Longitudinal electron beam and free electron laser microbunch measurements using off-phase rf acceleration

PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS, VOLUME 3, 032801 (2000)

Longitudinal electron beam and free electron laser microbunch measurementsusing off-phase rf acceleration

Kenneth N. Ricci* and Todd I. SmithStanford Picosecond FEL Center, W. W. Hansen Experimental Physics Laboratory, Stanford, California 94305-4085

(Received 2 February 2000; published 27 March 2000)

Magnetic dispersion followed by off-phase rf acceleration and an energy spectrometer were usedto measure the longitudinal density profile of bunched relativistic electron beams with a resolutionapproaching 100 fs. Various electron bunch shapes were measured by this method and comparedto bunch length measurements derived from the spectra of coherent transition radiation produced asthe bunches traversed a thin foil. A reasonable agreement was found between the two bunch lengthmethods. The off-phase rf acceleration method was then used to observe the modulated profile of amicrobunched electron beam at the exit of a far-infrared free electron laser oscillator. In a preliminarystudy of the relationship between optical cavity power and the microbunch distribution, the densitymodulation and the energy spread of the electron beam were seen to increase as the optical fieldstrength increased.

PACS numbers: 41.60.Cr, 29.27.–a

I. INTRODUCTION

In recent years the operation of many free electronlasers (FELs) and other accelerator-based light sourceexperiments has required the production of increasinglyshort picosecond and subpicosecond relativistic electronbunches and the concurrent development of subpicosec-ond electron beam diagnostics. This paper describes ap-plications of a novel subpicosecond beam diagnostic usingmagnetic longitudinal dispersion, an off-phase rf acceler-ator section, and an energy spectrometer.

Subpicosecond electron beam diagnostics range incomplexity from very simple, such as an inexpensivethermal detector, to very elaborate optical/electronicinstruments, such as the most advanced streak cameras.Since short picosecond electron bunches radiate morecoherent millimeter- and submillimeter-wave electromag-netic radiation than longer bunches, the relative electronbunch length can be minimized in an accelerator simply byadjusting the beam injection parameters while monitoringthe power of the coherent synchrotron radiation (CSR),coherent transition radiation (CTR), or other coherentradiation emitted by the beam at these frequencies [1–6].Other diagnostics have attempted to measure the absolutebunch length and exact bunch shape, or longitudinaldensity profile. Techniques currently used for this pur-pose include streak cameras, optical gating, and spectralanalysis of coherent radiation (CSR, CTR, etc.). All ofthese methods have succeeded in measuring subpicosec-ond bunch lengths, but they are limited in their ability

*Corresponding author. Telephone: (650)723-0209. FAX:(650)725-8311. Email address: [email protected]

1098-4402�00�3(3)�032801(9)$15.00

to observe the bunch shape. Optical gating techniquesrequire either extraordinarily good laser synchronization[7] or ambiguous pulse reconstruction [8], and they arecomplicated by the formation length and diffraction ofthe low-frequency components of the coherent fields [9].Spectral techniques avoid the synchronization difficultyby working in the frequency domain instead of the timedomain, but they suffer similar losses of low-frequencyfields. Furthermore, only certain classes of bunch shapescan be reconstructed unambiguously from their powerspectra [10]. A conventional streak camera attains highresolution in the time domain by using a ramped trans-verse electric field to transform a longitudinal (temporal)distribution of electrons into a more easily measuredtransverse distribution. With specialized optics designedby numerical simulation, resolutions of 200 fs haverecently been reported [11].

A longitudinal variation of the streak camera princi-ple has been used in multisection linear rf accelerators[12]. The last rf section is run off-phase so that the ac-celerating field is ramping up or down rapidly while arelativistic electron bunch passes through. Electrons en-tering the off-phase accelerator section receive an energyincrement that varies in proportion to their time of arrival.This transforms the beam’s temporal distribution into anenergy distribution which can be observed in an energyspectrometer. In practice, the initial energy spread of thebeam DEbeam limits the time resolution of this techniqueto Dt � DEbeam�a, where a is the maximum availableacceleration ramp (e.g., in keV�ps).

