X-ray Optics-Free FEL Oscillator

Old idea* X-OFFELO X-ray Optics-Free FEL Oscillator There is a need for an X-ray FEL oscillator to further the quality of X-ray beams. While SASE FELs demonstrated the capability of providing very high gain and short pulses of radiation and scalability to the X-ray range, the spectra of SASE FELs remains rather wide (~0.5%-1%) compared with typical short wavelengths FEL-oscillators (0.01% - 0.0003%). Absence of good optics in VUV and X-ray ranges makes traditional oscillator schemes with very high average and peak spectral brightness either very complex or, strictly speaking, impossible. In this paper, we describe the concept of X-ray optics-free FEL oscillator, discuss its feasibility, and present some initial results and plan for detailed computer simulations. *Originally presented at ICFA workshop, July 1-6, 2002, Chia Laguna, Sardinia, Italy Additional materials from the FEL prize talk at FEL 05 Conference, 2005, Stanford, CA, USA and FEL 07 conference at Novosibirsk, Russia

Dedication to abused (mechanically, thermally, verbally and also by radiation), stressed, damages, over-exploited, pushed to the limits, sworn-on MIRRORS which we used pushing the FEL oscillator limits to shorter and shorter wavelength and more and more intra-cavity power

Motivation: why an oscillator Key words: narrow Fourier-limited linewidth, single transverse mode, higher spectral brightness, higher stability, full wavelength tunability SASE FELs demonstrated the capability of providing very high gain, short pulses of radiation and scalability to very short wavelength - the FEL conference site is the best proof Meanwhile, the spectra of SASE FELs is rather wide (~0.1) compared with typical short wavelengths FEL-oscillators (0.01% - 0.001%) HGHG (or seeded) FELs depend on the availability of appropriate seed and lack the multi-decade tunability typical for SASE and oscillator FELs Higher (that on SASE FEL) average and peak spectral brightness can be achieved by keeping the FEL power constant while narrowing the linewidth

Motivation: why optics free Key words: no power limitation (before vacuum breaks and generate e - e + pairs), no wavelength limitations, no degradation of performance, ultimate Freedom Absence of good optics in VUV and X-ray ranges makes traditional oscillator schemes prohibitively complex or simply impossible Absorption in the mirrors coatings and the mirror substrates limits both average and peak power in FELs (power density, to be exact) Finally, optics is the only element in an FEL oscillator, which can not be fully controlled by accelerator physicist. Hence, the frustration! Michelle Shinn, 2005 Vladimir Litvinenko, 2000

Lasing Lines and Spikes OK-4-0.0072% RMS TESLA - 0.51% RMS LCLS @ 1.5 Å 0.015 nm @ 218 nm 0.55 nm @ 108 nm - 0.37% RMS Fourier limited 1 Lasing Line at 218.65 nm RMS linewidth: 0.0157 nm (including resolution) Intensity, normalized 0.8 0.6 0.4 0.2 FWHM=1.4*10-4 "!/!=7.18#10 $ 5 OK-4 FEL TESLA FEL 0 208 212 216 220 224!, nm Courtesy of J. Roβbach Courtesy of J.Walsh

120 Oscillator Full longitudinal coherence FEL pulse is much shorter than e-beam Fit: I(τ) = a 0 exp(-τ 2 /2σ 0 2 )+ a 1 exp(-τ 2 /2σ 1 2 ); a 0 =67; σ 0 =1.91 psec; a 1 =36; σ 0 =9.66 psec; 0.5 nsec 100 Intensity, a.u. Slice #4 80 60 40 20 FEL lght 3 fsec Fourier limited FEL pulses will be generated by 0-30 -20-10 0 10 20 30 τ, psec e - -beam LCLS TESLA FEL 10 msec 100 fsec e-bunch in an oscillator

P spont (ω) P in (ω) Feedback κ(ω,p) κ( ω o,p = 0) G( ω o ) >1 G(ω) Amplifier Oscillator Detailed analysis of the lasing linewidth of saturated oscillator is in: P out (ω) =G(ω). P in (ω) Current, I, A Wavelength, Å ~ 1 ~ 100 A Δω/ω ~ 10-3 Ko ~ 1.2 δω/ω Correlations length K(ω)= G(ω) κ(ω,p) K(ω) K(ω o ) 1- ω - ω o Δω 2 ( ) 2 P out (ω) P out (ω o ) 1- ω - ω o δω 2 ( ) 2 ~ 3 10-8 ~ 3 mm!!!

