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UNIVERSITY OF CALIFORNIA

Los Angeles

Experimental Characterization of the Saturating, Near Infrared,

Self-Amplified Spontaneous Emission Free Electron Laser:

Analysis of Radiation Properties and Electron Beam Dynamics

A dissertation submitted in partial satisfaction

of the requirements for the degree

Doctor of Philosophy in Physics

by

Alex Murokh

2002

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The dissertation of Alex Murokh is approved.

____________________________________Harold R. Fetterman

____________________________________George Morales

____________________________________Claudio Pellegrini

____________________________________

James B. Rosenzweig, Committee Chair

University of California, Los Angeles

2002

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Table Of Contents

CHAPTER I: Physics of SASE-FEL Systems (Introduction) ..................................-1-

I.1 EVOLUTION OF SYNCHROTRON RADIATION SOURCES..........................-2-

I.2 FEL THEORY OVERVIEW...................................................................................-5-

I.2.1 Spontaneous emission by a single electron.................................................-5-

I.2.2 The operating principle of the Free Electron Laser......................................-9-

I.2.3 1-D high gain FEL theory.........................................................................-11-

I.2.4 Concept of Self-Amplified Spontaneous Emission...................................-19-

I.2.5 3-D properties of SASE radiation.............................................................-23-

I.2.6 SASE-FEL temporal, spectral and statistical radiation properties.............. -27-

I.2.7 Start-up from noise and SASE gain definition..........................................-31-

I.3 EXPERIMENTAL PROGRESS IN SASE FEL AND MOTIVATION FOR THEVISA PROJECT (VISIBLE-TO-INFRARED SASE AMPLIFIER). ................... -35-

CHAPTER II: VISA Design and Development of the Experimental Base............-37-

II.1 VISA EXPERIMENTAL OBJECTIVES AND GENERAL DESIGN .................-38-

II.1.1 The ATF facility........................................................................................-38-

II.1.2 VISA undulator.........................................................................................-42-

II.1.3 FEL design performance and the experimental error budget.....................-45-

II.2 INTRA-UNDULATOR DIAGNOSTICS ............................................................-50-

II.2.1 Undulator table and the vacuum chamber.................................................. -51-

II.2.2 The conceptual design of the diagnostic probes........................................ -53-

II.2.3 Beam position monitors imaging optics.................................................... -55-

II.2.4 The signal strength considerations for OTR diagnostics........................... -58-

II.2.5 Testing YAG:Ce single crystal diagnostics............................................... -63-

II.2.6 SASE diagnostic tools and relay imaging system ..................................... -65-

II.2.7 Alignment laser system.............................................................................-69-

II.2.8 Data acquisition and control systems........................................................ -74-

II.3 MECHANICAL ALIGNMENT OF THE UNDULATOR...................................-77-

II.3.1 Error analysis for the trajectory walk-off ..................................................-77-

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II.3.2 Magnetic measurements and corrections...................................................-80-

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II.3.3 Interferometric alignment of the undulator sections..................................-85-

II.3.4 Using the steering magnets....................................................................... -89-

II.3.5 Reference laser alignment .........................................................................-90-

CHAPTER III: VISA Results and Analysis.............................................................-94-

III.1 INITIAL COMMISSIONING..............................................................................-95-

III.1.1 System installation and first results........................................................... -95-

III.1.2 Undulator position monitoring system....................................................-103-

III.1.3 Re-aligning the undulator........................................................................-106-

III.2 OPTIMIZATION OF THE SASE PROCESS....................................................-113-

III.2.1 SASE measurements at low gain.............................................................-113-

III.2.2 Characterization of the electron beam......................................................-116-

III.2.3 Obtaining higher gain, and measuring the gain length............................. -122-III.2.4 SASE radiation properties at high gain...................................................-126-

III.2.5 Anomalous bunch compression hypothesis............................................-132-

III.2.6 Review of the available bunch length measurement techniques ............... -135-

III.2.7 Measuring bunch compression with the CTR......................................... -139-

III.2.8 Measuring saturation ..............................................................................-144-

III.3 DATA ANALYSIS AND NUMERICAL SIMULATIONS...............................-148-

III.3.1 Self-consistent set of data, and preliminary analysis ............................... -148-

III.3.2 Start-to-end numerical simulations.......................................................... -153-III.3.3 Determining thermal emittance of the electron beam...............................-160-

III.3.4 SASE angular distribution ...................................................................... -163-

III.4 CONCLUSIONS..................................................................................................-165-

CHAPTER IV: Appendices .....................................................................................-168-

IV.1 ANGULAR DISTRIBUTION OF SPONTANEOUS EMISSION AT THEFUNDAMENTAL IN A PLANAR UNDULATOR .......................................... -169-

IV.2 UNDULATOR SPONTANEOUS RADIATION THROUGH THE FINITEAPERTURE........................................................................................................-174-

IV.3 2nd HARMONIC................................................................................................-177-

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IV.4 EQUATIONS OF MOTION BY THE SINGLE ELECTRON IN THE -FRAME,

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IN THE PRESENCE OF EXTERNAL FIELD...................................................-178-

IV.5 XIE NUMERICAL ALGORITHM FOR CALCULATING 3-D FEL GAIN LENGTHIN APPLICATION FOR VISA..........................................................................-180-

IV.6 TEMPERATURE CHANGE IN VISA UNDULATOR MAGNETS UNDER THE

DIRECT IMPACT OF THE ELECTRON BEAM ............................................. -182-

IV.7 TRANSITION RADIATION OFF A 45 MIRROR DUE TO A SINGLE ELECTRON.............................................................................................................................-184-

IV.8 ELECTRON BEAM TRAJECTORY SIMULATIONS...................................... -187-

IV.9 PROPOSED BEAM BASED ALIGNMENT ALGORITHM............................-188-

IV.10 FOURIER TRANSFORMATION OF THE SPECTRAL INTENSITY FUNCTION.............................................................................................................................-189-

References ....................................................................................................................-190-

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List of Figures

I.1 SASE Free Electron Laser is a promising next step in the evolution of the X-raysources (left). Spectral brightness of some existing light sources (right) compared

to the design parameters of the proposed 4th Generation sources................... -3-

I.2 Periodic trajectory modulation generates radiation at selected frequencies, whichadvance by an integer number of wavelengths with respect to electron, while it passesthrough a single undulator period.................................................................... -6-

I.3 A particle trajectory in the -frame in the presence of the external field (numericalsolution to the equations (IV.32) for the typical set of parameters). The initialposition has an offset z0 with respect to the zero-crossing of the standing wave

........................................................................................................................ -10-

I.4 Phase space trajectories given by (I.29). ......................................................... -13-

I.6 Temporal spikes formation in SASE-FEL process (GINGER simulations).... -28-

I.7 The spectral profile of a long bunch near saturation (Mathcad simulation) is wellcontained within ~ 2 bandwidth. In this case, z 4lc and one can observethe characteristic spectral pattern of spike interference (left). If the beam energyspread is large, the interference effect is partially washed out (right)............... -29-

II.1 A computer drawing of the ATF 1.6-cell gun (BNL-SLAC-UCLA design). Drivenby the frequency quadrupled Nd:YAG laser, the S-band RF Gun generatesaccelerating gradient up to 120 MeV/m .......................................................... -39-

II.2 The VISA experimental line has 3 sections: the electron beam is generated and

accelerated in gun-linac section, transported via 20 double-bend towards Beamline3, and matched into the VISA undulator ......................................................... -40-

II.3 Drawing of the ATF experimental hall. VISA shared Beamline 3 with anotherexperiment which made the space constrain one of the major challenges ....... -41-

II.4 Cutaway isometric projection of the VISA undulator section demonstrate both dipoleand quadrupole magnets array. The quadrupole axis could be adjusted horizontally,and shimming was used to compensate for vertical offsets ............................. -43-

II.5 GINGER simulations to determine quadrupole strength. VISA performance wassimulated for different values of the electron beam matched b-function inside theundulator. The electron beam parameters for the simulation are similar to given at

Table II.1, but for the case of 83 MeV electrons (600 nm SASE) ................. -44-

II.6 VISA 3-D power gain length dependence on electron beam current for differentbeam emittances calculated with Xie algorithm. The dotted line shows the upper

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limit on the gain length to achieve saturation within 4-m undulator................. -46-

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II.7 Mathcad simulation of beam centroid trajectory inside the VISA undulator (a beamis mismatched at the entrance by 100 m) ...................................................... -48-

II.8 Isometric layout of the VISA vacuum vessel and support system.................... -50-

II.9 Support system for the undulator segments ................................................... -51-