However, with an additional beam transformation from alongitudinally dispersive magnet section such as a chicane,the effect of initial beam energy spread can be removedfrom the final measurement. This idea was proposed byCrosson [13], and is illustrated in Fig. 1. In first-order

© 2000 The American Physical Society 032801-1

PRST-AB 3 KENNETH N. RICCI AND TODD I. SMITH 032801 (2000)

FIG. 1. A linear transformation of the longitudinal phasespace can transform a temporal slice of the bunch, such asthe segment containing point A, into a slice of the final energydistribution imaged in the spectrometer. Stretching of the phasespace in the dispersive section allows an off-phase acceleratorto remove the initial energy spread from the slice.

transport matrices, the chicane and off-phase accelerationtransform the longitudinal beam phase space as∑

1 0a 1

∏ ∑1 d

0 1

∏ ∑tE

∏�

∑t 1 dE

at 1 �1 1 ad�E

∏, (1)

where E is the energy coordinate relative to the mean en-ergy of the bunch, t is the relative time or longitudinalposition, and d is the longitudinal dispersion of the chi-cane (e.g., in ps�keV). Notice that if the accelerator andchicane are adjusted so that ad � 21, then the final en-ergy coordinate will be Efinal � atinit, with no first-ordercontribution from the initial energy distribution. This im-provement to the off-phase rf acceleration technique yieldsa resolution of

Dt � DEspec�a , (2)

where the resolution DEspec of the energy spectrometeris typically one or two orders of magnitude better thanDEbeam. This has extended the resolution of the off-phase acceleration technique down to the femtosecondrange and enabled a direct observation of the longitudinalprofile of subpicosecond electron bunches [14]. At thisresolution, it has become possible, for the first time, toobserve the detailed temporal profile of an electron beammicrobunched by the FEL interaction.

II. A COMPARISON OF TWO BUNCHMEASUREMENT TECHNIQUES

The new off-phase acceleration technique producedexcellent longitudinal beam data that were compared withthe results of a standard CTR spectral technique [15] inorder to evaluate the effectiveness of the CTR method.Measurements were made using the part of the Stanfordsuperconducting accelerator (SCA) shown schematicallyin Fig. 2. Bunches of 4 3 107 electrons were acceleratedto 21 MeV and bunched to picosecond length by the SCAfront end. The phase of the rf buncher and structures ofthe SCA front end were adjusted to vary the length andshape of the electron bunches, and for each setting the

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FIG. 2. Schematic diagram of part of the Stanford supercon-ducting accelerator

bunch was alternately measured by off-phase accelerationand by CTR.

For the off-phase acceleration measurement, the beampassed through the chicanes and off-phase accelerator andwas scanned across a thin tungsten wire at the focusof the energy spectrometer. The 1.3 GHz rf acceleratorwas run 90± off phase to provide an acceleration rampa � 105 keV�ps, and the chicanes were adjusted to pro-vide the longitudinal dispersion d � 20.0095 ps�keV.The chicane dispersion was calculated from the chicanegeometry and magnetic field and then optimized to withina few percent by tuning the chicane field until any en-ergy increment added at the SCA front end was exactlycanceled by the off-phase acceleration. This signaledthe achievement of the condition ad � 21 in the lineartransport matrices. For the estimated 5p mm mrad nor-malized transverse emittances of this beam, the energyspectrometer had an observed resolution of 0.05%. Ac-cording to Eq. (2), this corresponds to a time resolution of0.05% 3 21 MeV�105 keV ps21 � 100 fs.

For the CTR measurement, the chicanes were turnedoff, allowing the beam to travel in a straight line from theSCA front end to the CTR apparatus, shown schematicallyin Fig. 3. There the beam passed at a 45± incidentangle through a thin, polished aluminum foil, producingforward and reflected transition radiation. The reflectedCTR was collimated by a 50 mm diameter, 150 mmeffective focal length parabolic reflector and analyzed invacuum by a step-scanning Michelson interferometer todetermine its spectrum by the Fourier transform method.The Michelson interferometer used a 3 mm thick TPXplastic beam splitter and a second parabolic reflector tofocus the output light into a liquid helium cooled QMCInstruments1 InSb bolometer.

