Bekefi, G.

Fajans, J.

Hartmann, S.

Wurtele, J.S.

Xu, K.

DSpace@MIT

PFC/JA-87-19Wave Profile Modification (Optical Guiding)Induced by the Free Electron Laser InteractionF. Hartemann, K. Xu, G. Bekefi, J.S. Wurtele and J. Fajans*April 1987Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USAThis work was supported by the National Science Foundation, the Air Force Office ofScientific Research and the Office of Naval Research.Submitted for publication to Physical Review Letters.* Permanent address : Department of Physics, University of California, San Diego, LaJolla, CA. 92093Wave Profile Modification (Optical Guiding)Induced by the Free Electron Laser InteractionF. Hartemann, K. Xu, G. Bekefi and J.S. WurteleDepartment of Physics and Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts, 02139andJ. FajansDepartment of PhysicsUniversity of California, San DiegoLa Jolla, California, 92093AbstractModification of the transverse intensity profile of a single electromagnetic waveguide modeduring the free electron laser (FEL) interaction has been measured. This effect is thewaveguide analog to free space optical guiding. The studies were carried out at microwavefrequencies (8-12 GHz) in a free electron laser using a mildly relativistic electron beam of- 200 kV energy and - 1.0 A current. The probing of the RF fields was accomplished bysmall electric dipole antennas inserted in the interaction region. The observed intensityprofiles are compared with the measured FEL-induced phase shifts (wave refractive index).1One of the remarkable properties of the free electron laser (FEL), apart from its wave-length tunability and high efficiency, is the large phase shift which the resonant interactioninduces in the amplified electromagnetic wave. Under proper circumstances this phase shiftcan have a sign such that the electromagnetic wave is refracted towards the axis of theelectron beam, in a manner somewhat akin to the guiding properties of an optical fiber.This theoretically predicted 1,2,3,4,s behavior has important implications, but has yet tobe observed experimentally. Optical guiding 4'5 would mitigate the effects of diffraction,and thereby allow the length of FEL wigglers to exceed the Rayleigh range. Such longwigglers are needed if free electron lasers are to operate either in the vacuum ultraviolet(VUV) or at high efficiencies in the infrared wavelength regime.To date, indirect support for the phenomenon of optical guiding has come primarilyfrom two sources: computer simulations 4 , and measurements'' 8', of the FEL axial phasecharacteristics using interferometric techniques. Both approaches indicate the generalcorrectness of the concept. Bending effects observed in FEL oscillators 9 may also beexplained within the guiding model. To our knowledge this letter reports the first directmeasurements of FEL-induced profile modification of the electromagnetic wave.In the conventional sense, optical guiding refers to the focussing of an optical beamof such short wavelength that the proximity of the beam pipe is of little consequence. Thewaves are primarily transverse electromagnetic (TEM) and the transverse wave profiles areoften characterized by Gaussian-like shapes. In contrast, this letter addresses the questionof the wave profile when the free space wavelength is so long (- 3 cm) that only a singlevacuum waveguide mode can propagate freely. In our case it is the lowest TE 10 mode ofa rectangular waveguide which, in the absence of the FEL perturbation, is represented byEy = Eo sin(7rx/a) cos(wt - kz) (see Fig. 1). Wave profile modification is expected 10 inour microwave FEL experiment because of the large gain and phase shift per wavelength( - 1% for our parameters, as compared with < 10- 3 % in an optical FEL), and becausethe FEL-induced refractive index is enhanced by the ratio of the waveguide area to thebeam area.The FEL " is illustrated schematically in Fig. la. A Pierce thermionic electron gunis energized by a Physics International 615 MR Marx type accelerator. Focussing coils2compress the electron beam, and a pinhole emittance selector (0.25 cm in radius) removesall but the cold inner core of the beam. The ensuing 1.0 A, ~ 200 kV electron beamwith an energy spread < 0.5% is confined radially by an axial magnetic field B11 ~ 1.7kG. Beam excitation is provided by a 50 periods bifilar helical wiggler with a periodicitye, = 3.3 cm and a wiggler amplitude B, that can be varied from zero to ~ 1 kG. Forthe purpose of the present measurements the wiggler field is held constant at 250 G.Our FEL operates in the collective (Raman) regime where electron space charge mustbe considered. It is operated as a single pass amplifier. A wave launcher injects a monochro-matic signal at frequencies ranging between 8 and 12 GHz into the wiggler interactionregion. The rectangular waveguide (1.90 cm x 0.95 cm cross section) has a lowest modecutoff equal to 7.9 GHz. Thus only the fundamental TE 10 mode can propagate freely inthe empty waveguide since all the higher order modes are evanescent over the operatingfrequency range.The transverse profile of the electromagnetic mode is studied by means of two identicalelectric dipole antennas, oriented along the y