SUPERRADIANT EMISSION SCHEME, FREE ELECTRON SPIN-FLIP EMISSION OF - PowerPoint PPT Presentation

SUPERRADIANT EMISSION SCHEME, FREE ELECTRON SPIN-FLIP EMISSION OF RADIATION (FESFER) Avi Gover The FEL Knowledge Center for Radiation Sources and Applications Tel – Aviv University, Fac. of Engineering - Physical Electronics. June 2005

OUTLINE 1. SUPERRADIANT* EMISSION – RADIATION SCHEMES AND GENERAL FORMULATION. 2. STIMULATED–SUPERRADIANCE FEL OSCILLATOR. 3. FREE ELECTRON SUPERRADIANT SPIN–FLIP EMISSION OF RADIATION . * R. H. Dicke, Phys. Rev. 93 , 99(1954)

(b) Superradiant emission (a) Spontaneous emission λ λ N w λ N w l b λ w l b (a) (b)

PB-FEL I. Schnitzer, A. Gover, “The Prebunched FEL…”, NIMPR A237, 124 (1985) Wiggler B magnets k N Spent e-beam E B Bend CSR N b k Spent G.L. Carr et al, “High power e-beam THz radiation…”, Nature 420, 153 (2002) E

Other superradiant emission schemes • Coherent Smith-Purcell • Cerenkov Radiation • Transition Radiation • Cyclotron Resonant Emission (CRE)

Excitation of modes (Waveguide or Free Space) ( ) ( ) ( ) ∑ ~ ω = ω E r , C z , E r q q ± q ( ) ( ) ~ ( ) ∑ ω = ω H r , C z , H r q q ± q N N ( ) ( ) 1 ∑ ∑ ω − ω = Δ = − Δ out in W C C C q q qj qj P 4 = = j 1 j 1 q ∞ ( ) ( ) ( ) ~ ∫ Δ = − ⋅ ω * i t W e v t E r t e dt qj j q j − ∞ dW 2 ( ) 2 = ω q out P C ω π q q d ⎡ ⎤ + + 2 2 2 2 w ~ ~ x y x y = = − − + ϕ + 0 E E exp ⎢ ik i ikz ⎥ ( ) ( ) ( ) q 00 2 ⎣ ⎦ w z w z 2 R z

Useful Coherent Power from a spatially coherent source Filter 2 ΔΘ t 2 Θ coh 2a 2r coh 2r t L Coherent-Radiation Line - Source Target Plane

Spatially Coherent Spectral Power N N ( ) ( ) ( ) ( ) ∑ ∑ ω ω = ω + Δ ω + Δ i t out in 0 st C C C e oj C q q qe qj = = j 1 j 1 { dW 2 ( ) 2 = ω + q in P C ω π q q d 2 ( ) ( ) N ω + Δ ω ⋅ + ∑ i t 0 C e oj qe = j 1 ⎡ ⎤ ( ) ( ) ( ) N ω + ∗ ω ⋅ Δ ω ⋅ + + i t ∑ in 0 C C e oj c . c . ⎢ ⎥ ⎣ q qe ⎦ = j 1 ⎫ ⎡ ⎤ ( ) ( ) N + ∗ ω ⋅ Δ ω + ≡ ∑ in st ⎬ C C c . c . ⎢ ⎥ ⎣ q qj ⎦ ⎭ = j 1 ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ dW dW dW dW ≡ ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ q q q q ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ω ω ω ω ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ d d d d − in sp / SR ST SR st

Superposition of radiation wavepackets: a) Spontaneous emission b) Superradiance c) Stimulated emission d) Stimulated superradiance ( a) ( b ) out C q Δ out C C q 3 q Δ Δ C C q 3 q 2 Δ C q 1 Δ C q 2 Δ C 1 q ( c ) ( d ) Δ C q 4 Δ C q 3 Δ C out q 2 C Δ q C Δ st q 1 C q 3 Δ st C in q 1 C q in out C C q q