The results of these dual measurements are shownin Fig. 4 for three different settings of the SCA frontend. Figure 4(a) shows the three bunch shapes measureddirectly by the new off-phase acceleration technique. For

1Fast InSb detector type QFI�XB by QMC Instruments,West Sussex, England, mounted in dewar type HD-3 witha polyethylene window by Infrared Laboratories, Tucson,Arizona, 1993.

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PRST-AB 3 LONGITUDINAL ELECTRON BEAM AND FREE … 032801 (2000)

FIG. 3. Schematic diagram of the coherent transition radiation(CTR) measurement apparatus. As the beam passed at 45±

incidence through a thin, polished aluminum foil, CTR wasreflected from the foil into a parabolic mirror, which collimatedthe CTR and sent it through a Michelson interferometer.

clarity, bunch B1 has been shifted 2 ps to the left onthe graph. The jaggedness of B2 and B3 is due to rfnoise on the spectrometer wire and an intermittent 100 fsphase jitter between the beam and the rf accelerator duringspectrometer scans. In order to verify the sharpness of itspeak, bunch B1 was measured three times and averaged,removing much of the noise. The measured CTR spectrafor the same three bunches are shown in Fig. 4(c). Sincefrequencies near zero could not be detected, the CTRspectra have been normalized to a value of 0.5 near thefrequency 4.5 wave numbers for comparison with eachother and with the power spectra of B1, B2, and B3, whichwere computed numerically by taking the square modulusof the Fourier transform of the profiles in 4(a). Figure 4(b)shows the shapes of the three bunches calculated fromthe measured CTR spectra using the extrapolation andKramers-Kronig algorithm described in Ref. [15].

As expected, the shorter electron bunches emittedbroader CTR power spectra in the millimeter and submil-limeter wavelength range. Unfortunately, the measuredCTR spectra do not agree well with the calculated spec-tra. At low frequencies this is easy to understand—aFresnel calculation using the vectorial Smythe-Kirchoffapproximation [16] for wave propagation through two50 mm apertures separated by the 500 mm effective pathlength of the Michelson interferometer indicates thatdiffraction becomes severe for frequencies lower thanfour wave numbers. Measurements of the high frequencytails of the spectra were noisy because a backgroundof charged particle and gamma-ray noise, particularlyduring the observation of bunches 1 and 3, limited theeffective dynamic range of the bolometer to about 15 dB.Measurement of the higher frequencies was additionally

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FIG. 4. (Color) Comparison of off-phase acceleration and CTRbunch shape measurements. (a) At three different acceleratorsettings, bunch shapes B1, B2, and B3 were observed by thenew off-phase acceleration method. The peak heights havebeen normalized for ease in identifying their full width at halfmaximum (FWHM), given in parentheses (in picoseconds) foreach bunch. The black arrow in the upper left indicates thedirection of bunch travel (leading edge). (b) The shapes ofthe same three bunches were reconstructed by a CTR spectralmethod, which recovered the correct length and degree ofasymmetry for bunches B2 and B3, but could not distinguishbetween the original bunch shape and its temporal reflection.The spectral method also failed to discover the sharpness of thepeak and the shallow tail of bunch B1. (c) On a log scale, thenormalized numerical power spectra of measured bunch shapesB1–B3 are compared with the measured CTR spectral dataCTR1–CTR3 to show how detector response may affect bunchshape retrieval.

hampered by the nonlinearity of the InSb bolometer’sspectral response. Using a mercury vapor lamp in aBruker Fourier transform infrared (FTIR) spectrometer,

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and the SUNSHINE [17] coherent terahertz light sourcewith a Michelson interferometer similar to the one inFig. 3, the spectral response of the InSb detector was esti-mated over the range from 5 to 50 wave numbers; it wasfound to be approximately one order of magnitude lesssensitive at 30 wave numbers than at 10 wave numbers.This nonlinearity further reduced the effective dynamicrange of the detector for this application. A MolectronP1-75cc pyroelectric detector was substituted in place ofthe InSb bolometer and was found to have even greaternonlinearity over this spectral range.

