The Purpose of this talk The generation of the high-frequency resonant FEL wave by means of it s low-frequency wave as a pomp wave

Transcription

1

2

3

4

5

6

7

8

9

10

11

12

13 The Purpoe of hi alk The generaion of he high-frequency reonan FEL wave y mean of i low-frequency wave a a pomp wave

14 A free elecron laer ha wo reonan frequencie wih : λ 1, = ( 1 ± β β ) λ w In a waveguide: 1.The wo reonan frequencie are decried a: 1, = (1 ± β 1 X 1 + β cβ k ll w = x = ( β k ) 1 w β llγ ll = ll.the lippage eween he radiaion and he elecron eam can e conrolled ) 1 α

15 Piovella e al howed ha **If a wave a he upper frequency 1 i injeced ino he wiggler, no appreciale deviaion from he cuomary reul oained. **Bu, much more inereing i he iuaion, when a lowfrequency wave in injeced ino he wiggler. In hi cae, an inene and rong unching grow on he upper frequency. **Thi up-converion proce i maximum when he frequency raio i an ineger 1 = α. Thi mehod can e of mo pracical inere in he generaion of microwave of infrared radiaion, when convenional inpu ource are no eaily availale. The imulaion howed ha o generae radiaion a 430 Gh wih an inpu ource a 43 Gh: λ =10, cm N w = 100, aw = = 10 50mm, 1

16 Diadvanage of uing wave guide: producing a very high frequency wave may e oained 1. y increaing he lower frequency. y increaing α ** increae in α may e achieved y enhancing he iniial energy of he eam which reuled in he diminuion of he proce efficiency. = c ** ince k, and oh and k are quaniie wih a w very limied range of variaion, can no e increaed. The proce of up-converion in a waveguide FEL eem o e confined in he range of microwave or, a mo, UVA, u no in he regime of X-ray. 1

17 Q. Wha hould we do? Conrolling he diperion ad lippage of he wo reonan wave in he FEL y filling he wiggler caviy wih a plama, inead of uing a waveguide: 1, = (1 ± β 1 X 1+ β ) x = Advanage of hi cheme: p ( β γ k c) ll ll w one can reach high value of high frequency wihou increaing α oo much.

18 We aume a enuou elecron eam ravere hrough a plama wih n n p. We aume ha he plama efore injecion of he eam i in an equilirium ae wihou inernal curren and he eam i o weak ha i produce only mall deviaion from he equilirium ae. The plama i decried y he cold non-relaiviic elecron fluid equaion: n u p p + + u p ( n pu p ) = 0, e e up = E [ up ( B+ Bw )] m mc aw ikw B( Bw) = A( Aw ), Aw = (ˆ ee + c. c.), eˆ = xˆ + iyˆ,

19 The equaion for he elecron eam : d ( ) d = v ( ), dp ( ) e e c = E(, ) + ( A+ A ) 4 w d mc m c γ V e P = γ = ( A + c mc A w ),,

20 The longiudinal and ranvere componen of he elecric field in one-dimenion :, 4 ), ( J E c = π ), ( 4 p E ρ ρ π + = = = = + = N p p p p v en J u en J J J J 1 )) ( ( ) (,, δ Where i he eam curren in he charged hee model, I he urface deniy of he elecron on he ingle hee, and And are he inananeou poiion of he h plane and velociy of he h eam paricle. v J n

21 Wih, he diperion relaion of he yem i very near o ha of he cold unmagneied plama, which comprie and ( ), ).ˆ ( ˆ ) ( 1 ), ( e B u c e n n c a E c w p p ik w p w = + δ γ ).ˆ, ( 4 0 B u m c e m e n n w p p w p + = + + ρ π p w n n and p = c = p + k

22 wih: 1. ea A = Aeˆ + c. c., A = T mc,. aking he advanage of lowly varying envelope approximaion n n A p 0 T = = ~ i( A e A L e 1 i( k 1 ) i( k ) 1 ~ we deduce he nonlinear parial differenial equaion decriing he ineracion eween wo wave. + i ( k L L ) + A e c. c.

23 ( ), ) ( 1 ~ )] ( [ e n n a A k c ik w w = + + δ γ φ ( ), ) ( 1 ~ )] ( [ 0 e n n a A k c ik w w = + + δ γ φ ( ), ) ( 1 ] [ e n n i A ik L L L L = δ γ

24

25

26 [ ] ) ( ] [ ] [ ~ ~ ) ( k i k i w w w e A A e v ca d dp = = φ φ γ Wih ) ( 1, 0 1, 1, 1, p a k k w L L L + + = = = γ φ φ

27

28 Applicaion of

29

30

31

32

33

34