SLAC Summer School on Electron and Photon Beams Tor Raubenheimer Lecture #: Inverse Compton and FEL s
Outline Synchrotron radiation Bending magnets Wigglers and undulators Inverse Compton scattering Free Electron Lasers FEL Oscillators High gain X-ray FEL s Coherence and Seeding Lecture #1 Lecture # Lecture #3
Inverse Compton Scattering (ICS) Source Scatter a laser off a relativistic electron beam Two views: Compton (Thomson) scattering Undulator source with micron period» Characteristics very similar to undulator radiation with K < 1» Correlated emission angle and wavelength» Single (potentially narrow) emission line Challenge due to small cross-section for scattering 3
Compton Scattering SSSEPB, Applied July Physics -6, 35, 013 Spring 013 G. Stupakov 4
Inverse Compton Scattering (ICS) Source Consider a 50 MeV electron beam ( ~ 100) with a 1um laser (1 ev) directed at it counter propagating In the electron rest frame, the Doppler shifted photons have an energy of 0 /ev The electron recoil will be small with 00 ev photons Thomson If the photons are scattered in the lab frame, the scattered radiation is boosted by a factor of again 0 /4 kev! The laser wave looks like an undulator of period 0 / (x speed of light) 5
Inverse Compton Scattering Sources Two primary approaches to beam generation:» Ring-based with high rep rate but larger emittance» Linac-based with brighter beams» Very different technical challenges X-rays can be generated from 100 MeV beams rather than GeV beams Brightness of ICS source depends on electron source brightness For high energy s a linac is likely to provide a compact cost-effective path ThomX ICS design Many applications are dose limited and don t require huge fluxes MIT ICS design 6 6
ICS Sources around the World Many facilities exist; more are planned Y.K. Wu, Duke HiGS, Duke AIST, Japan MAX-IV SSSE Lyncean, CA PB, Applied Physics 35, Spring 013 July 7-6,
Some Existing or Planned ICS Sources Planned Existing Facility PLEIADES (LLNL) AIST LCS (Japan) TTX, Tsinghua U. (China) LUCX (Quantum Beam) Lyncean Tech (California) HIGS (Duke, NC) *NERL (UTNL, Tokyo) Type X-ray E (kev) Rep. Rate (Hz) Bunches/ pulse Source size (m rms) Spectral flux (approx.) Linac 10-100 10 1 10 10 8 10% BW Linac 10-40 10 1-100 40 10 7-10 9 4-10% BW Linac 4-48 0 1 5 10 7-10 8 ~10% BW SC linac ~5-50 1.5 Hz 100 (future 8x10 3 ) Ring 7-35 65 x 10 6 1 30-50 8 Commissioning 10 9 3-4% BW (future 5 x 10 11 ) Ring 1,000 10,000 1 x 10 6 1 700 10 8-10 10 ~10% BW Linac 10-80 10 10 4 75 x 60 10 9 -x10 10 few % BW *MIT SC linac 3-30 10 8 1.4 *MXI Systems (Tennessee) *PLASMONX (SPARC, Italy) *ThomX (France) *ELI-NP (Romania) 10 14 5% BW (>10 15 future ERL, FEL?) Linac 8-100 10 1 10 10 10 10% BW Linac 0-380 10 1 5-10 10 9 ~10% BW Ring 50-90 1 x 10 6 1 40-70 10 13 5% BW Linac 1,000 13,000 10 100 0 10 13 1% BW8
Undulator Radiation Z. Huang 9
Undulator ICS The scattered photon energy in the lab frame is (Compton scattering): Compton term E ~ 4 E L / (1 + ) for back scatter ( 1 =, =0) (Does not include laser field strength term) In an undulator, the parameter K describes the field strength: x = K/ * cos( w *s) In ICS, the laser electric field is parameterized by: a 0 = ee 0 /mc = x * a 0 = K with w = 0 / a 0 = 0.85x10-9 I 1/ [W/cm ] [m] where I = P L / L 10
Flux of ICS 11
Photon Emittance (Gaussian Beams) function 1
Flux of ICS (II) Collision usually limited by laser emittance (Rayleigh length), i.e. if the electron and laser sizes are matched at the waist, the laser beam increases in size much more rapidly away from the waist. Two limits: 1) laser pulse shorter than Rayleigh length, ) L >> z R Case (1): N = T * N e N L / ( e + L ) for round beams N 4 x 10 3 N e U L [J] / z R [m] assuming matched spots For example, 150 pc e -, 0.1 Joule 1 um laser in a 35 um spot 1e8 s (with I ~ 1 x 10 15 W/cm ) Case () solve for homework 13 G. Krafft, Reviews of Accelerator Science and Technology, Vol. 3 (010) 147 163
Spectrum of ICS (I) The total number of photons is conserved but the emission angles are shifted by the boost. 90-degree emission in beam frame is boosted to an angle of 1/ and, from p. 15, this has ½ the maximum energy http://members.home.nl/fg.marcelis/specrelpart.htm ½ the number of photons are emitted in the central cone of 1/ and the width of the cone for smaller energy deviations is ~ sqrt()/ For example, a 50 MeV e- beam scattering with a 1um laser 40 kev photons and the central cone of 300 urad has a spectrum of 0.1% Except 14
Spectrum of ICS (II) Measured spectrum from Lyncean Technologies ICS source Full x-ray spectrum, 4 mrad fwhm Peak x-ray energy =13.8 kev Electron beam energy = 7.85 MeV X-ray Energy in KeV 15
