Bekefi, G.

Fajans, J.

Knowles, D.S.

Wurtele, J.S.

Xu, K.

DSpace@MIT

PFC/JA-86-24Nonlinear Power Saturation and Phase(Wave Refractive Index) in the CollectiveFree Electron LaserJ. Fajans,*D.S.J.S. Wurtele, G. Bekefi,Knowles, and K. XuApril 1986Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USAThis work wasfice of Navaland the Hertzsupported by the National Science Foundation, the Of-Research, the Air Force Office of Scientific Research,Foundation.Submitted for publication to Physical Review Letters.*Present address: University of California, San Diego, PhysicsDepartment, La Jolla, CA. 92093.Nonlinear Power Saturation and Phase(Wave Refractive Index) in the CollectiveFree Electron LaserJ. Fajans* J. S. Wurtele, G. Bekefi, D.S. Knowles, K. XuDepartment of Physics and the Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139We report measurements of the nonlinear radiation intensity and phasein a collective (Raman) regime free electron laser (FEL). The helical wig-gler FEL generates up to - 100KW of RF power at a frequency of 9.3GHzand with an efficiency of - 10%. The experimental measurements agreewith computer simulations.PACS numbers:42.55Tb, 52.75Mb-Present address: University of California, San Diego, California1Free electron lasers (FELs) are currently under investigation because ofseveral remarkable properties, including their high efficiencies and outputpowers, and their inherent frequency tunability. In this paper we study thepower, saturation, energy bandwidth, and phase (refractive index) char-acteristics of a mildly relativistic, collective (Raman) regime free electronlaser.The small signal linear gain behavior of the device has been investigatedextensively.1 and is now well understood. The collective (Raman) nature ofthe experiment has been demonstrated by determining the influence of thelongitudinal space charge self-fields (beam plasma waves). In this paperthe nonlinear saturation of the FEL instability is examined by observingthe dependence of the FEL output power on the wiggler length, electronbeam current and beam energy. We find that the output power agrees,well with the predictions of the nonlinear theory of Kroll, Morton, andRosenbluth 2(KMR) and others,3 ,4 when the theory is suitably extended foruse with this experiment. Elsewhere, the KMR model was checked for aCormpton regime FEL (small longitudinal self-fields) with a different wigglerand waveguide configuration than ours.5We also examine the change induced by the FEL interaction in the ef-fective refractive index experienced by the electromagnetic wave. Changesin refractive index produce a cumulative phase shift in the wave which is2)measured experimentally. Not only do phase measurements constitute aninteresting test of FEL theory, but they are also relevant to the predictedphenomenon of optical guiding.6 An FEL employing optical guiding wouldrely on the electron beam to guide the emitted radiation in the same manneras light is guided on an optical fiber, thereby extending the FEL interac-tion length beyond that allowed by the Rayleigh diffraction limit. To ourknowledge, the phase measurements presented here are the first such mea-surements to be published for any FEL. The agreement found with theoryin both the linear and the nonlinear regions of operation directly confirmsthe FEL phase theory, albeit in a parameter regime quite different from theregime in which optical guiding is predicted to occur.The FEL is illustrated in Fig. -1. A thermionically emitting Pierce gunremoved from a SLAC klystron (model 343) is energized by the PhysicsInternational Pulserad 615MR high voltage facility. The ensuing 0.25cmradius electron beam is guided magnetically into a copper plated, 2.54cmID stainless steel evacuated drift tube which also acts as the cylindricalwaveguide. Beam integrity is maintained by a uniform axial guide fieldBil. Experimental measurements and electron gun computer simulationsiindicate that the beam energy spread is less than 0.5%. This, together withthe relatively high current density and modest beam voltage, assures oper-ation in the collective (Raman) regime. The 50 period circularly polarizedwiggler has a period of 3.3cm, and is generated by bifilar conductors wound3on the drift tube. The wiggler amplitude B, is varied