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Parametric behavior of a high gain 35 GHz free electron laser amplifier with guide magnetic field
366
Nuclear Instruments and Methods in Physics Research A250 (1986) 366-368 North-Holland, Amsterdam
PARAMETRIC BEHAVIOR OF A HIGH GAIN 35 GHz FREE ELECTRON LASER AMPLIFIER WITH GUIDE MAGNETIC FIELD Steven H. GOLD, Achintya K. GANGULY, Henry P. FREUND *, Arne W. FLIFLET,
Victor L. GRANATSTEIN **, Delbert L. HARDESTY and Allen K. KINKEAD
High Power Electromagnetic Radiation Branch; Plasma Physics Division, Naval Research Laboratory, Washington, D.C 20375-5000, USA
The linear gain of a millimeter-wave free electron laser (FEL) amplifier employing an intense relativistic electron beam has been measured as a function of the strength of the applied axial magnetic field. The experimental results, showing high growth rates (up to 1 .8 dB/cm) and suggesting broad instantaneous frequency bandwidth, are in good agreement with predictions of a three-dimensional theory for the FEL interaction. In the millimeter-wave region of the electromagnetic spectrum, free electron laser (FEL) amplifiers offer the potential of high gain, broad bandwidth, continuous tunability and extremely high power. A high-gain amplifier experiment employing a 900 keV (y = 2.75), 600 A solid electron beam in a 1 .08 cm circular waveguide, a 3 cm-period helical wiggler, and an axial magnetic field has previously reported tens of MW of amplified radiation at 35 GHz [1]. The experimental setup is illustrated in fig. 1 . A vertically-polarized 35 GHz signal wave is injected into the interaction waveguide in the fundamental TE°1 -mode. Operating as a traveling-wave amplifier with a wiggler field of 1.08 kG on axis (1 .16 kG averaged over the 3 mm beam radius) and an axial field of 11 .75 kG, a spatial growth rate of 1 .2 dB/cm was measured over a 30 cm variation of * Permanent address: Science Applications International Corp., McLean, VA 22102, USA. ** Permanent address: Electrical Engineering Dept., University of Maryland, College Park, MD 20742, USA.
interaction length, linearity was verified over a 200 X variation of injected signal, and a total gain in excess of 50 dB was observed [1]. In this paper, we report further experimental investigation of the parametric behavior of this FEL amplifier, and compare the results with the predictions of theory . The parametric behavior of a millimeter-wave FEL with an axial guide magnetic field is strongly affected by the presence of a resonance that occurs as the period of Larmor motion in the applied axial magnetic field approaches the period of the wiggler magnetic field. The effects of this gyroresonance on the electron trajectories were first studied by Friedland [2]. More recently, extensive theoretical studies of the effects of the axial field on the FEL instability, and of 3-D effects on both electron trajectories and on the FEL interaction, have been carried out [3,4] . Since the experiment of ref. [1] operates best at magnetic field values somewhat above gyroresonance where the gyroresonant effects strongly influence the electron orbits and the growth rate of the interaction, an investigation of the behavior of the FEL
MAGNETRON POLYETHYLENE WINDOW
/ ® MICROWAVE AXIAL FIELD COILS HORN
ANECHOIC---'CHAMBER __- ;
Fig. 1. Experimental configuration for high gain 35 GHz FEL amplifier measurements . 0168-9002/86/$03 .50 V Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
S.H. Gold et al. / A high gain free electron laser amplifier
interaction as a function of applied axial magnetic field is a sensitive experimental test of the FEL theory. In this paper, we study the parametric dependence of the linear gain of the FEL interaction on the value of axial magnetic field at constant voltage and wiggler field. In order to do this, we first measure the net gain of FEL configurations of different interaction lengths . Each experimental configuration includes a 21 cm entry taper of adiabatically increasing wiggler field at constant axial magnetic field, following by a region of constant wiggler and approximately constant axial fields . The uniform region merges into a region of gradually decreasing axial field at constant wiggler field, caused by ending the axial field magnet at a