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Avraham Gover (Tel-Aviv Univ.), Reuven Ianconescu (Tel Aviv Univ

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Avraham Gover (Tel-Aviv Univ.), Reuven Ianconescu (Tel Aviv Univ Super-radiant Pre-bunched Beam FEL in the Coherent- Spontaneous and Tapered-Wiggler Regimes Avraham Gover (Tel-Aviv Univ.), Reuven Ianconescu (Tel Aviv Univ. and Shenkar College), Moore Symposium on compact X-Ray FEL, UCLA Jan 2019 1 eSASE AND HIGH HARMONIC TES OPTION ALEXANDER A. ZHOLENTS Phys. Rev. ST Accel. Beams 8, 040701 (2005) e-SASE X-ray Buncher UV Uniform Wiggler Tapered Wiggler SP/SR TESSA Tapering Enhanced Superradiance 2 (a) Spontaneous emission (b) Superradiant emission (coherent spontaneous emission) 3 Formulation of Radiation mode Expansion 푬ෙ 풓, 휔 = ෍ 퐶ሙ푞 푧, 휔 푬෩푞(풓) Spectral (Fourier) ±푞 Frequency domain 푯ෙ 풓, 휔 = ෍ 퐶ሙ푞 푧, 휔 푯෩ 푞(풓) ±푞 ሙ 푑퐶푞(푧, 휔) 1 ∗ = − න 푱ෘ 풓, 휔 ∙ 푬෩푞(풓)dA 푑푧 4풫푞 표푢푡 푖푛 1 ∗ 퐶ሙ푞 휔 − 퐶ሙ푞 휔 = − න 푱ෘ 풓, 휔 ∙ 푬෩푞(풓)dV 4풫푞 out in - e Cq Cq ˆ ~ Er, Cq z,Eq r q 4 푁 Particulate current: 퐉 퐫, 푡 = ෍ −푒퐯푗(푡)훿 퐫 − 퐫푗(푡) 푗=1 푁 표푢푡 푖푛 1 Radiation wavepackets 퐶푞 휔 = 퐶푞 휔 − ෍ ∆풲ෙ푞푗 4풫푞 푗=1 ∞ ෙ ෩∗ 푖휔푡 ෙ (0) ෙ 푠푡 ∆풲푞푗 = −푒 න 풗෥푗 ∙ 푬푞 풓풋 푡 푒 푑푡 = ∆풲푞푗 + ∆풲푞푗 −∞ Spontaneous: ∞ (0) (0) (0) (0) (0) ෙ ෙ 푖휔푡푗0 Where: ෙ ෩∗ 푖휔푡 ∆풲푞푗 = ∆풲푞푒 푒 ∆풲푞푒 = −푒 න 풗푒 (푡) ∙ 푬푞(풓푒 (푡))푒 푑푡 −∞ 푁 푁 표푢푡 푖푛 0 푖휔푡0푗 푠푡 퐶푞 휔 = 퐶푞 휔 + ∆퐶푞푒 휔 ෍ 푒 + ෍ ∆퐶푞푗 푗=1 푗=1 Spectral radiant energy: 푑푊푞 2 2 푑푊푞 푑푊푞 푑푊푞 푑푊푞 = 푃 퐶표푢푡 휔 = + + + 푑휔 휋 푞 푞 푑휔 푑휔 푑휔 푑휔 푖푛 푠푝/푆푅 푠푡−푆푅 푠푡 5 Schematic description of the four radiative emission processes in the complex 표푢푡 푖푛 plane of the mode amplitude 퐶푞 , which is composed of 퐶푞 and the superposition of the particles radiation wave packets ∆퐶푞푗 : Spontaneous Emission Superradiance Stimulated Emission Stimulated – Super (Laser Amplifier) radiance A. Gover, Superradiant and stimulated-superradiant emission in prebunchedelectron-beam radiators PRST-AB 8, (030701) 2005 6 A Pulse Composed of a Periodic Train of NM Micro-Bunches f(t-t0) 7 Coherent SP-SR of Undulator Radiation For a finite train of periodic bunches: 2 2 2 2 푑푊푞 푁 푒 푍푞 푎 퐿 = 푤 푀 휔 2 푀 휔 2푠푖푛푐2 휃퐿Τ2 푑휔 16휋 훽 훾 퐴 푏 푀 푆푅 푧 푚 휔 휔 − 휔 2 0 휔0 ≅ 2훾푧 푐푘_푤 ∆휔 = 휔0Τ푁푤 Detuning parameter: 휃 휔 퐿 = − 푘푧푞 휔 − 푘휔 퐿 ≅ 2휋 푣푧 ∆휔 (Nw=# of undulator periods) ) Τ 1 푠푖푛 푁푀 휋휔 휔푏 Pulse train form-factor: 푀푀 휔 = 푁푀푠푖푛 휋휔Τ휔푏 nb nN M (NM=# of bunches in macropulse 푁푏 1 2 2 푖휔∆푡푗 −휔 휎 Bunching coeficient: 푀푏 휔 = ෍ 푒 = 푒 푡푏 푁푏 (Nb=# of particles in bunch) 푗=1 A. Gover, PRST-AB 8, (030701) 20058 The Macropulse Form-Factor Function Drawn for NM = 8 sin NM/ b MM NMsin / b 1 nb nN M 9 FINITE SIZE BUNCHING FACTOR A. Gover Erratum: Superradiant and stimulated-superradiant emission in prebunched electron-beam radiators. I. Formulation Phys. Rev. ST Accel. Beams 8, 030701 (2005)] 10 BUNCHING BY LASER MODULATION AND DISPERSIVE SECTION 0.67 n22 /2A Me A/ mod bn n1/3 0 0.67 nAMe 