Spectrum of ICS (III) There are four other terms that increase the spectrum (see p. 10): 1) The beam energy spectrum (change change boost) ) The laser incident angle (scales as ~ / 4 for backscatter) 3) The field strength variation of the laser ( ~ a 0 / ) 4) The electron beam emittance ( ~ ( / x ) ) Limits to achieving narrow energy spectrum, e.g. 0.1%: Term (1) can be typically limited to 0.1%, term () is weak for typical convergence angles, term (3) is important when a 0 ~ 0.05 (I ~ 10 15 W/cm ) at 1 um, and term (4) is important when focusing to small spots x < 35 um 16
Brightness of ICS The spot size depends on the overlap of the laser and electron beams: = ( e * L ) / ( e + L ) The angular divergence is dominated by the electron beam emittance ~ [( / x ) + / ] The pulse length (backscattering) is determined by the electron bunch length and the total flux is (for short pulses): N 4 x 10 3 N e U L [J] / z R [m] Using example from before B ~ 10 8 per (mm mrad 0.1% pulse) Low average brightness but high peak brightness and the brightness increases as better performance than 3 rd generation E >> 100 kev 17
ICS Brightness scales as Complements 3 rd generation light sources at high photon energy 1.E+18 Average brightness (ph/s*mrad^*mm^*0.1%bw) 1.E+17 1.E+16 1.E+15 1.E+14 1.E+13 1.E+1 1.E+11 1.E+10 1.E+09 SSRL BL4/7.0T SSRL Bend 1.5T ICE-X Example of ICS source average brightness 1.E+08 1.E+03 1.E+04 1.E+05 1.E+06 energy (ev) 18
Additional References Inverse Compton Scattering x-ray Sources Z. Huang and R.D. Ruth, Laser-Electron Storage Ring, Phys. Rev. Lett., 80:976-979 (1998). Roderick J. Loewen, A Compact Light Source: Design and Technical Feasibility Study of a Laser-Electron Storage ring X-ray Source, SLAC-Report-63 (003). W.J. Brown and F. V. Hartemann, Three-dimensional time and frequency-domain theory of femtosecond x-ray pulse generation through Thomson scattering, PRST-STAB, Vol. 7, 060703 (004). W. Graves, et al., MIT inverse Compton source concept, NIM, A608, (009). ThomX Conceptual Design Report, LAL/Soleil/ESRF/THALES Collaboration, LAL RT 09/8 (010). W. Graves, et al., High Repetition Rate Inverse Compton Scattering Source, presented at ICFA Future Light Sources 010 Workshop (FLS010), Stanford, CA, March, 010. G. Krafft, Reviews of Accelerator Science and Technology, Vol. 3, 147 163, 010 kw Lasers and laser cavities D. Rand, et al,, Cryogenic Yb 3+ - doped materials for pulsed solid state laser applications Optical Materials Express 1(3) 434-450 (011). J. Limpert, et al., The Rising Power of Fiber Lasers and Amplifiers, J. Sel. Top. Quantum Electron. 13(3), 537 545 (007). J. Limpert, et al., High Repetition Rate Gigawatt Peak Power Fiber Laser-Systems: Challenges, Design, and Experiment IEEE JSTQE 15, 1, 159 (009). F. Krausz, et al., Power Scaling of a high repetition rate enhancement cavity Opt. Lett., 35(1) (010). W. Putnam, et al., High intensity Bessel-Gauss beam enhancement cavities CLEO/QELS CMD1 (010). 19
The Free Electron Laser (FEL) 0
FEL Interaction (I) Undulator radiation is calculated ignoring other electrons and the resulting radiation field. Is there a way to couple the beam to the radiation field? dw = F ds = -e E v dt Need a component of the electron velocity aligned with the electric field Back to motion in an undulator (#1, p. 0): 1 z 1 x 1 K / K z 1 4 1 1 [1 K cos(sk u sin ) ( sk u )] 1
FEL Interaction (II) dw SSSEPB, > 0 July -6, 013 dw = 0 dw < 0
FEL Interaction (III) 3
Pendulum Equation Pendulum equation described the transfer of energy to and from the electrons as a function of the pondermotive phase Small amplitude oscillations sin s where K 0 k u a L k L with a L = ee 0 /mc L (sometimes refered to as a s ) Large amplitude oscillations oscillation frequency decreases as a function of amplitude K a Bucket height max L (1 K / ) which depends on the undulator strength and the laser field 4
Pendulum Equation (II) In general the electrons will simply oscillate in the bucket. However, if the initial energy of the electrons is higher than the resonant energy of the undulator energy loss on average Open circles are initial positions and stars are final positions No net energy transfer Energy loss by electrons From R. Ischebeck 5
Small Signal Gain Madey s theorem The small signal gain curve is the derivative of the sontaneous emission spectrum and gain is positive at positive detuning (higher beam energy) g ss ( ) K [ JJ ] u N 3 3 u I I A d dx sin x x where x N u Maximum gain at x ~ 1.3 or ~ 1/5N u Power grows as N u cubed 6
FEL Oscillator Resonant optical cavity allows radiation to build up as new electron bunches are passed through the undulator until saturation is reached 7