Di Lucchio, Laura

Gibbon, Paul

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ELECTRON EMISSION IN RELATIVISTIC LASER-DROPLETINTERACTIONSL. Di Lucchio, P. GibbonForschungzentrum Jülich GmbH, Institute for Advanced Simulation, Jülich SupercomputingCentre, D-52425 Jülich, GermanyUltrashort electron bunches created by the interaction of high-intensity, femtosecond laserpulses with plasma targets can be utilised as a powerful source of attosecond X-ray pulses. Thelatter can be produced by bombarding a secondary target with such electron bunches and have animmediate application in X-ray microscopy and ultrafast atomic dynamics studies. Recently, thegeneration of efficient attosecond bunches production by laser-illuminated droplets has becomefeasible due to the availability of both ultraintense and ultrashort laser pulses and of stabilisednanometer-sized droplet targetry at a number of laboratories.Figure 1: 3D electron density plot ofa 100nm size droplet illuminated bya 2-cycle pulse at I=1020W/cm2. Thebunches are represented by the coun-toured regions.In this work we analyze in detail the mechanism ofefficient generation of ultrashort dense electron bunchesfrom the surface of a small droplet illuminated by a two-cycle (fwhm = 5 fs) ultraintense Gaussian laser pulse. Incontrast to previous work in Ref.[1], our spherical nan-otargets have a solid-like density of n = 100nc , wherenc = 1.8×1021cm−3 is the critical density. Clusters with arange of sizes have been considered, starting with a muchsmaller radius than the laser focus, namely of 100-200nm, comparing their dynamics with clusters up to a 1 mi-cron radius, that is, a size comparable to the focus. Theintensity of the laser was varied between 1017− 1021 Wcm−2 to determine scaling behaviourfor the emitted particles’ energies and emission angles. Our simulations have been performedwith the particle-in-cell code EPOCH. The simulation box size was varied between 4 and 20µm,while the cell size was maintained at ≈ 8nm. The number of simulation particles was 34×106ions and electrons.A number of 3D simulations were made to test the dynamics of the electrons at early times.The bunches are emitted as every half-cycle of the laser pulse strikes the droplet, as foreseenin Ref.[1]. For smaller droplets, i.e. 100 nm size, the emitted bunches form narrow opticallyoverdense regions travelling together with the pulse at the rear side of the cluster, and tendto place themselves on the same plane as the incident wave already a few femtoseconds after41st EPS Conference on Plasma Physics P2.100Figure 2: 2D plot of electron density plots superimposed with laser energy density, just before, duringand soon after the interaction for a 100nm size droplet illuminated by a 2-cycle pulse at I=1020W/cm2the interaction (fig. 1). However, contrary to Ref. [1] at relativistic laser intensities, simulationresults do not agree with Mie scattering patterns for droplets whose radius is lower than λ/2.For such droplets, the inclination of the bunches appears to be deviated as soon as they leavethe surface, with an angle which depends on the size of the droplet and the intensity of thelaser. Since 3D simulations at such a high density as 100nc are computationally expensive, wehave performed 2D simulations in the plane of the electromagnetic wave where the most of thedynamics at later times ( ≈ 100− 200 fs) effectively occurs. These simulations show that theelectron bunches – which in this case are overdense – continue to interact with the laser pulseafter the emission – Fig. 2.Figure 3: Enhancement of absolute radial electric field as a function of the incident electric field E0 fora 100 nc droplet with R =100nm (a), 200nm (b), 500nm (c) and 1micron(d) in an incident plane wave ofconstant amplitude and wavelength λ = 800nm as a function of time and angle on the surface.The Mie scattering patterns for small droplets are computed assuming a linear dielectricconstant in the plasma region and so cannot account for any intensity-dependant behaviour inthe bunch emission – see fig. 3. Moreover, Mie theory is based on the assumption that R >> δ ,where R is the droplet radius and δ = c/ωp is the plasma skin depth. This condition can be fullysatisfied for droplets whose size is comparable or bigger than the laser focus, and in this case afair agreement is found between simulation results and Mie scatterig predictions. By contrast,simulations for 100-200nm droplets show a strong deviation from Mie theory predictions –Fig.4 – suggesting that this condition needs to be modified to R ∼ δr, where δr = γ1/2δ is41st EPS Conference on Plasma Physics P2.100Figure 