II.10 General schematics of the intra-undulator diagnostics .................................... -52-

II.11 Intra-undulator probe schematics ................................................................... -53-

II.12 The miniature silicon mirror polished to the laser quality ............................... -54-

II.13 Schematic of the BPM optics ......................................................................... -56-

II.14 Test of the BPM optics, focused on a reticle. The distance between small fiducialmarks is 100 m. The optical resolution was found about 20 m ................. -57-

II.15 BPM set-up at VISA undulator table. Space constrain was one of the major

experimental challenges: each pair of the consecutive BPM support brackets isseparated by only 1 cm.................................................................................... -58-

II.16 Comparison of the OTR signal to the non-attenuated SE background off a 45mirror behind the undulator. The images were taken with the same set-up, yet for thesecond image a thin foil was inserted in front of the mirror, to block off undulatorradiation. The SASE process was not taking place during this measurement -60-

II.17 Simulated performance of the OTR beam position monitors at magnification M = 2,for different values of beam charge and transverse size (assuming round spot). Thepercentage is given in terms of 8-bit CCD camera sensitivity (100% saturates thecamera) ........................................................................................................... -61-

II.18 SASE lasing at the intra-undulator BPM #8 (25 cm before the undulator exit). FELlight saturates the camera despite the filters and polarizer ............................... -62-

II.19 Scintillating spectra of YAG:Ce and LuAG:Ce single crystals measured at ATF,using 50 MeV electron beam for excitation of the media................................. -64-

II.20 Images of the electron beam taken with six different diagnostics in a short timeunder the stable operating conditions. The OTR image is clearly smaller than onesproduced with scintillators............................................................................... -65-

II.21 FEL diagnostics station includes joulemeter, spectrometer and CCD camera forSASE intensity, spectrum and angular distribution measurements, respectively.

Remote control flippers are used to multiplex between the diagnostics. At theundulator exit, the radiation is directed towards the diagnostics by the Faraday Cupmirror ............................................................................................................. -66-

II.22 Single cell of the relay imaging optical transport system (f = 25 cm) ............. -67-

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II.23 Photograph of the lens array. A flipper is activated between the lenses 3 and 4

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........................................................................................................................ -68-

II.24 Photograph of the kinematic plate with the lasers set-up. Both NIR and red laserbeams are coaligned, via cold mirror ............................................................... -70-

II.25 Schematic of the alignment lasers system ....................................................... -70-

II.26 Alignment laser spot near the undulator exit, with the waist nearly 2 meters upstream.Despite the hot spots, the overall profile closely resembles a Gaussian, as it isemitted from the fiber coupled diode .............................................................. -71-

II.27 Red alignment laser position measured inside the undulator for 20 minutes afterturning switch on. After first 10 minutes, the position stabilizes within 20 m........................................................................................................................ -73-

II.28 Schematics of the VISA shot-to-shot measurements, in this example SASEmeasured with joulemeter is recorded simultaneously with stripline sum signalintensity proportional to the beam charge ....................................................... -74-

II.29 Schematics of the S2000 spectrometer set-up. A Type 5 cable allows to connectsspectrometer inside the experimental hall to the labtop in the control room, viaEthernet/USB powered adaptors .................................................................... -75-

II.30 Histogram of the RMS trajectories walk-off, simulated for 60 random sets of: (a)FODO cells magnetic axis offsets not too exceed 50 m; and (b) undulator polefield values, each within the 0.4% off the nominal field strength of 0.75 T ..... -79-

II.31 Example of vast trajectory misalignment, which is entirely due to rather unfortunatecombination of dipole strength variations and FODO cell magnetic centerline offsets........................................................................................................................ -80-

II.32 Schematics of pulsed wire set-up. The current from pulsed source causes stretchedwire to oscillate inside the undulator. Oscillations propagate towards laser-powermeter location, were it is mapped on the scope ...................................... -81-

II.33 Pulsed wire signal from undulator sections 3 and 4 after the correction is completed.The wire trajectory misalignment is reduced to a fraction of the wiggling amplitude........................................................................................................................ -82-

II.34 Numerical simulation of the pulsed wire measurements and correction. For arandomly chosen error factor the initial wire trajectory (a) was numerically simulated,along with the corresponding electron beam trajectory (b). Pulsed wire trajectorywas straightened (c), by simulating an addition of shimming magnets. Although, thesame shimming action improves the electron beam trajectory (d), the correction is

less efficient then for the wire.......................................................................... -83-II.35 Results of 10 simulations of the pulsed wire trajectory correction, for different

random seeds of the initial undulator field errors ........................................... -84-

II.36 Tooling balls are attached to the undulator sections (top) to serve as fiducial marks in

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both planes. Positions of the tooling balls from different sections are determined

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with respect to the laser beam, which is a straight line (bottom) ...................... -86-

II.37 Operation principle of interferometric alignment system: a straightnessinterferometer (a) is used to determine the Wollaston prism transverse position withrespect to the interferometric laser beam; (b) a fixed length rod is used to map thedistance between the prism and an undulator fiducial mark. By measuring the rod

arcing (c) it is possible to determine in which prism position the rod is locatedexactly perpendicular to the laser beam .......................................................... -87-

II.38 Histogram of the trajectory walk-off, simulated for 60 random sets of undulator

section axis misalignments, each not exceeding x0max = 31 m . The median

trajectory walk-off is 60 m RMS ................................................................. -88-

II.39 Simulation of steering magnet use to correct the electron beam trajectory through theundulator, by centering the beam at the BPM locations. By applying a propersteering fields, the beam walk-off is reduced from 120 m RMS, down to negligiblysmall value of 20 m RMS ............................................................................ -89-

II.40Wire finder and laser finder in the calibration frame ...................................... -91-

III.1 Two sections of the undulator installed in the NSLS Magnetic Measurements Lab........................................................................................................................ -95-

III.2 First prototype of the intra-undulator diagnostic probe assembly.................... -96-

III.3 OTR image of the electron beam measured at BPM 2 (75 cm into the undulator).The halo is due to the spontaneous emission, but the central spot OTR is way abovethe noise level. ................................................................................................ -97-

III.4 Horizontal and vertical trajectories through the undulator measured when the chargetransmission was optimized with the 700 pC beam ........................................ -98-

III.5 Horizontal trajectories with the beam launched at the slightly different angles nearthe axis, as indicated by the alignment laser. The trajectory offset indicates that: (1)the alignment laser is off by about 200 m, and (2) there is a strong kick in themiddle of the undulator, which could not be attributed to the launching error . -99-

III.6 The best vertical trajectory is nearly straight (~ 200 m peak-to-peak) throughout theundulator length ............................................................................................. -100-

III.7 Beam envelope measurements show that the tune is slightly mismatched at theundulator entrance, and mismatch increases significantly in the second half of theundulator ........................................................................................................ -101-

III.8 First SASE observation at VISA. The signal intensity changes non-linearly with thecharge, and at around 250 pC exceeds calculated value for spontaneous emission byan order of magnitude .................................................................................... -102-

III.9 Optical fiducials at the undulator gap allow tracking the relative displacement of

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undulator segments with a 10 m accuracy .................................................... -104-

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III.10 CCD cameras installed to monitor the undulator segment motion in both vertical andhorizontal direction ......................................................................................... -104-

III.12 Custom vacuum pump set up allows control of the vacuum evacuation time at a ratenecessary to protect the undulator magnets from the vacuum loading pressure........................................................................................................................ -107-

III.13 The trajectory after the shut-down showed some improvement; nevertheless, itpossessed the same signature as previously measured. Namely, a strong kickremained between sections 2 and 3 ................................................................. -108-

III.14 Comparison of the geometric and magnetic centers of the undulator segments basedon CMM machine measurements ................................................................... -109-

III.15 Simulation of the trajectory due to the alignment error in a decent agreement with themeasurements. Poor fit at 2.75 m may be due to the off-axis roll-off in thequadrupole field ............................................................................................. -110-

III.16 Re-alignment procedure: the segments were monitored (a) to match the nominal axis

with 20 m accuracy, and significant trajectory improvement (b) was observed........................................................................................................................ -111-

III.17 Photograph of the SASE signal on the ATF framegrabber monitor, observed oncethe undulator re-alignment was nearly completed. The speckles are the consequenceof the coherent light reflected off a poor quality copper mirror ...................... -112-

III.18 Typical measured SASE spectrum displaying significant structure, with the centralwavelength varying in the range 830 - 832 nm. The structure is a signature of thelong bunch SASE regime ............................................................................... -113-

