Modulation of Harmonic Emission Spectra from Intense Laser-Plasma Interactions

Transcription

1 Modulation of Haronic Eission Spectra fro Intense Laser-Plasa Interactions T.J.M. Boyd and R. Ondarza-Rovira 2 Centre for Physics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, U.K. 2 ININ, A.P , México 80, D.F., Mexico Abstract. We report results fro a series of PIC siulations carried out to investigate the interaction of intense laser light with overdense plasa and in particular, aspects of the haronic eission spectru generated in these interactions. Recent observations of eission in this range by Watts et al. [] show eission above the 20th haronic extending to the 37th with conversion efficiencies of order 0 6 with this spectru showing distinct, if variable, odulation of between two and four haronics. This spectral feature proved highly sensitive to the incident intensity, with ore pronounced odulation at higher intensities. These authors also reported results fro a set of odel PIC siulations which showed a odulated eission spectru across the entire haronic range, but with a wider odulation bandwidth. In the results to be presented we report on features of the eission spectru across a wide paraeter range and its dependence on the detailed structure of the plasa density profile. While we do see evidence of a odulated spectru, this appears to be sensitive not only to the incident intensity but to the plasa density profile. In addition plasa eission present further coplicates the haronic eission spectru. Our results lead us to conclude that attepts to interpret odulation in eission spectra in ters of one particular theoretical odel and fro this to infer the dynaics of the critical surface ay be isguided. I. INTRODUCTION The interaction of high power laser pulses with ultradense plasa has proved a rich source of new plasa phenoena as varied as channel foration and the generation of intenselocalized agnetic fields. One of the earliest laser-plasa interactions to be studied in detail - and one of enduring interest - is the generation of ultiple haronics of the incident light. Different echaniss for haronic generation apply across differing intensity ranges and target characteristics but perhaps ost attention now attaches to haronic production by short intense laser pulses incident on solid targets. Short pulses without significant pre-pulse create target plasas free fro extensive underdense coronal regions.

2 Haronic generation is not only of intrinsic interest but holds proise as a diagnostic of plasa conditions in the surface interaction region and, potentially of other physical processes localized there. As well as targets of dense slab plasas the other deterinant for efficient haronic production is the brightness of the source. For light of intensity I and wavelength λ L, values of I λ 2 L in the range W c 2 µ 2 typically generate a haronic range of 50 haronics and Norreys et al. [2] detected haronics up to the 75th (with conversion efficiency of 0 6 ) for.053 µ wavelength light interacting with a solid target. Such a haronic range holds potential as a source of coherent XUV radiation. The haronics in the spectru of reflected light are generated by electrons accelerated across the vacuu-solid interface by the electric field of the pulse. The spectral characteristics of the reflected light are broadly understood. Conditions favouring optial haronic generation include intensities in the range W c 2 µ 2 with plasa densities of a few tens n c, where n c denotes the critical density. Typically this cobination of intensity and target plasa density gives rise to a spectru of 50 or ore haronics with a conversion efficiency of 0 6. An iportant transition takes place at an intensity threshold below which plasa expansion occurs thus creating a region of underdense plasa and above which channel boring and ponderootive steepening are doinant. Particle-in-Cell (PIC) siulations have been invaluable in understanding and characterizing this haronic eission. Gibbon [3] used this approach to good effect in identifying the physical echanis underlying haronic generation, attributing it to those electrons that ake vacuu excursions and then free-strea back into the target plasa. Gibbon s work showed that the current sources generating the haronics are localized just within the overdense plasa boundary. These siulations led to an epirical expression for the efficiency of highorder haronic generation η 9 0 5( I 8 λ 2 L) 2 (0/) 5 where I 8 denotes light intensity in units of 0 8 W c 2. In the work presented here we use a PIC code to further interpret aspects of the reflected light spectru and to extend these siulations over a wider range of paraeters. Boyd and Ondarza [4,5] exained in detail the effects of plasa line eission on the haronic spectru. Strong plasa eission was recorded, with haronics up to the fifth detected in both the reflected and transitted spectra. A robust feature of the reflected spectra appeared on the blue side of the plasa line between (.2-.6) ω p, where ω p is the plasa frequency. In this work jets of electrons of relativistic energy penetrating the ultra-dense plasa generated strongly nontheral Languir waves. The spectru of Languir waves was localized at the front edge of the plasa slab. This localization is iportant for the subsequent coupling of the plasa waves to the radiation field by eans of the steep density gradient in the (perturbed) peak density region. Fig. reproduces the spectru obtained by Boyd and Ondarza [5] showing the reflected haronic spectru and the plasa line for n e /n c = 30 and a 0 = 0.5. In this case the feature between ω p and 2ω p shows up as enhanced haronic lines between 8ω L and 2ω L, in contrast to the broad less well-resolved feature recorded for other choices of paraeters. We were propted to re-exaine the plasa line effects on the spectru by results reported 2

