Cooled-HGHG and Coherent Thomson Sca ering

Transcription

1 Cooled-HGHG and Coherent Thomson Sca ering using KEK compact ERL beam CHEN Si Institute of Heavy Ion Physics Peking University Seminar, KEK

2 Outline 1 Accelerator-based Light Sources 2 FEL review FEL Fundamental Standard HGHG cooled-hghg 3 Coherent Thomson Sca ering 4 Prelimnary simulation results by using KEK-cERL beam 35MeV case 125MeV case 5 Summary

3 Accelerator-based Light Sources Synchrotron Radiation Light Sources Synchrotron radiation: the electromagnetic radiation emi ed when relativistic charged particles travel through a curved path (M Borland, A Tutorial on Accelerator-Based Light Sources(talk), 211) In the last 6 years, accelerator-based light sources have evolved rapidly through four different generations The first three generation are mainly based on the synchrotron radiation generated by storage rings 1 st generation (197): parasitic to high-energy physics; 2 nd generation (198): dedicated machines; Radiations are mainly generated by bending magnets; 3 rd generation (199): dedicated and optimized machines; Radiations are mainly generated by insertion devices;

4 Accelerator-based Light Sources Next generation light sources Why we need the next generation light source? Scientific world requires light sources with higher brightness, be er coherence, shorter wavelength and pulse length, and purer spectrum Compact schemes and low costs How to satisfy the higher and higher requirement of light source users? Provide higher quality electron beam: Ultimate Storage Rings and Energy Recovery Linacs(ERL) Apply new mechanism of radiation: Free Electron Lasers(FEL) Combination of high quality electron beam and new radiation mechanism: ERL-FEL Preparation for the next generation light source Improvement of accelerator technologies: Electron gun, RF, superconducting technology, control system, cryogenic system, insertion device, etc Theory: basic theory and various mechanisms of FEL

5 Accelerator-based Light Sources Free Electron Laser Free electron lasers are now the premier source of tunable, intense, coherent photons of either ultra-short time resolution or ultra-fine spectral resolution, from the far infrared through to the hard x-ray rigime Compared with high performance 3 rd generation synchrotron radaiton light sources based on storage rings, FELs can provide as much as 1 11 in the peak brightness of the photon beam or by 1 6 in average brightness (a) peak brightness (b) average brightness ( Science and Technology of Future Light Sources, a White Paper by ANL, BNL, LBNL, SLAC collaboration, December 28)

6 FEL review FEL Fundamental Wiggler and Undulator A wiggler/undulator is a series of N w bends of alternating sign Electrons travels through the wiggler with a sinusoidal trajectory The strength parameter of wiggler/undulator: K eb λ u 2πmc Where B is the peak magnetic field, B(z) = B cos (2πz/λ u ) For K 1, it is wiggler; For K 3, it is undulator (1) (c) wiggler (d) undulator

7 FEL review FEL Fundamental Free Electron Laser Fundamental In a free electron laser the kinetic energy of a relativistic electron beam is transformed into an intense beam of electromagnetic radiation by wiggling the electrons transversely in an undulator The output wavelength of the FEL radiation in a planar undulator should satisfy the resonant condition, which is given in terms of the undulator period λ u, the relativistic energy factor γ E and the undulator strength mc 2 parameter K λ = λu K2 (1 + 2γ2 2 ) (2) Various machnisms of FEL: FEL Amplifier, FEL Oscillator, SASE, HGHG, EEHG, etc FEL Amplifier: hard to be tunable FEL Oscillator: limited by the mirrors for ultra-short wavelength and tunable FEL: SASE, HGHG, EEHG

8 FEL review FEL Fundamental SASE FEL SASE = Self Amplified Spontaneous Emission The main x-ray FEL light source by now: FLASH, LCLS, SACLA, Euro XFEL, etc The SASE radiation starts from initial shot noise in the beam As a result, the radiation has an excellent spatial coherence but a rather poor temporal coherence SASE FEL requires extremely high beam quality: beam energy several GeV, peak current ka, normalized beam emi ance 5-1 mm mrad, energy spread well below 1% rms

9 FEL review Standard HGHG High Gain Harmonic Generation First proposed by LH Yu in 1991 (L-H Yu, Phys Rev A 44, 5178 (1991)) First demonstrated at 3d harmonic of 8 nm at the NSLS(L H Yu et al, PRL, 91, 7481, 23) Figure: The scheme of HGHG