III.19 Fourier transform of the SASE spectra (left) results in the autocorrelation of thesignal temporal envelope (right). The full width of the autocorrelation pattern istwice the length of the radiation pulse, which is here lb ~550 m . The sharp peakin the autocorrelation profile indicate lack of phase correlation between the temporalradiation spikes .............................................................................................. -114-

III.20 Histogram of intensity distribution in SASE signal measured over 80 shots centeredaround 830-832 nm. By fitting the gamma function (I.83), one obtains M 4.6........................................................................................................................ -115-

III.21 Snap-shot of the ATF emittance measurement program shows the measured beamsize versus quadrupole current, and corresponding fit parameters, includingemittance ........................................................................................................ -116-

III.22 Vertical emittance, measured with the quadrupole scan, for different values of thesolenoid current............................................................................................... -117-

III.23 Longitudinal phase space at the output of the ATF linac, of a 200 pC electron beamsimulated with code PARMELA. One can observe a large head-to-tail energy spread

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( ~ 0.2% RMS), mostly due to the beam chirping by the linac RF phase;

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however, the uncorrelated energy spread ( )0 is smaller than 0.05% RMS........................................................................................................................ -118-

III.24 Beam current measured at the 2nd linac section, by chirping electron beam energyand measuring the dispersion dominated horizontal beam size after the bend. -120-

III.25 The radiation pulse is only 1.5 seconds long, which means, that less than 1/3 of theelectron beam charge contributes to the lasing process.................................... -121-

III.26 Change of the Beamline III tune, in attempt to get a better control of the dispersion.In the initial tune (top), all 8 quadrupoles in the dispersion section were on, while thenew tune (bottom) had only 3 quadrupoles operating in the dispersion section........................................................................................................................ -122-

III.27 Shot-to-shot measurement of SASE intensity at the undulator exit as a function ofbeam charge.................................................................................................... -124-

III.28 Tracking linac phase fluctuations, by monitoring the charge loss at the collimator. At

nominal phase (1), the electron beam looses only low energy tail at the collimator;when the linac phase is mistuned to make the beam energy smaller (2), large fractionof the beam is lost, and when the linac phase is mistuned in the opposite direction(3), all the beam charge is transmitted through ............................................... -125-

III.29 SASE intensity measurements along the undulator length. Radiation energy growsexponentially, with the gain length of 21.5 cm. Small increase in gain length can beseen in the last 0.5 m of the undulator ............................................................ -126-

III.30 Comparison of typical spectra at low and high gain ....................................... -127-

III.31 Fourier transforms of spectra shown in Figure III.30 .................................... -128-

III.32 Intensity fluctuations with gamma-function fits for low and high gain datarespectively...................................................................................................... -129-

III.33 Angular distribution of SASE signal at low gain (left) and in the high gain regime(right).............................................................................................................. -130-

III.34 When the beam momentum changes with respect to the nominal momentum p0, towhich the beam line is tuned, both, the linear compression coefficient R56 and energyspread in the beam change accordingly. If, for instance, the beam central momentumdecreases by 1 % off its nominal value (going from A to B), the compressioncoefficient become positive, and of significant value ....................................... -133-

III.35 Schematic of the FROG measurement. The pulse is split in two components, which

recombine in the doubling crystal, such that the 2nd harmonic horizontal profile is anautocorrelation of the pulse longitudinal structure. After doubling crystal, the signalis sent to vertically oriented spectrometer. The resulting FROG trace has a form

S ,( ) , which can be numerically analyzed to extract E t( ) ............................. -136-

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III.36 CTR interferometer configuration. CTR off the foil, intercepting the beam path

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inside the vacuum chamber is collimated (1-3), then split into the two components(4,5) of opposite polarization. Moving one arm of the interferometer allows one torecombine the two signals with variable phase offset (6-7), obtaining the CTR pulsetemporal autocorrelation profile from the Golay cell detector readings ........... -138-

III.37 CTR bunch compression monitor. The collimated CTR signal is reflected off a

vertical grid polarizer, to reduce the coherent undulator radiation and optical noise.Then it is focused into the Golay cell detector. A low pass filter on a remotecontrolled flipper can be inserted into the beam path, to determine upper limit in CTRspectrum ......................................................................................................... -140-

III.38 The transmission characteristics of the Golay cell opening window, and LPE-55 lowpass filter. For comparison, CTR spectral intensity is shown for 40 m, 100 m,and 330 m RMS Gaussian beams ................................................................ -141-

III.39 Simulation of the CTR signal, off the 150 pC Gaussian beam for different bunchlengths, including effects of the Golay cell window and low pass filter .......... -142-

III.40 Measurement of the CTR intensity as a function of linac RF phase. The signal

appears within 1.5 window, and sharply peaks up at the same phase, where theSASE lasing is optimized ............................................................................... -143-

III.41 First observation of saturation at VISA (March 15, 2001)............................... -144-

III.42 Shot-to-shot energy versus charge distribution obtained at diagnostic port 8. For theexponential gain measurements only the shots within the dashed line are considered,to minimize the effect of linac RF jitter............................................................ -145-

III.43 Comparison of the distributions obtained at the diagnostic port 7 and at theundulator exit. The qualitative difference in the distribution functions is an indirectevidence of saturation at the undulator exit...................................................... -147-

III.44 SASE intensity growth along the undulator length. At the undulator exit, the RMSSASE pulse energy was measured to be about 20 J, with the statistical distributionindicating saturation ....................................................................................... -149-

III.45 3-D power gain length dependence on electron beam current for different beamthermal emittances calculated with Xie algorithm. The dotted line shows themeasured gain length of 17.9 cm .................................................................... -150-

III.46 The three step numerical simulation of VISA experiment. PARMELA is used tosimulate the electron beam acceleration through gun and linac sections; then,ELEGANT reproduces the beam dynamics in the dispersive part of the beamline;and, finally, the code GENESIS simulates the SASE-FEL process in the VISA

undulator. The actual beam and radiation measurements (shown at the bottom of theFigure), are the boundary conditions for the simulation process .................... -154-

III.47 Bunch compression in the dispersive section simulated with ELEGANT. The initialparticle distribution generated by PARMELA (top) has chirp, due to the linac phasedetuning. The ELEGANT output (bottom) display strong compression in the core

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of the beam. The cut at the bottom of the distribution is due to the collimator -155-

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III.48 Beam current profile before and after compression, modeled with PARMELA andELEGANT...................................................................................................... -156-

III.49 Beam emittance evolution along the VISA dispersive section modeled withELEGANT. Dispersion term dominates the effective emittancegrowth............................................................................................................. -157-

III.50 Slice emittance plotted along the length of the electron beam. The beam corenormalized emittance does not exceed 4 m-rad ............................................ -158-

III.51 Measured SASE gain along the undulator length, plotted along with the RMS SASEintensity values simulated by multiple GENESIS runs (dashed line). Thick linescorrespond to the standard deviation of simulated intensity curves ................. -158-

III.52 As the linac phase increases, the beam central energy reduces,(a) and chirp is beinginduced. Beam scraping at the collimator, combined with the bunch compression(b), results in a Christmas tree shape of the SASE versus charge distribution (c),and similar shape can be found in the intensity versus wavelength measurements (d),where wavelength variation is due to changing beam energy .......................... -161-

III.53 Bunch compression efficiency depends on the thermal emittance in the electronbeam, as found with ELEGANT simulations .................................................. -162-

III.54 Measured SASE angular distribution (left) and far field radiation distributionsimulated with GENESIS (right), shown on the same scale ........................... -163-

III.55 Correlation in the lasing core of the beam between particle energy and transverseposition, generated in the dispersive section and simulated with ELEGANT .. -164-

IV.1 Azimuthal angular distribution of VISA spontaneous emission at fundamental..................................................................................................... -173-

IV.2 OTR off a 45 conducting surface can be found using image charge model... -184-

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List of Tables

II.1 Electron beam design parameters for VISA..................................................... -40-

II.2 VISA undulator parameters............................................................................. -42-

II.3 VISA expected performance, given by GINGER............................................ -45-

II.4 VISA design tolerances................................................................................... -49-

II.5 Manufacturer specified parameters of the alignment lasers............................. -69-

III.1 Total drift of the undulator segments measured through pump-down and all furtherinstallations .................................................................................................... -107-

III.2 Measured electron beam parameters after the linac.......................................... -119-

III.3 Comparison of SASE properties before and after the dispersive beamline sectiontune improvement ........................................................................................... -131-

IV.1 Coefficients for a numerical fit (IV.40)........................................................... -181-

IV.2 Material properties of Nd2Fe14B (* quantities are approximated with table data foriron)................................................................................................................ -182-

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ACKNOWLEDGMENTS

This thesis is due to the efforts of many, and, first of all, I would like to list other

members of the VISA experimental team. Given my inclination to do things in the last

minute, Aaron Tremaines discipline and commitment to schedule were essencial to VISA

success. Xijie Wang was a great host, staying up long hours to keep the experiment going

(I once took a picture of him at 5 a.m. in the control room). Finally, Heinz-Dieter Nuhn

joined the experimental team and brought into the ATF control room a high level of

expertise and a good fortune.