When applied to imperfect spectral data like this, theKramers-Kronig algorithm produces an artifact in itsbunch shape reconstruction. Every bunch has the sameextremely sharp rising edge, a result which is clearlynot physical. Furthermore, like any method based solelyon a power spectrum, the Kramers-Kronig algorithmcannot distinguish between any particular asymmetricpulse and its temporal reflection, which has an identicalpower spectrum. In spite of detection and algorithmshortcomings, there was sufficient optical informationto calculate the absolute electron bunch length and thedegree of asymmetry for the relatively simple shapesof B2 and B3. The sharp peak and shallow tail ofB1 produce more CTR at the high and low frequencyextremes, where the optical detection is poor, and soit is not surprising that these features are not wellreconstructed. The reconstruction CTR1 overestimatesthe FWHM of B1 by about 40%, but underestimatesthe temporal standard deviation st by 20%—st for thereconstruction CTR1 is 0.57 ps, while the actual deviationst is 0.71 ps for B1.

For smooth Gaussian bunches, the FWHM is always2.35 3 st , making these two statistical definitions ofbunch length equivalent. Clearly, the notion of absolutebunch length, a single statistical parameter describing theduration of the bunch, does not apply as well to irregulardistributions like B1. However, if the definition of bunchlength is taken to be the average of 2.35 3 st and thebunch FWHM, then the off-phase acceleration and CTRmethods yielded the same average bunch length in allthree cases to within a few percent. This comparisonshowed that, with imperfect optical data, CTR and otherspectral methods can correctly measure the electron bunchlength, but they miss significant details of the bunchshape, which can be observed by a direct method suchas the new off-phase acceleration technique.

III. RESOLUTION LIMITS

During the measurements in Sec. II of this paper, thesharpest bunch feature consistently resolved (the averagedtip of bunch B1) had a width of 130 6 10 fs. The reso-lution was limited mainly by the maximum available ac-celeration ramp a and the spectrometer resolution DE. Itis reasonable to assume that with a greater acceleration

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ramp or a smaller focus in the spectrometer, this resolu-tion would improve significantly. However, at resolutionsbelow 100 fs, care must be taken to consider second-order terms in longitudinal beam transport and couplingbetween the transverse and longitudinal phase spacesof the beam. Following the notation of Refs. [18,19],these terms will be described using the linear trans-port coefficients Rij and second-order coefficients Tijk ,where the subscripts i, j, k range over the six-dimensionalphase-space coordinates �x, �x, y, �y, t, E� of the beam. Forexample, the second-order contribution from the dimen-sionless �y momentum to the longitudinal position t after adrift section of length L is written as

Dt �L2c

� �y�2 � T544� �y�2.

Table I indicates the estimated size of all first- andsecond-order longitudinal terms for the measurement de-scribed in Sec. II of this paper. For brevity, the relevantcomponents of Fig. 2 have been entered into the table infive lumped sections: (i) the chicane section, whose pri-mary purpose is to provide the linear longitudinal disper-sion R56 � d as indicated in the table; (ii) a short driftsection with quadrupoles to transport the beam from thechicanes to the final accelerator section; (iii) the off-phase accelerator; (iv) another short drift section withquadrupoles to match the beam into the spectrometer; and(v) the energy spectrometer. Several entries in the tablemerit particular attention. The temporal terms R5j andT5jk after the off-phase accelerator are unimportant forthis type of measurement because the distribution of inter-est after that point is the energy distribution. The largestsecond-order terms in the table are the quadrupole focus-ing terms T511, T512, T533, . . . over a 6 m drift section afterthe chicanes, estimated at 60 fs each for the x, �x and y, �yphase spaces. Assuming a Gaussian electron distributionin all phase-space coordinates, the best expected resolu-tion including first- and second-order terms would be about140 fs, in good agreement with observations.

Since the focusing terms increase quadratically withtransverse emittance, significant improvement may be ex-pected with a better beam quality. Typical transverseemittances in the SCA are 5 10p mm mrad, but thenewest generation of linear accelerators can achieve trans-verse emittances on the order of 1p mm mrad, makingthe focusing terms negligible. Unfortunately, the situa-tion is not so hopeful for the nonlinear longitudinal dis-persion term T566 of the chicane. Some energy spread isneeded to produce a picosecond bunched beam, and thisenergy spread will cause a nonlinear smearing of the lon-gitudinal structure at the femtosecond level as the beampasses through a chicane. So, in higher gradient accelera-tors with lower emittances, the 140 fs resolution of thisoff-phase rf acceleration method could be improved to the20–30 fs level, where the limiting term will be the T566 ofthe chicane.

