High efficiency free electron lasers C. Emma IOTA/FAST Collaboration meeting May 10, 2018 Fermilab
Presentation Outline 1. Physics of tapered FELs 1.1.Motivation 1.2.Review of theory: 1-D, 3-D, and time dependent effects 2. Experimental studies 2.1.Past 2.1.1.Fresh-bunch self-seeding experiment (SLAC) 2.1.2.NOCIBUR experiment (BNL-ATF) 2.2.Present 2.2.1.TESSA-266 (Argonne) 2.3.Future 2.3.1.Opportunities at FAST 3. Conclusions
Motivation for high efficiency FEL High field Industrial FEL for Imaging single molecules via electrodynamics EUV lithography “diffraction before destruction” Redecke et al., Science 339, 6116, (2012) From Phys. viewpoints, A. Macchi, Physics 11, 13 (2018) From Hosler, Wood “Free electron lasers: beyond EUV lithography insertions”, Global Foundries Unexplored physics phenomena e.g. Semiconductor industry is a very radiation reaction occur when electrons large economic driver $2.0T global interact with an E-field close to the electronics maker Schwinger critical field E Schwinger = m 2 e c 3 Current technology uses EUV � 3 e = 1 . 3 × 10 18 V/m 2.1 A resolution from laser produced plasma Trypanosoma brucei cysteine protease cathepsine B sources. Expected cost is $15-20B Is being pursued actively at the for leading-edge fab. moment using PW lasers and LWFA Single Molecule Imaging Goal e-beams with interesting results e.g. 10 fs - 10 mJ - 2020 FELs being considered as an Cole et al , Experimental evidence of radiation reaction in the alternative but need to fulfill many collision of a high-intensity laser pulse with a LWFA electron beam PRX 8, 011020 (2018) requirements, one of which is high Aquila et al., “The LCLS single particle imaging roadmap” Stuct. Dynam. 2 , 041701 Poder et al “Evidence of strong radiation reaction in the field efficiency ~ 10 % of an ultra-intense laser”, arXiv:1709.01861
Undulator tapering for high efficiency FEL Untapered FEL Tapered FEL K High power Photons z Energy modulation Resonant interaction Tapered section Exponential Growth (Post-Saturation) e-beam Density modulation Exp Growth Coherent Radiation λ = λ u Tapered (1 + K 2 ) Resonance condition 2 γ 2 Section r • 1-D physics (BPN Opt Comm. 1984) described by single parameter ρ . � 2 � 1 / 3 � • Resonant interaction can continue past saturation by tapering the � ρ = 1 I K P sat = ρ P beam magnetic field K(z) to match the e-beam energy loss γ (z) I A 4 k u σ x γ • Some numbers: • Questions are: E e =250 MeV, I = 0.2 kA, λ = 250 nm, ρ ~ 0.5% • What is the max achievable efficiency? • For high efficiency applications we want > 20x in efficiency • What limits the max achievable efficiency? • How do you optimize the taper to achieve the max efficiency? to >10 %
1-D effects: How to choose the taper for max. power Power scaling in z 2 P rad = P 0 + P 1 ¯ z + P 2 ¯ post-sat regime Dominant for short Dominant for undulators or large seed long undulators
1-D effects: How to choose the taper for max. power Power scaling in � 2 � K P 2 = Z 0 λ u z 2 P rad = P 0 + P 1 ¯ z + P 2 ¯ ( f t sin ψ r ) 2 I post-sat regime 8 π γ σ e sin ψ r ∝ | K ′ | Dominant for short Dominant for Tapering Initial Condition undulators or large seed long undulators contribution contribution E
1-D effects: How to choose the taper for max. power Power scaling in � 2 � K P 2 = Z 0 λ u z 2 P rad = P 0 + P 1 ¯ z + P 2 ¯ ( f t sin ψ r ) 2 I post-sat regime 8 π γ σ e sin ψ r ∝ | K ′ | Dominant for short Dominant for Tapering Initial Condition undulators or large seed long undulators contribution contribution E 1.5 1 Normalized δγ 0.5 0 ψ r =0 − 0.5 ψ r = π /8 − 1 ψ r = π /4 − 1.5 − 1 − 0.5 0 0.5 1 ψ / π 1 f t for cold beam f t for warm beam 0.8 Trapping Fraction 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 ψ r / π