from zero to 300G.The FEL is operated in the amplifier mode. A microwave E-plane bendlauncher superimposes the input microwave signal onto the electron beamand converts the TEO, waveguide mode of the rectangular input waveguideto a linearly polarized, TE mode of the circular guide in the FEL. At theend of the wiggler known fractions of the power in the incident and orthog-onal polarizations are extracted by directional couplers, and measured bycalibrated crystal detectors. The system is driven by a 1OW traveling wavetube during the small signal measurements. To saturate the FEL withinapproximately one meter length, a high power (- 30KW) f =9.3GHz shortpulse magnetron is employed for the nonlinear studies.Figure 2 shows the FEL output-power as a function of the axial distancez for four different values of the electron beam current I and the corre-sponding power predicted by the computer simulations. The length of theinteraction region is adjusted by an axially moveable "kicker" magnet thatdeflects the beam into the waveguide wall. The current varies between 0.9Aand 5.5A. Since the output power and gain both decrease simultaneouslywhen the electron beam current is decreased, the saturation length is onlyweakly dependent on the beam current. Past the saturation point trappedparticle, electron "synchrotron" oscillations 2 cause the output power todecrease. The measured power levels are compared to the results of acomputer simulation that tracks 1024 particles in a single ponderomotive4wavelength, The numerical model is a modification of the KMR equations.The modifications are required for the particular parameter regime of thisexperiment, and include corrections for the excitation of a collective spacecharge wave on a finite radius beam, the transverse structure of the waveg-uide mode,7 three-dimensional wiggler fields, the axial guide magnetic fieldand the mildly relativistic electron beam. Three-dimensional effects areincluded by using appropriately calculated input parameters and analyticexpressions for the transverse electron motion.6 However, the simulationitself is one-dimensional and follows only the TEII waveguide mode. Thedetails of the model will be reported elsewhere.The output powers shown in Fig. 2 are determined at the fixed beamvoltage V that gives the greatest- gain at the beginning of the wiggler(z i 60cm). Note that this voltage need not be the voltage that givesthe maximum small signal gain because the device may already be appre-ciably saturated at z ~ 60cm. In addition, this maximum gain voltage isnot necessarily the voltage that gives the maximum output power alongthe entire wiggler length. In fact, the voltage that yields the maximumouput power increases steadily for wiggler lengths longer than the satura-tion length. This is shown in Fig. 3 where we plot the output power asa function of beam voltage for three axial positions. We see that both inthe data and in the simulations the voltage corresponding to peak powerincreases - 2% as z increases from 81cm to 155cm.5Figure 4 shows the FEL gain and the phase shift, as a function of thebeam voltage, when the experiment is operating in the small signal regime.Gain is observed at the operating point where the FEL instability can bemodeled as an interaction between an electromagnetic wave and an negativeenergy, slow space charge wave. A decrease in the output signal is obtainedat a somewhat lower energy where the electromagnetic wave interacts witha positive energy, fast space charge wave. The fine structure in Fig. 4 isdue to alternating constructive and destructive interference between theaforementioned waves.' This interference results from shifts in the wavephases.To directly measure these phase shifts, we use a microwave interferom-eter which mixes the RF output signal from the FEL with the RF inputsignal. As shown in Fig. 4b, the phase shifts extend over a wide range ofbeam energies, and they can be quite large, even when the FEL gain is nearunity. A characteristic of the collective (Raman) regime is that the phaseshift is near zero when the FEL interaction is strongest (i.e. at the largemaximum and minimum of Fig. 4a). This behavior is quite different fromthe phase behavior of an FEL operating in the single particle (strong pumpCompton) regime, where