1/2 max b,nmax 1/3 nmax ALEXANDER A. ZHOLENTS Phys. Rev. ST Accel. Beams 8, 040701 (2005) 11 Phase-merging enhanced harmonic generation Feng, C., Deng, H., Wang, D., & Zhao, Z. (2014). Phase-merging enhanced harmonic generation free-electron laser. New Journal of 12 Physics, 16(4), 043021. SP-SR HARMONIC POWER For: NNMw 2 n n2 b 0 z0 w dW ( ) dW ( ) q qn ddn 2 22 2 2 dWqn ( ) Ne 0aL w w 2 MM()b,n M d 16 0 z A em,q ( n ) Power of harmonic n: dWqn ( ) b Ptq,n p dN M n 222 2 I0 0 a w L w Mb,n 80 z A em,q ( n ) 13 ST-SR IN THE NONLINEAR REGIME 2 Pe N b mc 1 / T b 2 PCq,n q,nP q Self-consistent nonlinear model formulation for an infinite pulse or finite pulse with zero-slippage: dp dp q,n e 0 dz dz 14 TILTED PENDULUM EQUATION MODEL FOR TAPERED WIGGLER N.M. Kroll, P.L. Morton, M.N. Rosenbluth, IEEE J. Quant. Electron., QE-17, 1981 A. Gover, R. Ianconescu, A. Friedman, C. Emma, N. Sudar, P. Musumeci, C. Pellegrini, “Superradiant and stimulated-superradiant emission of bunchedelectron beams” arXiv-2018-1810.07566v1 (accepted Rev. Mod. Physics 2018) 15 ST-SR IN THE NONLINEAR REGIME 2nd ORDER PERTURBATIVE SOLUTION For short interaction length u z / L w : 22 Pq / P REF E (u) E (0) ST-SR SR TAPERING For 16 Uniform wiggler: maximal gain Stimulated Superradiance 17 Tapering Enhanced Stimulated Superradiance (TESSA): (0) r 18 Tapering Enhanced Stimulated Superradiance (TESSA):(0) / 2 19 Superradiance in the nonlinear regime (self interaction) - uniform wiggler 20 Tapering Enhanced Superradiance (TES) E. C. SNIVELY, J. XIONG, P. MUSUMECI, A. GOVER “Broadband THz Amplification and Superradiant Spontaneous Emission in a Guided FEL” (SUBMITTED) 21 Phase – space trajectories of a realistic bunch in a tapered wiggler FEL N. M. Kroll, P. L. Morton, M. N. Rosenbluth, IEEE J. Quant. Electron. 17, 1436 (1981) Y. Jiao et al, “Modeling and multidimensional optimization of a tapered free electron laser” PRST-AB 15, (050704) (2012) E. A. Schneidmiller, M. V. Yurkov, “Optimization of a high efficiency fel amplifier” PRST-AB 18, 03070 (2015) 22 TESSA: EXTENTION TO DISTRIBUTED BUNCH Bunches get trapped in the tapered undulator in ponderomotive buckets of the SP-SR generated harmonic radiation. f:t fraction trapped depends on phase between beam and radiation TAPERING SR Need to optimize ft ( r , mod )sin r N. Sudar, P. Musumeci et al “High Efficiency Energy Extraction …Tapered Undulator” PRL 117, 174801 (2016) OPTIMAL TAPERING PHASE Assume: mod trap For n ( A), 2 max z nmax 1 r 2 2mod 2trap *RIVER ROBLES - STUDENT UCLA PHYSICS DEPT. A Model Problem with a SAMURAI beam 3.2 μm 1 GeV, 800 A microbunched beam Focusing optics 320 nm radiation Short wiggler Tapered wiggler (10 periods, 24 cm) (125 periods, 3 m) K 10 K(0) 10 Non-tapered Undulator Radiation 320 nm PSP-SR 3.2 μm ● In undulator, beam slips back 10 radiation wavelengths ● Choosing tenth harmonic for resonance avoids “gaps” in the resulting laser distribution MODEL PROBLEM RESULTS ● Beam generates 2.4 GW of SP-SR radiation in the uniform wiggler which acts as seed radiation for the tapered wiggler ● An additional 13.4 GW is produced in the tapered wiggler ● Energy extraction efficiency: 2% Conclusions 1. High power coherent spontaneous superradiant emission (SP-SR) may be feasible at high UV harmonic (x30) of modulating laser. 