10 FEL review Standard HGHG High Gain Harmonic Generation Figure: Longitudinal phase space of a bunch in the HGHG process Electron bunch interacts with a seed laser in the first undulator and generates an energy modulation in the bunch Then the energy-modulated bunch travels through a dispersion section with well designed value of R 56 and the energy modulation is transferred to density modulation, which contains frequency components at harmonics of the seed laser The harmonic frequency component can be characterized by the bunching factor b n = e n2 σ 2 γ D2 /2 J n (nd γ) (3) where σ γ is the rms energy spread, D = 2πR 56 /(λ s γ ), and γ is the maximum energy modulation at the end of the modulator undulator

11 FEL review Standard HGHG Physic issues of HGHG Because of the presence of the beam energy spread, the bunching factor of HGHG decays exponentially with increasing n (ZT Zhao, etc Nature Photonics21215) The harmonic performance of HGHG is limited (n 1) Echo-Enabled Harmonic Generation(EEHG) is a probably way to improve the harmonic number Another method: using off-resonance laser modulation for beam-energy-spread cooling (HX Deng and Chao Feng, PRL 111, 8481)

12 FEL review cooled-hghg TGU TGU = Transverse Gradient Undulator First proposed by T Smith and co-workers at Stanford (J Appl Phys 5, 458 (1979)) Realized by canting the magnetic poles of a normal undulator, to give a linear x dependence of the undulator parameter K(x) K = 1 + αx (4) The idea of using TGU to reduce the effects of large beam energy spread from laser-plasma accelerator and ultimate storage rings was proposed by ZR Huang and co-workers(slac) (PRL 19, 2481 (212))

13 FEL review cooled-hghg Cooled-HGHG(HX Deng and Chao Feng, PRL 111, 8481) Compared with standard HGHG, the scheme of cooled-hghg has a dog-leg in front the modulator and a TGU to replace the traditional undulator Figure: The scheme of cooled-hghg K(x) K = 1 + αx = 1 + αη γ γ γ (5) where η is the dispersion strength of dog-leg Different x positions in the TGU have different resonant beam energy K 2 γ r(x) = γ + αη K 2 (γ γ) (6) + 2

14 FEL review cooled-hghg Cooled-HGHG(HX Deng and Chao Feng, PRL 111, 8481) Consider the longitudinal phase space resonant electron (γ, θ ) = (γ, θ ) arbitrary electron (γ, θ φ) = (γ, θ ) where φ is the phase advance of the off-resonance electron with respect to the resonant one φ = 4πN γ γ r γ For small θ, one has γ = γ γ sin θ = γ γθ γ = γ γ sin θ φ/2) = γ γ(θ φ/2) From the upper formulas, we can derive that γ γ γ γ = 1 2πN γ ( αηk2 γ K 2 1) (7) + 2 When we increase the value of αη and make the right side of Eq(7) to be unity, the beam energy spread is reserved because every electron satisfies the resonant condition Eq(2) By further increasing the αη, the right side of Eq (7) can be adjusted to zero and the energy spread will be fully cooled

15 FEL review cooled-hghg Beam-laser interaction in undulator(k Ohmi, SPring8/ SACLA seminar, Oct 3 213) Hamiltonian of particle motion in undulator and interact with laser H = (1 + δ) (1 + δ) 2 (p x ax ) γ 2 1 γ 2 (8) where a x = a u cos k us + a L sin k Lz, δ p p, z s ct Solve the Hamiltonian equation by, eg, Runge-Ku a integration method a dz (p ds = x x γ ) 2 + p 2 y + 1 γ 2 p s (p s δ) (9) dδ ds = 1 (p γ x ax ) dax p s γ dz (1) dx ds = (p x a x γ ) 1 p s (11) dp x ds = 1 γ p s (p x a x γ ) a x dx where p s (1 + δ) 2 (p x a x γ ) 2 p 2 y 1, a γ 2 x = â u(1 + αx) cos k us (12) a x z = klâ L sin k L z, a x x = âuα cos kus

16 FEL review cooled-hghg Effects of cooled-hghg(hx Deng and Chao Feng, PRL 111, 8481) 1D simulation of cooled-hghg (HX Deng and Chao Feng, PRL 111, 8481)

