TNSA laser driven ion acceleration Claudio Perego 21/09/2018 TNSA laser driven ion acceleration Theoretical modeling and analytical predictions Claudio Perego Dottorato in Fisica ed Astronomia: Seminario conclusivo 2° Anno Dipartimento di Fisica Università degli Studi Milano-Bicocca 25 Ottobre 2011 TNSA Laser Driven Ion Acceleration

Outline Introduction to TNSA Analytical Modeling Claudio Perego 21/09/2018 Outline Target Normal Sheath Acceleration Effective Modeling Introduction to TNSA Analytical Modeling Different Descriptions Passoni-Lontano Model New Insights Target Thickness Dependence Experiments Mass-limited targets Conclusions and Perspectives Intro – Parte generale sulla modellizzazione – Parte più specifica sullo spessore Target Normal Sheath Acceleration Effective Modeling

Outline Introduction to TNSA Analytical Modeling Claudio Perego 21/09/2018 Outline Target Normal Sheath Acceleration Effective Modeling Introduction to TNSA Analytical Modeling Different Descriptions Passoni-Lontano Model New Insights Target Thickness Dependence Experiments Mass-limited targets Conclusions and Perspectives Target Normal Sheath Acceleration Effective Modeling

Multi-MeV ion beams normal to the target surface Claudio Perego 21/09/2018 Introduction Target Normal Sheath Acceleration Effective Modeling Ultra-intense & Ultra-short Laser Pulse Focused on a thin solid target Conductor or insulator Multi-MeV ion beams normal to the target surface E.L. Clark et al., Phys. Rev. Lett. 84 (2000) A. Maksimchuk et al., Phys. Rev. Lett. 84 (2000) R. A. Snavely et al. Phys. Rev. Lett. 85 (2000) Ion Beam Features Normal direction Exponential spectrum with Multi-MeV cut-off High ion-per-bunch number > 1012 Low longitudinal (< 10-4 eVs) and transverse emittance (< 10-8 mrad) Low divergence < 15° Target Normal Sheath Acceleration Effective Modeling

Foreseen Applications Claudio Perego 21/09/2018 Foreseen Applications Target Normal Sheath Acceleration Effective Modeling L.Romagnani, et al. Phys. Rev. Lett. 95 (2005) Proton radiography Hadron-therapy Fast ignition PET isotopes … We need to control the beam parameters t S. V. Bulanov, et al. Phys. Lett. A 299 (2002) Target Need for Theoretical modeling M.Roth, et al. Phys. Rev. Lett. 86 (2001) Target Normal Sheath Acceleration Effective Modeling

Ions from target surface and substrate are accelerated up to MeV Claudio Perego 21/09/2018 Target Normal Sheath Acceleration (TNSA) Target Normal Sheath Acceleration Effective Modeling S.C. Wilks et al. Phys. Plasmas. 8 (2001) Front (Vacuum) Target Rear (Vacuum) Hot e- current Return current Accelerated Ions e- sheath - + Accelerated Ions + - Laser Pulse Espansione elettroni Nuvole elettroniche, separazione di carica, campi elettrici Accelerazione ioni 1)Faccia avanti e dietro 2)Protoni da strato di impurità + ioni Ions from target surface and substrate are accelerated up to MeV Target Normal Sheath Acceleration Effective Modeling

TNSA Theoretical Modeling Claudio Perego 21/09/2018 TNSA Theoretical Modeling Target Normal Sheath Acceleration Effective Modeling 9/21/2018 We need a reliable theoretical description of: Laser-Matter Interaction Hot Electrons Transport Ion Acceleration Target 2 possible ways: - + + - Numerical Simulation of Vlasov System Quite complete description of the physics Very high computational load, hardly feasible with a set of realistic parameters Simplified Models Analytical or semi-analytical solutions Prediction of Scaling Laws Lack of detail in the description of the system Target Normal Sheath Acceleration Effective Modeling