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TABLE I. Beam phase-space coupling coefficients for the beam transport used in longitudinal bunch profile measurements.Symbols used are L: effective path length of a beam transport section; f: effective focal length of a magnetic lens or dipole fringefield; b: spacing between chicane dipoles; r, u: bend radius and bend angle in chicane dipoles; y � bc: electron drift velocity;t, c: rf period and phase of the off-phase accelerator.

First order Rij Second order Tijk

Chicane R55 � 1 T51j � 0

R56 � d � 295 fs�keV T522 )L2c �x2 & 20 fs

R65 � 1 T533, T534, T544 )L2c � �y2 1

yf �2 & 20 fs

all other R5j , R6j � 0 T566 � 12

≠2L≠E2 ) �4r tan3u 1

6b tan2u

cos3u � �DE�2

2cE2 & 30 fs

all other T5jk � 0T6jk � 0

Quadrupoles and R55 � 1 T511, T512, T522 )L2c ��x2 1 � x

f �2� & 60 fsfirst drift section

R56 � 2≠y

≠E ø dchicane T533, T534, T544 )L2c �� y�2 1 � y

f �2� & 60 fs

R66 � 1 T566 )≠2y

≠E2L�DE�2

2c2 & 5 fs

all other R5j , R6j � 0 all other T5jk , T6jk � 0

Off-phase accelerator R55 � 1 T655 ) DE ~2p2t2 cos�c�

t2

R65 � a � 105 keV�psR66 � 1

all other R5j , R6j � 0

Second drift section R5j unimportant T5jk unimportantR6j � 0 T6jk � 0

Spectrometer DEspec

a � 100 fs T5jk unimportantT6jk � 0

IV. DIRECT OBSERVATION OF FELMICROBUNCHES

It is well known that undulator and optical fields in-teract with an electron beam in a free electron laser tomodulate the electron beam energy and density periodi-cally at the optical wavelength of the laser, forming mi-crobunches that coherently excite the optical field [20].The increasing optical field in turn increases the rate ofmicrobunching, providing the positive feedback mecha-nism for FEL gain, until the field-induced energy spreador energy loss of the beam causes enough of the currentto slip out of resonance with the optical bandwidth thatthe net gain drops to zero and the FEL saturates. Forthe case where large energy spread causes saturation, thebeam may overbunch— the optical field induces such alarge spread in electron drift velocities that microbunchesform and then disperse again before completing a passthrough the undulator. In a short-pulse FEL oscillatorwhere the electron bunch, optical pulse, and slippage dis-tance are close to the same length, the electron bunch co-herence at saturation will vary as a function of opticalpower, slippage length, and the desynchronism betweenthe optical pulse and electron bunch periods [21]. Whilethe occurrence of gain in an FEL confirms the existence ofmicrobunching, it has not been possible until now to ob-serve the density modulation directly, because the intervalbetween optical periods was too short. Instead, indirect

032801-5

measurements of modulation depth have been made byobserving the power spectrum of coherent transition radia-tion emitted from a beam microbunched in a mid-infraredSASE FEL [22]. Now, however, the complete longitu-dinal profiles of beams microbunched by the FIREFLYfree electron laser have been imaged using the dispersion-improved off-phase rf acceleration technique at the Stan-ford Picosecond FEL Center.

TABLE II. Typical FIREFLY parameters for 60 mm mi-crobunch observations.

Undulator period lu � 6 cmNumber of periods Nu � 25Undulator (K) Ku � 1.0Bunch charge 1.3 3 108e2

Electron bunch length 1.7 ps FWHMBeam energy 16 MeVInitial beam energy spread 130 keV FWHMBeam repetition rate 11.8 MHzOptical wavelength 60 mmSlippage length 1.5 mmOptical cavity length 12.7 mMaximum optical gain 1.3% per passCavity (Q) 30Intracavity optical power a �40 W

aEstimated cw average optical power extracted from the11.8 MHz pulsed electron beam at FEL saturation.