direction (Fig. 1b) so as to make them mostsensitive to the y component of the RF electric field. Each probe has a length of 0.1 cm ;cold tests show that the probes can detect spatial RF intensity variations as small as ~ 0.05cm. The signal from each probe is attenuated by a variable attenuator, then measuredby a calibrated crystal detector. The outputs from the crystal rectifiers are substractedfrom one another in a differential amplifier and then displayed on a fast oscilloscope. Inthe absence of the electron beam, the attenuators are adjusted to give a null reading onthe oscilloscope, so that any differences between the probe characteristics can be balancedout. With the FEL turned on, any observed residual signal corresponds to a change in theRF mode profile.The two probes are in the same z plane (40 periods from the wiggler entrance).One probe (the wall probe) is adjacent to the waveguide wall ; the other (inner) probeprotrudes midway into the waveguide, where the electron beam propagates. Because oftechnical limitations both probes are fixed in position relative to the waveguide. For thisreason we vary the position of the probes relative to the electron beam by moving theentire waveguide, wiggler and vacuum beamline transversely to the guiding magnetic field3B 11 . The axial position of the electron beam is held approximately constant. In this waythe FEL-induced perturbations of the mode profile can be scanned both in the x and ydirections. To be sure, this method of scanning causes the electron beam to be somewhatdisplaced from both the solenoid axis and the waveguide axis resulting in both precession 1 2and some loss of symmetry. However, since the maximum transverse displacements arenot large ( < 0.5 cm), this does not seem to pose a serious problem. In particular, thetotal gain of the system remains unchanged as we scan through the beam, indicating thatthe coupling is not affected by the displacement.The FEL is fired by discharging the Marx accelerator. Because of an RC droop,the beam energy falls gradually as is illustrated in Fig. 2a. Amplification (Fig. 2b), asmeasured by the inner probe, occurs at a beam energy for which the slow (negative energy)space charge wave on the beam is in near phase synchronism with the electromagneticwave 6'11 . This results in the gain peak marked G in Fig. 2b. Later in time, at a lowerbeam energy, one observes a dip corresponding to wave absorption. Here the wave energyis converted to electron kinetic energy, as is known to occur when the fast (positive energy)space charge wave is in synchronism with the electromagnetic wave.Figure 2c shows the corresponding oscilloscope trace obtained by subtracting the wallprobe signal from the inner probe signal as described above. We see that early and late intime, outside the energy range of the FEL interaction, the signals balance nearly perfectlyyielding a null output. Thus, the only measurable changes in the mode profile occur duringthe FEL interaction, where they can exceed ~ 25%. Comparing figures 2b and 2c, wesee that the largest profile modification (marked AI in Fig. 2c) is shifted away from thepeak RF gain (Fig. 2b) and coincides with the maximum observed phase shift (Fig. 2e,discussed below).In order to check the validity of these results, we dump the electron beam into thewaveguide walls by means of a magnetic kicker 6 ' placed 18 cm upstream of the probes.This allows the FEL-induced profile modification of the RF field to downconvert to thefundamental TE 10 mode, and a null signal results as shown in Fig. 2d (the other modesexcited by the FEL interaction are evanescent and die out exponentially within 1 or 2waveguide wavelengths from the kicker position). Because the wiggler interaction region is4shortened in this case, we increase the wiggler field by ~ 15% to maintain the same gainG as in Fig. 2a.In addition to the above intensity measurements we have performed axial phase shiftmeasurements. Using the inner probe, we determine the axial phase shift accumulatedby the wave inside the interaction region with respect to a fixed reference signal from theRF source 6 ''. This quantity is central to the guiding properties of the FEL. When theaccumulated phase shift reaches its maximum (see Fig. 2e), a peaking of the mode profilein the region of the electron beam is observed. Conversely, at the minimum of the phaseshift curve (Fig. 2e) we find a reduction in the electromagnetic wave profile at the beamposition. The phase measurements of Fig. 2e and the gain measurements of Fig. 2bagree with previously obtained results 6 '7 . Additional studies to those (not shown) havebeen carried out over a range of wiggler strength from 0 to 300 G. The amplitudes of theobserved phase shifts and profile modifications followed the increase in wiggler strength.The similarities between the phase shift and the profile modification seen in Fig. 2 aremaintained over this range of wiggler strength.The detailed structure of the transverse RF intensity profile during the FEL inter-action is obtained by scanning the inner probe across the electron beam. In Fig. 3a,the normalized intensity difference between the inner probe and the wall probe (AI/G)is plotted as a function of the