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Laser-Driven Ion Acceleration in Solids: Mechanisms and Analytical Models

This article explores the physics of laser-driven ion acceleration in solids, focusing on the Target Normal Sheath Acceleration (TNSA) mechanism. It discusses various analytical models to describe TNSA and the control of ion properties. Open issues and future applications are also discussed.

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Laser-Driven Ion Acceleration in Solids: Mechanisms and Analytical Models

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  1. Outline • Introduction • laser-drivenion acceleration physics • TNSA mechanism • Analytical models to describe TNSA • plasma expansion vsparticle acceleration in quasi-static field • A 1D quasi-static analytical model based on “bound electrons” • Comparisons with experimental results • Predictions for future applications • Conclusions

  2. 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!

  3. Ion acceleration mechanism(s!):general remarks SOME CRUCIAL ISSUES: solid target 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: effectivecharge separation - generation of intense electric fields - resulting ion acceleration Light ion layer pre-plasma (underdense) relativistic e- current Laser pulse return current 2 1 3 main pulse front surface rear surface pre-pulse

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

  5. Ion acceleration mechanism(s!):how to control their properties? Various possibilities can be explored: • 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)

  6. 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…)? How to describe the acceleration process theoretically? • - realization of suitable numerical simulations (Vlasov, PIC) • development of analytical models

  7. Theoretical description of TNSA How to develop analytical models of the acceleration process in TNSA? …generally speaking, two approaches are possible: • consider ions and hot electrons as an expanding plasma • described with fluid models • 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!

  8. Hydrodynamic models for TNSA These models (most popular from P. Mora) have been found very useful and are widely adopted to interpret experimental data. [P. Mora, Phys. Rev. Lett.90, 185002 (2003) J. Fuchs, et al., Nature Phys.2, 48 (2006)] Limits of this kind of description: • 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!!)

  9. 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 ionsform 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

  10. Hot electrons description:Boltzmann distribution/ infinite space …i.e.: on the problem of maximum ion energy Ni x regardless the dimensionality, final ion energy diverges !!! - isothermal models: introduce “truncation mechanisms” Y. Kishimoto, et al., Phys. Fluids26, 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)

  11. Role of “bound” electrons – 1 How to build a more self-consistent description?? Kinetic approach - consider the electron distribution function Ni only “trapped” ((r,p) < 0) e- are bound from the potential to the target; “passing” e- ((r,p) > 0) leave the system  (x) e- Y. Kishimoto, et al., Phys. Fluids26, 2308 (1983) x e- 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) tot(x)

  12. Role of “bound” electrons – 2 Any experimental evidence of “passing” vs “bound” electrons? “Dynamic Control of Laser-Produced Proton Beams” S. Kar et al., Phys. Rev, Lett., 100, 105004 (2008) “… 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. …” see also M. Borghesi’s talk!! and K. Quinn et al. PRL (2009) …then, in usual conditions a globally neutral target with only “bound” electrons develops

  13. 1D 1T trapped electron model – 1 only the density of “trapped” e- enters Poisson eq.; integrating over  < 0 we get the trapped e- density ntr((r))

  14.  = x/D(Dfrom ) 1D 1T trapped electron model – 2implicit analytical solution Spatial extention of the electron cloud [L. Bertagna, Master thesis, (2009) Politecnico di Milano ]

  15. 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)] proton imaging of rear field experimental data best reproduced by PIC simulations assuming a field which becomes zero at a finite distance h ≈ 20 m from the rear surface LULI t (ps) interaction CPA1 I ≈ 3.51018 W/cm2  ≈ 1.5 ps 1 - 40 m, Al, Au bent foils Te≈ 500 keV int ≈ 6-7 MeV E ≈ 3 1010 V/m

  16. 1D 1T trapped electron model – 4 • - determination of f from the knowledge of 0 • - 0related 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 ZNi - Ncold = NL 0 * laser in(x) (x) Thot x - w 0 xf max value of the potential inside the target max value of trapped electron energy =

  17. 1D 1T trapped electron model – 5 Analytical solution in the ultra-relativistic limit (appropriate near and inside the target for typical parameters) “Theory of Light-Ion Acceleration Driven by a Strong Charge Separation” M. Passoni, M. Lontano, Phys. Rev. Lett., 101, 115001 (2008) maximum ion energy ion energy spectrum

  18. 1D 1T trapped electron model – 6 The maximum electron energy e,max = * as a scaling law How to obtain e,max = * ? Difficult both theoretically and experimentally… - 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 EL is the laser energy

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

  20. 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!