Enabling Technologies and Ideas ERLs with low emittance and high brightness beams (in R&D stage) High Gain FEL Amplifiers (VISA, FLASH, LEUTL. LCLS) Electron Out-Coupling (N.A. Vinokurov, 1985) Suggested by M. Tigner in 1965: Pursued by Stanford U, BINP, Jefferson Lab, JAERI, BNL, Cornell U, KEK, LBNL, Daresbury, Erlangen and more... Parameter range Energy 3,6,9 20+ GeV Beam current 0.001-1 A Emittances, ε 0.01-1 Å. rad σ E /E 0.0001-0.1% Peak current 0.001-1 ka G. Kulipanov et al. MARS @ 6 GeV ε ~ 0.05 Å. rad σ E /E ~ 20 ppm

Gap 5 mm total 0.3 T for 30 GeV 10 to 20 GeV e x 325 GeV p 130 GeV/u Au erhic erhic detector 2 x 200 m SRF linac 4 (5) GeV per pass 5 (4) passes BeamPolarized dump e-gun Possibility of 30 GeV low current operation Common vacuum chamber 20 GeV e-beam 16 GeV e-beam 12 GeV e-beam 8 GeV e-beam 5 mm 5 mm 5 mm 5 mm 9 9 STAR V.N. Litvinenko, EICC meeting, Stony Brook, NY, January 11, 2010 4 to 5 vertically separated recirculating passes

Enabling Technologies and Ideas Low Emittance ERLs High Gain FEL Amplifiers (VISA, TESLA, LEUTL ) saturation occurs at Courtesy of P.Emma P out ~ e 14 P spont ~ 10 6 P spon C.Pellegrini, NIM A475 (2001) 1 Electron Out-Coupling

Enabling Technologies and Ideas Low Emittance ERLs (in design stage) High Gain FEL Amplifiers (VISA, TESLA, LEUTL ) Electron Out-Coupling (N.A. Vinokurov, 1985) modulator θ Electron out- coupling

OFFELO #1 High Gain Ring FEL oscillator Multiple wigglers separated by second order achromatic bends Suggested by N.A. Vinokurov in 1995, Nucl. Instr. and Meth. A 375 (1996) 264 1.5 Å Ring FEL

Ring FEL - low energy For a low energy beams (and rather long wavelength) it is conceivable to modulate the beam using a short wiggler, turn it around, and to amplify the modulation and the resulting optical power in a high gain amplifier High Gain FEL Modulated e-beam Modulator Wiggler Photons Used e-beam Fresh e-beam

Proposed Optics Free FEL based on R&D ERL fitted in accelerator cave in BLDG 912 at BNL FIR Light OFFELO loop ebeam Modulator Amplifier ERL loop Optics functions in isochronous loop for OFFELO Laser Light SRF Gun ebeam 19.8 m SRF Linac ebeam Dump " (m) 30. 25. 20. 15. 10. 5. 0.0 Isochronous bend 20 Mev Win32 version 8.51/15 04/07/07 14.43.29 " x " y Dx Dx 0.0 2. 4. 6. 8. 10. 12. 14. 16. s (m)! E/ p 0c = 0. Table name = TW 10. 5. 0.0-5. -10. -15. -20. -25. -30. Dx (m), ddx/ d! (m) (PARMELA simulation) Charge per bunch, nc 0.7 1.4 5 Numbers of passes 1 1 1 Energy maximum/injection, MeV 20/2.5 20/2.5 20/3.0 Bunch rep-rate, MHz 700 350 9.383 Average current, ma 500 500 50 Injected/ejected beam power, MW 1.0 1.0 0.15 Normalized emittances ex/ey, mm*mrad 1.4/1.4 2.2/2.3 4.8/5.3 Energy spread, de/e 3.5x10-3 5x10-3 1x10-2 Bunch V.N. Litvinenko, length, ps FLS 2010, SLAC, March 4, 2010 18 21 31