Claudio Pellegrini and Max Cornacchia are Godfathers of VISA experiment. They

provided intellectual guidance, resources, and protected the collaboration from the outside

and from within. Jamie Rosenzweig, my graduate advisor, guided me through every step in

my career, as a physicist. He didnt took a thing for granted, and was quickly getting into

the essence of every problem I was up against (even if it was womens hockey). Among

other important contributions to VISA experiment, Jamie put together a start-to-end simulation

team including himself, Ron Agustsson and Sven Reiche. Their work enlightened with

understanding the most controversial results obtained at VISA. Both, Jamie and Sven,

helped me with writing and editing of this manuscript.

This is an experimental thesis, and it would not be happening without a good pair of

hands. Brendan Dix and Pedro Frigola equipment handling skills were outstanding. Don

Davis, Ben Polling and Bob Harrington provided essential technical assistance. All the ATF

personal was very supportive: Ilan Ben-Zvi carried the experiment through the budget gaps,

Bob Malone built VISA control system, Mark Montenagno assisted with electronic equipment,

Marcus Babzien helped with optical diagnostics, Karl Kusche with infrastructure, and Bill

Cahill kept us out of troubles. Finally, Vitaliy Yakimenko helped to perform diagnostic

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tests, and also designed the beamline tune which turned out to be a winner.

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Other people and laboratories contribution is most valuable. Roger Carr (SLAC) built

the undulator, Marcus Libkind (LLNL) designed the vacuum chamber, George Rakowsky

(BNL) carried the magnetic measurements, and Robert Rulands team (SLAC) did the

undulator alignment. Erik Johnson, Arthur Toor and Lowell Klaisner played a major role in

development of delicate diagnostic probes. George Skaritka helped with the design of

VISA hardware, and resolved space conflicts between multiple experimental systems.

Aside of VISA, I am affiliated with UCLA Particle Beam Physics Laboratory (PBPL)

for number of years. Within this group, my working environment was enriched by the

stream of characters. The graduate students that climbed the ladder before myself are Gil

Travish, Reinshan Znang, Eric Colby, Nick Barov, Mark Hogan, and Aaron Tremaine. Gil

is a star of my early days in PBPL, among other things he turned me into a Mac user; also,

Eric was very supportive during my thesis-hunting days in Chicago. Scott Anderson and I

started graduate school the same year and shared many experiences, including a cab ride in

Boston. Pedro Frigola organized great PBPL outdoor adventures; and Aaron organized the

best adventure of Xiodang Ding. Sven Reiche drove RV through the Golden Gate Bridge;

nevertheless, he is yet to learn how to play a good Terran. Other PBPL members, whose

company made my graduate school a great experience are: Ron Agustsson, Gerard Andonian,

Salime Boucher, Travis Holden, Pietro Musumeci, Soren Telfer, Matt Thompson, and all

new people who just recently joined the group.

... Some green piece activists consider scientists a burden to the society. I dont know

about the society, but we are certainly burden to those close to us. I thank my parents for

tolerating two physicists in the family (my brother, Igor, happens to be my first physics

instructor). And, of course, none of this work would be possible if it wasnt for an infinitepatience and support by my beloved wife Lena.

-xvii-

Finally, I thank my friends who are always there when the bell rings.

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PUBLICATIONS

J. B. Rosenzweig, A. Murokh and C. Pellegrini,A Proposed Dielectric-LoadedResonant Laser Accelerator, Phys. Rev Let. 74, 2467-2471, 1995

A. Murokh et al.,Bunch Length Measurement of Picosecond Electron Beams from a

Photoinjector Using Coherent Transition Radiation, Nucl. Instr. and Meth. A 410,452-460, (1998).

M. Hogan et. al.,Measurements of High Gain and Intensity Fluctuations in a SASEFree-Electron Laser, Phys. Rev. Lett. 80, 289-293, (1998).

A. Tremaine et. al., Observation of Self-Amplified Spontaneous-Emission InducedElectron-Beam Microbunching Using Coherent Transition Radiation, Phys. Rev.Lett. 81, 5816-5820, (1998).

A. Murokh et al., Photon Beam Diagnostics for the VISA FEL, Proceedings of 1999Particle Accelerator Conference, New York, March 1999, IEEE, 2480-2482, (1999).

A. Murokh et al.,A Diagnostics System to Measure SASE-FEL Radiation PropertiesAlong the 4-meter VISA Undulator, Proceeding of Free Electron Lasers 1999,Hamburg, August 1999, Elsevier, (II)119-120, (1999).

A. Tremaine et al., Status and Initial Commissioning of a High Gain 800 nm SASEFEL, Nucl. Instr. and Meth. A 445, 160-163, (2000).

A. Murokh et. al.,Limitations on Resolution of YAG:Ce Beam Profile Monitor forHigh Brightness Electron Beam, Proceedings 2nd ICFA Advanced AcceleratorWorkshop, Los Angeles, November 1999, World Scientific, 564-580, (2000).

P. Frigola et al.,Initial Gain Measurements of an 800 nm SASE FEL, VISA, Nucl.Instr. and Meth. A 475, 339-342, (2001).

A. Murokh et. al.,Limitations on Measuring a Transverse Profile of Ultra-denseElectron Beams with Scintillators, Proceedings of 2001 Particle AcceleratorConference, Chicago, June 2001, (accepted for publication).

A. Tremaine et. al.,Measurements of a 800 nm SASE FEL, Proceedings of 2001Particle Accelerator Conference, Chicago, June 2001, (accepted for publication).

A. Murokh et. al., Measuring FEL Radiation Properties at VISA-FEL, Proceedingsof 2001 Particle Accelerator Conference, Chicago, June 2001, (accepted forpublication).

R. Carr et al., Visible-Infrared Self-Amplified Spontaneous Emission Amplifier FreeElectron Laser Undulator, Phys. Rev. ST AB 4, 122402, (2001).

A. Tremaine et. al., Saturation Measurements of an 800 nm SASE FEL, ProceedingsFree Electron Laser Conference 2001, Darmstadt, August 2001, (accepted for

-xix-

publication).

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ABSTRACT OF THE DISSERTATION

Experimental Characterization of the Saturating, Near Infrared,

Self-Amplified Spontaneous Emission Free Electron Laser:

Analysis of Radiation Properties and Electron Beam Dynamics

by

Alex Murokh

Doctor of Philosophy in Physics

University of California, Los Angeles, 2002

Professor James B. Rosenzweig

In this work, the main results of the VISA experiment (Visible to Infrared SASE

Amplifier) are presented and analyzed. The purpose of the experiment was to build

a state-of-the-art single pass self-amplified spontaneous emission (SASE) free electron

laser (FEL) based on a high brightness electron beam, and characterize its operation,

including saturation, in the near infrared spectral region. This experiment was

hosted by Accelerator Test Facility (ATF) at Brookhaven National Laboratory, which

is a users facility that provides high brightness relativistic electron beams generated

with the photoinjector.

During the experiment, SASE FEL performance was studied in two regimes: a

long bunch, lower gain operation; and a short bunch high gain regime. The transition

-xx-

between the two conditions was possible due to a novel bunch compression mechanism,

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which was discovered in the course of the experiment. This compression allowed

the variation of peak current in the electron beam before it was launched into the 4-m

VISA undulator. In the long bunch regime, a SASE FEL power gain length of 29

cm was obtained, and the generated radiation spectral and statistical properties were

characterized.

In the short bunch regime, a power gain length of under 18 cm was achieved at

842 nm, which is at least a factor of two shorter than ever previously achieved in this

spectral range. Further, FEL saturation was obtained before the undulator exit. The

FEL systems performance was measured along the length of the VISA undulator,

and in the final state. Statistical, spectral and angular properties of the short bunch

SASE radiation have been measured in the exponential gain regime, and at saturation.

One of the most important aspects of the data analysis presented in this thesis

was the development and use of start-to-end numerical simulations of the experiment.