  21. 1T trapped electron modelComparison with experimental data Experimental data from T. Ceccotti, Ph. Martin (CEA Saclay): fixed pulse duration (25 fs) and focal spot with UHC: BWD TNSA! BWD H+ [M. Passoni et al., AIP Conf. Proc. (in press)]

  22. Experiments with reduced wavelength and different spot size Wavelength: 528 nm (2w) Pulse width: 400 fs Max intensity (Il2): ~4.8*1018 Wcm-2mm² Temporal contrast: >1010 From J. Fuchs presentation at ULIS ’09 (2 weeks ago), and here yesterday! 1/5 spot 3mm 3mm Spot size (FWHM) ~ 4.4mm Spot size (FWHM) ~ 0.9mm

  23. EPM ∝ILaser Direct Proton maximum energy [MeV] Au 2mm thick Al 2mm thick Al 0.5mm thick Experiments with reduced wavelength and different spot size Need only ~ 1/10 energy to accelerate the protons. 5.5 MeV protons From J. Fuchs presentation Only 0.8 J ~ 7J

  24. 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

  25. - our model 1T trapped electron modelComparison with experimental data Quasi-monoenergetic MeV carbon beams [B. M. Hegelich et al., Nature439, 441 (2006)] - our model C5+ ions estimated layer thickness: < 5 nm [T. Ceccotti et al, Phys. Rev. Lett. 99, 185002 (2007)] Use of Ultrahigh-Contrast Laser Pulses and thin targets electron energy distribution (PIC) No fitting parameters used!

  26. 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”

  27. Pulse energy – intensity plane:TNSA beyond 1021 W/cm2: ? Example : 100 MeV protons with Ti:Sa (=800 nm); I = 4x1021 W/cm2; EL = 5 J

  28. 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 = 1x1022 W/cm2; EL = 50 J; = 15 fs (focal=4 µm) (3 PW system); Rep. rate 5 Hz (with 1010 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

  29. 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. A357, 339 (2006) • A.P. Robinson, et al., Phys. Rev. Lett.96, 035005 (2006) • - hold forshort 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…

  30. 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

  31. Experimental Results (Fuchs J.) In following tables there are predictions using (1) nominal pulse energy in φ* scaling law or (2) effective pulse energy:

  32. Comparison between experimental point and UR model predictions (1)

  33. Comparison between experimental point and UR model predictions (2)

  34. Expected results from UR model (scaling law for φ* with NOMINAL pulse energy)

  35. Comparison theoretical vs. experimental results (scaling law for φ* with NOMINAL pulse energy) 2.3 6.9 11

  36. Expected results from UR model (scaling law for φ* with EFFECTIVE pulse energy)

  37. Comparison theoretical vs. experimental results (scaling law for φ* with EFFECTIVE pulse energy) 2.3 6.9 11

  38. From Ph. Martin’s talk…. Linear scaling law Next decade ? BWD H+ Wanna get 100 MeV ? Just build up a 1PW laser (but clean !) theory

  39. 1T trapped electron model – 7Comparison with experimental data Proton spectra with different laser parameters - model [M. Nishiuchi, et al., Phys. Lett. A, 357, 339 (2006)] [R.A. Snavely, et al., Phys. Rev. Lett., 85, 2945 (2000)]

  40. 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. A357, 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

  41. Further theoretical references… …not exaustive list… “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. Plasmas15, 082702 (2008) V. F. Kovalev, et al., JETP,95, 226 (2002) S. Betti, et al., Pl. Phys. Contr. Fus. 47, 521 (2005)

  42. 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 andcontrol 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

  43. 1T trapped electron model – 7Comparison with experimental data Proton spectra with different laser parameters - model [M. Nishiuchi, et al., Phys. Lett. A, 357, 339 (2006)] [P. McKenna, et al., Phys. Rev. E, 70, 036405 (2004)] [R.A. Snavely, et al., Phys. Rev. Lett., 85, 2945 (2000)] M. Passoni, M. Lontano, Phys. Rev, Lett., 101, 115001 (2008)

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