X-ray vortices from nonlinear inverse Thomson scattering

Transcription

1 JLab semar 8/7/6 X-ray vortces from olear verse Thomso scatterg Yoshtaka Tara Natoal Isttute of Advaced Idustral Scece ad Techology (AIST) Vstg scetst: Msssspp State Uversty ad Jefferso Lab.

2 Optcal vortex Characterstcs Formg a helcal wave frot. Carryg a orbtal agular mometum (OAM). Total agular mometum = OAM mħ + sp agular mometum ħ o the paraxal approxmato. B. J. McMorra et al., Scece 33 () 9. Beams Laser, 3 kev electro, kev X-ray, Terahertz radato, Cold eutro. Applcato Optcal tweezer, quatum etaglemet, etc.

3 Optcal vortex Geerato Cyldrcal les, Spral phase plate, Fork gratg, Electromagetc radato from a electro. Laguerre Gaussa beam B. J. McMorra et al., Scece 33 () 9. E = + C ( ) ( ) p z z ω z ω ( z) ω ( z) R exp r kr z ( z + z ) R m L m exp r Ths term represets the helcal wave frot. exp ( m ) exp ( p + m + ) r ta OAM operator: L z = = m z z R

4 3 Iterferometer CCD Irs Referece lght Les f Beam spltter Laser Vortex lght Irs Fork gratg Mrror

5 4 Iterferece patter OAM value Plae wave + vortex Sphercal wave + vortex Vortex + vortex

6 5 Purpose Geerate hgh eergy X-ray vortex (more tha MeV) ad develop ts applcato. Applcato possblty X-ray dchrosm, Nuclear physcs, Sold state physcs, Geerato of postro vortex va par producto.

7 6 How to geerate X-ray/gamma-ray vortex Helcal udulator Hgh eergy electro, more tha GeV, s requred f MeV gamma ray vortex geerats. Iverse Thomso/Compto scatterg betwee plae wave electro ad optcal vortex laser Already proposed by U. D. Jetchura ad V. G. Serbo. PRL 6 3 (). Nolear verse Thomso/Compto scatterg betwee plae wave electro ad tese crcularly polarzed laser (ot vortex) Newly proposed by Y. Tara ad M.Katoh.

8 What s mportat to geerate X-ray vortex? Helcal moto of the relatvstc electro. X-ray vortex geerato by a helcal udulator was proposed 8. Hgher harmoc carry ±(-)ħ OAM. 7 B. M. Kcad, J Appl. Phys (977). S. Sasak et al., PRL. 48 (8).

9 POP expermet at BESSY-II Iterferece patter betwee secod harmocs from helcal udulator (vortex beam) ad fudametal from plaar udulator (o vortex beam). Photo eergy was 99 ev. 8 J. Bahrdt et al., PRL 348 (3).

10 Helcal moto of electro Also t s duced by the tese crcularly polarzed laser feld. Electro orbts r = (x, y, z) x y z ( η) = x ( ) + r ( η) = y ( r ) ( η) = z + β η s k η cos k η sgh - : postve helcty sgh +: egatve helcty η = z + ct k = π λ / a hk ( μm) ( ) 9.85 λ I W/cm λ : Wavelegth of crcularly r = a : Laser stregth parameter a = I : Itesty of the laser Hgh eergy X-ray vortex wll be produced by olear verse Thomso scatterg! polarzed laser 9 E. Esarey et al., PRE (993).

11 Emtted by a sgle electro a arbtrary orbt ( ) ( ) ( ) { } ( ) = c t r t t kr R k e E ω β ε π ω exp d exp 3 3 emtted radato of Agular freq. ω : r to the observato pot Dstace from org of R : ( ) ( ) ( ) ( ) ψ β η η ψ ε π λ ω kr C p J k k k k kr R c N k e E ± + = ± + = = = = = 3 exp s s cos s exp 3 ( ) ( ) ( ) ( ) ψ η η ψ ε π λ ω kr C p J h a k k kr R c N k e E ± + = ± + = = = ' 3 exp s exp 3 / λ η N = the perod teractg wth theelecctros Number of : N Electrc feld

12 Polarzato ad OAM characterstcs Electrc feld the x-y plae E + Stokes parameter S ( C ) ( ) 3 cos + C C cos C C C cos = = S ( C cos + C ) + ( C cos C ) C cos + C = ( C cos + C ) exp { ψ + kr + ( ) } ( C cos C ) exp { ψ + kr + ( + ) } e e + e ± e x ± e y = : Harmoc umber Postve helcty carry (-)ħ OAM Negatve helcty carry (+)ħ OAM. γ s s γ s cos - Postve helcty Negatve helcty

13 Spatal dstrbuto γ s s γ s cos = = γ s s γ s cos γ s s 3-3 =3-3 3 γ s cos Aular profle of hgher harmoc s due to the phase sgularlty.

14 Characterstcs of X-rays Agle Helcty <.6/γ.4/γ < <.47/γ Postve helcty Negatve helcty Fudametal ( = ) N 6 x photos/sec x photos/sec E -3 MeV.6-.7 MeV OAM Secod ( = ) ħ N x photos/sec x photos/sec E -6 MeV MeV OAM ħ 3ħ a =. N = 5 γ = λ =. μm Pulse wdth of the laser =.7 ps 3 N e = 9 electros/sec

15 4 Where ca we do expermet? JLab? BNL? Secod harmoc from olear verse Thomso scatterg was observed. But, they probably do t realze t s X-ray vortex.

16 Nolear verse Thomso X-rays at BNL Aular shape of the secod harmocs was measured. Ths wll be X-ray vortex. Electro beam γ = 8 E = 3 kev (λ =.95 m) Laser λ =.6 µm, pulse eergy = J, ω = µm, pulse wdth = 5 ps (FWHM), I =.4 x 6 W/cm, a =.6 5 M. Babze et al., PRL (6). Y. Saka et al., PRSTAB 8 67 (5).

17 Expermetal demostrato Iterferece patter measuremet betwee the cdet X-ray vortex ad dffracted X-ray from the wre. X-ray 5 µm few µm tugste wre Detector (.85 m from source) 5 µm Wre X-ray.5 m 3 σ = µm σ = µm 3 Y (µ m) Y (µ m) σ: rms beam sze of the electros X (µ m) X (µ m) -

18 7 Are X-ray vortces geerated at uverse? X-ray vortex ca be geerated f relatvstc electro ad tese crcularly plarzed electromagetc wave coexst. For example, eutro star, quasar, ad superova. Crab Nebula, Wkpeda

19 8 Cocluso X-ray vortex ca be geerated by olear verse Thomso scatterg of the tese crcularly polarzed laser. Secod harmocs of the olear verse Thomso scatterg was observed at BNL. A caddate of the expermetal demostrato s a terferece measuremet of the X-ray vortex usg a metal wre.