2. High power extraction may be attainable in a Tapering Enhanced Superradiant (TES) scheme where the bunched beam is trapped by its own generated SP-SR. 3. The advantage of TES is self phase matching to the bunch train. 4. Can be companion to e-SASE facility. 5. Consider option of oscillator (TESO). No need for seed. 28 RESERVE 29 Analytic Output Predictions ● Spontaneous power in normal wiggler: 2.4 GW ● Power gained in tapered wiggler: 13.4 GW ● Radiation wavelength: 320 nm ● Radiation pulses: 250 ● Pulse spacing: 320 nm Experimental Setup Numbers ● Microbunching period: 3.2 microns ● Normal wiggler period: 24 mm ● Input beam energy: 1 GeV ● Wiggler periods: 10 ● Average bunch current: 800 A ● Resonant wavelength: 320 nm ● Bunch charge: 200 pC ● Normalized vector potential: 10 ● Tapered wiggler period: 24 mm ● Wiggler periods: 125 ● Norm. vector potential (entrance): 10 ● Resonant wavelength: 320 nm EXTENTION TO DISTRIBUTED BUNCH 1/2 1/2 Pq 8P q (0) P SR P SR 2 2 1 02 L w a w (0) PSR I 0 f r ,A / n) 40 A em ( n ) 0 A/ mod 0 z 0 / 2A 2 z 0 / n max n max A ALEXANDER A. ZHOLENTS Phys. Rev. ST Accel. Beams 8, N.040701 Sudar, (P.2005 Musumeci) et al “High Efficiency Energy Extraction …Tapered Undulator PRL 117, 174801 (2016) 32 eSASE AND HIGH HARMONIC TES OPTION ALEXANDER A. ZHOLENTS Phys. Rev. ST Accel. Beams 8, 040701 (2005) X-ray Buncher UV Uniform Wiggler Tapered Wiggler SP/SR TES 33 Phase-merging enhanced harmonic generation Feng, C., Deng, H., Wang, D., & Zhao, Z. (2014). Phase-merging enhanced harmonic generation free-electron laser. New Journal of 34 Physics, 16(4), 043021. Mesured multi-bunch coherent Smith-Purcell linewidth (MIT - S.E. Korbly et al PRL 2005) 4 for mfb 240GHz f fb / NM 28MHz f / for 1/ mNM 1.310 14 1.7 GHz 1.7 GHz 550 14 550 35 SR and ST-SR of Undulator Radiation For a finite train of periodic bunches: 2 2 2 2 푑푊푞 푁 푒 푍푞 푎 퐿 = 푤 푀 휔 2 푀 휔 2푠푖푛푐2 휃퐿Τ2 푑휔 16휋 훽 훾 퐴 푏 푀 푆푅 푧 푚 푑푊푞 푁푒 푎 2푍푞풫푞 = 퐶ሙ푖푛 휔 푤 퐿 푀 휔 푀 휔 푠푖푛푐 휃퐿Τ2 푐표푠 휑 − 휃퐿Τ2 푑휔 푞 2휋 훽 훾 퐴 푏 푀 푆푇−푆푅 푧 푒푚푞 휔 휔 − 휔 2 0 휔0 ≅ 2훾푧 푐푘_푤 ∆휔 = 휔0Τ푁푤 Detuning parameter: 휃 휔 퐿 = − 푘푧푞 휔 − 푘휔 퐿 ≅ 2휋 푣푧 ∆휔 (Nw=# of undulator periods) ) Τ 1 푠푖푛 푁푀 휋휔 휔푏 Pulse train form-factor: 푀푀 휔 = 푁푀푠푖푛 휋휔Τ휔푏 nb nN M (NM=# of bunches in macropulse 푁푏 1 2 2 푖휔∆푡푗 −휔 휎 Bunching coeficient: 푀푏 휔 = ෍ 푒 = 푒 푡푏 푁푏 (Nb=# of particles in bunch) 푗=1 A. Gover, PRST-AB 8, (030701) 2005 Uniform wiggler: maximal extraction 37 RUBICON/NOCIBUR EXPERIMENT N.
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