of radiation is feasible even with V1 0 = 0, as observed in refs . [1,2]. Following the TWC amplifier experiment at MIT, we constructed an oscillator experiment at Tel Aviv University . The oscillator apparatus is based on the traveling-wave FEM experimental setup [4]. In this paper we present frequency modulation (chirping) observed in the TWC oscillator experiment at Tel Aviv University . 2. The oscillator experiment The TWC oscillator employs a Pierce type electron gun. A low-energy electron beam (8 keV) is injected on-axis into the periodic waveguide. The electrons acquire initial transverse velocity by a small kicker coil at the entrance to the interaction region . The oscillator experiment employs the same inductive periodic waveguide used at MIT [1,2]. It consists of an array of metal posts in a rectangular waveguide (WR90) as shown in Fig. 1 . The beam is contained by a uniform axial magnetic field (4 .2 kG) produced by a solenoid . The electron beam is collected at the exit of the interaction region by a collector which measures the current. The parameters of the oscillator experiment at Tel Aviv University are listed in Table 1 . In comparison with the parameters of the amplifier experiment at MIT, the main differences between the two setups are: (a) the TWC oscillator, unlike the TWC amplifier, requires a strong kicker magnet as a means to spin-up the electron beam in order to acquire an initial transverse velocity component V 1 o # 0; (b) with the same waveguide and electron beam energy,
0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V . All rights reserved SSDI 0168-9002(93)E1101-3
11 . EXPERIMENTAL RESULTS
E. Jerby et at. /Nucl. Instr. and Meth . i n Phys. Res A 341 (1994) 115-118 TO OSCILLOSCOPE
Fig. 1 . A principal scheme of the traveling-wave cyclotron (TWC) free-electron maser.
ATTENUATOR LOW-PASS FILTER
~~
MIXER
TO OSCILLOSCOPE
LO
00
the oscillator tends to operate at higher frequency, and in a stronger axial magnetic field than the amplifier (9.4 GHz at 4.2 kG vs . 8.2 GHz at 3 .1 kG); (c) the oscillator interaction region is much shorter than the amplifier interaction region (54 cm vs . 170 em); and (d) a theoretical analysis indicates the possibility that the two experiments operate in different TWC regimes; the amplifier interacts with a forward wave near cutoff with F/_,,,= 0, whereas the oscillator operates with V10 =A 0 and interacts with a backward wave near the , IT mode (where ßo a -Tr/p where p is the waveguide period). The RF power produced in the TWC oscillator is detected by means of the apparatus shown in Fig. 2. The TWC output signal is sampled by a 20 dB crosscoupler and attenuated by a 30 dB attenuator in each arm. One arm measures the total RF power of the order of - 400 W inside the cavity . The other arm is used to analyze the frequency characteristics of the TWC oscillator . In this arm, the TWC signal is mixed with a fixed frequency signal from a local oscillator (LO). The output of this arm is the intermediate frequency (IF) signal . Its frequency is given by
pendent TWC oscillator frequency with the fixed 9 .41 GHz local oscillator frequency. Fig. 3c shows the IF local frequency (3) evaluated by measuring 1/T where T is the nth period of the IF signal in Fig. 3a. The IF frequency follows the e beam energy trace in Fig. 3b . This indicates that the frequency chirp is a consequence of the electron energy sweep near the peak of its Gaussian pulse. The slow time dependence of the electron velocity Ve(t) results in a corresponding sweep of the TWC resonance frequency &a(t) in accordance with the transcendental tuning equation am(t) = ca e + Ve(t)t30(w(t)) derived from Eq . (1).
(3) where ca LO is the LO frequency. In the experiment, 0LO is tuned to 9.41 GHz. The IF signal is filtered by the internal 20 MHz low-pass filter of a Tektronix TDS 540 digital oscilloscope .
Table 1 Parameters of the TWC oscillator experiment e beam
3. The FM effect
energy current pulse width
8 keV 0.2 A 1 ms
Magnet
solenoid cyclotron frequency kicker
4.2 kG 11 .4 GHz
Waveguide
rectangular metal post array periodicity length
0.9 X 0.4 in .z
em wave
frequency in cavity power
9 .41 GHz
WIF = 0-J - wLO>
A typical result of the mixed TWC oscillator output (the IF signal) is shown in Fig. 3a. The frequency sweep during the TWC pulse is clearly observed . The electron beam energy trace is shown in Fig. 3b . Two local zeros are observed in the IF signal at approximately the same level of electron energy in the leading and the trailing edges of the electron voltage pulse. These zeros represent the intersection of the time-de-
LOCAL OSCILLATOR
Fig. 2. The microwave diagnostic setup of the TWC oscillator experiment .
4. Discussion In this experiment we demonstrate a frequency modulation effect in the TWC oscillator output which
5 kA turns see Fig. 1 20 mm 54 cm 400 W
E. Jerby et al. I Nucl. Instr. and Meth . to Phys. Res A 341 (1994) 115-118 7 80 7 73 % 76 7,
76S~ I,` _ 6E Cd
7
t
I
60 Sl5
1
I
1
1
1
400
425
450
475
500
t
[us]
t
[us]
[us]
Fig. 3. Experimental results. (a) The IF signal output . (b) The electron gun voltage trace. (c) The IF signal temporal frequency (the dots represent the reciprocal of the period of the IF signal in (a). The solid line is their 2nd order regression curve) .
results from the variation of the electron gun voltage. In a future practical device, this modulation could be achieved by a separate low-current control electrode in the electron gun. Frequency modulation might be a useful feature of TWC devices in many applications including radar, electronic warfare, communication, and cyclotron resonance heating. This feature is added to the other useful TWC properties, such as the low-voltage highefficiency operation, and low sensitivity to electron spread . Hence, the TWC is expected to be a practical free-electron maser device for useful applications .
Further experimental and theoretical studies are being conducted in order to evaluate the TWC features and to develop new TWC devices in various frequency bands and power level regimes.
Acknowledgements This work is supported by the Israeli Ministry of Energy and by the Belfer Center for Energy Research . II . EXPERIMENTAL RESULTS
E. Jerby et al. I Nucl. Instr. and Meth. t o Phys . Res . A 341 (1994) 115-118
References [1] E . Jerby and G. Bekefy Proc . SPIE, Vol . 1872 (1993) p . 276. [2] E . Jerby and G . Bekefi, Cyclotron maser experiments in a
periodic waveguide and references therein, Phys . Rev . E (Dec . 1993) . [3] E . Jerby et al., Linear model of periodic waveguide cyclotron maser, submitted for publication in Phys . Rev . E. [4] E . Agmon, H . Golombek and E . Jerby, Nucl . Instr . and Meth . A 331 (1993) 156 .