Fernandez, J.C.

Focia, R.J.

Johnson, R.P.

Montgomery, D.S.

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PSFC/JA-01-17OBSERVATION OF MULTIPLE CASCADE STEPSOF THE LANGMUIR DECAY INSTABILITYIN A LASER PLASMAR. J. Focia,1 D. S. Montgomery,2J. C. Fernández,2 and R. P. Johnson21Plasma Science & Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USA2Los Alamos National LaboratoryLos Alamos, New Mexico 87545 USAJuly 2001This work was supported by the Los Alamos National LaboratoryContract No. E29060017-8F. Reproduction, translation,publication, use and disposal, in whole or part, by or for the UnitedStates Government is permitted.To appear in Physical Review Letters.1Observation of Multiple Cascade Steps of the Langmuir DecayInstability in a Laser PlasmaR.J. Focia, D.S. Montgomery1, J.C. Fernández1, and R.P. Johnson1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts021391Los Alamos National Laboratory, Los Alamos, New Mexico 87545Stimulated Raman scattering (SRS) can be non-linearly coupled to other parametric instabilities, suchas the Langmuir decay instability in which an electron plasma wave (EPW) decays into acounterpropagating EPW and a copropagating ion acoustic wave. This process can result in a cascade ofcounter and copropagating EPWs. We have unambigously observed this cascade using collective Thomsonscattering. For the conditions of the study we observed two cascade steps. The Thomson spectra is wellcorrelated with measurements of the backscattered SRS light as expected since SRS drives the process.PACS Codes: 52.35.Fp, 52.35.Mw, 52.70.KzPreprint - Submitted to the PRL 5/15/01Control of parametric laser-plasma interactions is essential to the success of inertialconfinement fusion (ICF) [1]. Stimulated Raman scattering (SRS) is one such interactioninvolving the resonant decay of an incident electromagnetic wave (EMW) into a scatteredEMW and an electron plasma (or Langmuir) wave (EPW). SRS is undesirable not onlybecause it can cause losses in drive energy and illumination symmetry but also because it cantrap and accelerate electrons that could preheat the fusion capsule. The onset and scaling ofSRS has been the subject of much investigation [2].In quasi-homogeneous ignition-relevant plasmas, the EPW amplitude can be largefor moderate SRS reflectivity so that saturation by nonlinear mechanisms is expected and2observed [3,4]. One possible source of non-linearity is coupling of SRS to other parametricprocesses via wave-wave interactions. One such mechanism is the Langmuir decay instability(LDI) [5], where the daughter EPW from SRS decays into an EPW and an ion acoustic wave(IAW). LDI occurs when the amplitude of the primary EPW exceeds a threshold that isproportional to the product of the damping rates for the secondary EPW and IAW. Thegrowth rate for LDI is maximized when the daughter EPW and IAW are propagatingantiparallel and parallel, respectively, to the primary EPW. Subsequent EPW decays due toLDI are possible if their amplitudes exceed the threshold. In this Letter we use theterminology that an EPW generated by LDI is called an LDI cascade step and, collectively,more than one cascade step is called LDI cascade. The LDI cascade can saturate SRS sincewave energy from the SRS EPW couples into secondary EPWs and IAWs that are non-resonant with the SRS process. The saturation effect is strongest when the daughter wavesare strongly damped. Backward propagating EPWs presumed to be from LDI have beenobserved [6] and LDI has been observed in ionospheric plasmas [7]. Observation ofLangmuir turbulence in a laser-produced plasma has been reported recently [8]. However, itcould not be established whether strong turbulence or weak LDI cascade was observed inthose experiments due to inhomogeneity [9].In this Letter, we present the first unambiguous observations of multiple LDIcascade steps driven by SRS backscatter. The experiment was conducted at the Los AlamosNational Laboratory (LANL) using the TRIDENT laser facility [10]. In the experiment, apreformed plasma is illuminated with a nearly diffraction-limited single hot spot (SHS) laser[11] to drive SRS in a plasma. The SHS laser focal spot is characterized by a speckle width ofFλ0≈2.5±0.15 µm and speckle length of 7F2λ0≈75µm, where λ0 is the