specific axial location, and then ends where the electron beam intercepts the drift tube wall . In order to measure the linear properties of the system, the amplitude of the input signal is controlled to ensure that the system operates far from saturation . Thus, we can assume local linearity of the FEL interaction with a growth rate typical of the local values of the axial field B., the wiggler field B and the beam energy . The measured total gain for such a system is assumed to result from the line integral of the local growth rates along the length of the experiment, minus any launching losses . Since a specific configuration incorporates regions of lower axial fields, down to perhaps half of . the uniform value before the beam is collected on the drift tube wall, such data could be directly compared with the results of a simulation, but less easily with analytic theory. However, by determining the net change in gain due to a length differential, at uniform axial field, between two systems of different total lengths, it is possible to determine values that can be directly related to the predictions of linear theory . This procedure has been considered in more detail elsewhere [5] . We compare these results with predictions of a fully 3-D theory for the growth rate of the FEL instability for the same experimental parameters [4] . Fig . 2(a, b) shows measurements of total gain as the axial magnetic field in the uniform portion of the interaction region is varied between 10 and 15 kG (compared to a resonant value of < 9 kG), for systems of lengths 66 and 54 cm. (The defined length L begins at the start of the wiggler entry taper, and ends at the half-field point of the axial field exit taper .) The total gain is defined here as the ratio (in dB) of the vertically polarized 35 GHz output radiation to the injected signal wave . (In fact, the FEL amplifies a left-circularlypolarized wave [6], so that only half of the input signal is effective, and only half of the circularly-polarized output signal is measured. Thus, the true gain could be considered to be 6 dB larger than the plotted values.) Fig. 2(c) shows the experimental growth rate, in dB/cm, that results from subtracting the measured gains for the shorter system [fig. 2(b)] from those for the
367
60 50
L = 66 .05 cm P , =46±10W
_ 40 m 9 2
am
30
1
20 10 10 01 60, 50
m
40
11
12
13
14
15
L = 54 .15 cm P ; =460 ± 80W
z 30
á
20 10
s m W
á m x
30 m
Fig . 2. Growth rates at 35 GHz as a function of Bz for the FEL amplifier operating at B, _ (1 .08 t 0.04) kG and y = (2 .75 f0.05) : (a) measured gain for L = 66.05 cm ; (b) measured gain for L = 54.15 cm ; (c) comparison of experimental growth rates with values predicted by theory for B, =1 .08 kG, y = 2.75, I = 600 A. longer system [fig. 2(a)], and dividing the results by the 11 .9 cm length differential. Fig. 2(c) also includes a line representing the predictions of the 3-D FEL theory [4J for the same experimental parameters. The agreement between the experimental data and the parametric behavior predicted by theory is good . However, the theoretical growth rates are typically 50% larger than the experimental values. This discrepancy may be due to several approximations that were employed to make the theory analytically tractable, including the assumption of a thin moncenergetic beam with axicentered electron trajectories . In particular, the inclusion of finite energy IX . RAMAN/GUIDE FIELD FELS
368
S.H. Gold et al. / A high gain free electron laser amplifier
and pitch angle spreads in the beam would result in lower predicted growth rates. It is apparent that end effects strongly influence the data in fig. 2(a, b) . The vanishing of the theoretical gain at -13.3 kG corresponds to the vanishing of the ponderomotive potential, and marks the transition between the anomalous regime above gyroresonance in which the FEL instability couples the electromagnetic wave to a space charge wave that is itself driven unstable by the combination of axial and wiggler magnetic fields [3], and the ordinary regime at still larger values of B, in which the FEL interaction is a parametric instability coupling the electromagnetic wave to the stable negative-energy beam space charge wave . (The anomalous regime is predicted [3] to offer broader instability bandwidths and larger growth rates.) Figs . 