3 e-05 e Figure : Reflected haronic spectru for n e /n c = 30 and a 0 = 0.5. by Watts et al. []. In this work using light intensities up to W c 2 incident on a solid surface, haronics up to the 37th were recorded with a conversion efficiency 0 7. The striking feature of the spectra at the highest intensity is a distinct if irregular odulation with a frequency between 2 and 4 ties that of the incident light (Fig. 2). Watts et al. found that although odulations peak at different haronics they were observable across the entire spectral range although their published spectra show only a part of this range, and that at relatively low conversion efficiencies. Figure 2: Modulation of haronic spectra, for a laser-dense plasa interaction, I λ 2 L 09 W c 2 µ 2, fro Watts et al. []. The corresponding spectru at Iλ 2 L 08 W c 2 µ 2 in contrast shows only weak odulation. In conjunction with these observations they siulated the eission spectru for conditions approxiating those in the experient apart fro their choice of thickness of the siulated plasa which was only one wavelength across. In addition they used a pulse with a sine-squared teporal profile. The siulated spectra showed a clear odulation with an 3

4 aplitude that increased with laser intensity. In contrast to previous work using the sae code where odulations were attributed to internal reflections of transitted light within the plasa box (Lichters et al. [6]), Watts et al. suggest that the odulation structure is intrinsic to haronic generation. For a plasa one wavelength thick and with density n e = 3n c they record odulations at between 4 and 5 haronics for Iλ 2 L 09 W c 2 µ 2 across a spectral range of = 40 whereas for Iλ 2 L 08 W c 2 µ 2 this range contracts to about = 7, too liited to discern odulation even if it were present. These authors undertook a correlation of the odulated spectra with an exaination of the dynaics of the critical surface, showing that surface odes excited by nonlinearities could have relatively large aplitudes. For the higher intensity studied, it appeared that haronics at = 4,5 were doinant. Fro this they concluded that the oscillating-irror odel of haronic generation proposed by Bulanov et al. [7] was capable of interpreting the odulation observed. The spectra reported by Watts et al. and the inferences drawn by the propted us to look again at spectra fro our earlier siulations. The PIC code we use, like the Pfund-Lichters code used by Watts et al., ebeds the Bourdier technique to allow for oblique incidence but in contrast to theirs, our siulation plasa can be up to ten wavelengths in extent, with the plasa density raped at the front surface. Vacuu gaps extend fro both the front of the rap and the planar rear surface of the plasa to the walls of the siulation box. The initial electron teperature was chosen to be kev and we used a gaussian pulse of variable length. The noralized quiver velocity a ( I 8 λ 2 L) /2 lay in the range with slab densities between 4 n c and 64 n c. The ions fored a neutralizing background. Our attention focused on the effect of the plasa density on the odulated spectra. Given the wealth of detail in the spectra presented in ters of the dependence of the odulation on laser light intensity and pulse length as well as on the density and the density profile, it is perhaps worth highlighting at the start the principal finding fro our work e-05 e-07 e Figure 3: Haronic odulation for a 0 = 0.5,n e /n c = 0 and τ p = 7 fs. This is evident fro Fig. 3 in which a 0 = 0.5, n e /n c = 0 and the pulse length τ p = 7 fs. 4

5 The spectru shows clear and unifor odulation with an average odulation frequency of 3.3 ω L for a plasa with ω p = 3.2ω L. We contend that the spectru of reflected light shows haronic structure odulated at the Languir frequency. To support this interpretation we carried out siulations across a range of intensities and pulse lengths. In all of these we used a plasa slab 4 wavelengths thick without any density raping. Fig. 4 shows spectra for runs with a 0 = 0.6 and n e = 9n c and 9 n c respectively. 0. (a) 0. (b) e-05 e-05 e-07 e Figure 4: Haronic odulation for a 0 = 0.6, τ p = 7 fs, (a) n e /n c = 9 and (b) n e /n c = 9. These spectra are odulated at frequencies of 3.3 ω L and 4.4 ω L, consistent with the Languir frequencies for these densities. Note in passing that for this cobination of paraeters the level of plasa line eission is low enough for the haronic spectru to be relatively unperturbed. With increasing density the haronic range narrows correspondingly until a point where just one odulation cycle persists as in Fig. 5 for a 0 = 0.5,n e /n c = 64 with a pulse length of 7 fs. For this density the plasa line is centred on = 8 and we see the effects of the Languir wave spectru on neighbouring haronic lines, notably on the blue wing. Apart fro the strength of the plasa line, this spectru shows soewhat siilar structure to that in Fig.. It now appears that the detail in the spectru identified by Boyd and Ondarza [5] as the cobination line is nothing other than the aplification of individual haronic lines in the spectru by the nontheral Languir waves excited in the supra-dense plasa. If we wish to reproduce spectra showing several cycles of odulation at higher densities we need to generate eission spectra at higher a 0. However the cobination of higher intensity and increased plasa density results in the Languir wave being ore strongly driven and at the sae tie significantly broadened. Siple linear estiates of the bandwidth of Languir waves ω, excited by a bea of fast electrons give ω ( V b /v b )(n e /n c ) /2 ω L for a bea velocity v b with velocity spread V b. Our PIC siulations show strongly driven Languir waves at the front edge of the plasa slab and this localization is crucial for coupling to the radiation field by the steep gradients in the perturbed peak density zone (cf. Boyd and 5