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FIG. 5. A gray-scale image of 60 mm FIREFLY microbunches focused in the energy spectrometer. The energy distribution ofthe final beam, dispersed horizontally in this image, exhibits the time profile of the beam at the undulator exit. The light coloredvertical bars are regions of higher electron density (microbunches). The two horizontal white arcs are optical artifacts (reflectionsfrom the edge of the scintillator). The scale and arrow at the bottom of the image indicate picoseconds and the direction of bunchtravel.

For these measurements, the energy spectrometer in-strumentation was upgraded from a slow-scanning tung-sten wire to a scintillator screen and camera which canacquire an energy spectrum in 30 ms. This eliminatedrf electrical noise and the rf�beam phase jitter on mil-lisecond and longer time scales. FIREFLY was oper-ated at wavelengths between 51 and 60 mm, as measuredwith an ARC2 far-infrared diffraction grating monochro-mator. For other FIREFLY parameters, see Table II. Theelectron beam was coupled into and out of the FIRE-FLY optical cavity using the electromagnetic chicanesillustrated in Fig. 2. The second chicane, at the out-put end of the FIREFLY undulator, was adjusted to pro-vide 20.018 ps�keV longitudinal dispersion. A beam of1.3 3 108 electrons per bunch excited the FIREFLY laserand was microbunched in the undulator. At the exit of theundulator, apertures reduced the current to about 5 3 107

electrons per bunch to trim the transverse emittance andpermit a better resolution at the spectrometer. After thebeam received an off-phase acceleration of 56 keV�ps, itsenergy distribution was imaged on a YAG:Ce scintillatorscreen at the focus of the spectrometer. A monochromecharge-coupled device (CCD) camera3 with a triggered30 ms electronic shutter was used to select and integrate atrain of 350 bunches from the 11.8 MHz pulsed electronbeam. In principle, with a fast gated intensified camera,it would be possible to observe the longitudinal profile ofa single bunch this way.

2SpectroPro VM-504 Monochromator by Acton ResearchCorporation, Massachusetts, 1993.

3Pulnix TM-7AS CCD camera from Pulnix America Inc.,Sunnyvale CA 1999

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A typical image of 60 mm FIREFLY microbunches isshown in Fig. 5. The strongest beam modulation usu-ally occurred at the peak of the electron bunch, but insome cases, such as the 60 mm modulated profile shownin Fig. 6, the microbunches were distributed asymmetri-cally with the maximum modulation shifted toward ei-ther the leading or trailing edge. No strong correlationhas yet been found between the occasional microbunchingasymmetry and any controlled FEL parameter. When theFIREFLY wavelength was changed from approximately60 to 51 mm by adjusting the electromagnetic undulatorstrength without adjusting beam energy or other parame-ters, the spacing of the microbunches shortened accord-ingly, as shown in Fig. 6.

FIG. 6. (Color) Normalized beam current density with mi-crobunching at 60 and 51 mm. These data were averaged from60 horizontal slices through images like Fig. 5. Note that themodulation amplitude varies along the electron bunch. The ar-row indicates the direction of bunch travel.

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V. ANALYSIS OF MICROBUNCHOBSERVATIONS

Microbunches at 60 mm spacing were observed for avariety of FEL parameters and found to be extremely sen-sitive to changes in the optical cavity desynchronism, asindicated by Fig. 7(a). Here, desynchronism is definedas the repetition period of the electron beam minus theround-trip time of the optical cavity, so that desynchro-nism increases as the cavity length decreases. It is dif-ficult to determine the absolute desynchronism while theFEL is operating, but the relative desynchronism can beprecisely adjusted by changing the optical cavity length.(Note that the round-trip optical path length changes bytwice as much as the cavity length changes.)

At relatively small desynchronism, where the saturatedoptical field was strongest (relative cavity length 0 to21 mm), and at large desynchronism, where the satu-rated optical field was weak (relative cavity length 27to 210 mm), no microbunches were observed, but beammodulation up to 12% was measured for intermediate val-ues of the desynchronism. These data imply that themicrobunches at large desynchronism were too small tosee above background noise and that the microbunchmeasurement at small desynchronism was disrupted byFEL-induced energy spread. The disappearance of mi-crobunches at strong optical fields also suggests the pos-sibility of overbunching, but careful consideration of thebeam energy spread shown in Fig. 7(b) rules out thisconjecture.