2(a) and 2(b) each show substantial net gain occurring at values of axial field larger than this zero. However, the rate of growth determined by the difference between the two experimental values is negligible, and theory suggests that the gain at 35 GHz is very small and may vanish in this region . The net gain at Bz > 13 .3 kG is believed to be due to the region of downward tapered axial magnetic field that is a part of each system ; that is, for large values of BZ, most of the gain actually occurs at lower fields at the end of each system, rather than at the nominal value of Bz indicated in fig. 2(a, b) . Similarly, such end effects appear to account for the apparent shift of the gain maximum to higher B, between figs . 2(a) and 2(b), since the total gain for the shorter system at a particular value of uniform B, is more dominated by gain occurring in the end region at values of Bz lower than the nominal value. The presence of substantial gain at 35 GHz as the resonant interaction frequency is varied over a wide range by changing the value of axial field, suggests that the amplifier has a broad instantaneous frequency bandwidth. However, the direct measurement of the frequency bandwidth is precluded by the fixed frequency of the driver magnetron. As an alternative, the evident correlation between theory and experiment encourages one to address the question of amplifier bandwidth theoretically. The approximate resonant coupling frequencies for the FEL interaction are given by the intersection of the pump-shifted beam line, w = (k + kW) vZ, with the electromagnetic waveguide mode, w2 = w2 + k 2c 2. Here (w, k) are the angular frequency and wave number for the electromagnetic mode, kW = 2ir/XW, where XW is the wigger period, vz is the electron axial velocity, c is the velocity of light, and w./2v is the cutoff frequency of the TE I1 mode in the interaction waveguide. Fig. 3 shows the theoretical growth rate as a function of frequency for a number of values of axial magnetic field. (Note that fig. 3 was calculated for B, =1 .04 kG rather than 1 .08 kG.) At higher axial fields, which imply
Fig. 3. Theoretical gain versus frequency at representative values of B, for B, =1 .04 kG. operation further from gyroresonance, the transverse wiggle velocity is lower, reducing the gain . However, the parallel velocity is higher, moving the upper intersection of the beam line with the waveguide mode to higher frequencies . Due to the broader nature of the FEL interaction for this range of experimental parameters, the entire frequency span between the two intersections becomes unstable, resulting in very broad amplification bandwidths . As B, is reduced, the transverse velocity increases, increasing the strength of the interaction. However, the parallel velocity decreases, shifting the upper intersection to lower frequencies and reducing the effective growth bandwidth. Finally, below - 11 kG, the beam line no longer intersects the waveguide mode, and coupling becomes progressively weaker and narrower bandwidth as the two lines separate . In conclusion, the parametric dependence of the linear growth rate of a high-gain millimeter-wave FEL amplifier as a function of axial magnetic field has been measured . Gain per unit length as high as 1 .8 dB/cm has been observed, producing total gain of up to 50 dB. Good agreement has been observed between these results and the predictions of a three-dimensional linear theory for the FEL interaction. The experimental data suggests, and the theory predicts, that the interaction has very broad instantaneous bandwidths, extending over more than a full octave in many cases. Acknowledgement This work was supported by the US Office of Naval Research. References
[1] S.H . Gold, D.L. Hardesty, A.K. Kinkead, L.R. Barnett and V.L . Granatstein, Phys. Rev. Lett . 52 (1984) 1218 . [2] L. Friedland, Phys . Fluids, 23 (1980) 2376 . [3] H.P. Freund, P. Sprangle, D. Dillenburg, E.H . daJornada, R.S . Schneider and B.L . Berman, Phys . Rev. A26 (1982) 2004 . [4] H.P. Freund and A.K. Ganguly, Phys . Rev. A28 (1983) 3438 . [5] S.H . Gold, W.M. Black, H.P . Freund, V.L. Granatstein and A.K . Kinkead, Phys . Fluids 27 (1984) 746. [6] S H. Gold, Rev . Sci. Instrum . 57 (1986) 36 .