The Bunch Form-Factor ( ) ( ) ∞ 2 Δ ( ) ⎛ ⎞ 0 W ω dW ω = ' 1 ' i t ' ∫ = ⋅ ω M f t e dt ⎜ ⎟ qe 2 q 2 0 M ( ) N ⎜ ⎟ b 2 0 0 ω π ω b ⎝ ⎠ P d 8 2 − − ∞ × t q SR ( ) 4 ω := M e ) ( ) ( ( ) = − π 2 2 for a Gaussian e-beam bunch distribution : f t exp t t / t 0 0 b b ( ) ( ) ω 2 = − ω 2 2 / M exp t 2 1 b b 0.8 0.6 ω M ( ) 0.4 0.2 0 0 1 2 3 4 5 6 ω ω t b

The Macropulse Form-Factor for a Pulse Composed of a Periodic Train of N M Micro-Bunches f(t-t 0 ) ⎛ ⎞ dW 2 N ( ) ( ) ( ) ( ) ⎜ ⎟ 2 = Δ ω ω 2 ω 2 q 0 W M M ⎜ ⎟ ω π qe b M ⎝ ⎠ P d 8 q SR ( ) Δ ω πω ω / 1 ( ) sin N = ω = M b M ( ) πω ω ω M / N sin n nN M b b M

The Macropulse Form-Factor Function Drawn for N M = 8

Spatially Coherent Spectral Power For PB-FEL : 2 ⎛ ⎞ ⎛ ⎞ 2 2 2 dW N e Z ( ) ( ) eB L ⎜ ⎟ ⎜ ⎟ = ω 2 θ q b q 2 w M sinc L 2 ⎜ ⎟ ⎜ ⎟ ω π β γ b 2 ⎝ ⎠ ⎝ ⎠ d 16 mc k A z w em SR θ = ω v - k - k / z z w For CSR : 2 ⎛ ⎞ ⎛ ⎞ 2 2 2 ⎡ ⎤ 4 dW N e Z ( ) ( ) eB L d ⎜ ⎟ = ⎜ ⎟ ω θ q b q b M sinc L 2 ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ω π βγ θ b ⎣ ⎦ ⎝ ⎠ ⎝ ⎠ d 4 mc A d L em SR θ = ω v z k - / z

Line-Shape Function PB-FEL CSR ( ( ) ) θ ω 2 sin c L 2 2 ⎡ ⎤ ( ) d θ sinc L 2 ⎢ ⎥ θ ⎣ ⎦ d L Δ ω ( ) θ = π ω − ω Δ ω L 2 0

Synchrotron Radiation Generation electron(s) Intensity ⏐ E 2 ⏐ E/N Electric field N super-radiant enhancement THz time freq. (1/time) W.D. Duncan and G.P. Williams,”Infra-red Synchrotron Radiation From Electron Storage Rings”, Applied Optics 22, 29l4 (1983).

Schematic of the TAU table-top Prebunched-Beam Free Electron Maser.

PB – FEM SUPERRADIANCE MEASUREMENT

PB-FEL STIMULATED SUPERRADIANCE MEASUREMENT

STIMULATED– SUPERRADIANCE FEL OSCILLATOR

Stimulated-Superradiance PB-FEL Oscillator P(0) = R rt P(L) P(L) P out = TP(L) Wave packet e-bunch

The Pendulum Equation model – Saturated PB-FEL Ψ 2 d = − Ψ 2 K sin s 2 dz d Ψ θ = dz k a a / 2 = w s K γγ β s 2 z z ~ 1 ω ⎛ ⎞ e E ω 2 e 2 P ⎜ ⎟ = = a ⎜ ⎟ s μ ε mc mc ⎝ A ⎠ em