laser wavelength (5273nm for the SHS interaction laser) and F is the focal ratio of the focusing optic. The plasmainitial conditions are homogeneous on the scale of the laser focal spot volume where theinteraction occurs, and enables the observation of fine spectral structure associated with LDIcascade. This removes any ambiguity due to inhomogeneity when interpreting the data. Theinitial conditions of these plasmas have been thoroughly characterized elsewhere [11]. Theconditions for our experiment were also monitored as described below. The EPW spectrumfrom SRS and LDI is measured using collective Thomson scattering, and structure isobserved in the spectra consistent with LDI cascade. Up to two LDI cascade steps areinferred from the measurements presented here.A schematic of the experimental setup is shown in Fig. 1. The plasma is formed byvaporizing a thin foil target and heating it with a line-focused λ=527 nm laser beam. Thisheater beam is defocused so as to create a plasma with density scale lengths transverse andparallel to the interaction laser focal spot of ~200 µm and ~1000 µm, respectively. Thus, theplasma is considered quasi-homogeneous over the interaction volume of the SHS. Thetargets used were ~1 mm in diameter and ~6.5 µm thick parylene (C8H8). The heater beamhas a flat-topped pulse profile with duration of 1.2 ns full-width at half maximum (FWHM).At a time 200 ps after the heater beam is turned off the interaction beam (λ=527 nm),having a Gaussian pulse width of 200±10 ps FWHM, is focused into the plasma through anf/4.4 lens perpendicular to the plasma flow (i.e. parallel to the original surface of the target).The location of the SHS was ~400 µm in front of the target, resulting in ne/nc≈3.1-3.2% asinferred from the backscattered SRS data shown later. Here, ne is the electron density and nc(≈4 x 1021 cm-3) is the critical density above which light does not propagate. The ultraviolet(λ=351 nm) Thomson probe beam is also a Gaussian pulse with a 200±10 ps FWHM,4coincident in time with the interaction beam, and is focused into the plasma through anf/4.5 lens. The Thomson scattered light is collected through the full aperture of thecollection optic (f/4). The Thomson scattering diagnostic was set up to look only at theforward propagating EPWs, i.e. those propagating in the same direction as the interactionlaser. Although we do not image the backward propagating EPWs their presence is inferredfrom the resultant Thomson spectrum.Thomson scattering is a resonant process that requires frequency, ω and wavevector, k& matching be satisfied [12]. Frequency and wave vector matching cannot beachieved with arbitrary probe and collection angles. To calculate the resonance points andthus the probe and collection angles required, we use the usual dispersion relation for an EMwave in a plasma and kinetic dispersion relations for EPWs and IAWs. The focal ratio of theprobe and collection optics allows for a finite range of wave vectors (and frequencies for thescattered light) to participate in the Thomson scattering. The Thomson probe was set up toinvestigate plasma densities near ne/nc≈3%. The probe beam was focussed into the plasmaat 50±6.3 degrees and the scattered light was collected at 63±7.1 degrees, which allowedprobing waves parallel to ko (the free space wave number of the SHS beam) from 1.34ko to1.76ko. We calculate that our diagnostic would allow resolution of the SRS EPW and up tothree subsequent forward-propagating LDI cascade steps. Half of the Thomson scatteredlight was sent to a time-resolved diagnostic that integrated over the scattered wave vectors,and the other half was sent to a diagnostic that resolved the wavelength versus angle on thecollection optic (effectively ω vs. k&) and was time-integrated over the duration of the probepulse. The latter was accomplished by imaging the optic plane of the collection lens, ratherthan its focal plane [13]. This diagnostic was useful for obtaining the dispersion properties of5the LDI cascades, and in understanding any structure observed in the time-resolved (wave-vector integrated) Thomson spectra.The backscattered SRS spectrum from a typical shot in a regime where LDI cascadewas observed is shown in Fig. 2. For our present discussion, λ represents