Nuclear Instruments and Methods in Physics Research A250 (1986) 366-368 North-Holland, Amsterdam
PARAMETRIC BEHAVIOR OF A HIGH GAIN 35 GHz FREE ELECTRON LASER AMPLIFIER WITH GUIDE MAGNETIC FIELD Steven H. GOLD, Achintya K. GANGULY, Henry P. FREUND *, Arne W. FLIFLET,
Victor L. GRANATSTEIN **, Delbert L. HARDESTY and Allen K. KINKEAD
High Power Electromagnetic Radiation Branch; Plasma Physics Division, Naval Research Laboratory, Washington, D.C 20375-5000, USA
The linear gain of a millimeter-wave free electron laser (FEL) amplifier employing an intense relativistic electron beam has been measured as a function of the strength of the applied axial magnetic field. The experimental results, showing high growth rates (up to 1 .8 dB/cm) and suggesting broad instantaneous frequency bandwidth, are in good agreement with predictions of a three-dimensional theory for the FEL interaction. In the millimeter-wave region of the electromagnetic spectrum, free electron laser (FEL) amplifiers offer the potential of high gain, broad bandwidth, continuous tunability and extremely high power. A high-gain amplifier experiment employing a 900 keV (y = 2.75), 600 A solid electron beam in a 1 .08 cm circular waveguide, a 3 cm-period helical wiggler, and an axial magnetic field has previously reported tens of MW of amplified radiation at 35 GHz [1]. The experimental setup is illustrated in fig. 1 . A vertically-polarized 35 GHz signal wave is injected into the interaction waveguide in the fundamental TE°1 -mode. Operating as a traveling-wave amplifier with a wiggler field of 1.08 kG on axis (1 .16 kG averaged over the 3 mm beam radius) and an axial field of 11 .75 kG, a spatial growth rate of 1 .2 dB/cm was measured over a 30 cm variation of * Permanent address: Science Applications International Corp., McLean, VA 22102, USA. ** Permanent address: Electrical Engineering Dept., University of Maryland, College Park, MD 20742, USA.
interaction length, linearity was verified over a 200 X variation of injected signal, and a total gain in excess of 50 dB was observed [1]. In this paper, we report further experimental investigation of the parametric behavior of this FEL amplifier, and compare the results with the predictions of theory . The parametric behavior of a millimeter-wave FEL with an axial guide magnetic field is strongly affected by the presence of a resonance that occurs as the period of Larmor motion in the applied axial magnetic field approaches the period of the wiggler magnetic field. The effects of this gyroresonance on the electron trajectories were first studied by Friedland [2]. More recently, extensive theoretical studies of the effects of the axial field on the FEL instability, and of 3-D effects on both electron trajectories and on the FEL interaction, have been carried out [3,4] . Since the experiment of ref. [1] operates best at magnetic field values somewhat above gyroresonance where the gyroresonant effects strongly influence the electron orbits and the growth rate of the interaction, an investigation of the behavior of the FEL
MAGNETRON POLYETHYLENE WINDOW
/ ® MICROWAVE AXIAL FIELD COILS HORN
ANECHOIC---'CHAMBER __- ;
Fig. 1. Experimental configuration for high gain 35 GHz FEL amplifier measurements . 0168-9002/86/$03 .50 V Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)
S.H. Gold et al. / A high gain free electron laser amplifier
interaction as a function of applied axial magnetic field is a sensitive experimental test of the FEL theory. In this paper, we study the parametric dependence of the linear gain of the FEL interaction on the value of axial magnetic field at constant voltage and wiggler field. In order to do this, we first measure the net gain of FEL configurations of different interaction lengths . Each experimental configuration includes a 21 cm entry taper of adiabatically increasing wiggler field at constant axial magnetic field, following by a region of constant wiggler and approximately constant axial fields . The uniform region merges into a region of gradually decreasing axial field at constant wiggler field, caused by ending the axial field magnet at a specific axial location, and then ends where the electron beam intercepts the drift tube wall . In order