Two electrons with a small energy difference DE moveat slightly different velocities,

Dy

y�

1g2

DEE

, (3)

with relativistic factor g. After they traverse an undulatortrajectory of length Nulu�1 1 K2�, their longitudinalphase shift with respect to each other is

Df � 4pNuDEE

, (4)

where Df is given in radians of the optical wavelength

l0 �lu�1 1 K2�

2g2. (5)

Here Nu, lu, and K are the number of periods, periodlength, and dimensionless field strength [20] of theundulator. In the case of field-induced energy spread,the electrons do not move uniformly with respect to eachother but are accelerated as a function of their phaserelative to the optical wave. In the limit of a continuous-wave (cw), weak optical field, the acceleration a is nearlyuniform on an electron at resonance with the undulatorfield, so that the velocity varies linearly as Dy � aT andthe phase shift varies as Df ~

12 aT 2 �

12 yT , where T

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FIG. 7. (Color) (a) Measured microbunch modulation ampli-tude and FEL power as a function of optical cavity length.Since the absolute cavity desynchronism was difficult to de-termine during FEL operation, the relative cavity length wasdefined as zero at the smallest desynchronism (longest cavitylength) where stable lasing occurred. Modulation percent isdefined as one-half of the maximum peak-to-peak variation inelectron beam density divided by the mean density over onewavelength. Power indicates the cw average of the intracav-ity optical power extracted from the 11.8 MHz pulsed elec-tron beam. The relative FEL power was monitored with afar-infrared detector, and an absolute calibration was estimatedfrom the observed efficiency (defined below). (b) FEL-inducedbeam energy spread and efficiency as a function of optical cav-ity length. Efficiency is defined as the FEL-induced change inthe mean electron energy divided by the initial mean electronenergy.

is the time elapsed during transit. Then the phase shift atthe undulator exit due to a uniform acceleration is relatedto the final induced energy spread by

Df � 2pNuDEind

E. (6)

When optimal bunching occurs, the maximal phase shiftof some of the electrons must reach 6p radians [20].

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Plugging this into Eq. (6) and solving for the expectedenergy spread, we find

DEind

E� 6

12Nu

(7)

for optimal bunching. This expression must be takenonly as a conservative lower limit on the energy spreadrequired to achieve optimal bunching because electronacceleration in a strong optical field is not uniform and,particularly, because of the unique properties of short-pulse FEL oscillators.

It is generally known that at large desynchronism theoptical field in a short-pulse FEL oscillator is stronglyasymmetric [21], and the peak of the optical pulseinteracts with the electron bunch only at the end ofthe undulator. In this situation, much of the energyspread (first integral of acceleration) is imparted to thebeam too late to microbunch the beam (second integralof acceleration) effectively. At small desynchronism,the optical pulse tends to be nearly symmetric andsignificantly shorter than the slippage length due to theeffect known as lethargy [21], so that the effective FELinteraction length is reduced. This increases the opticalbandwidth and also requires a larger field-induced energyspread to achieve optimal bunching in the shorter effectiveundulator length.

The FEL-induced electron energy spread and FEL ef-ficiency were determined by comparing the beam energydistributions with and without FIREFLY lasing, as shownin Fig. 8. For the 25-period undulator of FIREFLY,Eq. (7) predicts that strong bunching should not appearuntil the induced energy spread approaches 62%, or 4%

FIG. 8. (Color) Typical measured beam energy spreads withand without FIREFLY lasing. The unperturbed beam had anenergy spread of about 130 keV FWHM as shown by theequal-area fit. (The spectrometer camera was saturated forthis measurement.) With FIREFLY lasing at this particulardesynchronism, the induced energy spread was 4.4% and theFEL efficiency (mean energy loss of the beam) was 0.7%.