the free spacewavelength of the measured scattered light, i.e. λ=2πc/ω, where c is the speed of light. Forthis shot the laser peak intensity was I≈1.92x1015 W/cm2 and the measured SRS reflectivitywas R≈3.2%. Thomson scattering from thermal levels of ion acoustic waves from similarshots indicated an initial electron temperature of Te≈350±50 eV, decreasing to ~230±50 eVover the duration of the probe pulse. The SRS spectrum starts at ~659 nm has an intensityweighted centroid of ~657 nm Using the measured SRS wavelengths and Te, we estimatekLλD≈0.27, where kL is the wavenumber of the SRS Langmuir wave, and λD is the electronDebye length.A rough estimate of the Langmuir wave density fluctuation can be obtained from theSRS reflectivity, and compared to estimates of the LDI threshold as a consistency check [4,14]. We calculate 2/122max ])//(4[)/( LknnkRnn oco∆=δ =0.021 is sufficient to exceed theLDI threshold of 2/12/1 )/()/(4)/( pLiaiaDLLDI vvknn ωωλδ = =0.018. In these equations Rmax isthe maximum reflectivity, ∆k is the actual spectral width of the SRS (i.e. the observedspectral width corrected for instrument resolution), n is the electron density, ko and nco arethe wave number and critical density of the incident beam, L is the interaction length,(νia/ωia) is the ratio of the IAW damping to its real frequency, and (νL/ωp) is the ratio of theLangmuir wave damping to the plasma frequency. The SRS spectrum clearly showscurvature towards shorter wavelengths over the duration of the laser pulse and there is an6abrupt change in the curvature at time t≈-10 ps. From the SRS spectrum we infer that theplasma density is ne/nc~0.032. The decrease in the SRS wavelength with time is accountedfor by the measured decrease in Te. For these conditions the expected separation betweenthe SRS EPW and the first forward propagating EPW from LDI cascade would be ~9.7±0.8Å.The time-resolved Thomson spectrum corresponding to the SRS spectrum in Fig. 2unambiguously shows the signature of LDI cascade (see Fig. 3a). A horizontal lineout of thisimage where the cascade separation is indicated is shown in Fig. 3b. From the SRS data andan ideal calculation (i.e. using linear theory and resonance matching) we would anticipate theSRS EPW to initially occur at a Thomson wavelength of ~405.1 nm and the observed data isin close agreement. The slight discrepancy in the Thomson wavelength for the SRS EPW(~0.5 nm) is within the uncertainties in the absolute calibration of the SRS and Thomsondiagnostic wavelength scales.  As indicated in Fig. 3b, the spacing between the SRS EPWand the second cascade is ~10.6 Å and is in excellent agreement with the ideal calculation.The curvature in the Thomson spectrum closely follows that in the SRS spectrum. Althoughthe time axes in Figs. 2 and 3a are not absolutely calibrated with each other, there is anabrupt change in the Thomson spectrum correlated with that in the SRS spectrum. The LDIdoes not start immediately with the SRS most likely due to being below threshold for theinteraction, or due to thermal detuning as indicated by the change in the SRS wavelengthwith time.The time-integrated Thomson spectrum corresponding to the SRS and time-resolvedThomson spectra shown in Figs. 2 and 3a, respectively, also shows the signature of LDIcascade (see Fig. 4). Two distinct waves are observed separated in both frequency (Thomson7wavelength) and wave vector (position on the collection optic). The initial spacing inwavelength (∆λ≈10.6 Å) and wave vector (∆k/ko≈-0.13) is consistent with the idealcalculation using the density estimated from the SRS spectrum and the early timemeasurement of Te. The other characteristics of the spectrum can be modeled using lineartheory and resonance matching by assuming a fixed density and a decreasing temperature.The finite focal ratio of the SHS focusing lens allows for a range of wave vectors andfrequencies to participate in the SRS interaction.  