The dynamics of the ATF electron beam was modeled starting from the photocathode,

through acceleration, transport, and inside the VISA undulator. The model allowed

simulation of SASE process for different beam conditions, including the effects of

the novel bunch compression mechanism on the electron beam 6-D phase space

distribution. The numerical simulations displayed an excellent agreement with the

experimental data, and became key to understanding complex dynamics of the SASE

FEL process at VISA.

-xxi-

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CHAPTER I: Physics of SASE-FEL Systems (Introduction)

The evolution of the electron beam sources is directed towards increasing the 6-D phase

space density of the beam. Even though the most compact phase-space electron beams are

at present far away from fundamental performance limits, the development of photo-injectors

during 1980's [1] opened up new prospects for increasing the electron beam brightness. At

the present time advanced photo-injector facilities produce electron beams with an order of

magnitude denser phase space population in all three dimensions [2] compared to the most

advanced thermionic guns. This new technology has stimulated rapid development in the

high brightness beam applications [3], including FEL (Free Electron Lasers).

In this chapter we review the theory of FEL, and discuss goals and historical momentum

behind FEL research.

-1-

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I.1 EVOLUTION OF SYNCHROTRON RADIATION SOURCES

The instantaneous radiated power by a relativistic electron, subject to an external force, is

described by a generalized Larmor formula [4],

P =2e2

60m2c3

dp

dt

2

2dp

dt

2

. (I.1)

It is easy to seem see that, if one is in business of extracting radiation from the relativistic

electron beam, the process will be more efficient if the force applied transversely to the

particle velocity,

P = 2

e

2

60m2c3

F 2 + 12F||2

. (I.2)

In particular, a static magnetic field produced in a bending magnet deflects the electron beam

trajectory, thus forcing the beam to produce a synchrotron radiation. The spectrum of

synchrotron radiation is generally broad band, but sharply dropping below the characteristic

wavelength

c 23

meceB2

~ 2000

2

[nm]. (I.3)

From (I.3) one can find that ultra-relativistic >>1( ) electron beams can produce synchrotron

radiation in deep UV and X-ray regions. This technique has enabled construction of

storage-ring based 2nd Generation short wavelength light sources [5].

As an electron passes through an undulator magnet with the periodic magnetic field, the

synchrotron radiation band narrows to the set of selected frequencies, enhancing the generated

radiations spectral brightness by many orders of magnitude (Figure I.1). Improvements of

-2-

the electron beam emittance in the storage rings, combined with the growing users demand

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for the source brightness, led to the development of the 3rd Generation light sources based

on the spontaneous emission from the undulator [6] magnets. Over a dozen 3rd Generation

Light Sources are presently operating or under construction in many laboratories throughout

the world, and their use has created rapid progress in new branches of applied sciences,

such as protein crystallography [7].

So far, only the synchrotron radiation from individual electrons in the beam has been

considered. For the undulator emission at the short wavelengths, the collective effects in the

electron beam do not affect the spontaneous undulator radiation properties. Indeed, the

electrons within the beam are randomly spaced along the beam bunch length, which is, as a

rule, much longer than the wavelengths of interest. As a consequence, the undulator emission

from the presently operating synchrotron radiation sources is incoherent.

Figure I.1: SASE Free Electron Laser is a promising next step in the evolution of the X-ray

sources (left). Spectral brightness of some existing light sources (right) compared

to the design parameters of the proposed 4th Generation sources.

-3-

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However, in 1970 J. Madey demonstrated [8] that inside the undulator, the electron

beam can undergo microbunching while being irradiated by the coherent light of the same

frequency as the spontaneous emission fundamental wavelength. The microbunches would

radiate in phase with each other, thus generating coherent emission. Such a device was

named Free Electron Laser (FEL). The FEL process can increase the efficiency of the

undulator radiation by many orders of magnitude. An FEL can operate as an amplifier of

an existing coherent source, or it can also operate as an oscillator when coupled to the

optical cavity. Throughout 1980s there has been a significant progress in the development

of FELs in both amplifier and oscillator configuration [9,10,11]. However, both technologies

can not be extended into the X-ray spectral region, since neither existing coherent sources

nor optical resonators are available at such short wavelengths.

Further development of FEL theory [12,13] suggested the possibility of SASE (Self-

Amplified Spontaneous Emission) FEL, which allows coherent amplification of the self-

generated spontaneous emission by many orders of magnitude in a single passage of an

electron beam through the undulator. Such devices open up the potential for the development

of 4th Generation X-ray sources of unprecedented peak brightness [14,15].

-4-

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I.2 FEL THEORY OVERVIEW

In this section we discuss radiation from a single electron, 1-D high gain FEL theory, and

review some relevant results of 3-D SASE FEL theory.

I.2.1 Spontaneous emission by a single electron

The typical field of the planar undulator can be approximated on axis by

B =B0ycos kuz( ) , (I.4)

whereku is a wavenumber corresponding to the undulator period u. In this idealized case,the Hamiltonian of an electron travelling through the undulator is independent from its

transverse position and one can find the equations of motion directly from the canonical

momentum conservation,

Px0 = px eAx = 0 px = eAx =eB0

kusin kuz( ) . (I.5)

Noting that the magnetic field does not change the overall energy of the particle, one can

solve (I.5) for the horizontal motion of a relativistic electron inside the undulator:

x K

kucos kuz( ) and x =

K

sin kuz( ) . (I.6)

The deflection strength of a single undulator period can be defined through the undulator

parameter K, defined as

KeB0

kumc, (I.7)

-5-

which is the normalized vector potential magnitude of the undulator field. The transverse

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oscillations of the electron in the undulator, reduce its longitudinal velocity:

z = 2 x

2 +K2

42cos 2kuz( ) , (I.8)

where K242

is an average longitudinal velocity within the undulator. The effective

Lorentz factor, which gives the correct average longitudinal velocity, depends on the undulator

parameter Konly,

2 1

1 2= 2

1

1 + K2 2

. (I.9)

u

n

Figure I.2: Periodic trajectory modulation generates radiation at selected frequencies, which advance

by an integer number of wavelengths with respect to electron, while it passes

through a single undulator period.

Using (1.1), one can calculate the overall energy loss by an electron travelling through

the undulator of lengthLU:

-6-

ET 2e2kuK

2Nu

60, (I.10)

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whereNU is the total number of periods.

While synchrotron radiation is generally broad band (1.3), a periodic undulator structure

superimposes a coherency condition (Figure I.2). For any given emission angle , theundulator structure amplifies only the frequencies at which the wave front advances an

integer number of wavelengths with respect to the electron as it travels through a period,

nn = u1

cos ( )

n ( ) u

22n1+ K

2

2+ 22

.

(I.11)

The spontaneous emission spectrum resembles that one of a synchrotron radiation from a

single undulator cell [16] but is discrete. For the on-axis radiation 0( ) , additional

symmetry takes place, and only odd harmonics are present.

From here on, only the fundamental harmonic r will be considered. For the purpose

of quantitative analysis we recall a general expression for the far field angular spectral

fluence by the moving electron [4,17]:

d2E

dd=

2e2

32 30cdte

i t nr c( )n

+

2

. (I.12)

From the electron kinematics (1.6 - 1.8), it can be shown, that in a small angle large

approximation

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were kr ( ) is a fundamental harmonic wave number, ,( ) define the observation angle,

a xsin ( ) ycos ( ) , and the integration variable is changed to = kuz .

This rather complex expression can be integrated (see Appendix 1) and the result

(IV.17) is displayed here:

dE

d=

4e2Nuku2K2

0 1+ K2

2 +2( )3 ( ) (I.14)

The new independent variable is an energy normalized azimuthal angle , and the

function ( ) , defined in the Appendix IV.1, includes integration over the angle .

The resonant wavelength increases for larger angles, as can be seen from (I.11). As a

result, one can define the coherent angle c , such that within this angle the radiation

bandwidth will not exceed the on-axis linewidth of the radiator,

T=Nur

c

1

Nu

( )

= r ( ) rr

= 2 2

1+ K2 2( )

c =1+ K2 2

Nu. (I.15)

For the typically large number of undulator periods c

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I.2.2 The operating principle of the Free Electron Laser

When a beam of many electrons travels through the undulator, the longitudinal position

of different particles is generally uncorrelated; therefore, each particle in the beam contributes

to the beam spontaneous emission with a random phase. Such a source is intrinsically

incoherent, and for a large number of particles, the total energy generated by the beam is

expected to be the energy generated by a single electron (I.17), multiplied by a number of

particles in the beam, EcNe [18]. Introducing the phase correlation to the electron beam

longitudinal distribution, can potentially make the radiation process much more efficient.