to measure the linear properties of the system, the amplitude of the input signal is controlled to ensure that the system operates far from saturation . Thus, we can assume local linearity of the FEL interaction with a growth rate typical of the local values of the axial field B., the wiggler field B and the beam energy . The measured total gain for such a system is assumed to result from the line integral of the local growth rates along the length of the experiment, minus any launching losses . Since a specific configuration incorporates regions of lower axial fields, down to perhaps half of . the uniform value before the beam is collected on the drift tube wall, such data could be directly compared with the results of a simulation, but less easily with analytic theory. However, by determining the net change in gain due to a length differential, at uniform axial field, between two systems of different total lengths, it is possible to determine values that can be directly related to the predictions of linear theory . This procedure has been considered in more detail elsewhere [5] . We compare these results with predictions of a fully 3-D theory for the growth rate of the FEL instability for the same experimental parameters [4] . Fig . 2(a, b) shows measurements of total gain as the axial magnetic field in the uniform portion of the interaction region is varied between 10 and 15 kG (compared to a resonant value of < 9 kG), for systems of lengths 66 and 54 cm. (The defined length L begins at the start of the wiggler entry taper, and ends at the half-field point of the axial field exit taper .) The total gain is defined here as the ratio (in dB) of the vertically polarized 35 GHz output radiation to the injected signal wave . (In fact, the FEL amplifies a left-circularlypolarized wave [6], so that only half of the input signal is effective, and only half of the circularly-polarized output signal is measured. Thus, the true gain could be considered to be 6 dB larger than the plotted values.) Fig. 2(c) shows the experimental growth rate, in dB/cm, that results from subtracting the measured gains for the shorter system [fig. 2(b)] from those for the
367
60 50
L = 66 .05 cm P , =46±10W
_ 40 m 9 2
am
30
1
20 10 10 01 60, 50
m
40
11
12
13
14
15
L = 54 .15 cm P ; =460 ± 80W
z 30
á
20 10
s m W
á m x
30 m
Fig . 2. Growth rates at 35 GHz as a function of Bz for the FEL amplifier operating at B, _ (1 .08 t 0.04) kG and y = (2 .75 f0.05) : (a) measured gain for L = 66.05 cm ; (b) measured gain for L = 54.15 cm ; (c) comparison of experimental growth rates with values predicted by theory for B, =1 .08 kG, y = 2.75, I = 600 A. longer system [fig. 2(a)], and dividing the results by the 11 .9 cm length differential. Fig. 2(c) also includes a line representing the predictions of the 3-D FEL theory [4J for the same experimental parameters. The agreement between the experimental data and the parametric behavior predicted by theory is good . However, the theoretical growth rates are typically 50% larger than the experimental values. This discrepancy may be due to several approximations that were employed to make the theory analytically tractable, including the assumption of a thin moncenergetic beam with axicentered electron trajectories . In particular, the inclusion of finite energy IX . RAMAN/GUIDE FIELD FELS
368
S.H. Gold et al. / A high gain free electron laser amplifier
and pitch angle spreads in the beam would result in lower predicted growth rates. It is apparent that end effects strongly influence the data in fig. 2(a, b) . The vanishing of the theoretical gain at -13.3 kG corresponds to the vanishing of the ponderomotive potential, and marks the transition between the anomalous regime above gyroresonance in which the FEL instability couples the electromagnetic wave to a space charge wave that is itself driven unstable by the combination of axial and wiggler magnetic fields [3], and the ordinary regime at still larger values of B, in which the FEL interaction is a parametric instability coupling the electromagnetic wave to the stable negative-energy beam space charge wave . (The anomalous regime is predicted [3] to offer broader instability bandwidths and larger growth rates.) Figs . 