Power, W 5 10 5 4 10 5 3 10 5 2 10 5 1 10 5 FEL simulation results for OFFELO at BNL R&D ERL GENISIS simulations Power, W 5 cm undulators period and 0.7 nc electron beam at rep. frequency 9.38 MHz the GENESIS simulation gives: wavelength 29 microns, peak power 2 MW and average power 400 W. For full current mode operation rep. rate 703.75 MHz we obtain 30 kw far infrared in CW mode. Peak power reaches 2 MW 0 0 10 20 30 40 50 Pass 2.5 2 Peak power, MW Close to the Fourier limited spectrum The central wavelength 29μm and FWHM 0.35%. 50 40 Intensity 1.5 1 Intensity, a.u. 30 20 0.5 0 0 5 10 15 20 25 30 Optical pulse 10!, µm 0 28 28.5 29 29.5 30 Spectrum

High Gain Ring FEL oscillator - cont. Three-bend isochronous achromat (positive, negative, positive bends) Plus 2 nd order aberrations

Ultimate Ring FEL Turning around strongly modulated beam high energy beam does not work Used e-beam Feed-back Wiggler Photons High Gain FEL Used e-beam Fresh e-beam Photons

OFFELO #2 Suggested by V. N.Litvinenko in 2001 Feedback from the out-put to the input of such FEL amplifier with κ fb ~10-6 is sufficient to make the oscillator * When κ fb. G >1, the system oscillates Å-scale Feed-back Use lower energy e-beam with very low charge (few pc), peak current (few A) and emittance (ε n ~10 nm) for the feed-back The feed-back-beam is energy-modulated and carries-on the modulation to the entrance of the FEL Radiator Photons High Gain FEL 0.5 GeV e-beam Source Fresh 10 GeV scale e-beam Used e-beam Photons

Alternative Feed-back scheme Use beam with necessary energy for effective energy modulation (i.e. use of a typical wiggler) Decelerate the feed-back beam to much lower energy (let s say ~100 MeV) where synchrotron radiation is mitigated Turn the beam around, accelerate it to radiate in the radiator, decelerate it and dump it Low energy pass ERL dump Photons High Gain FEL source ERL Radiator Modulator Fresh e-beam Used e-beam

Feed-back Requirements Preserving the phase correlations at the lasing wavelength High order achromatic isochronous lattice and rather low energy spread in the beam Long pulses and low peak current to avoid CSR effects Preserving the phase correlations at the lasing wavelength Use of sextupoles to compensate for time delay related to betatron oscllations High stability for arc magnets in the returning pass (potentially permanent magnets with trim coils) Effective modulation and aperture limitations High-K wiggler with large gap for passing of the laser beam Free-space IR Laser-based or mmwave pump as the modulator-wiggler Reasonable e-beam energy for avoiding space charge effect and the de-synchronization by synchrotron radiation Low peak current Low field in the arcs Reasonable β-functions Jitter of the system should not exceed the electron bunch duration New types of photo cathode driver Long bunches for feed-back e-beam Reasonably low RF frequency Reasonable e-beam for radiating at the designed wavelength (as low as 1Å) Micro-wiggler for mid-range energies Free-space IR Laser-based or mmwave pump as the modulator-wiggler