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FWHM, in good agreement with Figs. 7(a) and 7(b). Forrelative cavity lengths less than 26 mm, the optical fieldsaturated at low intensity because the large desynchro-nism decreased the coupling of the electron beam withthe peak of the optical pulse, lowering the optical gain. Asmall field-induced energy spread was enough to decreasethe gain to zero and cause saturation. At relative cavitylengths near 24 mm, the desynchronism was nearlyoptimal for coupling of the electron beam to the opticalpulse, and the highest optical gain (1.3% per pass) wasobserved. Higher initial gain enabled the FEL interac-tion to proceed to larger energy spreads and strongermicrobunching before reaching saturation. Smallerdesynchronism also produced a shorter optical wavetrain with a broader gain spectrum. At relative cavitylength 0, FIREFLY had an optical bandwidth of 3.5% asmeasured with the ARC monochromator. This bandwidthcorresponds to a wave train 14 periods long, indicatingthat the optical pulse had shortened enough to reducethe effective FEL interaction length by 45%. RecallingEq. (7), the energy spread needed to fully bunch the beamin a 14-period undulator is at least

DEE

� 61

2Neff� 63.5% , (8)

or 7% FWHM. The 5.5% energy spread measuredat this desynchronism was still insufficient to produceoverbunching.

However, the increased energy spread had an ad-verse effect on the measurement, because femtosecondlongitudinal resolution can be achieved only when thesecond-order beam transport terms are small. For themeasurements shown in Fig. 7, the T566 coupling frombeam energy to longitudinal position in the chicanebecame significant as the energy spread exceeded 4%FWHM. With chicane parameters r � 42 cm, u � 0.39,b � 13 cm (from Table I), the T566 temporal distortionwas

µ4r tan3u 1

6b tan2u

cos3u

∂�DE�2

2cE2� 190 fs

whenDEE

� 60.02 , (9)

which smeared out the 200 fs separation between 60 mmmicrobunches. Since this distortion increased quadrati-cally with energy spread, it cut off the observable mi-crobunches sharply as the relative cavity length wasincreased from 24 to 22 mm. As the cavity lengthapproaches zero and the optical field continues to increase,the microbunching is also expected to increase, but thiscannot be observed using the phase-acceleration methodunless steps are taken to trim the induced energy spreadafter the undulator and before the off-phase accelerator.

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VI. CONCLUSIONS

The longitudinal beam dispersion of a magnetic chi-cane and an off-phase linear accelerator section have beenused with an energy spectrometer to measure the longi-tudinal density profile of relativistic electron bunches atthe Stanford superconducting accelerator with a resolutionapproaching 100 fs. This diagnostic was used to observea variety of bunch shapes produced by beam manipula-tion at the accelerator front end and was compared withanother standard subpicosecond bunch measurement tech-nique: the spectral analysis of CTR. The new off-phaseacceleration technique yielded similar results for overallbunch length measurement, but offered a direct view ofthe bunch shape that was far superior to the bunch shapeinformation inferred from CTR.

The accuracy and effectiveness of the new off-phaseacceleration technique were further demonstrated by mak-ing the first direct time-domain observation of the pro-file of an FEL microbunched electron beam. Trains upto 13 microbunches long were resolved at separations of51 and 60 mm, conclusively showing a resolution betterthan 170 fs and temporal linearity of the technique overa range of several picoseconds. In the first experimentalstudy of microbunching as a function of desynchronismin an FEL oscillator, the saturated optical power, beamenergy spread, and beam modulation amplitude increasedas desynchronism decreased, at rates which indicated again-bandwidth limited saturation process instead of lon-gitudinal overbunching of the beam.

In higher gradient accelerators with smaller emit-tances, this improved off-phase acceleration measurementtechnique could be extended to resolutions of tens offemtoseconds, with the ultimate resolution limited bysecond-order terms in the beam transport such as thenonlinear longitudinal dispersion (T566) of a magneticchicane. This femtosecond beam diagnostic may be use-ful in accelerator facilities that require well-characterizedultrashort electron bunches for coherent terahertz lightgeneration, fast IR�UV�x-ray light sources, or highcurrent density applications such as FEL, SASE FEL, andhigh brightness beams.

ACKNOWLEDGMENTS

The authors wish to thank Eric R. Crosson for his rolein extending the wavelength capability of FIREFLY for

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this experiment and Takuji Kimura for assistance in mak-ing microbunch measurements. Funding was provided inpart by ONR Grant No. N000140-94-1-1024.

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Longitudinal electron beam and free electron laser microbunch measurements using off-phase rf acceleration