Part XI. Optimising Femtosecond K α Sources

Transcription

1 Part XI Optimising K α Sources 333 / 353

2 K α sources Goals: maximize # photons < 100 fs pulse length minimize spot size (magnification) maximize throughput (ave. power) 334 / 353

3 Applications of femtosecond K α sources Electron transport diagnostic (Fast Ignitor scheme) Real-time x-ray diffraction Bio-medical imaging (> 50 kev) 335 / 353

4 Inner shell excitation by fast electrons 2p K α 1s hot e 336 / 353

5 Model of femtosecond K α generation N Kα (I, Z) = 0 N H (I )f H (E, T H )I K (Z, E)f K (Z, E)dE N H (I ) f H (E, T H ) T H (I ) hot electrons hot electron distribution hot electron temperature I K (Z, E) K α quantum efficiency (# photons/electron) f K (Z, E) K α emission factor I obs /I K self absorption cf: G. H. McCall, J. Phys. D (1982) 337 / 353

6 Hot electrons Absorbed laser energy: PIC simulations show: U abs = η a U L N H T H = const. η a 40 60%(10 15 < I λ 2 < Wcm 2 µm 2 ; θ = 45 0 ; L/λ = 0.3) f (E) = (πet H ) 1/2 exp( E/T H ) T H 100(I 18 λ 2 µ) 1/2 kev N H (I λ 2 µ) 1/2, since U L I focal area = const. 338 / 353

7 Scaling of hot electron temperature T hot (kev) IOQ-99 Experiments LLNL-00 T h(fkl) T h(w) T h(gb) T RAL-99 h(b) IOQ-97 CELV-96 MBI-00 RAL-96 STA-92 LLNL-99 IOQ-00 CELV-96 MBI-95 MBI-97 LULI-97 IOQ-96 INRS-99 LULI-94 LLE I (Wcm m ) 339 / 353

8 K α emission from solid targets Quantum efficiency Green & Cosslett (1968): ( ) 5/3 E I K = N(Z) 1 E K Replace with fit to Monte-Carlo simulations using monoenergetic electrons: I K Z 4/3 E 3/2 (196) Emission factor f K I obs I K = f (E/E K ) { 1, EK < E < 20E K 0, otherwise (197) E K = K-shell ionization energy Z / 353

9 K α emission factor N em /N gen shows universal behaviour with Z emission factor U scat.depth / abs. length U Ti Cu Ag Ta Normalised electron energy U E/E k 341 / 353

10 Solution Normalize energies to K-shell ionization energy: U E E K U H k BT H E K Putting together results (1) (5) gives: 20/UH N Kα (Z, U H ) az 0.6 U 1/2 H [ = az 0.6 e U 1 H e 20U 1 H Ue U/U H du 1/U H ( ) U 1/2 H + U 1/2 H ( U 1/2 H + 20U 1/2 H )] 342 / 353

11 Photon reabsorption leads to optimal electron energy N(U H ) U H opt = 6.4 no absorption U max = U H = k B T H /E k 343 / 353

12 Analytical model of intensity optimum scaling Reich, Gibbon, Uschmann, Förster, Phys. Rev. Lett. 84, 4846 (2000) Photon yield: N Kα (I, Z) Z 2.73 I 3/ U exp( U/U H )du, where U H is the hot electron temperature normalised to the K-shell ionization energy: Find: U H = k BT hot E k I 1/2 Z 2.2. U opt H 6.4 I opt const Z 4.4 I opt (W/cm 2 ) atomic number Z 344 / 353

13 Particle-in-cell + Monte-Carlo model τ d I, λ, τ p hot electron generation PIC-code Plasma (n e, L/ λ ) Laser e - e - Kα K α production X-ray image Solid (z) Time dependence f hot(e,t) MC-code K α (x,t) time intensity Total K -yield 345 / 353

14 Optimal laser intensity for K α yield with constant energy on target yield (photons / sr) Ti Cu Ag Ta E L = 200mJ τ p = 60fs (Ti-Sa) L/λ = 0.3 θ = 45 o laser intensity (W/cm 2 ) 346 / 353

15 X-ray pulse duration with thick targets photons / fs (a.u.) % of emission over time (fs) Afterglow 90%-pulse duration (fs) laser intensity (W/cm 2 ) 347 / 353

16 Sub-100 fs pulses with foil targets 10 7 photons sr -1 fs time (fs) W/cm W/cm W/cm 2 Compromise between high yield & ultrashort duration gives: I opt Z 2.4 (τ X τ p ) 5/4 Wcm 2 d opt 3Z 1/2 (τ X τ p ) 5/4 nm 348 / 353

17 Emission region of a 6.4 kev K α burst Fe-Target Ti:Saphir Laser: 200 mj 100 fs W/cm 2 (Uschmann, Feurer) Intensities [a.u.] x [ m] K measured K simulated laserprofile 349 / 353

18 K α yield optimisation using a controlled prepulse Ziener et al., Phys. Rev. E (2002) K signal (V) Si Prepulse delay (ps) K signal (V) Ti Prepulse delay (ps) K signal (V) Co Prepulse delay (ps) E L = 200 mj, λ = 0.8 µm, θ = 45 o I 0 = Wcm 2, I prepulse = Wcm / 353

19 Density scale lengths calculated from isothermal expansion model L/ Si Ti Co d (ps) see : Bastiani et al., PRE 56, 7179 (1999) Schlegel et al., PRE 60, 2209 (1999) 351 / 353

20 Calculated Kα yield for different density scale-lengths K -photons / sr * Co n/n c = L/ K -photons / sr * n/n c = 20 n/n c = L/ Si 352 / 353

21 Experimental Kα yields f/electron/sr K/4 sr experiments K Efficiency Z Overall x-ray conversion efficiency ε K = ε f 4πN h E K U L 353 / 353