Indeed, if all the electrons in the beam radiate at the same phase, the source become

completely coherent, and the overall energy scales like EcNe2 , which is a significant

enhancement for a typical beam of 109

particles.

One way to introduce a phase correlation into the electron beam longitudinal distribution

is to irradiate a beam propagating through the undulator with the horizontally polarized

coherent forward travelling wave of the same frequency as the fundamental line of the beam

spontaneous emission. To illustrate the physical principle it is useful to consider both

undulator field and external radiation in the

-frame, or more specifically in the frame

moving forward along thez-axis with the velocity (I.9). The magnetic field of the

undulator (I.4) looks like a backward plane wave, when transformed into the -frame, and

has the following properties:

Ex = Ex cBy( )

By = By Ex

c

z = z + c t( )

eEx =Kmec2k1e

i k1 z + 1 t( )

eBy = Kmeck1ei k1 z + 1 t( )

k1 ku

(I.18)

-9-

By the same token, the forward travelling laser radiation of wavelength r =u

22, when

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Lorentz transformed into the -frame, become of the same frequency as the undulator field:

Exl =E0le

i krzwrt( )

Byl = E0l

cei krzwrt( )

eEx l Kl mec2k1e

i k1 z w1 t( )

eByl = Klmec2k1e

i k1 z 1 t( )

Kl eE0

l

krmec2 .

(I.19)

As a result, both fields combined produce a standing wave component, which generates

a sinusoidal ponderomotive well alongz-axis. Consequently, in addition to the fast motion

in the wiggler field, an electron of a random phase undergoes slow ponderomotive drift

towards the phase zero-crossing of the standing wave (see Figure I.3 and Appendix IV.4).

A randomly distributed initial electron beam is subject to a periodic modulation of the

longitudinal phase space distribution (microbunching), which travels at effective velocity

in the lab frame. Formation of the microbunches enhances the spontaneous emission

efficiency and the initial forward travelling wave (a seedof the FEL) is thus amplified.

z0

-z0

x0

0

0

-x0

Figure I.3: A particle trajectory in the -frame in the presence of the external field (numericalsolution to the equations (IV.32) for the typical set of parameters). The initial

position has an offset z0 with respect to the zero-crossing of the standing wave.

-10-

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I.2.3 1-D high gain FEL theory

Here we closely follow references [16,19] andanalyze the FEL system in the lab frame.

When a single electron is passing through the undulator, its kinematic energy is invariant,

when it is subject to the magnetic forces only (neglecting radiation losses). If the presence

of the external radiation field (I.19) is added, the energy exchange between the electron and

a field must be accounted. The work done by the field on the particle is

mec2 = eE v . (I.20)

Substituting expressions (I.6) and (I.19) into (I.20) one obtains

=KlKkrc

2sin 2( ) sin ( )[ ] , (I.21)

where = kuz is a period normalized longitudinal position, and is a fast oscillating phase

kr+ ku( )z rt+0 . (I.22)

It is useful to replace with the new energy variable , defined as

r

r;

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ponderomotive; hence, one is interested in a period-averaged phase advance

0 sin 2( ) (I.25)

One can verify, that does not change when the particle is at resonant energy r,

dd

2 . (I.26)

Substituting (I.25) into (I.21) results in the following expression,

dd

2Kl Kku

2 + K2( )sin +0 sin 2( )( ) sin +0 sin 2( ) 2( )[ ]. (I.27)

Once again, the fast oscillating terms periodic in do not contribute to the particle-field

interaction. Using the Bessel function expansion (IV.7) and keeping only slowly varying

terms, one obtains the so-called pendulum equations, which describe the evolution of the

period-averaged phase and energy of a particle through the undulator in the presence

of the external field (I.19),

d

d = 2dd

= 2 sin +0( ) ,

(I.28)

where 2 2KlK JJ[ ]

2 + K2( )defines a pendulum frequency, and JJ[ ] is given by (I.17).

If the electron energy is not far away from the resonant energy r, and is sufficiently

close to the nearest zero-phase crossing, the particle periodically oscillates inside the separatrix

shown in Figure I.4. Such particles are trapped inside the so-called ponderomotive bucket,

and thus participate in the FEL interaction. In this model, the vertical half-size of the

-12-

separatrix max , define the upper limit on the electron-radiation energy exchange: if the

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electron looses more energy than max , it falls outside the separatrix and does not participate

in the FEL interaction.

Equations (I.28) can be derived from the Hamiltonian

H= 2 + 2 cos ( ) . (I.29)

Ponderomotive Phase

0

3

Figure I.4: Phase space trajectories given by (I.29).

To complete the set of FEL equations, we need to consider the evolution of the external

field, which can be generally affected by the particles motion, and therefore can not be

considered constant. To satisfy (I.19) the vector potential of the external field A z,t( ) can be

written

Ax z,t( ) = iE0

l

krce

ikrz ct( )

= iKlmec

e eikr zct( )

. (I.30)

-13-

The changes in the field through the FEL interaction can be included in (I.30), by simply

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considering the dimensionless field parameter Kl as a complex varying amplitude of the

radiation field Kl = Kl z,t( ) . It is also most practical to use a slowly varying phase and

amplitude (SVPA) approximation, and require that changes in Kl are insignificant over a

single undulator period,

1

c

t

Kl

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D+Kl z,t( ) =

2reKkr

eikr zct( )

sin kuzj( )j

3 r,rj( )j

, (I.36)

where the sum is taken over all particles in the electron beam, and re =e2

40mec2 is the

classical electron radius.

It is of the interest to evaluate the changes in the field amplitude averaged over many

undulator periods. For this purpose, we introduce a new variable z z ct, which can be

interpreted as a longitudinal position relative to the reference particle moving through the

undulator with the resonant energy r. One can integrate (I.36) over all the electrons within

the z -slice of volume V = z b , chosen such that

(a) the beam average density does not change throughout the volume V ;

(b) the variation of the field complex amplitude Kl is small, for the duration of the time

interval that it takes the radiation wavefront to pass through the volume V .

Both conditions, combined with (I.31), set a range for the choice of z :

1

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yields

D+

Kl z, t( ) ireK[JJ]

kr Ve

i j+0[ ] j

j V . (I.39)

By introducing the electron beam density in the laboratory frame, ne Ne V[ ]

V, one

obtains the equation for slow evolution of the FEL complex field amplitude,

D+Kl z,t( ) i

K[JJ]renekrr

e i j +0[ ]

. (I.40)

Combined with (I.28), this expression completes the set of 2Ne +1 FEL equations.

One can rewrite these equations in the dimensionless form, by using the following substitutions:

A Kl z,t( )i

22K JJ[ ]

2 + K2( )e

i 0

z 2 .

(I.41)

The dimensionless constant is left for the moment undefined. With new variables the

pendulum equations (I.28) for each individual electron becomes

djdz

= j

djdz

= Aei j + A*e

ij

. (I.42)

The D+

operator in equation for a field complex amplitude evolution (I.40) can be rewritten

for the new set of variables z ,( ) :

D+ = z

+ 1c

t

= 2ku z+ 1

2

(I.43)

-16-

In the steady state regime, the phase derivative of A is defined by the wavelength offset with

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respect to the resonant value r,

A

ir

1

A . (I.44)

Introducing a -normalized frequency detuning factor ,

1

2r

1

, (I.45)

one obtains an expression for the complex field amplitude,

d

dz+ i

A = K2[JJ]2 rene

83ku2r

3 e i j . (I.46)

Now the free parameter can be chosen to symmetrize equations (I.42) and (I.46),, namely

K2[JJ]2 rene

8ku2r

3

1 3

. (I.47)

As a result, one obtains a complete, symmetrized and dimensionless set of 2Ne +1 FEL

equations:

djdz

= j

djdz

= Aei j + A*e

ij

d

dz+ i

A = e ij .

(I.48)

To solve the FEL equations analytically a set of macro-variables need to be introduced. In

addition to complex field amplitude A ,

-17-

A =i

2 2K JJ[ ]

2 + K2( )eEl

krmec2 e

i0 , (I.49)

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it is convenient to introduce electron beam bunching factor B and energy modulation ,

B = e i j

= j e i j .

(I.50)

Generally these variables are small, unless the system is in saturation; hence, the FEL

equations can be linearized as follows,

d

dzB = i

d

dz

=

A

d

dz+ i

A = B .