( ) H = 1+ K (s) o c Preserving the phase correlations - patricle motions is well known p 2 o c 2 + 2E o δe + δe 2 + P 2 2 { x + P y } e c A s + δe {x,p x }, {y,p y }, {τ = (t o (s) t),δe} v o dτ ds = H δe ( ) ; dt o ds = 1 v o. τ exit τ input = M 5 (x,p x, y,p y,δe) δs turn = cδ(τ exit τ input ) < FEL δs turn FEL ; δs turn = δs turn (δe) + δs turn (ε x,y ) + δs HO (δe,ε) + δs random ; Example : L =100m; =10 10 m; ε =10 10 m rad; σ E = 0.01% 1. Energy spread and compaction factors δe δs turn (δe) = L R 56 E + R 566 δe E 2 δe + R 5666 E 3 +... ; α c = R 56 ( 0,L) <10 8 ; R 566 ( 0,L) <10 4 ; R 5666 ( 0,L) <1... -> second order isochronous system

M T SM = S; 2. Emittance effects Linear term: comes from symplectic conditions σ 0 0 S = 0 σ 0 ; σ = 0 1 1 0 0 0 σ [ ] δs turn (ε x,y ) = η η 0 1 x + f (ε ) + O(ε 2 ) 1 0 x η < 10 5 m ; η < 10 5 β[m] β[m]; It is not a problem to make the turn achromatic with η=0 and η =0 It is a bit more complicated to make the condition energy independent. An elegant solution - sextupoles combined with quadrupoles with K 2 =K 1 /2η: x = K 1x + K 2 (( x + η δ) 2 y 2 ) 1+ δ ( ) = K 1 x + O(x 2, y 2 ) O(x 2, y 2, xy,η 2 ) 0 y = K 1y + 2K 2 y η δ + x 0 = K 1 y + O(xy) 1+ δ Solution is a second order achromat (N cell with phase advance 2πM, M/N is not integer, etc.) with second order geometrical aberration cancellation L FEL ~ 1Å

Sextupole 2. Emittance effects x = a x δs 2 L o x 2 + 2 y 2 ds β x (s) cos( ψ x (s) + ϕ x ) + η( s) δe ; y = a y E o Dipole Quadratic term β y (s) cos( ψ y (s) + ϕ y ). Sextupoles* in the arcs are required to compensate for quadratic effect sextupole kick + symplectic conditions give us right away: Sextupoles located in dispersion area give a kick ~ x 2 -y 2 which affect the length of trajectory. Two sextupoles placed 90 o apart the phase of vertical betatron oscillations are sufficient to compensate for quadratic term with arbitrary phase of the oscillation Δ x sext = K 2 l ( x 2 y 2 ) δs = η(s) Δ x sext = η(s)k 2 l ( x 2 y 2 ) 1 2 L ( x 2 + y 2 )ds η(s n )( K 2 l) n ( x 2 (s n ) y 2 (s n ))ds 0 o This scheme is similar to that proposed by Zolotarev and Zholetz. (PRE 71, 1993, p. 4146) for optical cooling beam-line and tested using COSY INFINITY. It is also implemented for the ring FEL: A.N. Matveenko et al. / Proceedings 2004 FEL Conference, 629-632 n Four sextupoles located in the arcs where dispersion are sufficient to satisfy the cancellation of the quadratic term in the non-isochronism caused by the emittances. Fortunately, the second order achromat compensates the chromaticity and the quadratic term simultaneously. In short it is the consequence of Hamiltonian term: x 2 y 2 h g(s) δ C x δ a 2 x 2 2 + C δ a 2 y y 2

Emittance effects 1. The fact that e-beam passes only once (in contrast with storage rings) allows to use very strong nonlinear elements in the system 2. The compensation required only at the exit of the turn, i.e. there is no parasitic density modulation anywhere in the arc, hence no coherent radiation and wake-fields. This is very positive effect of smearing caused by the non-zero emittances Single particle effects - conclusion OFFELO is feasible Higher order terms must be taken into account (using exact analytical expressions or symplectic high order integrators) to ensure the result Stability of power supplies and the quality of the magnets may require special R&D