Outline Introduction to TNSA Analytical Modeling Claudio Perego 21/09/2018 Outline Target Normal Sheath Acceleration Effective Modeling Introduction to TNSA Analytical Modeling Different Descriptions Passoni-Lontano Model New Insights Target Thickness Dependence Experiments Mass-limited targets Conclusions and Perspectives Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 TNSA Models (I) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Among the TNSA models we can find some common features: The description is focused on the acceleration phase Laser-matter interaction and hot electron transport phases set up the initial conditions: Hot electron distribution, usually Maxwell-Boltzmann Hot electron temperature, usually ponderomotive scaling Assumption of planar symmetry: 1-dimensional description Target Normal Sheath Acceleration Effective Modeling

TNSA Models (II) Fluid Approach Quasi-static Approach Hybrid Models Claudio Perego 21/09/2018 TNSA Models (II) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Fluid Approach Target described as a fluid plasma The hot electron fast expansion drives the motion of the ion population J.E. Crow et al., J. Plasma Phys. 14 (1975) P. Mora, Phys. Rev. Lett. 90 (2003) P. Mora, Phys. Rev. E 72 (2005) T. Grysmayer et al. Phys. Rev. E. 77 (2008) Quasi-static Approach Bulk i+ Fixed Bulk Ions and thermal hot electrons Accelerated test Ions in a static electric field Only the first stages of the process described Anticipo già che i modelli tendono a descrivere solo la fase di accelerazione. Le fasi antecedenti sono tenute in considerazione dalle ipotesi del modello (distribuzione e temperatura elettroni caldi) + Hot e- cloud + + + M. Passoni & M. Lontano, Laser & Part. Beams, 22 (2004) M. Lontano & M. Passoni, Phys. Plasmas, 13 (2006) J. Schreiber et al., Phys. Rev. Lett 97 (2006) Hybrid Models A.P.L. Robinson et al., Phys. Rev. Lett. 96 (2006) B.J. Albright et al., Phys. Rev. Lett. 97 (2006) TNSA Laser Driven Ion Acceleration

Models Compared Remarks: Input Parameters Claudio Perego 21/09/2018 Models Compared Target Normal Sheath Acceleration Effective Modeling 9/21/2018 A database of experimental measurements of the peak ion energy have been compared to the theoretical predictions provided by six different models C. Perego et Al., Nucl. Instr. & Methods A, 653 (2011) Remarks: Mora Isothermal Mora Adiabatic Schreiber Input Parameters Some are provided by the experimental papers Some others cannot be measured and need to be estimated Results depending on the arbitrary choice of the estimates Passoni-Lontano Albright Scaling Robinson Interaction and Transport Phases No complete or reliable modeling of such physical processes The models describe TNSA starting from simple assumptions Need to improve the connection to those two phases Experimental Theoretical Target Normal Sheath Acceleration Effective Modeling

Passoni-Lontano Quasi-Static Model Maximum Ion Energy Relativistic Claudio Perego 21/09/2018 Passoni-Lontano Quasi-Static Model Target Normal Sheath Acceleration Effective Modeling 9/21/2018 M. Lontano & M. Passoni, Phys. Plasmas, 13 (2006) M. Passoni & M. Lontano, Phys. Rev. Lett 101 (2008) M. Passoni et al., New J. Phys. 12 (2010) 1D, Ion fixed, static longitudinal field Sheath truncation Issue, divergent potential Solution of Poisson equation with bound electrons charge density Finite potential difference, analytical prediction for the peak energy Most energetic electrons lost by the system e- lost e- bound + + + + Relativistic Non-Relativistic Maximum Ion Energy Target Normal Sheath Acceleration Effective Modeling

Quasi-Static Model (II) Claudio Perego 21/09/2018 Passoni-Lontano Quasi-Static Model (II) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 QN Plasma Left Boundary Depends only on: The hot electron temperature The bounded electron maximum kinetic energy Estimates: Ponderomotive Scaling S.C. Wilks et al. Phys. Rev. Lett 69 (1992) Empirical Scaling M. Passoni et al., Phys. Rev. Lett 101 (2008) Concludo dicendo che cerchiamo quindi di aggiungere dettaglio alla parte iniziale del processo We need further detail in the description of laser-matter interaction and hot electron transport phases Target Normal Sheath Acceleration Effective Modeling

