Active Medium Acceleration

Transcription

1 Active Medium Acceleration Levi Schächter Department of Electrical Engineering Technion - Israel Institute of Technology Haifa 3, ISRAEL

2 Outline Acceleration concepts Wake in a medium Frank-Hertz, LASER & Acceleration Space-charge wave in resonant medium Wake & Saturation Dynamics & Saturation Active enhancement of the Q-factor BNL-ATF PASER experiment

3 Classification of Acceleration Concepts Inverse Radiation Processes Slow Wave -- Cerenkov -- Smith-Purcell Fast Wave: -- FEL -Cyclotron Transition Radiation Laser Wakes Laser Wake-Field Plasma Wake-Field Plasma Beat Wave Dielectric Wake-Field

4 Wake in a medium Passive Dielectric Cerenkov Radiation Decelerating Force Reaction Field E = q dec 4πε R γ 1 Resistive Material Eddy Currents Decelerating Force R Reaction Field Eddy currents E = q dec 4πε R ( γβ ) 3 ση R 1 Active Medium Negative Resistivity Induced Polarization Accelerating Force R Reaction Field "Polarization" Narrow band L. Schachter, PRE, 53, p.647(1996)

5 Frank-Hertz, LASER and Acceleration Frank-Hertz LASER Light Amplification by Stimulated Emission of Radiation L. Schachter, Phys. Lett. A., 5, p.355(1995) PASER Particle Acceleration by Stimulated Emission of Radiation

6 Wake in a resonant medium εω ( ) A z ε r dω + ω ω ω p ω + 1 jω e εω ( ) ε r -1/β =.1 jωω ( t z/ v) β ω cs, Im(ω)/ω Four -. Poles: ε r - 1/β ε r -1/β =.5 R = 1.5 cm f = 4 GHz f p = 1 GHz Re(ω)/ω Two waveguide modes Two resonance modes Amplitude [a.u.] 1-1 f = 4 GHz R = 1.5 cm time [nsec] L. Schachter, PRE, 6, p.15 () Amplitude [a.u.] *1 5-5 f = 4 GHz R = 1.5 cm time [nsec] No growth off-resonance

7 Space-charge wave in a resonant medium Basic Concept: Space-charge wave propagating in a lossy waveguide leads to resistive-wall instability. Resonant absorption of atoms or molecules may be used for amplification or acceleration Gas plasma frequency Im[ε 1/ (ω)] Im[ε(ω)] Resonant frequency Re[ε(ω)] Im[ε 1/ (ω)] ω/ ω ε( ω) =ε Beam plasma frequency r pb, = 3 mεγ + ω ω p, g ω Line width pb, ( ω kv ) + jωω ω J ( ω, k) = jωε E ( ω, k) z ω en L. Schachter, Phys. Lett. A, 77, p.65 () z 1

8 Space-charge wave in a resonant medium ω ω pb, 1 εω k ( ) 1 c = ( ω kv) ε( ω) TEM SC Im[ε 1/ (ω)] Im[ε(ω)] Re[ε(ω)] Im[ε 1/ (ω)] ω/ ω TEM: SC: Im( k) Im(k) = = ω Im c ω p,b v [ ε( ω) ] Im 1 ε( ω) L. Schachter, Phys. Lett. A, 77, p.65 ()

9 Space-charge wave in a resonant medium Example: Amplifier µ=.5 Debye ω /π =15 GHz ω 1 /π =1MHz Im(k EM ) = 3.36cm -1 ω p,b /π = GHz Im(k SC ) =.54cm -1 =>.47dB/cm 1W input, 11cm interaction =>1MW Im[ε 1/ (ω)] Im[ε(ω)] Re[ε(ω)] Im[ε 1/ (ω)] ω/ ω L. Schachter, Phys. Lett. A, 77, p.65 ()

10 Space-charge wave in a resonant medium Example: Accelerator Same as above Im(k EM ) = 3.36cm -1 ω p,b /π = GHz Im(k SC ) =.54cm -1 =>.47dB/cm 1W input =>.15MV/m 11cm interaction =>45MV/m 4nsec,1mm beam L. Schachter, Phys. Lett. A, 77, p.65 () Im[ε 1/ (ω)] Im[ε(ω)] Re[ε(ω)] Im[ε 1/ (ω)] ω/ ω

11 Space-charge wave in a resonant medium Asymmetric Modes ω ω 1 p εω ( ) 1 c ( ω kv ) ε ( ω ) R pb, ns, k = TM 1 : p 1 = TM 11 : p 11 =3.83 Im(k SC,max )R b 1-1 TM TM γ Frequency of Peak Im(k SC ) [GHz] TM TM L. Schachter, Phys. Lett. A, 77, p.65 () γ

12 Wake & Saturation Quasi-linear approach Amplified Wake Gradient [V/m] ω τ 1 E 3 TT sat 31 p Cm 1 1[MV/m] 1 [ ] p TT.1[ nsec] 1 L. Schachter, PRL, 83, p.9 (1999)

13 Self-consistent dynamics Interaction of a single-mode with a bunch of electrons d jχ i a = α e dξ 1 jχ d i d a γ = a e c.c. γ 1 dξ i + + dξ i = α Kinetic Energy EM Energy d 1 1 χ = Ω dξ i β β i p Energy conservation L. Schachter, PRL, 87, (1)