Random effects Quantum fluctuations of synchrotron radiation Ripples in the power supplies Intra-beam scattering Wake-fields CSR Others

Synchrotron Radiation FEL ~ 1Å Energy of the radiated quanta ε c [kev ] = 0.665 B[T] E e 2 [GeV ] Number of radiated quanta per turn N c 2παγ 89.7 E[GeV] Radiation is random -> the path time will vary The lattice should be designed to minimize the random effects ( ) 2 ε N c c δs rand E e 2 R 2 56(s,L) R 56 (s,l) is the longtudinal dispersion from azimuth s to L R 2 56(s,L) < It looks as the toughest requirement for the scheme to be feasible 2 N c E e ε c R 2 56(s,L) <2.25 10 5 m E e 3 / 2 [GeV ] B 1 [T]

Synchrotron Radiation - cont... but for FEL ~ 1Å E e = 0.5GeV; B =100GS R 2 56(s,L) /L <0.64 10 4 This value is already close to that of the 3 rd generation rings: ESRF: α c = 1.99 10-4 APS: α c = 2.28 10-4 Spring 8: α c = 1.46 10-4 THUS - the arcs should have ~ 60-100 bending magnets Three-bend isochronous achromat (positive, negative, positive bends) N gives σ δs = σ cδt ~ 4 10 2 Å for α o = π /100; γ =1000 σ δs = σ cδt ~ 2.4Å for α o = π /20; γ =1000

Feed-Back radiation FEL ~ 1Å Energy Modulation of the feed-back e-beam should not be a problem - the FEL power is high and a few wiggler periods will do the job For efficient feed-back the spectral intensity of the coherent feed-back radiation should be significantly larger than the spontaneous radiation at one-gain length d 2 F dθdψ Spontaneous radiation from ONE GAIN Length E e ~ 10 GeV; L G ~ 1-5m; l W ~ 5 cm, I peak ~1 ka, N w ~ 100 photons secmr 2 0.1%BW 1.74 1014 N 2 w E 2 e [GeV ] I[A] F(K) ~10 23 Radiation into the TEM mode from σ =100 fsec e-beam with β opt ~ 1.5 m; Δλ/λ= λ/2ps ~ 3 ppm F mode photons sec Coherent radiation from the feed-back e-beam E e ~ 0.5 GeV; N w ~ 100; λ W ~ 0.6 mm*, L w ~ 6 cm; I peak ~1 A ~ 1.5 1015 Number of the coherently radiating electrons is defined by the beam current, the slippage length and the degree of the density modulation (M) N e (coh) =1.3 10 6 Feedback mode ~ 5 10 19 M 2 photons Maximum Oscillator Gain per Pass can be 10 3 10 4 sec * 1.2 mm for 20 GW mm-wave pump

Crude Number Crunching FEL ~ 1Å Feed-back at M~1 FEL with gain G=10 6 F inp ~ 5 10 19 photons sec P inp ~ 16 kw [ ] F photons out ~ 5 10 25 sec P out ~ 16 [ GW ] Better Number Crunching (in progress) From ERL, main beam 15 GeV, Radiator 3 ka, 0.4 mm rad 5 mm period, K w =0.77, h=91 m LCLS type wiggler, 3 cm period, K w =3.08, 30-40 m λ FEL =1Å Modulator 5 mm period, K w =0.77, h=1 m Radiator Genesis 3 1 GeV beam Zero initial field Wave propagation FEL amplifier Genesis 3 Fresh 15 GeV beam & EM wave from the radiator From ERL, feed-back beam 1 GeV, 3 A, 0.03 mm rad Wave propagation Modulator Genesis 3 Fresh 1 GeV beam Wave from the Amplifier Beam Propagation MAD-X, PTC, Elegant, Tracy 3, CSR-track.