4: Electron emission angles as a func-tion of laser intensity and droplet size (red= 100nm, magenta= 200 nm, cyan= 300nm,green=500nm, violet=1µm), compared withmodels discussed in the text. Solid lines repre-sent simulation points, dashed horizontal linesthe Mie theory prediction. Black and blue linesrepresent predictions of Eq.1 and Eq.2 , respec-tively.the effective skin depth taking into account the induced transparency effect which occurs forrelativistic intensities. The effective plasma frequency is ωrp = ωp/γ1/2 and therefore for γ =√1+a20 ≈ 5− 20, we have δr ≈ 40− 60nm, which is of the same order as R for the smallerdroplets. In this case it makes more sense to apply a relativistic interaction model such as theponderomotive scattering of electrons by an intense field at laser focus[3].The scattering angle of a single electron in the laser focus in vacuum is given byθ0 = arctan√21+β0(γγ0 −1)γ− γ0(1−β0) , (1)where γ0 and β0 are the initial energy and normalised transverse momentum of the particle,respectively. For an electron initially at the rest on the droplet surface, γ0 = 1 and β0 = 1, inwhich case Eq.1 reduces to θ0 = arctan√2/(γ−1), as displayed by the black curve in Fig.4.As soon as the bunches leave the droplet they are exposed to the field of the scattered laserpulse, in a similar manner to electrons driven by a short laser pulse reflected from a finite-sizedplane target, as described in Ref. ([4]). In the case of small droplets with R < λ/2 most ofthe pulse is actually transmitted, so that the highest field gradients are in the rear side vacuumregion, where also most of the electrons are expelled. The electron bunches have high (nb > ncr),implying that they will still be subject to ponderomotive while sitting between phases of thelaser field. During the co-propagation with the laser pulse they lose part of their longitudinalmomentum and of their density, thus lowering their inclination.In Ref[4] this effect is related to the characteristic parameters of the bunches, namely thenumber of particles Nb they contain and their longitudinal thickness db. As long as the elec-trons kinetic energy overcomes the electrostatic potential energy of the bunch (Coulomb barrierthreshold) , that is, Nbεe > e2N2b/db , the normal component of the momentum is progressively41st EPS Conference on Plasma Physics P2.100reduced by an amount corresponding to the space-charge force contribution from the ionizeddroplet. For a 100nm droplet and a laser intensity I = 1019 Wcm−2 one can estimate Nb ≈ 108and db ≈ 100nm (corresponding to a duration of 300 attoseconds) from the simulations, andthe corresponding threshold energy of 1.4 MeV is easily overcome. Defining p⊥ = py sinθ andp‖ = px sinθ as the components of the momentum along the perpendicular and tangential direc-tions with respect to the droplet surface (see Fig. 5), these are modified by the space charge viathe relations: p′⊥ ≈ p⊥−e2Nbm/cdm; p′⊥ = p′y sinθ ′; p′‖ = p′x sinθ ′ = p‖, giving a final emissionangle varies according to θ ′ = arctan(py′/px′).Figure 5: Geometry of bunch deflection due tospace chargeIn conclusion, droplets with R< λ/2 emit elec-tron bunches at angles differing significantly fromvalues expected from linear Mie theory, follow-ing instead trajectories which deflect towards thelaser axis in the relativistic regime through a com-bination of ponderomotive scattering and space-charge deflection after emission. This transitionfrom the Mie-scattering-dominated and the rela-tivistic nanodroplet regime is fully summarized inFig. 4.AcknowledgementsThe authors acknowledge computing resources under grant VSR-JZAM04 and thank Dr. HZilken and the visualization team of the Jülich Supercomputing Centre, for assistance with therendering for the 3D simulations.References[1] T.V. Liseykina, S.Pirner, D.Bauer, Relativistic Attosecond Bunches from Laser-IlluminatedDroplets, PRL 22, 2010.[2] P.W.Barber, S.C.Hill, Light Scattering by Particles:Computational Methods, World Scientific, Sin-gapore, 1990.[3] F.V.Hartemann et al, Nonlinear ponderomotive scattering of relativistic electrons by an intenselaser field at focus, Phys. Rev. E, 1995.[4] A.A.Andreev, K.Y.Platonov, Generation of electron nanobunches and short-wavelength radiationupon reflection of a relativistic intensity laser pulse from a finite-size target, Optics and Spec-troscopy, 2013, Springer41st EPS Conference on Plasma Physics P2.100

Electron emission in relativistic laser-droplet interactions

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Electron emission in relativistic laser-droplet interactions

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