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)

(a) Spontaneous emission (b) Superradiant emission

(a) Nw λ Nw λ λ λw (b) lb lb

PB-FEL

• I. Schnitzer, A. Gover,

“The Prebunched FEL…”, NIMPR A237, 124 (1985)

Wiggler magnets Spent e-beam k B

E

N Bend Spent e-beam k B Nb

E

CSR

G.L. Carr et al, “High power THz radiation…”, Nature 420, 153 (2002)

Other superradiant emission schemes

• Coherent Smith-Purcell
• Cerenkov Radiation
• Transition Radiation
• Cyclotron Resonant Emission (CRE)

Excitation of modes (Waveguide or Free Space)

( ) ( ) ( ) ( ) ( ) ( )

∑ ∑

± ±

= =

q q q q q q

z C z C r H r H r E r E ~ , , ~ , , ω ω ω ω

( ) ( )

∑ ∑

= =

Δ − = Δ = −

N j qj q N j qj in q

• ut

q

C C C

1 1

4 1 W P ω ω

( ) ( )

( )

∫

∞ ∞ − ω

⋅ − = Δ dt e t t e

t i j q j qj

r E ~ v

*

W

( )

2

• ut

q q q

C 2 d dW ω π = ω P

( ) ( ) ( )

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ϕ + + − + − = = ikz i z R 2 y x ik z w y x exp z w w

2 2 2 2 2 00 q

E E ~ ~

Useful Coherent Power from a spatially coherent source

2a

2ΔΘt

Coherent-Radiation Line - Source Target Plane Filter

2rt 2Θcoh 2rcoh

L

Spatially Coherent Spectral Power

( ) ( )

( )( )

∑ ∑

= =

Δ + Δ + =

N j st qj N j t i qe in q

• ut

q

C e C C C

• j

1 1 ω

ω ω ω

( )

{

( )( )

( )

( )( )

( ) ( )

st q SR ST q SR / sp q in q N 1 j st qj in q N 1 j t i qe in q 2 N 1 j t i qe 2 in q q q

d dW d dW d dW d dW . c . c C C . c . c e C C e C C 2 d dW

• j
• j

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω ≡ ≡ ⎭ ⎬ ⎫ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∑ + ω Δ ⋅ ω + + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ∑ ⋅ ω Δ ⋅ ω + + ∑ ⋅ ω Δ + + ω π = ω

− = ∗ = ω ∗ = ω

P

Superposition of radiation wavepackets: a) Spontaneous emission b) Superradiance c) Stimulated emission d) Stimulated superradiance

• ut

q C

1 q C Δ 2 q C Δ 4 q C Δ

in q C

• ut

q C in q C st 1 q C Δ st 3 q C Δ

( c )

( d ) 1 q C Δ

2 q C Δ

3 q C Δ

• ut

q C

• ut

q C 3 q C Δ q 1 C Δ 2 q C Δ ( a) ( b )

3 q C Δ

( )

2 2 b q 2 qe SR q

N ) ( M 8 1 d dW ω Δ ⋅ π = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω P W

The Bunch Form-Factor

( )

( )

2 t exp M

2 b 2 2 b

/ ω − = ω

for a Gaussian e-beam bunch distribution :

b

t ω

M ω

( )

e t

2

− ω

2

4 × := 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 M ω ( ) ω

( )

( ) (

)

b 2 b 2

t / t t exp t f π − =

( )

( )

∫ = ω

∞ ∞ − ω ' t i ' b

dt e t f M

'

The Macropulse Form-Factor for a Pulse Composed of a Periodic Train

• f NM Micro-Bunches

( )( )

( ) ( )

2 M 2 b 2 qe q 2 SR q

M M 8 N d dW ω ω ω Δ π = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω W P

( ) ( ) ( )

b M b M M

sin N N sin M ω πω ω πω = ω / /

M b

nN 1 n = ω ω Δ

f(t-t0)