(I.51)

The solution of the set of equations (I.51) is straightforward. Substituting out the other

variables, one obtains a linear differential equation for the dimensionless field amplitude A :

d

dz+ i

d2

dz2A = i A (I.52)

The equation can be solved trivially, by assuming a solution form A ~ eiz

, which leads to

a cubic equation for the eigenvalues of (I.51),

( )2 1 = 0. (I.53)

In the case = 0 , (I.53) yields

1 = 1, 2 = 1 i 3

2, 3 =

1+ i 32

, (I.54)

and the overall expression for the field amplitude evolution is

-18-

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A z( ) =1

3A 0( ) +

B 0( )

k i 0( )k

k=1

3

e ikz . (I.55)

One can see that for the large z the K= 3 term will dominate as it exhibits an exponential

growth:

A z >>1( ) ei

z 2

3A 0( )+

B 0( )

3 i 0( )3

e

3

2z

. (I.56)

The expression given in (I.56) demonstrates exponential amplification of the initial field

amplitude A 0( ) , underlining the basic operating principle of the FEL amplifier.

If one do not ignore a frequency detuning term in the cubic equation (I.53),, it is easy

to show, that frequency offset has to be small for the effective FEL amplification to take

place,

rr

2 . (I.57)

For instance, for

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laser field present ( A 0( ) = 0 ). Such a process, known as a Self-Amplified Spontaneous

Emission (SASE), has the advantage of being self-seeded and, thus, enabling generation of

coherent radiation at the spectral regions not available to the conventional laser sources (for

example, far-IR or X-rays).

For an exponentially growing SASE signal, from (I.56) one can find a dimensionless

intensity of the radiation field I A A , due to random bunching factor B 0( ) ,

I gA B 0( )2e

3z. (I.58)

In this expression gA defines the power coupling into the amplified mode. For SASE of a

monoenergetic beam, one obtains from (I.56) gA =1

9 . The power gain length during the

exponential growth in real units can be expressed

Lg =u

4 3. (I.59)

While converting equation (I.58) into physical units, the evolution of the SASE radiation

pulse spectral bandwidth, , has to be taken into the account [20], which yields

dP

d

= gAe

z Lg dP

d

NOISE

. (I.60)

Using (I.58) and (I.49), one can estimate the effective noise power generated in a z -slice

of the beam,

dP

d

NOISE

kr

2 mec2( ) 2 + K2( )

2cneb

16ku2r

3

B 0( )2

0( ). (I.61)

The average bunching factor of a random particle distribution can be found 18

-20-

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B 0( )2

1

Ne2 e

ij

j=1

Ne

2

=1

Ne. (I.62)

As long as condition (I.37) is satisfied, the ratio of initial bunching to the effective noise

bandwidth (I.15), in the z -slice is independent of a slice length,

B 0( )2

0( )

1

2nebc. (I.63)

As a result, by substitution of (I.63) into (I.61), one finds a simple expression for the initial

shot noise spectral power [20]:

dP

d

NOISE

1D

=rmec

2

2 , (I.64)

which turns out to be a function of the dimensionless FEL parameter only.

Of course, in both cases, whether the FEL operates as an amplifier or in SASE regime,

the exponential growth shown in the equations (I.56) and (I.60) has to be restricted to some

maximum value, in order to preserve energy conservation. The amplification of the radiation

field inevitably takes the energy away from the electron beam, increasing the electron beam

detuning with respect to the amplified radiation. From (I.11), one can conclude that if the

electron beam energy is reduced to r 1 ( ) , it does not radiate within the FEL bandwidth

(I.57), and no further amplification can take place. The FEL process reaches saturation, and

the field amplitude reaches its maximum value A ~1 [21]. At saturation, SASE radiation

intensity has a simple dependence on the universal scaling parameter 13,

PSAT

PBEAM, (I.65)

-21-

where PBEAM =Ib

emc2 is the instantaneous power in the electron beam. Too reach saturation,

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it takes approximately Nu ~ 1

undulator periods [20], so that the saturation length is

roughly given by

Lsat

u

(I.66)

In Figure I.4 a numerical simulation of the SASE process is shown for the VISA

design parameters (see Chapter II). The curve can be separated in three parts: undulator

regime (lethargy), exponential gain regime, and saturation. In the undulator regime, the

radiation growth is mostly due to the incoherent spontaneous emission (IV.20), the radiation

intensity increases linearly, and all three solutions of the cubic equation (I.55) are equally

important. At around two power gain lengths from the undulator entrance, the exponential

term (I.56) begins to dominate, and the system exhibits exponential growth. Typically at

about 20 gain lengths the exponential growth slows down and the system enters saturation

regime, where energy exchange between the electron beam and the radiation field periodically

reverses sign. In saturation, the linearized equations (I.51) are not valid.

It is important to investigate the limits of validity of the equations (I.48). Throughout

the derivation process the number of assumption was made, including the following:

the transverse distribution in the electron beam was considered uniform and stationary;

the finite emittance and energy spread in the electron beam were not considered;

the radiation field was approximated by a plane wave, neglecting diffraction;

the small slippage approximation was used, when the electron beam bunch length lb

was much larger than the relative displacement of the radiation field with respect to the

beam throughout the undulator length (rNu

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this manuscript. In the next sections we state the most general results concerning this

issues, generated through both theoretical work and numerical studies and reported in the

referenced publications.

0.10

1.0

10

102

103

104

105

106

107

0 1 2 3 4

Radiation

Intensity,

A.U.

Dist ance [m]

Undulator

regime

Exponent ial gain

regime

Sat uration

regime

Figure I.5: A numerical simulation of the SASE-FEL process obtained with GENESIS. One

can see linear growth followed by exponential gain and eventual saturation.

I.2.5 3-D properties of SASE radiation

With a finite transverse profile of the electron beam, one finds that corrections are

necessary to the 1-D treatment. In previous sections the radiation field, A , was approximated

as the plane wave. In 3-D approach, the field is given by a superposition of exponentially

growing guided modes [20]. For efficient lasing, a SASE coherent bandwidth criterion

(I.57) has to be satisfied, which, combined with (I.15), places a limit on the angular spread

-23-

in the fundamental mode:

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4r

u. (I.67)

If the transverse size of the electron beam, r, is small, the emitted radiation diffracts at theangle d =

r r

, which can be larger than (I.67), reducing the beam-radiation coupling. On

the other hand, a moderate amount of diffraction is required to establish FEL transverse

coherence. As a consequence, the 3-D gain length increases due to the diffraction by some

fraction ,

Lg =Lg 1 +( ) (I.68)

As such, the 3-D FEL parameter can be defined as 1+

. Most of the 1-D results can

be generalized to include the 3-D effects, by simple substitution of ,Lg( ) with , Lg( ) .

Following [22], it is useful, to introduce dimensionless beam radius a through the ratio

of the radiation pulse Rayleigh range, ZR , to the 3-D gain length:

a2

2

ZR

2 Lg

. (I.69)

(The meaning of normalization factor2

will become clear in Section I.2.7). For the beam

with Gaussian transverse intensity profile the dimensionless waist radius is

a =xLgr

. (I.70)

In the large beam limit a >> 1( ) , diffraction is negligible and interaction between the different

transverse fractions of the electron beam is weak. As a result SASE process give rise to

many coexistent transverse modes (the number of modes is on the order of 1 a2

[27]), and

-24-

there is no transverse coherence in SASE radiation during the exponential growth. In the

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opposite limit a

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In the case of a symmetric and matched electron beam, the two conditions, (I.73) and (I.71),

combined define a limitation on the beam emittance:

x xx x > lc . (I.80)

-27-

In this limit, different temporal fractions of the radiation pulse engage in the SASE process

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independently, resulting in formation of temporal spikes (Figure I.6). The spikes are formed

from the start-up noise, and as a consequence their phases and amplitudes are random. It

was shown in [25], that a separation between the spikes can not exceed the cooperation

length lc . For each individual spike, the longitudinal profile of the electron beam is

uniform; therefore, in the long bunch limit (I.80) the SASE process treatment given in

previous sections is valid, and so are the basic results.

SASE intensity

start-up exponential gain saturation

Figure I.6: Temporal spikes formation in SASE-FEL process (GINGER simulations).

The spectral bandwidth of the SASE signal at start-up resembles that of spontaneous

emission

1

Nu. When system enters the exponential gain regime, the SASE bandwidth

narrows down, and then slowly evolves as

2 Nu

[20], until it reaches the limit given

in (I.78). The spectrum profile of a long bunch has a lot of structure, reflecting the random

-28-

nature of the temporal spikes, as it is shown in Figure I.7. Thermal effects in the electron

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beam, such as a large energy spread (of the order of ) or emittance, reduce the overall

SASE radiated energy and partially remove the SASE spectral modulation.