the phase shift is largest at maximum gain.In Fig. 5a we show the phase shift as a function of distance withinthe wiggler. The FEL power saturates at z - 100cm. However, even inthe saturated regime the phase continues to change, thus demonstrating6continued bunching of the electron beam by the FEL interaction. In Fig.5b and c we plot the power and phase shift as a function of beam voltageat a fixed distance z = 104cm. We note that the phase shifts illustratedin Figs. 4 and 5 are relative to the phase the electromagnetic wave wouldhave in the absence of the FEL interaction. A positive shift denotes areduction in the phase velocity of the wave, and thus an increase in theeffective refractive index, and vice versa for a negative phase shift.In conclusion, we have studied the power saturation of a collective freeelectron laser. The experimental results are in very good agreement withthe predictions of an extended one dimensional numerical model which in-cludes the essential three dimensional physics for this experiment. We havealso studied the phase behavior of-the FEL, and find that these measure-ments are also correctly predicted by the FEL theory. Such measurementsare a good test of nonlinear FEL theory, and they are also relevant to thepredicted phenomenon of optical guiding.This work was supported by the National Science Foundation, the Officeof Naval Research, the Air Force Office of Scientific Research, and the HertzFoundation.7References'J. Fajans, G. Bekefi, Y. Z. Yin, and B. Lax, Phys. Rev. Lett. 53, 246(1984) and Phys. Fluids 26, 1995 (1985).2N. M. Kroll, P. L. Morton, and M. R. Rosenbluth, IEEE J. QuantumElectron. QE-17, 1436 (1981).3W. B. Colson, IEEE Jour. Quantum Electron. QE-17, 1417 (1981).4D. Prosnitz, A. Szoke, and V. K. Neil, Phys. Rev. A 24, 1436 (1981).sT. J. Orzechowski, E. T. Scharlemann, B. Anderson, V. K. Neil, W. M.Fawley, D. Prosnitz, S. Yarema, D.B. Hopkins, A. C. Paul, A. M. Sessler,and J. S. Wurtele, IEEE Jour. Quan. Electron. QE-21, 831 (1985).'E. T. Scharlemann, A. M. Sessler, and J. S. Wurtele, Phys. Rev. Lett. 54,1925 (1985).7J. S. Wurtele, E. T. Scharlemann, and A. M. Sessler, to be published inthe Proceedings of the Seventh Annual Free Electron Laser Conference,Tahoe City, California 1985.'H. P. Freund, S. Johnston, and P. Sprangle, IEEE J. Quant. Electron.QE-19, 322 (1983).'J. Fajans and G. Bekefi, submitted for publication in Phys. Fluids.8FiguresFIG. 1. Schematic of the collective FEL experimental set-up.FIG. 2. Microwave power as a function of wigger length z for four currents,with B, = 188G, Bj = 1512G, and f = 9.3GHz. The points are fromexperiment, the lines from simulation: o o I = 5.5A; 4+ I = 3.7A;E I = 2.5A; AA I = 0.9A.FIG. 3. Power as a function of beam energy for three values of wigglerlength z. The solid lines are from the experiment,the dashed lines arefrom simulation. Here B, = 187G, B11 = 1470G, I = 4.5A, Pi = 32KWand f = 9.3GHz.FIG. 4. The small signal gain and relative phase shift as a function of beamvoltage. The solid lines are from the experiment,the dashed lines arefrom theory.9 B, = 122G, B1 = 1510G, I = 3.5A, f = 11.1GHz.FIG. 5. Nonlinear phase measurements; (a) phase vs. z at -y = 1.301; (b)phase vs voltage at z = 104cm; (c) power vs. voltage at z = 104cm. Thesolid lines are from the experiment,the dashed lines are from simulation.B, = 176G, B11 = 1450G, I = 4.1A, Pin = 27KW and f = 9.3GHz.9(I)00Uz 0ULUU- M-.JI9(-LaJr~a2IzLUILUI-LUJLUJzDJz0LwLua-LUJcDJ11090- ++++/++ ++ +-+0 +50-w+ mass>+ w'/ A A A& AAAAis---30 - -0 40 80 120 160z (cm)Fig. 2Fajans et al(a)80-40z=81cm0(b)40 -40-z=155 cmS1.291 1.296 1.301 1.306BEAM VOLTAGE l+(C)CFig. 3Fajans et a]I I0.9 1.0NORMALIZED VOLTAGEFig. 4Fajans et al3.02.01.008060.40.2+300+ 2(YI (a)- ----- ----  - -- - ----- \ -- IzLI-0-a-00I.-w+. 0*o0-\0'-20'\ (b)- -I I0.8 I.90 130Z (cm)1.288 1.294BEAM VOLTAGE1.300Y=1+eV/moc 21.306Fig. 5Fajans et alp-4d'O*r50 170(b)-- (c)wooI I I I0--4080Lii001-(a)waf1%e - -*040

Nonlinear power saturation and phase (wave refractive index) in the collective free electron laser

http://dspace.mit.edu/bitstream/1721.1/94892/1/86ja024_full.pdf

Nonlinear power saturation and phase (wave refractive index) in the collective free electron laser

Abstract

Similar works

Full text

Available Versions

DSpace@MIT