Numerical investigation of protonacceleration using ALaDyn code

P. Londrillo∗∗

∗∗ INAF and INFN, Sezione Bologna

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Bologna activity

Computational and theoretical modeling:G. Turchetti, S. Sinigardi, F. Rossi (Phys. Dep. Unibo), P. Londrillo (INAF), A. Sgattoni(FIRB).

Collaborations:M. Sumini (Unibo), P. Dattoli (ENEA), P. Bolton (JAEA-Kyoto), S. Bulanov(JAEJA-Kyoto), C. De Martinis (INFN-MI), D. Giove (INFN-MI)

Partecipation in the LILIA project (LNF-INFN);

Computational Activity :The Aladyn and Jasmine codes.

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A short overview of acceleration physical regimes

The absorption of laser energy-momentum by plasma electrons is based on twodistinct mechanisms:(i) A direct heating following the field induced quiver velocity (fast time scale, dominantin linear polarized pulses), scaling with the adimensional vector potentiala0 = Ae/mc2 i.e. (I)1/2.(ii) A energy-momentum transfer by the ponderomotive force (the radiation pressureforce component), scaling as a2

0. This component can dominate even at lower

intensities for circular polarized (CP) pulses (Macchi et al. 2005).

For laser pulses interacting with solid thin solid targets, the first mechanism (enforcedby the second, at higher intensities), one has the TNSA classical regime.

For higher intensity for LP laser or at any intensity for CP laser and sufficiently thintargets, the RPA dominated regime comes in.Based on 1D models, this regime is the most efficient and can provide mono-energeticproton energy spectra. However, in multi-dimensional case, it is prone to instabilitiesand many nice properties can be lost.To date, no experimental result is available with clear identification of a ’pure’ RPAregime.

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For thick target new physical regimes come into play (hole-boring, shock waves,solitons). These regimes are no yet well understood, but recent experiments with CO2

laser pulse opened renewed interest.

For very thick plasma targets at near-critical densities (NCD), induced relativistictransparency leads to a complete absorption of the laser energy (channeling).

–Notes on computational issues.–Our objectives.

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Numerical results in 2D-TNSA scaling laws

In the study of TNSA regime, the main ordering parameters are expected to be:(i) the laser intensity I (or Power P ),(ii) the target structure expressed in terms of the areal density σ = (ne/nc)(L/λ).In the work (Esirkepov et al, PRL 96, (2006)), a first systematic numerical investigation hasbeen performed to select optimal target design for efficient proton acceleration. Optimalparameters are:(i) Pulse length Lp of the order of the laser spot diameter D,and(ii) σopt = 3 + 0.4(I/I1)1/2, I1 = 1.3 ∗ 1018W/cm2

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Numerical investigations of 3D TNSA regimes

No systematic investigations have been performed in 3D. We started a numerical studylooking to more restricted objectives:

Laser pulses in the low-medium power range P (TW ) ∈ [50, 250], where a scaling with√P is expected;

Double layer in the micron range, with attached near-critical material (a silicon foam).The presence of a foam layer, as suggested by Nakamoura et al.Phys.Pl. 2010, helps protonacceleration.A parametric 2D numerical study have been performed by Sgattoni et al.,in preparation

(2011).

By taking as reference the laser-target model parameters considered in 2D case, wehave extended the configuration to 3D, on the expectation that some scaling between2D and 3D can provide a useful guide for a more extended 3D study.

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3D TNSA

The basic reference model contains:

A linear polarized pulse with fixed length τ = 25fs and waist w = 3µm. Intensity is inthe range I(W/cm2) ∈ [1020, 1021], corresponding to the adimensional vectorpotential a0 ∈ [10− 30].

The target has a three-layer structure:- a foam with near critical density n/nc = 2,

- a high−Z ’solid’ material with density n/nc = 40 and a hydrogen coat with n/nc = 9

where λ2nc ≃ 1021/cm3.

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3D-TNSA

The electrons and protons distribution on the (x, y) plane. Model parametersa0 = 30, I = 1.8 ∗ 1021W/cm2, Lt = 0.5µm, Lfoam = 2µm

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3D TNSA

The time story of the proton max energy, at a fixed laser intensitya0 = 10, I = 2 ∗ 1020W/cm2, for different foam thickness.

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The proton 3D energy spectra

The proton energy spectrum at the intensity I = 8. ∗ 1020W/cm2, with Emax = 31mev

(left), and at the intensity I = 1.8. ∗ 1021W/cm2, with Emax = 58mev (right).

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Scaling laws of 3D-TNSA

The 3D scaling of max and average proton energy with the laser intensit intensity (left),compared with the equivalent 2D scaling (right).

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Channeling in near-critical plasmas

A laser pulse propagating in an overdense plasma n/nc = 1− 3 with intensity parametera >> 1, experiences the relativistic induced transparency and is totally absorbed by theplasma particles in a length Lch ≃ Lp.Experiments : Willingale et al.,PRL 2006, Yogo et al.,Phys.Rev. 2008, Fukuda et al.,PRL 2009

Modeling : S. Bulanov et al., Phys.Pl. 2010, Nakamura et al. et, PRL 2011

The electron and proton density on the (x, y) plane during the channel formation.

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The accelerating mechanisms

During the channel formation, only a part 50%− 70% of the laser energy goes to particles.The remaining part is used to form a quasi-static vortex-like magnetic field.

The azimuthal magnetic field Bφ on the orthogonal (y, z) plane, at two different positions(x = 45µ, and x = 52µ) on the channel exit.

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(left): the exiting electrons produce a TNSA-like regime.(right) an inductive Ex > 0 field is produced by the B field: expanding on the (y, z) plane:∂tEx = ∂yBz − ∂zBy

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NCD: the accelerated proton beam

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NCD: the proton beam spectrum

Left : the energy spectrum for case P = 150TW, n/nc = 1, giving a maximum protonenergy Emax ≃ 70mev and average energy < E >≃ 10mev

Right : the energy spectrum for case P = 198TW, n/nc = 2, giving a maximum protonenergy Emax ≃ 90mev and average energy < E >≃ 12mev

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NCD: scaling relations

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