Physics of coherent radiation by relativistic electron bunches

Transcription

1 Physics of coherent radiation by relativistic electron bunches. F. Shul ga RuPAC-008 Akhiezer Institute for Theoretical Physics ational Science Center Kharkov Institute of Physics and Technology Kharkov, Ukraine How does Electron Radiate? Coherent beam - beam radiation Backward Compton scattering undulator radiation On radiationless motion of accelerated electrons bunch Positron source 1

2 Relativistic Electron Field Potential e z + γ ikzvt 3 ikr c e d re k ikzvt γ k z ikzvt cos z πγ e e dz k ze π e e d J 0 k K 0 k z γ k ( ) ( )

3 How Does Electron Radiate? The excitation is small c vrel c v γθ << 1 scat v ( c v) t t λ Δ Δ c c γ λ l c γ λ λ γθscat 1 The excitation is increased l c γ λ γθ >> 1 scat The excitation is strong ε 5GeV 3 lc ~10 cm for ω ~1MeV l ~1 cm for ω ~1KeV c 3

4 Coherence Length R l c γ ω crystal amorphous media dω dω B H LPM ω ε ω 4

5 Radiation in Coulomb field of relativistic particle lc γ λ l eff c!!! 3 eff lcγ γ λ U( r) α r ( ) U r α + + γ ( z vt) 5

6 Coherent radiation in crystal and at electron collision with a short bunch crystal atomic string bunch ϑ e ε RT F. Shul ga, D. Tyutyunnik, JEPT Lett. 78(003)700., Proc. of SPIE, v. 5974(005)60. 6

7 Coherent radiation at electron-beam collision e l c B dω B 0 L I. Ginzburg, G. Kotkin, S. Polityko, V. Serbo Phys. Lett. B86 (199) 395 Phys. Rev. E51 (1995) 493 e B 1 c << 7

8 Suppression of coherent radiation (analog of LPM-effect) ϑ e ε ( ) + ξ+ ξ + dω π ξ ξ + 1 e ξ 1 ln 1 1, ξ γϑ, l c L dω 6 e m e 4e ln m γϑ << 1 γϑ >> 1 ε5 Gev, L0.1 cm, 0.01 cm, 10 10, ω 4 c γ 50 kev, γϑ L 1. Shul ga, D. Tyutyunnik. JETP Lett. 78 (003) 700. im B7 (005) 15 8

9 Coherent radiation in a thin crystal p 0 a a lc a p ' γϑ << 1 ϑ Ze, R ε dω γϑ, γϑ << 1 e 3π ( γϑ ) 6ln, γϑ >> 1 dω p lc p ' >> a γϑ >> 1 γϑ suppression of CR 1 A. Akhiezer,. Shul ga et al. Sov. J. Part. ucl. 10 (1979) 9

10 Beam-beam monitoring u dω 6 e 3 ( ) e u γϑ e sh dω 3π 3πm u u 10

11 Beam-size dependence e Δ e u γϑ << 1 dω d 1 πδ e Δ ( ) dω u Δ e sh e d dω 3π m Δ u dω 6 8 e 3π m Δ ln ( Δ ) u Δ ( ) u Δ << u Δ >> u 11

12 Conclusions Beam-beam collision and CR Beam-crystal collision and CR analogy Born approximation Semiclassical approximation coherent radiation suppression of CR e e 1 c << 1 c >> γϑ << 1 γϑ >> l c eff γ ω 3 γ ω long-distance effect Beam-beam monitoring Beams-sizes dependence of CR applications 1

13 v Radiation of Charge Distribution at r( ) r( ) t+ T t + T e k I dωdο 4π J rt e t r r t ( ) (, ) υ( ) ( ) i( ωt kr() t ) 3 ikr I dt e υ t d k e r () ( ) r t+ T r t + υt ( ) ( ) T π i( ωt kr() t ) 3 ikr I δ( ω kυ ωn ) dte υ t d re r T n 0 () ( ) π ω n n T 13

14 Classically Radiationless Motion of Oscillating Charge r t T r t ( + ) ( ) 1. Spherically symmetrical charge distribution (G.Schott 1933) 1 4π R ( r) δ( r R) 3 ikr 1 dre r k sin ωnr ω R ( ) ( ) n ω n π n T The radiation is absent for π R kn π T. r r R, nonspherically symmetrical charge distribution, ( ) ( ) G.Goedecke, Phys.Rev 1964 A.Devaney, E.Wolf, J.Math.Phys

15 Backward Compton Scattering (Quantum Theory) e ω θ Ω Ω ω ε +... ar0 ε' ω ε ε' ω ω T dωdo Ω ε ω m ε' ε ωm ω m E ' ε 50Mev Ω 1ev ω m 4 εε ' Ω m ω ε ' ε ω ω m 900kev 15

16 Backward Compton Scattering Undulator Radiation dωdo + e 4π i( ωt kr() t ) k v t e dt γϑ << 1 e () Ω e ω δ δ cos dωdo 4π q q q q ω kv δ ω γ ϕ W q ( ) Ar0 ω ω ω T 1 1 dω Ω ωm ωm ωm E ' W( q) v ( t) e iqt dt e i( v0 ) t v Ω Ω () t Re Ae ε. Shul ga, D. Tyutyunnik. Phys. Lett. A36 (004) 87. 4γ Ω ω 16

17 Suppression of Radiation at Undulator Motion r t+ T r t + υt υ υ ( ) ( ), Пластинка: ( z ) ( kl ) 3 ik kz 1 sin z z dke + ( r) ( π) δ( k ) k LLL k x y z z ω kυ Ω n ω n 4π γ T n Отсутствие излучения: kl z z πγ Lz π T Lz 1 γ T Подавление излучения при ω ω n : 4π γ k L ωθ n γ L L 1 T > T L > 4π γ 17

18 18

19 Positron Source Problem 19

20 Positron Source from Pencil-like Target.Shul ga, V.Lapko Phys.Lett.A v.359, p.8-9 (006) Pencil-like target A.Mikhailichenko (003) 0