A constraint at the left boundary of Poisson equation is provided Claudio Perego 21/09/2018 Further Hypotesis Target Normal Sheath Acceleration Effective Modeling 9/21/2018 1-Laser-Matter Interaction The laser energy is partially absorbed and distributed among the hot electrons QN Plasma 2-Electron Transport The hot electron population expand through the target reaching the quasi-static equilibrium 3-Ion Acceleration A constraint at the left boundary of Poisson equation is provided A relation for is obtained: Target Normal Sheath Acceleration Effective Modeling

Theoretical Result Relativistic Result Observations: Claudio Perego 21/09/2018 Theoretical Result Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Relativistic Result Observations: Physical support to the behavior . A connection to key parameters is provided . The modeling of such parameters could open some interesting paths The normalization is still unknown, the system is not closed yet, we need to use the empirical scaling for . Target Normal Sheath Acceleration Effective Modeling

Partial Conclusions: TNSA Modeling has been presented and investigated Claudio Perego 21/09/2018 Partial Conclusions: Target Normal Sheath Acceleration Effective Modeling 9/21/2018 TNSA Modeling has been presented and investigated Theoretical models quantitative comparison: The Passoni-Lontano quasi-static model turns out to be a convenient scheme to predict the peak energy Limited knowledge on interaction and transport phases Passoni-Lontano quasi-static description Introduction of further details in the theoretical basis of the model New relation for the parameter , which connects the model to some key parameters of the system as . Modeling of such parameters can extend the model predicting capability Target Normal Sheath Acceleration Effective Modeling

Outline Introduction to TNSA Analytical Modeling Claudio Perego 21/09/2018 Outline Target Normal Sheath Acceleration Effective Modeling Introduction to TNSA Analytical Modeling Different Descriptions Passoni-Lontano Model New Insights Target Thickness Dependence Experiments Mass-limited targets Conclusions and Perspectives Target Normal Sheath Acceleration Effective Modeling

Target Thickness Energy Dependence Claudio Perego 21/09/2018 Target Thickness Energy Dependence Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Optimum thickness Targets thicker than the optimum Targets thinner than the optimum High contrast M. Kaluza et al. Phys. Rev. Lett. 93 (2004) I. Spencer et al. Phys. Rev. E 67 (2003) J. Fuchs et al. Nat. Phys. 48 (2006) D. Neely et al. Appl. Phys. Lett. 89 (2006) T. Ceccotti et al. Phys. Rev. Lett. 99 (2007) Target Normal Sheath Acceleration Effective Modeling

Transport model (I) The laser pulse heats up electrons Claudio Perego 21/09/2018 Transport model (I) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 The laser pulse heats up electrons The electrons expand through the target with almost collisionless dynamics The divergence of the hot electron beams has been studied experimentally Estimating the volume occupied by the hot electrons we can evaluate the hot electron density at the accelerating surface Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 Transport model (II) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Due to the charge separation, the fast electron reflux back into the target while the quasi-static equilibrium is reached This affects the hot electron density at the accelerating sheath The minimum time required for the formation of the accelerating field is We assume that the electrons travel at speed , and that the rise time of the electro-static field is For thin targets ( ) the electron reflux is more effective Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 Transport model (III) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 In an infinite target the electrons cover a longitudinal distance during the field formation We evaluate the density of hot electrons for the infinite target In the real target the volume is longitudinally shrinked and the actual density is multiplied by the factor The description can be strongly refined Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 Results (I) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 It is now possible to predict the thickness dependence with the quasi-static model We obtained the hot electron density at the sheath as a function of divergence angle and target thickness depends on and via the equation (relativistic) Now we can evaluate and compare it to the experimental measurements The normalization is still unknown. We need to evaluate it imposing that the scaling holds for some thickness Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 Results (II) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 J. Fuchs et al. Nat. Phys. 48 (2006) The agreement with the experimental measurements is remarkable in some cases may depend on the reflux dynamics The normalization issue should be solved to perform more reliable comparisons T. Ceccotti et al. Phys. Rev. Lett. 99 (2007) M. Kaluza et al. Phys. Rev. Lett. 93 (2004) Electron Divergence 15° 30° 45° Target Normal Sheath Acceleration Effective Modeling