17 Coherent Thomson Sca ering Coherent Thomson Sca ering(k Ohmi, TUPME13, Proceeding of IPAC213) In order to generate ultra-short wavelength radiation, extramely short undulator period length λ u or large beam energy γ is required As shown in the resonant condition Eq(2), λ r λu 2γ 2 Short period undulator: in-vacuum undulator; superconducting undulator, etc Another method of generating short wavelength radiation using relatively small beam energy is Thomson Sca ering, which is the process of head-on collision of beam and laser pulse (λ 1) emits radiation with shorter wavelength λ R = 1 + a2 1 λ1 (13) 4γ2 where a 1 = ea/mc is the normalized vector potential of the laser field When the beam has longitudinal density modulation equal to the wave length λ R, the radiation from Thomson sca ering becomes coherent

18 Coherent Thomson Sca ering Coherent Thomson Sca ering(k Ohmi, TUPME13, Proceeding of IPAC213) Hamiltonian for particle-laser interaction H = (1 + δ) (1 + δ) 2 (p a γ ) 2 1 γ 2 (14) a is the vector potential for laser or undulator for undulator: a u,x = a u cos k us; for laser field traveling to the beam direction: a L,x = a L cos (k L s ωt + ϕ) = a L cos (k L z + ϕ), where z = s ct; for laser field traveling against the beam direction: a L,x = a L cos ( k L s ωt + ϕ) = a L cos (k L (z 2s) + ϕ); For Gaussian laser pulse, a L = a L, exp( z2 2σ 2 z ) or a L = a L, exp( (z 2s)2 ) 2σz 2 Applying the vector potential of both undulator and laser and solving the Hamiltionian equation of particle motion, one can get: x = H p x = p x a x /γ p s z = H δ = δ p s p x = H x = δ = H z = 1 p x a x /γ a x γp s p s z where p s = (1 + δ) 2 (p a γ ) 2 1 γ 2

19 Coherent Thomson Sca ering Coherent Thomson Sca ering(k Ohmi, TUPME13, Proceeding of IPAC213) Radiation field emi ed by Thomson sca ering is calculated from particle motion using the Heaviside-Feynman expression: E i(x, t) = e 4πϵ [ Ri R 3 i + Ri c d dt ( Ri R 3 i + 1 c 2 d 2 dt 2 ( Ri R i )] (15) where R i = x o x i is a vector between observer (x o ) and electron (x i ) and observer time and electron local time is connected by t = t i + Ri c ct = s z i + R i Total electric field at observer position is given by summation for all electrons N e E(x o, t) = E i(x o, t) i=1

20 Prelimnary simulation results by using KEK-cERL beam KEK-cERL Parameters and scheme of KEK-cERL parameters Energy bunch charge emi ance bunch length values 35MeV (1st stage) 125MeV (2nd stage) 245 (2-turn design) 77pC (1st stage) 77pC (2nd stage) 1mm mrad (77pC) 1 3ps 15fs (by compressor) The slice energy spread chosed for simulation is 35keV and a maximum energy modulation of 21keV is introduced by seed laser in a Modulator TGU with period length λ u = 4cm and period number N u = 15

21 Prelimnary simulation results by using KEK-cERL beam 35MeV case 35MeV E (MeV) σ E /E γ(mev) λ s (µm) 35 1E-3 6 σ E 16 Here, 1D simulation (ϵ z ) was applied Dog-leg dispersion strength η = 2 and optimized TGU transverse gradient α = 16, αη = 32 Optimized dispersion strength of chicane R 56 17e 4 The normalized vector potential of TGU and seed laser are a u = and a L = 11747e 4 1e+6 cooled-hghg standard-hghg 14 cooled-hghg standard-hghg 12 1 bunching factor 1 1 count of marco-particle number harmonic number z (µ m)

22 Prelimnary simulation results by using KEK-cERL beam 35MeV case 35MeV Consider 3D simulation with transverse emi ance ϵ x = 1mm mrad 1e+6 cooled-hghg standard-hghg 14 ε x = ε x =1e bunching factor count of marco-particle number harmonic number z (µ m) By increacing dog-leg dispersion strength η but keeping the value of αη, the effect of non-zero transverse emi ance can be counteract Here, we use η = 25 and α = 128 1e+6 ε x = ε x =1e-6 14 cooled-hghg standard-hghg 12 bunching factor 1 1 count of marco-particle number harmonic number z (µ m)