displacement along the small dimension of the waveguide( y-axis). We see that the effect is maximum in the center, and rapidly decays outside ofthe electron beam. Similar behavior is seen by scanning along the x-axis (Fig. 3b). Whenthe beam is dumped upstream of the probes, the intensity difference falls by more than anorder of magnitude and shows no spatial structure (Fig. 3a), indicating that the measuredeffect is indeed generated by the electron beam. The experimental data is convenientlyfitted by Lorentzian curves which are then used to construct the normalized RF intensityprofiles shown in Fig. 4. The first profile (1) corresponds to the situation marked by arrow1 in Fig. 2c, where both gain and guiding are present. The second profile (correspondingto arrow 2 of Fig. 2c) shows absorption and anti-guiding. The dashed curves, displayed forcomparison, represent the measured unperturbed input mode profiles. The data shown forpoints 1 and 2 are representative of the type of wave profile modification that we observeduring the FEL interaction.5The above phase and intensity measurements are obtained with the FEL operating inthe linear regime (input powers in the watt range). We have also measured the same quan-tities in the saturated regime (input powers in the kilowatt range). The results obtainedin the saturated regime are consistent with those described in Figs. 2, 3 and 4.In conclusion, we have observed the redistribution of the RF electromagnetic waveintensity induced by the FEL interaction. This effect has been measured at several fre-quencies between 8 and 12 GHz and at input power levels ranging from a few watts (linearregime) to several kilowatts (saturated regime). In our experiments, we have observedthat the intensity profile modifications follow the variation of the FEL-induced axial phaseshifts. We also note that the corresponding effective refractive index is large only close tothe FEL resonance and for that reason it has some similarity with the anomalous refractiveindex observed in the neighborhood of an atomic transition. Finally, it is noteworthy thatin the collective (Raman) regime, unlike the single particle Compton regime, the phaseshift is large only away from the point of maximum gain and it is here that we find thelargest modification of the transverse mode profile.This work was supported by the National Science Foundation, the Air Force Office ofScientific Research and the Office of Naval Research.6References[1] P. Sprangle and C.M. Tang, Appl. Phys. Lett. 39, 677 (1981).[2] W.M. Kroll, P.L. Morton and M.W. Rosenbluth, IEEE J. Quantum Electron. 17,1436 (1981).[3] D. Prosnitz, R.A. Haas, S. Doss and R.J. Gelinas, in Free Electron Generutors ofCoherent Radiation, Physics of Quantum Electronics Vol. 9, edited by Stephen F. Ja-cobs, Murray Sargent III and Marlan 0. Scully (Addison-Wesley, Reading, Mass.,1982), p. 10 4 7 .[4] E.T. Scharlemann, A.M. Sessler and J.S. Wurtele, Phys. Rev. Lett. 54, 1925 (1985).[5] G.T. Moore, Nucl. Inst. and Meth. in Phys. Res. A239, 19 (1985).[6] J. Fajans and G. Bekefi, Phys. Fluids 29, 3461 (1986).[7] J. Fajans, J.S. Wurtele, G. Bekefi, D.S. Knowles and K. Xu, Phys. Rev. Lett. 57,579 (1986).[8] T.J. Orzechowski, E.T. Scharlemann and B.D. Hopkins, Phys. Rev. A35, 2184(1987).[9] B.E. Newnam, R.W. Warren, R.L. Sheffield, J.G. Goldstein and C.A. Brau, Nucl. Inst.and Meth. in Phys. Res. A237, 187 (1985) ; also R.W. Warren and B.D. McVey,submitted to the Eighth International FEL Conference, Glasgow, Scotland (1986).[10] J. Fajans, J.S. Wurtele, G. Bekefi, D.S. Knowles and K. Xu, Bull. Am. Phys. Soc.31, 1481 (1986).[11] J. Fajans, G. Bekefi, Y.Z. Yin and B. Lax, Phys. Fluids 28, 1995 (1985).[12] J. Fajans, D.A. Kirkpatrick and G. Bekefi, Phys. Rev. A32, 3448 (1986).7Figure CaptionsFig. 1 a) Schematic of the free electron laser experiment, ; b) arrangement of the electricdipole antenna probes.Fig. 2 Oscilloscope traces (see text). The experimental parameters are B11 ~ 1.7 kG, B, ~250 G, I ~ 1.0 A and f = 10.40 GHz.Fig. 3 Normalized differential RF intensity as a function of the transverse displacement.Fig. 4 Transverse intensity profiles reconstructed from the data shown in Figs. 2b and c(arrows 1 and 2), and Fig. 3.8WAVELAUNCHER SOLENOIDBIFILAR HELICALWIGGLERPR99BESBEAM'APERTUREFOCUSSING COILSTHERMVIONICPIERCE GUN (a)(b)Fig. 1Hartemann, Xu, Bekefi, Wdurtele, Fajans1 2KICKER ONF - 4TIME (/is)Fig. 2Hartemann,L&J0I--J010Xu, Bekefi, Wurtele, FajansII--Zcrwz--z=Z Qz Cz--zH-LL(Icf)0-0G(a)(b)(c)(d):e)O-2 0 2DISPLACENT ALONG Y AXIS (mm)-2 0DISPLACEMENT ALONG X2AXIS (mm)Q30(b)4Fig. 3Hartemann, Xu, Bekefi, Wurtele, Fajans- -0(KICKER ON- - - - --0.20-(a)0.10-O.D- 44ftoLL.LL-zw0zQ3CO.2C, **) : i I . I0QICO.c-46I a I I -- 0O 2AXIAL Y POSITION (mm)-5 0 5AXIAL X POSITION (mm)10Fig. 4Hartemann, Xu, Bekefi, Wurtele, Fajans2.0,----------------------TEKc INPUT MODE1021.50.5 -0.6.zwzI-4 42.01.51T0 ,INPUT %MODE _---1.00.5100.0-

Wave profile modification (optical guiding) induced by the free electron laser interaction

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Wave profile modification (optical guiding) induced by the free electron laser interaction

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