1. Energetic ions from next generation ultraintense ultrashort lasers: scaling laws for TNSA Matteo Passoni 1,2,3, Maurizio Lontano 3, Luca Bertagna 1, Alessandro Zani 1 1 Dipartimento di Energia, Politecnico di Milano 2 Istituto Nazionale di Fisica Nucleare (INFN) Milano 3 Istituto di Fisica del Plasma, CNR, Milano

2. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 2 Outline - Introduction laser-driven ion acceleration physics TNSA mechanism - Analytical models to describe TNSA plasma expansion vs particle acceleration in quasi-static field - A 1D quasi-static analytical model based on “bound electrons” Comparisons with experimental results Predictions for future applications - Conclusions

3. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 3 Laser-driven ion acceleration in solids targets If an ultraintense and ultrashort laser pulse hits the surface of a thin solid film, intense and energetic (Multi-MeV) ion beams are effectively produced The accelerated ions possess unique properties!

4. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 4 Ion acceleration mechanism(s!): general remarks 1 2 3 Laser pulse solid target front surface rear surface 1: laser pulse-front surface interaction - generation of relativistic e - population - role of pulse properties (intensity, energy, prepulse, polarization) - role of target properties (density, profile, thickness, mass) 2: electron propagation in the target - role of electron properties (max. energy, spectrum, temperature) - role of target properties - return current 3: effective charge separation - generation of intense electric fields - resulting ion acceleration pre-plasma (underdense) Light ion layer relativistic e - current return current main pulse pre-pulse SOME CRUCIAL ISSUES:

5. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 5 Ion acceleration mechanism(s!): TNSA – RPA IF THE e - POPULATION IS DOMINATED BY A THERMAL SPECTRUM… (quite “natural” experimentally…) Target Normal Sheath Acceleration mechanism (TNSA) IF THE THERMAL e - POPULATION IS “SUPPRESSED”… (is it “feasible” experimentally…?) Radiation Pressure Acceleration mechanism (RPA) …accelerating field due to strong charge separation between hot electrons expanding in vacuum and the bulk target …accelerating field due charge separation induced by the balance between radiation pressure and electrostatic force

6. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 6 Ion acceleration mechanism(s!): how to control their properties? - Laser pulse different combinations of pulse energy, intensity, duration linear polarization to have a thermal component (TNSA) circular polarization + normal incidence to suppress it (RPA) - Target ultrathin targets (with ultrahigh contrast!) can be used: “enhanced TNSA” (“hotter” electrons) “light sail” RPA (vs “hole boring” RPA with thick targets) “partially trasmitted pulse” regimes target density and structure can influence the process multilayers (control of the ion spectrum and species) mass limited (control of the accelerating field) nanostructured (e.g. to change the density parameter) Various possibilities can be explored:

7. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 7 TNSA: still a number of open issues! - which are the most effective laser absorption process at the target front surface? Dependence on pulse properties?? - role of pre-pulse/pre-plasma? - differences between front and rear acceleration? - role of target properties (thickness, density, structure…)? - realization of suitable numerical simulations (Vlasov, PIC) - development of analytical models How to describe the acceleration process theoretically?

8. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 8 Theoretical description of TNSA How to develop analytical models of the acceleration process in TNSA? …generally speaking, two approaches are possible: 1)consider ions and hot electrons as an expanding plasma described with fluid models 2)describe in detail the accelerating field as a quasi-static electric field set up by the hot electrons This is the approach of the present work!

9. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 9 Hydrodynamic models for TNSA Limits of this kind of description: These models (most popular from P. Mora) have been found very useful and are widely adopted to interpret experimental data. - accelerated ions are a thin layer rather than a semi-infinite plasma - empirical acceleration time can be unphysical in several regimes: - too short for very short pulses (tens fs), - too long for the most energetic part of the spectrum with long pulses (few ps) - divergent maximum ion energy (see below!!) [P. Mora, Phys. Rev. Lett. 90, 185002 (2003) J. Fuchs, et al., Nature Phys. 2, 48 (2006)]

10. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 10 Quasi-static theoretical models for TNSA The following physical picture can be assumed: - hot electrons create a non-neutral region, source of an electric field - light ions form a thin layer, the main target is made of heavier ions - during the characteristic acceleration time of the light ions hot electrons almost isothermal (cooling important at longer times), heavier ions almost immobile - until the number of accelerated light ions is much lower than the number of hot electrons, the field is not heavly affected the accelerating field can be assumed as quasy-static, light ions treated as test particles

11. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 11 Hot electrons description: Boltzmann distribution/ infinite space …i.e.: on the problem of maximum ion energy regardless the dimensionality, final ion energy diverges !!! - - isothermal models: introduce “truncation mechanisms” Y. Kishimoto, et al., Phys. Fluids 26, 2308 (1983) M.Passoni, M.Lontano, Laser Part. Beams 22, 171 (2004) M. Lontano, M. Passoni, Phys.Plasmas, 13,042102 (2006) M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008) x NiNi

12. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 12 Role of “bound” electrons – 1 - consider the electron distribution function only “trapped” (  (r,p) < 0) e - are bound from the potential to the target; “passing” e - (  (r,p) > 0) leave the system Y. Kishimoto, et al., Phys. Fluids 26, 2308 (1983) How to build a more self-consistent description?? Kinetic approach  (x) x NiNi e-e- e-e-  tot (x) lost at ∞ “E.S. field distribution at the sharp interface between high density matter and vacuum” M. Lontano, M. Passoni, Phys.Plasmas, 13, 042102 (2006)

13. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 13 Role of “bound” electrons – 2 “… A small fraction of the hot electron population escapes and rapidly charges the target to a potential of the order of Up preventing the bulk of the hot electrons from escaping. …” “… All targets were mounted on 3 mm thick and 2 cm long plastic stalks in order to provide a highly resistive path to the current flowing from the target to ground. …” “Dynamic Control of Laser-Produced Proton Beams” S. Kar et al., Phys. Rev, Lett., 100, 105004 (2008) Any experimental evidence of “passing” vs “bound” electrons? …then, in usual conditions a globally neutral target with only “bound” electrons develops see also M. Borghesi’s talk!! and K. Quinn et al. PRL (2009)

14. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 14 1D 1T trapped electron model – 1 only the density of “trapped” e - enters Poisson eq.; integrating over  < 0 we get the trapped e - density n tr (  (r))

15. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 15 1D 1T trapped electron model – 2 implicit analytical solution  = x/ D ( D from ) Spatial extention of the electron cloud [L. Bertagna, Master thesis, (2009) Politecnico di Milano ]

16. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 16 1D 1T trapped electron model – 3 [L. Romagnani, et al., P.R.L. 95, 195001 (2005) M. Borghesi, et al., Fus. Sc. & Techn. 49, 412 (2005)] interaction CPA 1 I ≈ 3.5  10 18 W/cm 2  ≈ 1.5 ps 1 - 40  m, Al, Au bent foils T e ≈ 500 keV  int ≈ 6-7 MeV E ≈ 3  10 10 V/m t (ps) experimental data best reproduced by PIC simulations assuming a field which becomes zero at a finite distance h ≈ 20  m from the rear surface proton imaging of rear field LULI

17. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 17 1D 1T trapped electron model – 4 - determination of  f from the knowledge of  0 -  0 related to the hot electron parameters inside the target as far as the front side (-  w = - w/ D <  < 0) - ions and cold electrons form provide a positively charged background density ZN i - N cold = N L (x)(x) x  in (x) 0- w ** 00 xfxf T hot laser max value of the potential inside the target max value of trapped electron energy =

18. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 18 1D 1T trapped electron model – 5 Analytical solution in the ultra-relativistic limit (appropriate near and inside the target for typical parameters) maximum ion energy ion energy spectrum “Theory of Light-Ion Acceleration Driven by a Strong Charge Separation” M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008)

19. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 19 1D 1T trapped electron model – 6 The maximum electron energy  e,max =  * as a scaling law - Make use of proper numerical simulations of laser-target interaction - From the analysis of several published results (starting with observed proton energies and using the model to infer  * ) we get the fitting (valid for the “ordinary” TNSA regime…) A=4.8, B=0.8, where E L is the laser energy How to obtain  e,max =  * ? Difficult both theoretically and experimentally…

20. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 20 Pulse energy – intensity plane: present day experiments [1] [23] [24] [25] [26] [27] [29] [30] [28] …agreement within 10 % M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008)

21. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 21 Dependence on intensity: present day experiments [ From M. Borghesi et al., Plasma Phys. Contr. Fus. 50, 024140 (2008)] There is a combined variation of pulse energy & intensity!

22. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 22 1T trapped electron model Comparison with experimental data [M. Passoni et al., AIP Conf. Proc. (in press)] Experimental data from T. Ceccotti, Ph. Martin (CEA Saclay): fixed pulse duration (25 fs) and focal spot with UHC: BWD TNSA! BWD H +

23. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 23 Experiments with reduced wavelength and different spot size Spot size (FWHM) ~ 4.4  m 3m3m Spot size (FWHM) ~ 0.9  m 3m3m Wavelength: 528 nm (2  ) Pulse width: 400 fs Max intensity (I 2 ): ~4.8*10 18 Wcm -2  m² Temporal contrast: >10 10 1/5 spot From J. Fuchs presentation at ULIS ’09 (2 weeks ago), and here yesterday!

24. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 24 Experiments with reduced wavelength and different spot size ∝ I Laser EPM Direct Au 2  m thick Al 2  m thick Al 0.5  m thick Proton maximum energy [MeV] 5.5 MeV protons Only 0.8 J ~ 7J Need only ~ 1/10 energy to accelerate the protons. From J. Fuchs presentation

25. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 25 Experiments with reduced wavelength and different spot size Preliminary theoretical interpretation of these experiments… - General trend well reproduced - Underling physics seems to be nicely captured

26. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 26 1T trapped electron model Comparison with experimental data - our model C 5+ ions estimated layer thickness: < 5 nm Quasi-monoenergetic MeV carbon beams [B. M. Hegelich et al., Nature 439, 441 (2006)] - our model electron energy distribution (PIC) [T. Ceccotti et al, Phys. Rev. Lett. 99, 185002 (2007)] Use of Ultrahigh-Contrast Laser Pulses and thin targets No fitting parameters used!

27. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 27 TNSA: dependence on laser parameters Pulses with fixed duration (25 fs) and focal spot: prediction of max. ion energy vs. intensity In these conditions, combined variation of pulse energy & intensity Effective dependence on intensity changes with the “decades”

28. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 28 Pulse energy – intensity plane: TNSA beyond 10 21 W/cm 2 : ? Example : 100 MeV protons with Ti:Sa ( =800 nm); I = 4x10 21 W/cm 2 ; E L = 5 J

29. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 29 Predictions for applications: hadrontherapy with TNSA? Possible path to reach 250 MeV protons and 10 nA current with “usual” TNSA: Ti:Sa ( =800 nm); I = 1x10 22 W/cm 2 ; E L = 50 J;  = 15 fs (focal=4 µm) (3 PW system); Rep. rate 5 Hz (with 10 10 protons/pulse in the selected energy interval) …these requirements could be even less demanding if “improved” schemes of TNSA can be adopted at these laser parameters

30. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 30 Conclusions - Quasi-static models give simple expressions for the TNSA maximum ion energy and for the energy spectrum others exist…B.J. Albright, et al., Phys. Rev. Lett. 97, 115002 (2006) J. Schreiber, et al. Phys. Rev. Lett. 97, 045005 (2006) M. Nishiuchi, et al., Phys. Lett. A 357, 339 (2006) A.P. Robinson, et al., Phys. Rev. Lett. 96, 035005 (2006) - hold for short time (in this sense, complementary to fluid models) - A 1D quasi-static model of TNSA has been developed: experimental results in good agreement with the expectations predictions for future applications are easily feasible - Further improvements in several directions are possible: magnetic fields, max e - energy, 2T, 3D, space charge effects, expanding target.. Work in progress…

31. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 31 THANK YOU FOR YOUR ATTENTION! And thanks to the co-workers! Maurizio Lontano, Luca Bertagna, Alessandro Zani for more details… matteo.passoni@polimi.it www.nanolab.polimi.it

32. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 32 Experimental Results (Fuchs J.) In following tables there are predictions using (1) nominal pulse energy in φ* scaling law or (2) effective pulse energy:

33. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 33 Comparison between experimental point and UR model predictions (1) Experiment al point E L [J] I [10 20 W/cm 2 ] Iλ 2 [I/10  m 2 ] f S [  m] E max,TEO [MeV] E max,EXP [MeV] 12.502.456.850.9 (T.F.)14.2310.5 21.751.724.80.9 (T.F.)10.99.5 33.253.28.90.9 (T.F.)17.259.5 41.751.724.80.9 (T.F.)10.99 50.8 2.20.9 (T.F.)5.85.7 60.8 2.20.9 (T.F.)5.85.9 70.8 2.20.9 (T.F.)5.85.2 82.50.10.34.4 (Direct)1.752 94.80.20.54.4 (Direct)3.24 105.50.230.634.4 (Direct)3.62 1190.3714.4 (Direct)5.47 128.50.350.94.4 (Direct)5.16 139.50.414.4 (Direct)5.710

34. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 34 Comparison between experimental point and UR model predictions (2) Experimenta l point E L [J] I [10 20 W/cm 2 ] Iλ 2 [I/10  m 2 ] f S [  m] E max,TEO [MeV] E max,EXP [MeV] 12.502.456.850.9 (T.F.)10.910.5 21.751.724.80.9 (T.F.)8.159.5 33.253.28.90.9 (T.F.)13.349.5 41.751.724.80.9 (T.F.)8.159 50.8 2.20.9 (T.F.)4.25.7 60.8 2.20.9 (T.F.)4.25.9 70.8 2.20.9 (T.F.)4.25.2 82.50.10.34.4 (Direct)1.32 94.80.20.54.4 (Direct)2.54 105.50.230.634.4 (Direct)2.82 1190.3714.4 (Direct)4.47 128.50.350.94.4 (Direct)4.26 139.50.414.4 (Direct)4.610

35. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 35 Expected results from UR model (scaling law for φ* with NOMINAL pulse energy)

36. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 36 Comparison theoretical vs. experimental results (scaling law for φ* with NOMINAL pulse energy) 2.3 6.911

37. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 37 Expected results from UR model (scaling law for φ* with EFFECTIVE pulse energy)

38. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 38 Comparison theoretical vs. experimental results (scaling law for φ* with EFFECTIVE pulse energy) 2.36.911

39. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 39 From Ph. Martin’s talk…. BWD H + Wanna get 100 MeV ? Just build up a 1PW laser (but clean !) Linear scaling law Next decade ? theory

40. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 40 1T trapped electron model – 7 Comparison with experimental data [R.A. Snavely, et al., Phys. Rev. Lett., 85, 2945 (2000)] [M. Nishiuchi, et al., Phys. Lett. A, 357, 339 (2006)] - model Proton spectra with different laser parameters

41. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 41 Other quasi-static models… “Theory of Laser Acceleration of Light-Ion Beams from Interaction of Ultrahigh-Intensity Lasers with Layered Targets ” B.J. Albright, et al., Phys. Rev. Lett. 97, 115002 (2006) - extention of the 2T model to describe layered targets “Analytical Model for Ion Acceleration by High-Intensity Laser Pulses “ J. Schreiber, et al. Phys. Rev. Lett. 97, 045005 (2006) - surface charge model exploiting radial symmetry for the electric field “The laser proton acceleration in the strong charge separation regime ” M. Nishiuchi, et al., Phys. Lett. A 357, 339 (2006) - approach analogous to the 1T model to interpret experiments “ Effect of Target Composition on Proton Energy Spectra in Ultraintense Laser-Solid Interactions “ A.P. Robinson, et al., Phys. Rev. Lett. 96, 035005 (2006) - study of the effects of a non negligible proton density in the target

42. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 42 Further theoretical references… “Ion acceleration in expanding multi-species plasmas” V. Yu. Bychenkov et al., Phys. Plasmas, 11, 3242 (2004) “Ion acceleration in short-laser-pulse interaction with solid foils “ V. T. Tikhonchuk, et al., Plasma Phys. Controlled Fusion 47, B869 2005. “Collisionless expansion of a Gaussian plasma into a vacuum” P. Mora, Phys. Plasmas 12, 112102 (2005) “Thin-foil expansion into a vacuum” P. Mora, Phys. Rev. E 72, 056401 (2005) “Test ion acceleration in a dynamic planar electron sheath ” M.M. Basko, Eur. Phys. J. D, 41, 641 (2007) “Nanocluster explosions and quasimonoenergetic spectra by homogeneously distributed impurity ions” M. Murakami & M. Tanaka, Phys. Plasmas 15, 082702 (2008) …not exaustive list… V. F. Kovalev, et al., JETP, 95, 226 (2002) S. Betti, et al., Pl. Phys. Contr. Fus. 47, 521 (2005)

43. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 43 Arguments for discussion The field of laser-based ion acceleration is extraordinary active…some examples: - elimination of the pre-pulse to allow: - efficient TNSA front acceleration - more efficient electron heating - use of ultrathin targets (promising to increase ion properties) - production and control of a “true ion beam” - Achievement of monoenergetic collimated low-emittance ion beams - investigation of new accelation schemes (e.g. Radiation Pressure Acceleration, RPA, other kinds of targets) - construction of satisfactory theoretical descriptions of these issues - development of the possible applications

44. Matteo Passoni COULOMB 09, Senigallia, 16.06.2009 Matteo Passoni 44 1T trapped electron model – 7 Comparison with experimental data [R.A. Snavely, et al., Phys. Rev. Lett., 85, 2945 (2000)] [P. McKenna, et al., Phys. Rev. E, 70, 036405 (2004)] [M. Nishiuchi, et al., Phys. Lett. A, 357, 339 (2006)] - model Proton spectra with different laser parameters M. Passoni, M. Lontano, Phys. Rev, Lett., 101, 115001 (2008)