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  • 32 SUMMER 2002

    REATING MATTER from the vacuum,taking an atomic scale motion picture ofa chemical process in a time of a fewfemtoseconds (1 fs = 10-15 sec) or unravelingthe complex molecular structure of a singleprotein or virus. These are some of the newexciting experiments envisioned with a novel

    radiation source, the X-ray free-electron laser (FEL). John Madey and collaborators built the first FEL in the

    1970s. It is a powerful and challenging combination of parti-cle accelerator and laser physics and technology. Untilrecently FELs have been operating at infrared or near ultravi-olet wavelengths. A combination of theoretical, experimen-tal, and technological advances has made possible theirextension to the X-ray region. X rays have allowed us to seethe invisible for almost a century. With their help we havebeen making great progress in understanding the propertiesof materials and of living systems. Today the best sources ofX rays utilize synchrotron radiation from relativistic electronbeams in storage rings. The most advanced, so called thirdgeneration facilities, combine storage rings and undulatormagnets, and are used by thousands of scientists around theworld.

    USEFUL AS THEY ARE these facilities havelimitations. The minimum X-ray pulse duration isabout 50 picoseconds (1 ps = 10-12 sec), and the num-ber of photons that one can focus on a small sample islimited. Future experiments will need X-ray pulses with a

    With advances

    in technology,

    it is now possible

    to realize the

    dream of a fully

    coherent X-ray

    laser.

    X-ray Free-Electron Lasers

    by CLAUDIO PELLEGRINI & JOACHIM STHR

    C

  • BEAM LINE 33

    large number of photons focused on a sample as small as amolecule, squeezed in a time a thousand times shorter, tostudy the dynamics of atomic and molecular processes. X-rayfree-electron lasers can satisfy these requirements, as shownin the table.

    AN FEL CONSISTS OF A LINEAR acceleratorfollowed by an undulator magnet, as shown in thefigure. The undulator has a sinusoidal magnetic fieldof period w, usually a few centimeters, and amplitude Bw,typically about 1 tesla. In this field a single electron movesalong a sinusoidal, oscillating trajectory, and radiates an elec-tromagnetic wave-train with a number of waves equal to thenumber of undulator periods, Nw. The wavelength of thisspontaneous radiation is equal to the undulator periodreduced by a relativistic contraction factor inversely propor-tional to the square of its energy. This makes it easy toshorten the wavelength by increasing the electron beamenergy, and for GeV electron beams one can produce

    Principles, Properties and Applications

    ElectronAccelerator

    ElectronBeam

    E-MRadiation

    UndulatorMagnet

    Schematic representation of a SASE free-electron laser.

  • 34 SUMMER 2002

    wavelengths of about 1 , the size ofan atom. The radiation is within anarrow wavelength band, equal tothe inverse of the number of undu-lator periods, which for an X-ray FELcan be a few thousand. The radiationwithin this energy band is very wellcollimated, with an opening angle ofa few microradians. The number ofphotons spontaneously emitted fromone electron within this energy bandand angle is however rather low,about one photon per 100 electrons.In an FEL the electron beam has alarge number of electrons, about 109

    to 1010. In this case a phenomenon ofself-organization of the electrons,known as the FEL collective insta-bility, can greatly increase the num-ber of photons per electron and thetotal X-ray intensity. This instabil-ity transforms an electron beam witha random electron position distrib-ution into one in which the electronsare clustered in groups regularly

    spaced at about 1 , producing whatcould be called a 1-dimensional rel-ativistic electron crystal. The radi-ation from this crystal has new andexciting properties.

    Consider an ensemble of elec-trons propagating through an undu-lator. The total radiation field theygenerate is the sum of the fields gen-erated by all electrons. When theelectrons enter the undulator, thereis no correlation between theirposition and the X-ray radiationwavelength. As a result the fieldsthey generate superimpose at ran-dom, with a partial cancellation, asshown at the left in the next figure.What the beam produces in this caseis called spontaneous undulatorradiation, and its intensity is pro-portional to the number of electrons,Ne.

    If we could order the electrons sothat they were all within a fractionof the radiation wavelength, or

    Third Generation SASE-Free- Short pulse SASE-Electron Free-Electron

    Laser Laser

    Wavelength range, nm 1-0.1 1-0.1 1-0.1

    Emittance, nm-rad 2 0.03 0.03

    Pulse length, ps 15-30 0.06 0.01

    Average brightness 1020 1022 1021

    Peak brightness 1023 1033 1033

    Peak power, W 103 1010 1010

    Some typical characteristics of the undulator radiation from third-generation ring-based lightsources, and free-electron laser light sources. The emittance is in nm rad; the pulse length in picoseconds; the average and peak brightness are in photons/sec/mm2/mrad2/0.1% bandwidth;the peak power in watts.