The physical description can be improved in many ways … Claudio Perego 21/09/2018 Results (III) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 D. Neely et al. Appl. Phys. Lett. 89 (2006) In other cases the agreement is not satisfactory The electron divergence angle doesn’t affect heavily the dependence No domain of applicability is pointed out from the comparisons LOA Experimental Campaign April-June 2011 Electron Divergence 15° 30° 45° The physical description can be improved in many ways … Target Normal Sheath Acceleration Effective Modeling

Possible Improvements Claudio Perego 21/09/2018 Possible Improvements Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Collisional and radiative effects can influence the hot electron distribution even at such short timescales. Collisional and radiative stopping power Target material information The hot electrons density profile can be modeled in longitudinal and transverse direction Gaussian or Breit-Wigner transverse profile Exponential attenuation in the longitudinal direction The refluxing electrons may be re-heated up by the laser …Other key aspects of the hot electron dynamics cannot be described in a straightforward way (instabilities, magnetic effects…) Target Normal Sheath Acceleration Effective Modeling

Rear Face Thermal Emission Claudio Perego 21/09/2018 Mass-Limited Targets Target Normal Sheath Acceleration Effective Modeling 9/21/2018 It has been shown that using mass-limited targets the acceleration can be more effective Maximum proton energy and conversion as well as the hot electron temperature increase reducing the surface area of the target This can be the effect of transverse reflux of the electrons at the target boundaries S. Bouffechoux et Al., Phys. Rev. Lett, 105 (2010) Rear Face Thermal Emission Target Normal Sheath Acceleration Effective Modeling

Claudio Perego 21/09/2018 Lateral Reflux model Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Hot electrons are confined by the target lateral surface The hot electron density is amplified by a factor Measurements show a temperature increase which should be taken into account Target Normal Sheath Acceleration Effective Modeling

Outline Introduction to TNSA Analytical Modeling Claudio Perego 21/09/2018 Outline Target Normal Sheath Acceleration Effective Modeling Introduction to TNSA Analytical Modeling Different Descriptions Passoni-Lontano Model New Insights Target Thickness Dependence Experiments Mass-limited targets Conclusions and Perspectives Target Normal Sheath Acceleration Effective Modeling

Conclusions A simple hot electron transport model has been proposed Claudio Perego 21/09/2018 Conclusions Target Normal Sheath Acceleration Effective Modeling 9/21/2018 A simple hot electron transport model has been proposed Informations about target thickness and electrons divergence are implemented in Passoni-Lontano predictions The experimental results are partially reproduced Mass-limited targets can improve TNSA acceleration Our model for the electron transport can explain such an effect The measured energy increase is greater than our predictions The description needs to be improved Further physical details can be implemented while some aspects of the dynamics require numerical studies A consistent way to close the system is still needed The laser-matter interaction modeling is neither precise nor reliable Target Normal Sheath Acceleration Effective Modeling

Perspectives Analytical Work Numerical and Experimental Work Claudio Perego 21/09/2018 Perspectives Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Analytical Work Hot electrons stopping power effects and density profiling implementation Laser-matter interaction description Stable and reliable initial conditions 3D solution of the electrostatic problem (Poisson-Boltzmann theory) Consistent closure of the system Numerical and Experimental Work Parametric studies to understand the dependencies New scaling laws for the initial conditions Weight of instabilities and magnetic effects Validation of the Analytical results Target Normal Sheath Acceleration Effective Modeling

Thank You!!! The End Claudio Perego 21/09/2018 Target Normal Sheath Acceleration Effective Modeling 21/09/2018 Thank You!!! Target Normal Sheath Acceleration Effective Modeling

LOA Experiment (II) Pre-Heating Results Pump Energy: Claudio Perego 21/09/2018 LOA Experiment (II) Target Normal Sheath Acceleration Effective Modeling 9/21/2018 Pre-Heating Results Pump Energy: Pre-heating Beam Energy: Pre-heating Beam Intensity: Al targets different thicknesses: s The results for different thicknesses show a similar behavior Energy drop up to 100-150 ps delay Slight increase for higher delays Strong instability with preheating …Simulation being performed Target Normal Sheath Acceleration Effective Modeling