2(a) and 2(b) each show substantial net gain occurring at values of axial field larger than this zero. However, the rate of growth determined by the difference between the two experimental values is negligible, and theory suggests that the gain at 35 GHz is very small and may vanish in this region . The net gain at Bz > 13 .3 kG is believed to be due to the region of downward tapered axial magnetic field that is a part of each system ; that is, for large values of BZ, most of the gain actually occurs at lower fields at the end of each system, rather than at the nominal value of Bz indicated in fig. 2(a, b) . Similarly, such end effects appear to account for the apparent shift of the gain maximum to higher B, between figs . 2(a) and 2(b), since the total gain for the shorter system at a particular value of uniform B, is more dominated by gain occurring in the end region at values of Bz lower than the nominal value. The presence of substantial gain at 35 GHz as the resonant interaction frequency is varied over a wide range by changing the value of axial field, suggests that the amplifier has a broad instantaneous frequency bandwidth. However, the direct measurement of the frequency bandwidth is precluded by the fixed frequency of the driver magnetron. As an alternative, the evident correlation between theory and experiment encourages one to address the question of amplifier bandwidth theoretically. The approximate resonant coupling frequencies for the FEL interaction are given by the intersection of the pump-shifted beam line, w = (k + kW) vZ, with the electromagnetic waveguide mode, w2 = w2 + k 2c 2. Here (w, k) are the angular frequency and wave number for the electromagnetic mode, kW = 2ir/XW, where XW is the wigger period, vz is the electron axial velocity, c is the velocity of light, and w./2v is the cutoff frequency of the TE I1 mode in the interaction waveguide. Fig. 3 shows the theoretical growth rate as a function of frequency for a number of values of axial magnetic field. (Note that fig. 3 was calculated for B, =1 .04 kG rather than 1 .08 kG.) At higher axial fields, which imply
Fig. 3. Theoretical gain versus frequency at representative values of B, for B, =1 .04 kG. operation further from gyroresonance, the transverse wiggle velocity is lower, reducing the gain . However, the parallel velocity is higher, moving the upper intersection of the beam line with the waveguide mode to higher frequencies . Due to the broader nature of the FEL interaction for this range of experimental parameters, the entire frequency span between the two intersections becomes unstable, resulting in very broad amplification bandwidths . As B, is reduced, the transverse velocity increases, increasing the strength of the interaction. However, the parallel velocity decreases, shifting the upper intersection to lower frequencies and reducing the effective growth bandwidth. Finally, below - 11 kG, the beam line no longer intersects the waveguide mode, and coupling becomes progressively weaker and narrower bandwidth as the two lines separate . In conclusion, the parametric dependence of the linear growth rate of a high-gain millimeter-wave FEL amplifier as a function of axial magnetic field has been measured . Gain per unit length as high as 1 .8 dB/cm has been observed, producing total gain of up to 50 dB. Good agreement has been observed between these results and the predictions of a three-dimensional linear theory for the FEL interaction. The experimental data suggests, and the theory predicts, that the interaction has very broad instantaneous bandwidths, extending over more than a full octave in many cases. Acknowledgement This work was supported by the US Office of Naval Research. References
[1] S.H . Gold, D.L. Hardesty, A.K. Kinkead, L.R. Barnett and V.L . Granatstein, Phys. Rev. Lett . 52 (1984) 1218 . [2] L. Friedland, Phys . Fluids, 23 (1980) 2376 . [3] H.P. Freund, P. Sprangle, D. Dillenburg, E.H . daJornada, R.S . Schneider and B.L . Berman, Phys . Rev. A26 (1982) 2004 . [4] H.P. Freund and A.K. Ganguly, Phys . Rev. A28 (1983) 3438 . [5] S.H . Gold, W.M. Black, H.P . Freund, V.L. Granatstein and A.K . Kinkead, Phys . Fluids 27 (1984) 746. [6] S H. Gold, Rev . Sci. Instrum . 57 (1986) 36 .