23 Cool-HGHG and Coherent Thomson Sca ering Prelimnary simulation results by using KEK-cERL beam 35MeV case Radiation performance of 35MeV beam Parameters of the collision laser: λr = 2mm, ar = The peak current of electron beam: Ipk = 77pC Output wavelength 424nm, pulse length 2µm 7fs Field Strength Field Strength 3 15 "fort15" u ($4*1e6): Ex Ex "fort15" u ($4*1e6): ct (µm) ct (µm) Figure: 1D results of radiation Field Strength -35 Field Strength "fort15" u ($4*1e6):5 "fort15" u ($4*1e6): Ex Ex ct (µm) ct (µm) Figure: 3D results of radiation with transverse emi ance ϵx = 1mm mrad and optimized value of αη

24 Prelimnary simulation results by using KEK-cERL beam 125MeV case 125MeV E (MeV) σ E /E γ(mev) λ s (µm) E-4 6 σ E 164 For 1D simulation (ϵ z ), dog-leg dispersion strength η = 2 and optimized TGU transverse gradient α 48, αη = 96 Optimized dispersion strength of chicane R e 5 The normalized vector potential of TGU and seed laser are a u = 2897 and a L = 35739e 5 bunching factor phase space after dispersion chicane 1e+6 "bfcalctxt" u 1:2 12 "histtxt" u ($1*1e6):2 1 8 bunching factor 1 γ-γ harmonic number z (Symbol mm)

25 Prelimnary simulation results by using KEK-cERL beam 125MeV case 125MeV Consider 3D simulation with transverse emi ance ϵ x = 1mm mrad 1e+6 ε x = ε x =1e-6 12 cooled-hghg standard-hghg 1 1 bunching factor 1 1 count of marco-particle number harmonic number z (µ m) By increacing dog-leg dispersion strength η but keeping the value of αη, the effect of non-zero transverse emi ance can be counteract Here, we use η = 2 and α = 48 1e+6 ε x = ε x =1e-6 12 cooled-hghg standard-hghg 1 bunching factor 1 count of marco-particle number harmonic number z (µ m)

26 Cool-HGHG and Coherent Thomson Sca ering Prelimnary simulation results by using KEK-cERL beam 125MeV case Radiation performance of 125MeV beam Parameters of the collision laser: λr = 2mm, ar = 2897 The peak current of electron beam: Ipk = 77pC Output wavelength 2128nm, pulse length 2µm 7fs Field Strength Field Strength 2e+6 2e+6 "fort15" u ($4*1e6):5 "fort15" u ($4*1e6):5 15e+6 15e+6 1e+6 1e+6 5 Ex Ex e+6-1e+6-15e+6-15e+6-2e+6-2e ct (µm) ct (µm) Figure: 1D results of radiation Field Strength Field Strength 5 15 "fort15" u ($4*1e6):5 "fort15" u ($4*1e6): Ex Ex ct (µm) ct (µm) Figure: 3D results of radiation with transverse emi ance ϵx = 1mm mrad, η = 2 and α = 48

27 Cool-HGHG and Coherent Thomson Sca ering Prelimnary simulation results by using KEK-cERL beam 125MeV case Radiation performance of 125MeV beam By further increasing the dog-leg dispersion strength η = 25 and α = 384 Field Strength Field Strength 1 8 "fort15" u ($4*1e6):5 "fort15" u ($4*1e6): Ex Ex ct (µm) ct (µm) Figure: 3D results of radiation with transverse emi ance ϵx = 1mm mrad, η = 25 and α = 384 Field Strength Field Strength 5 15 "fort15" u ($4*1e6):5 "fort15" u ($4*1e6): Ex Ex ct (µm) ct (µm) Figure: 3D results of radiation with transverse emi ance ϵx = 1mm mrad, η = 2 and α = 48

28 Summary Summary and future work Summary The theory of cooled-hghg and coherent Thomson sca ering was briefly reviewed Some preliminary results of applying cooled-hghg and coherent Thomson sca ering to KEK-cERL were presented A lot of work to do Parameters should be further optimized Ultra-short pulse (a o-sec pulse) generation The feasibility to realize the idea to KEK-cERL

29 Acknowledgment Special thanks to Prof Kazuhito Ohmi He provides the idea of Coherent Thomson Sca ering and a simulation code `tomsan He also provides me the funding of living and working at KEK Thanks to Dr Demin Zhou for many useful discussion on this work Thanks to all people in KEK You make me feel like at home

30 The End