The Macropulse Form-Factor Function Drawn for NM = 8

Spatially Coherent Spectral Power

( ) ( )

w z z

k

• k
• v

/ ω θ θ ω γ β π ω = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ 2 16

2 2 2 2 2 2 2

L sinc M A k L mc eB Z e N d dW

b em w z w q b SR q

( ) ( )

z z k

• v

/ ω θ θ θ ω βγ π ω = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

2 4 2 2 2

2 4 L sinc L d d M A L mc eB Z e N d dW

b em b q b SR q

For PB-FEL: For CSR:

Line-Shape Function

( )

2

2 L sinc L d d ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ θ θ

CSR

( )

ω Δ ω − ω π = θ 2 L

ω Δ

( ) ( )

2 L c sin

2

ω θ

PB-FEL

Electric field time

• freq. (1/time)

electron(s)

super-radiant enhancement

N

E/N Intensity ⏐E2 ⏐

Synchrotron Radiation Generation

W.D. Duncan and G.P. Williams,”Infra-red Synchrotron Radiation From Electron Storage Rings”, Applied Optics 22, 29l4 (1983).

THz

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) = RrtP(L) P(L) Pout = TP(L) Wave packet e-bunch

The Pendulum Equation model – Saturated PB-FEL

Ψ − = Ψ sin K dz d

2 s 2 2

dz dΨ = θ

2 1 em s

A P 2 mc e mc ~ e a ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ε μ ω = ω = E

2 z z s w s

2 / a a k K β γγ =

Ultimate Energy Extraction Efficiency Scheme in PB-FEL

Saturation Dynamics of a Single e-Bunch in a fixed wiggler length for different Ks (stored power ~ Ks

4)

θ0 3π ψ0 = K 1.7 =

2 2 4 6 8 10 5 5 10

θ ψ θ0 3π ψ0 = K 3.273 =

2 2 4 6 8 10 5 5 10

θ ψ θ0 3π ψ0 = K 4.316 =

2 2 4 6 8 10 5 5 10

θ ψ θ0 3π ψ0 = K 4.706 =

2 2 4 6 8 10 5 5 10

θ ψ θ0 3π ψ0 = K 5.013 =

2 2 4 6 8 10 5 5 10

θ ψ

Bistability of PB-FEL Oscillator

P(L) = P(0)/Rrt P(L) = P(L;P(0)) Psat2 Punst Psat1 P(0) P(Lw)

CLOSED-TRAJECTORIES SATURATION STABLE POINT

OPEN-TRAJECTORIES SATURATION STABLE POINT

Rrt = 0.97 G-1 = 0.005

Oscillation build-up in Stimulated Superradiance FEL Oscillator

Fixed Detuning Saturation Detuning Control

• Post

FREE ELECTRON SUPERRADIANT SPIN–FLIP EMISSION OF RADIATION.

Electron Spin Resonance Emission Frequency

( ) [ ] ( )

THz 2 f , GHz 10 ' f 100 , kGauss 5 . 3 B : For : cos c k For ck ' B ' B

s s z s z s z z s z s z z

= = ⇒ = γ = = Θ Θ ω = ω β − ω γ = ω =

' B g '

z B s

μ = ω h

In the e-rest frame: In the lab frame:

( )

' cos ' 1 1

s z z s z z s s

ω γ β ω β γ ω ω + = Θ − =

Free Electron Spin-Flip Emission of Radiation (FESFER)

Axially polarized Acceleration Bz

ωs ωs

Transversely polarized Acceleration

e* e*

Bb

e*

ωb

8mW/A I P 2THz, f FOR ; ω e I P

b max s s b max

= ⇒ = = h

“π/2 pulse section”

Radiation Bz Radiation

Ratio of SR-FESFER to SP-ECR

( ) ( )

[ ] ( ) ( )

2 2 2 2 2 2 2 2 2

2 2 1 1 2 2 1 1 2 2 4 1

s s n b s s s n b SP c q SR SP s q s s s s B s q z em SR SP s q

NP mc r N P N P N mc r d dW d dW P N P N L c g c Z Z v L A d dW ω ε π ω ε π ω ω θ γ μ ω ε μ π ω h h ≈ + − = + − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

∗ +

) ( sin e ˆ σ ˆ

' q /

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.