1-D effects: How to choose the taper for max. power Power scaling in � 2 � K P 2 = Z 0 λ u z 2 P rad = P 0 + P 1 ¯ z + P 2 ¯ ( f t sin ψ r ) 2 I post-sat regime 8 π γ σ e sin ψ r ∝ | K ′ | Dominant for short Dominant for Tapering Initial Condition undulators or large seed long undulators contribution contribution E Take home messages from 1-D theory 1.5 1 Normalized δγ 0.5 (1) Resonant phase ψ r sets the speed of the taper and 0 the size of the bucket ψ r =0 − 0.5 ψ r = π /8 − 1 ∴ Trade-off between number of electron trapped and how ψ r = π /4 − 1.5 quickly the electrons are decelerated − 1 − 0.5 0 0.5 1 ψ / π (2) Power scales like (f t sin ψ r ) 2 1 f t for cold beam f t for warm beam 0.8 Trapping Fraction ∴ Increasing the trapping by e.g. pre-bunching can increase P 0.6 0.4 (3) Power scales like I 2 / σ e2 =I 2 / βε n 0.2 ∴ Brighter beam/smaller beta conducive to high efficiency 0 0 0.1 0.2 0.3 0.4 0.5 ψ r / π
1-D effects: trade-offs and design considerations No tapering “Slow” tapering “Fast” tapering ψ r = 0 ψ r = 22 . 5 ◦ ψ r = 80 ◦ P ∝ z 2 P ∝ e z/Lg “Slow” taper In 1-D theory, with a No tapering “Fast” taper has strikes the balance judiciously chosen taper efficiency is the larger net energy between total you can continue to same as saturation loss but smallest energy loss and increase power by fraction captured trapping fraction adding undulators
3-D effects: diffraction limits to the 1-D model E-beam refractive index n 0 =1 e-beam n � e i ψ � K n − 1 = χ 2 k E γ Microbunching and trapping Growth of field reduces guiding sets limit on max. E field must be kept high to maintain good guiding E max ≈ Z 0 I K P rad = 2 π E 2 σ 2 γ cos ψ r r 1 λ Z 0 Exp 0.8 Growth D. Prosnitz, A. et al, Phys. Rev. A 24, 1436 (1981) Scharlemann, T. et al, Phys. Rev. Lett. 54, 17 (1981) 0.6 E/E max Fawley W.., NIMA 375 (1996) Yiao, J., PRSTAB. 15 , 050704 (2012) Schneidmiller, et al., PRSTAB. 18 , 030705 (2015) 0.4 “Low gain” “High gain” Take home messages from 3-D theory Tapered Tapered 0.2 Section Section 0 0 5 10 15 20 25 Limit on field and radiation growth region in contrast with 1-D z/Z R theory 1 0.8 Needs to be considered for long undulators L u >> Z R 0.6 P/P max 0.4 Want to extract energy (taper) as fast as possible to outrun 0.2 diffraction limit 0 0 5 10 15 20 25 z/Z R
Time Dependent effects: limits to the 1 frequency model Electron beam shot noise and synchrotron motion � cos ψ ( z, t ) � I ( t ) � sin ψ ( z, t ) � φ ′ ( z, t ) ∝ E ′ ( z, t ) ∝ I ( t ) E ( z, t ) γ ( z, t ) γ ( z, t ) z = 160 m * z= L w Amplitude and phase modulations 10 8 * z=0.75 L w z = 120 m of the radiation field * z=0.5 L w z = 80 m 10 6 P H l L @ a.u. D Resonance between sideband radiation and synchrotron motion 10 4 Radiation field saturation from 100 reduced optical guiding gives ~ - 10 - 5 0 5 10 constant L synch Dl ê l @ * 10 - 3 D “ …the electron motion in a FEL will become chaotic when the sideband amplitude exceeds a certain threshold. This, in turn, will result in significant electron detrapping. Since it is the deceleration of the trapped electron bucket Sideband Instability that provides the energy for the radiation in the case of tapered wigglers, detrapping will cause loss of amplification for the FEL signal” S. Riyopoulos, C.M. Tang, Phys. Fluids (1988) “ Chaotic electron motion caused by sidebands in free electron lasers”
Time Dependent effects: limits to the 1 frequency model Electron beam shot noise and synchrotron motion � cos ψ ( z, t ) � I ( t ) � sin ψ ( z, t ) � φ ′ ( z, t ) ∝ E ′ ( z, t ) ∝ I ( t ) E ( z, t ) γ ( z, t ) γ ( z, t ) 7 Single Frequency Amplitude and phase modulations Time Dependent 6 of the radiation field 5 P/P beam [%] 4 Resonance between sideband 3 radiation and synchrotron motion 2 1 Radiation field saturation from 0 reduced optical guiding gives ~ 0 2 4 6 8 10 12 14 z/<L synch > constant L synch Take home messages from TDP theory Sideband instability can cause second saturation of radiation power in tapered FEL Sideband Instability Want to reduce the sideband growth along tapered undulator to S. Riyopoulos, C.M. Tang, Phys. Fluids (1988) “ Chaotic electron continue extracting power motion caused by sidebands in free electron lasers”
Presentation Outline 1. Physics of tapered FELs 1.1.Motivation 1.2.Review of theory: 1-D, 3-D, and time dependent effects 2. Experimental studies 2.1.Past 2.1.1.Fresh-bunch self-seeding experiment (SLAC) 2.1.2.NOCIBUR experiment (BNL-ATF) 2.2.Present 2.2.1.TESSA-266 (Argonne) 2.3.Future 2.3.1.Opportunities at FAST 3. Conclusions
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