Ultimate Energy Extraction Efficiency Scheme in PB-FEL

Saturation Dynamics of a Single e-Bunch in a fixed wiggler length for different K s 4 ) (stored power ~ K s θ 0 θ 0 θ 0 θ 0 θ 0 3 π 3 π 3 π 3 π 3 π ψ 0 ψ 0 ψ 0 ψ 0 ψ 0 = = = = = = = = = = 0 0 0 0 0 K K K K K 4.706 1.7 3.273 4.316 5.013 10 10 10 10 10 5 5 5 5 5 θ θ θ θ θ 0 0 0 0 0 5 5 5 5 5 10 10 10 10 10 ψ ψ ψ ψ 2 2 2 2 0 0 0 0 2 2 2 2 4 4 4 4 6 6 6 6 8 8 8 8 ψ 2 0 2 4 6 8

Bistability of PB-FEL Oscillator P(L) = P(0)/R rt P sat2 P(Lw) P(L) = P(L;P(0)) P unst P sat1 P(0)

CLOSED-TRAJECTORIES SATURATION STABLE POINT

OPEN-TRAJECTORIES SATURATION STABLE POINT

R rt = 0.97 G-1 = 0.005

Oscillation build-up in Stimulated Superradiance FEL Oscillator Post - Saturation Detuning Control Fixed Detuning

FREE ELECTRON SUPERRADIANT SPIN–FLIP EMISSION OF RADIATION .

Electron Spin Resonance Emission Frequency In the e-rest frame: ω = μ h ' g B ' s B z In the lab frame: = B ' B z z [ ( ) ] ω = γ ω − β ω ' ck s z s z z s ω γ ( ) ' = ω Θ ω = For k c cos : s 0 z z s − β Θ s 1 cos z Θ = For 0 : ( ) ω = + β γ ω 1 ' s z z s 0 = γ = ⇒ = = B 3 . 5 kGauss , 100 f ' 10 GHz , f 2 THz z s s

Free Electron Spin-Flip Emission of Radiation (FESFER) Axially polarized Radiation Acceleration ω s e* B z Transversely polarized Acceleration Radiation “ π /2 pulse section” ω s e * e* B z B b ω b I P = = ⇒ = P b ω ; FOR f 2THz, 8mW/A h max I max s s e b

Ratio of SR-FESFER to SP-ECR 2 ⎛ ⎞ ⎛ ⎞ μ ε ω μ [ ] s ' dW ( ) ( ) 1 L Z g ⎜ ⎟ ⎜ ⎟ = ⋅ ∗ θ − + ˆ ˆ q 0 0 σ e sin 2 2 2 0 s 0 B s 2 1 c L N P N P ⎟ ⎜ ⎟ ⎜ + ω π q γ s s 0 s 0 d 4 A v Z c 2 ⎝ ⎠ ⎝ ⎠ em z q / SP SR ( ) ω s π ω − + dW d ( ) 2 2 r h N 1 P N P 1 q = SP SR b ( ) s s 0 s 0 ε ω c 2 dW d mc N 2 2 n q SP π ω r h 1 ≈ b 2 s NP ε s 0 2 mc 2 2 n

CONCLUSIONS • SUPERRADIANT EMISSION FROM femto/pico-SEC E-BEAM BUNCHES IS A PROMISSING HIGH POWER THz RADIATION SCHEME. • FORMULATION FOR THE CALCULATION OF COHERENT SPECTRAL CHARACTERISTICS OF ANY KIND OF RADIATION SCHEMES WAS PRESENTED. A STIMULATED-SUPERRADIANCE OSCILLATOR SCHEME PROVIDES • ULTIMATE RADIATIVE CONVERSION EFFICIENCY (WITH ENERGY RETRIEVAL SCHEMES). • A RADIATION EMISSION SCHEME FROM ACCELERATED ELECTRONS IS PROPOSED: FREE ELECTRON SPIN-FLIP EMISSION OF RADIATION (FESFER). • A SHORT BUNCH OF POLARIZED ELECTRONS CAN PROVIDE ENHANCED (SUPERRADIANT) SR-FESFER RADIATION, WITH APPRECIABLE INTENSITY RELATIVE TO CRE RADIATION .