Conclusions FEL oscillator without optics seems to be scientifically feasible R&D is required to check very important technical details Feed-Back e-beam It is at the very edge of current capabilities A long few pc bunch with few A peak current with ε n ~ 0.01 μm rad is needed. Could it be achieved by?: by using slice emittance of a few-psec, a few pc bunch by the the collimating the beam in current sources using negative electron affinity photo-cathodes

No mater how closely I study it, No mater how I take it apart, No matter how I brake it down - IT REMAINS CONSISTANT Robert Fripp, King Crimson, Indiscipline, 1981 There is the need for Optics-free FEL oscillator

LCLS Parameters Undulator Type planar NdFe:B planar NdFe:B Wavelength 15 1.5 Å Norm. RMS Emittance 1.2 1.2 mm mrad Peak Current 3.4 3.4 ka Electron Energy E 4.54 14.35 GeV Average b -Function 7.3 18 m/rad s E /E (X-rays) 0.47 0.13 % Pulse Duration (FWHM) 230 230 fs Pulses per macropulse 1 1 Repetition Rate 120 120 Hz Undulator Period 3.0 3.0 cm Peak Field 1.32 1.32 T FEL parameter r 1.45 0.50 10-3 Power Gain Length 1.3 4.7 m Saturation Length 27 86 m Peak Power 19 8 GW Average Power 0.61 0.25 W Coherent Energy per Pulse 2.6 2.3 mj Coherent Photons per Pulse 27.9 1.1 10 12 Peak Brightness 0.64 8.5 10 32 ** Average Brightness 0.2 2.7 10 22 ** Transverse RMS Photon Beam Size 40 33 µm Transverse RMS Photon Beam Divergence 3.4 0.42 µrad

Dedication (Serious) to the inventor of the phrase MIRRORS DEGRADATION to the free electrons - the pure substance which does not care about the wavelength and the intensity of radiation, the heat stress, the absorption, the losses, the reflectivity and do not need conditioning

Feed-Back Arcs- cont. Low beam current and small emittance provide for a toy - size of the magnetic system for the arcs β x,y 100m ε x, y 10 10 m; σ x, y < 0.1mm gap ~ 1 mm Magnets (dipoles and quadrupoles) can be 2 x 4 cm 2 in cross-section

FEL oscillator without optical resonator The linewidth of oscillator (~10-100 ppm) The pulse length is ~ 1/10 of the e-bunch (i.e. 10 fsec for 100 fsec e-bunch) Broad band and fast tunability No average and peak power limits imposed by optics Diffraction & Fourier limited X-ray beams * Determined by the ratio between feed-back and spontaneous radiation

Single pass Ångstrom-class FELs at erhic Average lasing power is a problem! @ 1Å (12 kev) It is from 0.6 MW to 1.3 MW Energy, GeV 20 15 10 Wavelength, Å 0.5 1 0.87 1.8 2 4 Bunch length, psec 0.2 0.2 0.27 0.27 0.4 0.4 Peak Current, ka 5 5 3.75 3.75 2.5 2.5 Wiggler period, cm 2.5 3 2.5 3 2.5 3 SASE gain length, m SASE Saturation length, m Saturation power, GW 7.5 4.3 5.5 3.3 3.7 2.4 100 60 76 47 51 34 7.7 19 6.4 14 4.5 9 DOK, gain length, m 3.5 1.4 1.5.65.51.25 DOK, saturation length, m 47 19 21 9 7 3.5

BNL R&D ERL beam parameters R&D prototype ERL (PARMELA simulation) Charge per bunch, nc 0.7 1.4 5 Numbers of passes 1 1 1 Energy maximum/injection, MeV 20/2.5 20/2.5 20/3.0 Bunch rep-rate, MHz 700 350 9.383 Average current, ma 500 500 50 Injected/ejected beam power, MW 1.0 1.0 0.15 Normalized emittances ex/ey, mm*mrad 1.4/1.4 2.2/2.3 4.8/5.3 Energy spread, de/e 3.5x10-3 5x10-3 1x10-2 Bunch length, ps 18 21 31

High Gain Ring FEL oscillator - cont. 1.5 Å Ring FEL 50 nm Ring FEL