/ 44 / 44

Figure I.7: The spectral profile of a long bunch near saturation (Mathcad simulation) is well

contained within ~ 2 bandwidth. In this case, z 4lc and one canobserve the characteristic spectral pattern of spike interference (left). If the beam

energy spread is large, the interference effect is partially washed out (right).

In the short bunch limit z lc

2

, only a single temporal spike is typically present. In

this limit, the spectral bandwidth is dominated by the Fourier transform limit z c , and

the spectral profile is smooth. The assumption of beam longitudinal uniformity, used in the

derivation of the FEL equations, does not hold in this limit, because a significant fraction of

the radiated energy leaves the region of interaction due to slippage. In this limit some

results have to be reevaluated. For instance, the energy growth rate of a short pulse was

found different from pure exponential behavior [25],

E

SHORT

z( )

exp 4.4z

2 3z13

Lg

z5 3 . (I.81)

In the limit of a short bunch, the power at saturation (I.76) is also reduced due to the

-29-

slippage by a factor ofs ,

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s 2z lc 1. (I.82)

One important consequence of the random nature of spikes is its role in fluctuations of

the SASE intensity. Each slice of the length lc is an independent radiation source with

100% intensity fluctuation expected; as a result, over the length of the beam one obtains

characteristic gamma-distribution [26], for the intensity fluctuations summed over many

independent sources:

p E( ) =MM

M( )E

E

M1

1

Ee

ME

E, (I.83)

whereMcan be approximated as a number of temporal spikes (assuming that full transverse

coherence of SASE radiation is established). In the long bunch limitMis large, Mlb

lc>> 1

(here lb is a full bunch length, different from RMS value z ), and the distribution function

(I.83) become similar to Gaussian. In a short bunch limit, on the other hand, the distribution

parameterM is near unity and the expression (I.83) reduces to the negative exponential,

which is the intensity distribution function expected from a single temporal spike.

If saturation is achieved, the saturation length and power fluctuations depend on the

number of spikes in the beam, as well. In a short bunch regime, fluctuations of the

saturation length can be as large as few gain lengths [25], and scale as

SAT 2Lglc

2z. (I.84)

For the long bunches, both LSAT and PSAT are relatively stable quantities.

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I.2.7 Start-up from noise and SASE gain definition

If 3-D effects are taken into account, the start-up from noise of SASE FEL requires

some additional considerations. It takes about two 3-D gain lengths, Lg for the exponentially

growing term in (I.56) to become dominant. As a result, the effective shot noise power can

be expressed in terms of the power of spontaneous emission after the first two gain lengths

[27], within the coherent angle c ,

dP

d

NOISE

02 dP

dd

z=2 Lg

SPONT

, (I.85)

where the angle 02

defines the coupling of SE into the fundamental amplified SASE mode.

It is convenient to modify this expression. From (IV.20), one can find a SE power

within the coherent angle for an electron beam of current Ib ,

Pc eIbkr

40

K2JJ2

1+ K2 2. (I.86)

Noting, that the expression (I.47) for the 1-D FEL parameter can be rewritten through

electron beam current and cross-section,

=8

Ib

IA

K[JJ]

1+ K2 2

2r

2

r2

13

, (I.87)

one can reduce the right-hand side of (I.85) to the following useful expression,

dP

d

NOISE

C a( ) 1+ ( )2mc2

2

. (I.88)

Here C a( ) is a coupling coefficient, which can be estimated by evaluating the diffraction of

SE over the first 2 gain lengths:

-31-

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C a( ) =ZR

2

2 Lg

dz

z2 +ZR2

0

2 Lg

=2 a2

tan

1 2a2

. (I.89)

If the electron beam is small a > 1( ) 1, and the shot noise power (I.88) reduces to the 1-D limit, as anticipated.

To draw an analogy to with conventional lasers, one can define the gain of the SASE

FEL system as the ratio of spectral output powerdP

d

f

to the effective noise power,

G dP

d

f

dP

d

NOISE

. (I.91)

When the monoenergetic system is in the exponential gain regime, the expression for the

amplification gain is straightforward,

G z( ) gAez 2Lg

. (I.92)

However, if there is deviation from the exponential growth due to system imperfections, or if

it is near saturation, it is often desirable to estimate gain based on the measured power

-32-

output Pf . In addition, the assumption that the coefficient gA is equal to1

9only applies

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when energy detuning is negligible ( = 0 ). For an electron beam of large energy spread,

the coupling coefficient can be as large as unity, and generally depends on the beam phase

space distribution [28]. In the general case, to determine gain, one can convert (I.91) into

the experimentalist-friendly format, by applying (I.88) and (I.70),

G1

3

2

Ib

IA

Lg

u

mec2

Pf krc( )

f

K2[JJ]2

1+ K2 2tan

1Lgr

2x2

, (I.93)

where SASE radiation output power Pf

, bandwidth ( )f

, and a gain length Lg , are

measured parameters.

It is interesting to examine gain at saturation, in the 1-D approximation; using

PSAT

Ibe

mec2 and radiation bandwidth of

SAT

~ 2 , as was defined by (I.65)

and (I.57), respectively. Then, the expression (I.93) reduces to the well understood result:

GSAT =lc

re

Ib

IA. (I.94)

Notice, thatIb

reIAis the linear density of charge in the electron beam, and Nlc lc

Ib

reIAis

just the number of electrons in a single spike. As FEL process amplifies spontaneous

emission by forcing the electrons in the beam to radiate coherently, the amplification gain is

limited to the number of electrons that can radiate in phase, GSAT = Nlc .

It is often desirable to estimate the gain length, if the only measured values are beam

charge Q, and SASE radiation energy at the undulator exit Ef. In this case, assuming long

bunch in the exponential gain regime, with a flat top profile, one can approximate (I.93) as

following:

G1

3

4 3

Ec

Ef

tan1 2

Lg

ZR

Lg

Nuu, (I.95)

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UV, and recently achieved saturation at the wavelength of 93 nm.

The VISA (Visible to Infrared SASE Amplifier) experiment at BNL Accelerator Test

Facility (ATF) was initiated to demonstrate SASE FEL operation at near-infrared wavelengths,

with the beam dynamics directly scalable towards future X-ray FEL projects. A novel

undulator design allowed a full advantage to be taken of the low emittance ATF electron

beam. With saturation in less than 4-m, the power gain length shorter than 18 cm was

expected. Also, due to conveniently chosen 800 nm fundamental wavelength, VISA could

utilize commercially available sophisticated optical diagnostic tools for most of the detailed

measurements of the FEL radiation properties.

The experimental progress in FEL is accompanied with a continuing advance of particle

and electromagnetic field numerical modeling codes. One important accomplishment of

VISA was the generation of a start-to-end numerical model of the experiment. A computational

routine involving three different codes, which will be discussed in the last chapter of this

manuscript, enabled reproduction of the experimental results in great detail from the

photocathode surface, all the way beyond the undulator exit.

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CHAPTER II:

VISA Design and Development

of the Experimental Base

As an introduction it is important to state, that VISA experiment started on sheer

enthusiasm and did not attract any significant funding, until most of the experimental base

has been built in a close collaboration of many institutions. The following is an incomplete

list of people and institutions which formed VISA collaboration:

Brookhaven National Laboratory (BNL)

M. Babzien, I. Ben-Zvi, D. Davis, B. Hurrington, E. Johnson, R. Malone, M. Montenigmo,

G. Rakowsky, J. Skaritka, X. J. Wang,, V. Yakimenko;

Lawrence Livermore National Laboratory (LLNL)

L. Bertolini, J. M. Hill, G. P. Le Sage, M. Libkind, A. Toor, K. A. Van Bibber;

Stanford Linear Accelerator Center (SLAC)

R. Carr, M. Cornacchia, B. Dix, L. Klaisner, H.-D. Nuhn, B. Poling, R. Ruland, B.

Scott, A. Trautwein;

UCLA Department of Physics and Astronomy (UCLA)

R. Agustsson, P. Frigola, A. Murokh, P. Musumeci, C. Pellegrini, S. Reiche, J.

Rosenzweig, A. Tremaine.

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II.1 VISA EXPERIMENTAL OBJECTIVES AND GENERAL

DESIGN

VISA experiment was proposed in 1998 [41] to build and operate SASE-FEL with

fundamental wavelength in the near-IR spectral region. The main objectives of the experiment

were to perform a complete test of SASE-FEL theory and to benchmark simulation tools.

Its goals were stated as follows:

1. Reach FEL saturation in Self Amplified Spontaneous Emission mode.

2. Measure radiation pulse intensity and intensity fluctuations versus undulator length

and charge.

3. Determine start-up noise, looking for possible new effects.

4. Measure radiation