This will result in some fixed initial spreadin both ω and k of the SRS EPW. As time progresses Te and, to a lesser degree, ne/ncdecrease. The major effect is due to the reduction in the EPW dispersion as a result of thedecrease in electron temperature, i.e. thermal flattening. In an underdense plasma, thefrequency of the SHS laser and SRS EM waves are much greater than that of the SRS EPW.To satisfy resonance matching as Te decreases, the change in the SRS EPW wave numberwill be relatively small. For any subsequent EPWs generated by LDI, a small change infrequency will result in a large change in wave number. For example, assuming a decrease inTe of 100 eV (from 350 eV), the ideal calculation shows that the relative change in ∆λ and∆k/ko of the second LDI cascade to that of the SRS EPW are 0.94 and 7.1, respectively.Thus, the narrow ∆λ, broad ∆k/ko time-integrated spectrum is characteristic of an EPWgenerated by LDI combined with thermal flattening of the EPW dispersion and not someother source of EPWs. The actual change in ∆λ and ∆k/ko shown in Fig. 4 do not exactlymatch the ideal calculation most likely due to uncertainties in the actual Te in the SHS.However, the qualitative behavior is consistent with linear theory.Now that LDI cascade is established, a parameter study is necessary to understandthe scaling of the number of cascades with plasma parameters and the possible role of LDI8in limiting SRS. A wealth of data was generated from this experiment under various plasmaand laser conditions. Presentation of this data is outside the scope of this Letter and will bepresented elsewhere in a longer article.In summary, we have observed multiple LDI cascade steps from the decay of theEPW generated by SRS. The data presented in this Letter shows excellent agreementbetween the backscattered SRS, time-resolved Thomson, and time-integrated Thomsonspectra.The Authors are indebted to the TRIDENT operations staff in LANL Group P-24for their hard work, expertise, and dedication, which led to another successful round ofexperiments. We also thank the Target Fabrication in LANL Group MST-7 for supplyingthe targets used in the experiment. The lead author is grateful to Prof. A. Bers of MIT foruseful discussions and for his efforts in establishing the MIT/LANL research collaborationthat allowed participation in the SHS experiments. This work was supported by LANLContract E29060017-8F.[1] J. Lindl, Phys. Plasmas 2, 3933 (1995).[2] H.A. Baldis, E.M. Campbell, and W.L. Kruer, in Physics of Laser Plasma, Handbook ofPlasma Physics (North-Holland, Amsterdam, 1991), Vol. 3, Chap. 9.[3] J.C. Fernández et al., Phys. Rev. Lett. 77, p. 2702 (1996), Phys. Plasmas 4, p. 1849 (1997),and Phys. Plasmas 7, p. 3743 (2000).[4] R.K. Kirkwood et al., Phys. Rev. Lett. 77, p. 2706 (1996).9[5] D.F. DuBois and M.V. Goldman, Phys. Rev. Lett. 14, p. 544 (1965), and Phys. Rev. 164, p.207 (1967).[6] K.S. Baker et al., Phys. Rev. Lett. 77, p. 67 (1996), and Phys. Plasmas 4, p. 3012 (1997).[7] D.F. DuBois, et al., Phys. Plasmas 8, p. 791 (2001), and P.Y. Cheung et al., Phys. Plasmas 8,p. 802 (2001).[8] S. Depierreux et al., Phys. Rev. Lett. 84, p. 2869 (2000).[9] D.S. Montgomery, Phys. Rev. Lett. 86, p. 3686 (2000), and D. Pesme et al., Phys. Rev. Lett.86, p. 3687 (2000).[10] N.K. Moncur et al., App. Opt. 34, p. 4274 (1995).[11] D.S. Montgomery et al., Laser and Particle Beams 17, p. 349 (1999).[12] J. Sheffield, Plasma Scattering of Electromagnetic Radiation (Academic Press, NewYork, 1975).[13] D. M. Villeneuve et al., J. Opt. Soc. Am. B 8, 895 (1991) and D. M. Villeneuve et al.,Phys. Rev. Lett. 59, 1585 (1987).[14] S. J. Karttunen, Phys. Rev. A 23, 2006 (1981).10Figure 1.  Schematic diagram of the single hot spot experiment.11Figure 2.  The SRS spectrum observed on shot number 12805.  The normalizedfrequency scale ωES/ωo (ωo is the angular frequency of the SHS laser) shows the expectedelectrostatic wave frequency for a given wavelength.12(a)(b)Figure 3.  (a) Time-resolved Thomson spectrum from shot number 12805 showing theforward propagating EPW from SRS and the second LDI cascade.  (b) A horizontallineout taken where the cascade separation is indicated in (a).13Figure 4.  Time-integrated Thomson spectrum from shot number 12805 showing theforward propagating EPW from SRS and the second LDI cascade.

Observation of Multiple Cascade Steps of the Langmuir Decay Instability in a Laser Plasma

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Observation of Multiple Cascade Steps of the Langmuir Decay Instability in a Laser Plasma

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