14 Self-consistent dynamics Energy conservation in the presence of Active Medium Photon Density d a nph ω γ = i dξ α nmc e Kinetic Energy EM Energy Energy in Medium Electron Density L. Schachter, PRL, 87, (1)

15 Self-consistent dynamics The effect on the population inversion d jχ i 1 a = α e + σ nphd a dξ d a a γ 1 i d 1 jχ dξ + α = α γ i i = ae + c.. c dξ Inversion equation ( σ nphd) d a nph ω γ 1+ + i = dξ α nmc e d n = a σ dn mc n dξ α ω ph e ph L. Schachter, PRL, 87, (1)

16 Self-consistent dynamics d jχ i 1 a = α e + σnphd a dξ d 1 jχ i γ = ae c.c. i + dξ d a nph ω γ i = d 1 1 dξ α nmc e χi =Ω Kinetic Energy ( γ ) EM Energy Energy in Mediu dξ β β m i p d a mc nph σdne nph dξ = α ω L. Schachter, PRL, 87, (1)

17 Self-consistent dynamics en λ = 1 µm, = 3, int = 1[ Ω ], el = 1 = = 4.8[A], acc = 1 GV/m T 5 el [ ] d λ Z N I E [ ] IZint d eeaccd α = 84.5, a a.6 α = mc / e λ mc 5 N el ne =.3 1 m πrb λ π(.1λ) λ d a mc nph = σdne n dξ α 3 mc 6 σ [ Nd : YAG] = 5 1 m,.4 1 ω 3 4. ω ph n ph [m ] ph 5[J/cm ] w

18 Self-consistent dynamics Power [MW] ζ Gradient [GV/m] 1 Average Energy [MeV] ζ.5 γ/(<γ> 1) [%] L. Schachter, PRL, 87, (1) Relative Population Inversion [%] ζ Gradient [GV/m]

19 Q-factor enhancement The energy stored in the cavity of a laser is much higher (Q) by the extracted energy. Significant fraction of the energy is wasted by the various optical components. Efficiency of a single acceleration module can be fairly small. Number of accelerated bunch in one micro-bunch macro-bunch quasi-coherent wake. Proposed concept: combine the cavity of the laser and the acceleration module, to one unit. Different perspectives: - recycle some of the energy - active enhancement of the Q-factor - quasi-coherent wake External Laser Traveling-wave Acceleration Module Active Medium

20 Q-factor enhancement Tapered laser laser pulse λ M = d External Laser Traveling-wave Acceleration Module Active Medium Normalized Field α =. v gr =. 4c input laser output t / τ EM α =. v gr =. 5c input laser output t / τ EM α =. v gr =. 6c input laser output t / τ EM Conditions for self-consistent field: (I) (II) Amplifier compensates for all radiation loss External laser compensates for beam-loading L. Schachter, PRE (4) η KIN = = U LASER U + U ACTIVE 1+ 1 Q 1 U U OUT KIN

21 Q-factor enhancement - Peak efficiency independent of κ 1 /κ - Sensitivity External Laser Traveling-wave Acceleration Module Active Medium 1..8 Q = 5 ( ) κ F β gr =.5 / κ = 1. ( ) κ F / κ = 1. β gr =.5 Q = 5 β gr =.5 Q = 5 ( ) / κ = 1.. κ F Efficiency.6.4 Q = 5 ( ) κ F / κ =.5 β gr =.9. Q = 1 ( ) κ F / κ =.1 β gr = q / q q / q q / q High Q: (I) High efficiency (II) Reduced sensitivity - Peak efficiency dependent on β gr - Sensitivity L. Schachter, PRE (4)

22 BNL-ATF PASER experiment 1 cm 4.5 cm 4 cm CO Laser Accelerator FEL CO Mixture Diagnostics

23 BNL-ATF PASER experiment Ferro-electric cathode & gas excitation CO Laser Accelerator FEL CO Mixture Diagnostics

24 BNL-ATF PASER experiment 1 Jz (, r z,) t = qv δ ( r rν ) δ[ z zν Vt] π r ν ( ) P = π drr dze( rztj,, ) ( rzt,, ) = qv E r, z+ Vtt ; z z z ν x sinc M P x β 1 x R dxsinc Re jx 1 b = 1 β ε QV π F β λ x ε β β λ sinc 4πε λ β ν ν F( u) 1 1( ) 1( ) u [ K u I u ] CO Laser Accelerator FEL CO Mixture Diagnostics

25 BNL-ATF PASER experiment η Cer Act N N η µ 1 r d el el.5[%] γ -1 M Rb w ( π rel d) [ ] el ph % γ-1 ω N R 1, d =.5m, λ 1.6µm, 1 el b 1µm, γ 139, L 3mm 3 3 ph 1 pulse..., w 1 J/m, µ.1 CO Laser Assumptions: (I) T much longer than e-pulse duration (II) Linear medium Accelerator FEL CO Mixture Diagnostics

26 Summary In an active medium a particle may be accelerated: Frank-Hertz, LASER and PASER Wake in an active medium may be amplified Space-charge charge wave in a resonant passive medium may become unstable (resonant absorption instability) Wake saturation in an active medium Self-consistent equations (e, field and active medium) Active enhancement of the Q-factor Q of an acceleration module PASER experiment few percents energy change