    Undulator Radiation Characteristics

  • BEAM LINE 35

    separated by a wavelength, the radi-ation fields would superimpose inphase, as shown at the right in thefigure. The intensity is then propor-tional to the number of electronssquared, a huge gain. The effect issimilar to what you would have dur-ing a large party if instead of hav-ing all the people talking casually,producing a lot of noise, you couldorganize them in a well performingchoir, all persons singing exactly thesame note in perfect tune. Theresults would probably break all theglasses and windows in the room!

    While we do not know how tocontrol the electron position at thengstrom level, we can convenientlylet nature order the electrons for us,using the FEL collective instability.The way it works is: o Electrons propagating through the

    undulator interact with the elec-tromagnetic field generated byother electrons. The interactionchanges their energy, and thechange is modulated at the X-raywavelength.

    o Within the undulator the trajec-tory of electrons with larger(smaller) energy is bent less(more). As a result the electronswill bunch together within awavelength.

    o The electromagnetic fields emit-ted by the bunched electronssuperimpose in phase, and thetotal field amplitude increases.Thus the electron energy changeis larger, and the bunching mech-anism is stronger.The end result is that the ampli-

    tude of the electromagnetic fieldgrows exponentially. The growthrate is called the gain length and isthe most important FEL parameter.

    The exponential growth saturateswhen all the electrons are wellordered, and sing perfectly in tune!

    The instability can start with theaid of an external electromagneticfield, in which case the system is ahigh gain FEL amplifier, or it canstart from the random synchrotronradiation noise produced by theelectron beam at the undulatorentrance, a Self Amplified Sponta-neous Emission FEL (SASE-FEL). Aone-dimensional theory of a SASE-FEL, describing all its propertieswith a single parameter , wasdeveloped in 1984 by RoldolfoBonifacio, Claudio Pellegrini andLorenzo Narducci.

    In the X-ray region is about10-3 or less. This means that satu-ration is reached in about 1000undulator periods, and that onethousandth of the electron beamkinetic energy is transformed intophotons. Consider as an example a1 X-ray SASE-FEL with 15 GeV elec-tron energy, and ~10-3. In this casethe number of photons per electronwithin the same frequency band andangle is about 1000, a gain of 100,000over the spontaneous radiation case.

    The instability develops if theelectron beam has an energy spreadsmaller than , and a radius andangular spread similar to that of the

    The superposition of the fields generatedfrom many electrons; on the left is thespontaneous radiation case, on the rightthe free-electron laser case.

  • 36 SUMMER 2002

    X-ray beam. The gain must also belarge enough to overcome radiationlosses due to diffraction. This meansthat as the FEL wavelength is reducedthe electron beam must satisfy morestringent , and this requires avoid-ing damaging collective effects in theaccelerator. Operating an X-ray SASE-FEL is a balancing act between con-trolling the unwanted collectiveeffects in the accelerator, and lettingthe FEL instability develop in theundulator.

    IN A WORKSHOP held atSLAC in 1992 to discuss the pos-sibility of developing advanced,fourth generation X-ray sources,Claudio Pellegrini showed thatusing a novel electron source, thephotoinjector, developed by JohnFraser, Richard Sheffield, and EdwardGray at Los Alamos, and the newlinac technologies developed for theSLAC linear collider, it was possibleto build a 1 X-ray SASE-FEL. A studygroup coordinated by HermanWinick developed this concept, call-ing it the Linac Coherent LightSource (LCLS). A design groupdirected by Max Cornacchia contin-ued the project development until itsapproval by the Department ofEnergy. A group at DESY in Germanyalso became interested in this workand developed its own SASE-FEL pro-ject as part of the TESLA linear col-lider project.

    The first experimental observa-tions of the FEL instability were donein 1998 by a UCLA-Kurchatov group,which demonstrated exponentialgain over about 4 gain lengths, in a60 cm long undulator, at a wave-length of 16 mm. A much larger gain,3105 at 12 m, was obtained in the

    same year, using a 2 meter long un-dulator by a UCLA-Kurchatov-LANL-SSRL group. In 2000-2001 three SASE-FELs have reached a gain largerthan 107 and

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