6 0. (a) 0. (b) e-05 e-05 e-07 e-07 e e Figure 5: Haronic odulation for a 0 = 0.5,n e /n c = 64, (a) τ p = 7 fs and (b) τ p = 25 fs. Ondarza [5]). As the plasa eission line becoes ore strongly driven it odifies the haronic spectru in the region of the plasa frequency (cf. Fig. ). This in turn eans that one has to look for odulation cycles at frequencies well above ω p. As we have rearked already the nuber of haronic lines (above a conversion efficiency of 0 6, say) reduces with increasing density so that the spectral window available is squeezed fro both ends. Fig. 6 shows a ore strongly driven result (a 0 =.0) for densities n e = 25n c and n e = 50 n c. The plasa line is now evident and affects neighbouring haronic lines so that in Fig. 6a with ω p /ω L = 5 the first full odulation cycle appears at = 8. Three cycles with an average odulational frequency of 5.3 ω L can be resolved above a conversion level of 0 6. For n e = 50n c, ω p /ω L 7. and there are now just two cycles above this level with an average odulational frequency of 8 ω L. 0. (a) (b) 0.00 e-05 e e Figure 6: Haronic odulation for a 0 =.0, τ p = 7 fs, (a) n e /n c = 25 and (b) n e /n c = 50. At yet higher intensities (a 0 = 2.0) and densities n e = 64n c, plasa line eission is broader 6

7 again than in Fig. 6. The haronic spectru above a conversion level 0 6 now extends to approxiately = 60 (Fig. 7). However at this intensity not only is in the plasa line a strong feature but its second haronic is strong enough to perturb the line spectru. Consequently one can resolve only 3 odulation cycles with an average frequency of 8.7 ω L e-05 e Figure 7: Haronic odulation for a 0 = 2.0,τ p = 7 fs, and n e /n c = 64. In all the cases discussed thus far, the PIC siulation plasa has been in the for of a slab. We have also exained the effect on the odulation of a raped density profile to check the clai by Watts et al. that density raping served to suppress the effect. We too found a coparable decay in odulation as the thickness of the rap is increased. Fig. 8 shows our result for a 0 = 0.5, n e /n c = 0 for different thickness of rap ; (a) = 0.2λ L and (b) = 0.4λ L. Fro this it is evident that although soe odulation persists when a rap of thickness 0.2λ L is present, the effect disappeared copletely in Fig. 8b. (a) (b) e e Figure 8: Haronic odulation for a 0 = 0.5,τ p = 7 fs, n e /n c = 0, (a) = 0.2 λ L and (b) = 0.4 λ L. 7

8 II. CONCLUSIONS Our siulations lead us to conclude that the odulations we see in the haronic spectru ste fro the effect of Languir waves excited in the plasa slab. We have shown that the odulation frequency varies with the plasa density as n e /2 over a wide range. The odulation is evident for choices of intensity and pulse length for which plasa line eission does not distort the spectru to any arked degree. On this interpretation the odulation frequency affords a easure of plasa density as distinct fro the clai by Watts et al. of its potential as a diagnostic of the dynaics of the critical surface. The presence of a density rap a fraction of a wavelength thick appears to suppress the odulation as Watts et al. found. We see this as consistent with our interpretation in that the presence of a rap ensures that there is no longer a unique plasa density at the surface. Acknowledgents One of us (ROR) acknowledges support fro CONACyT under Contract No F. REFERENCES [] Watts I. et al., Phys. Rev. Lett. 88 (5), 5500 (2002). [2] Norreys P. A. et al., Phys. Rev. Lett. 76, 832 (996). [3] Gibbon P., Phys. Rev. Lett. 76, 50 (996). [4] Boyd T.J.M. and Ondarza-Rovira R., in Proceedings, International Conference on Plasa Physics, Nagoya, Septeber 996, edited by H. Sugai and T. Hayashi (Japan Society of Plasa Science in Nuclear Fusion Research, Nagoya, 997), Vol. 2, p. 78. [5] Boyd T.J.M. and Ondarza-Rovira R., Phys. Rev. Lett. 85 (7), 440 (2000). [6] Lichters R. et al., Phys. Plasas 3, 3425 (996). [7] Bulanov S. V. and Nauova N. M., Phys. Plasas, 745 (994). 8