Threshold of the 2ωpe instability in a laser produced plasma

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THRESHOLD OF THE 2c.+

H.C. PANT**

, K. EIDMANN,

Max-Planck-Illstitlct

Received

INSTABILITY

IN A LASER PRODUCED PLASMA*

P. SACHSENMAIER

fiir Plasmaphysik,

17 November

COMMUNICATIONS

Buratom

Association.

and R. SiCEL 8046 Garchinx,

Fed. Rep. tierrnarl~’

1975

3 ?WL

~ITUSSIOII from various plane targets irradiated by a 20 J, 5 ns neodymium laser pulse has been investigated. The onset of jwhemission and an increase in intensity by five orders of magnitude is observed at a laser intensity 22 X1013Wcm, the threshold intensity predicted for excitation of the 2wpe instability.

Parametric instabilities are expected to constitute a major source of collision-free light absorption in laser-heated fusion plasmas (access to the very extended literature may be found in refs. [ 1,2]. Such instabilities should be excited only in a radiation field whose intensity exceeds a certain threshold value. In laser-produced plasmas, inaccessible as they are, theirexcitation might be detected by scattered radiation from waves which are generated in the plasma as a result of instability. At threshold the intensity of scattered radiation should grow from noise to a large value. Though parametric instabilities have been considered in the context of scattered radiation observed at frequencies fwL, wL, $oL and 2wL [3-91, no clear threshold behaviour has ever been reported*. Evidence obtained for the presence of parametric instabilities from hard X-ray and fast-ion production reported in ref. [9] and from other experiments is only indirect, mainly qualitative and difficult to correlate with specific instabilities. Since the existence of a well defined threshold is basic to parametric instabilities and characteristic of the type of the instability, and since its measured value may illustrate the validity of the theoretical approach, we should like to report here the * Presented at the 8th Int. C’onf. on Laser Plasma Fusion. x;* Warsaw, klay 19923 (1975). On leave from Bhabha Atomic Research Centre, Bombay, India. * A threshold of about 1OL3 W cm2 was reported for stimulated Brillouin scattering by Ripin et al. [ lo]. This case will be discussed in detail by Sigel et al. [lo]. 396

of

experimental observation of the threshold behavrout in the case of $wJ_ emission from a laser-produced plasma. The measured threshold intensity agrees with the predicted threshold of the 2tipe instability. The results were obtained in the Garching neodymium laser experiment under identical conditions and with methods similar to those described pr-eviously in the context of studies of o,_ [ 121 and 20, [ 131 emission. Laser pulses (wavelength h = 1.06 p. spectral width = 30 8) of 5 ns duration were focussed onto plane targets of solid deuterium, plexiglass (C,02H8). carbon, and copper by an aspheric f‘/l lens with a focal length of 75 mm. The pulse energy was varied by attenuation with filters in the range 0.1 --20 J. With a pulse energy of 20 J a maximum intensity of 4 X 1014 W cm--2 could be reached in the focal plane ot the lens. The intensity of $w,_ radiation backscattered through the focussing lens was monitored with a Valve 56 TWP photomultiplier with a S20 cathode, its angular distribution and polarization were determined within the solid angle of the focussing lens by photographing the intensity distribution in the plane of the lens on Kodak IN plates by a technique described earlier [ 12,131, and its spectral shape was measured by a ZeisssJena 3-prism spectrograph (type F&sterling I). Its spatial origin was also studied with side-on photographs of the target, the $wL radiation being isolated by an interference filter. Typical plasma parameters and the scattering properties of the plasma at frequencies other than $o,_ may be taken from refs. [ 12.131. The investigation [ 141 yielded the following major

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OPTICS COMMUNICATIONS

results: 1) At a laser energy of N 1 J, corresponding to an intensity of 2 X 1013 W cmU2, emission of fw,_ radiation starts with a threshold character. 2) Side-on photographs are consistent with the assumption that iw,_ radiation is generated at an, (n, is the so-called critical density defined by mpe = wL, ape = electron plasma frequency) in agreement with previous observations [3,4]. 3) 3 oL radiation is linearly polarized to better than 90% in the same direction as the incident laser beam. 4) The angular distribution is diffuse, unlike collimated backscatter at wL [ 121 and also unlike 2wL which is preferentially radiated at the specular angle [ 131. The only correlation with backscatter at wL seems to be an enhanced conversion efficiency for $wL in the presence of strong collimated backscatter, i.e. in the presence of a spatially coherent stading wave field and ion sound waves excited by stimulated Brillouin scattering [ 121. 5) In general, $wL radiation is found to be a double line [ 141, with the blue component being of lower intensity than the red one. The blue component is shifted by Ah = -10 _&relative to the calculated $oL center wavelength; the shift of the red component decreases with the atomic number of the target material (typical values are Ah 2 +40 A for copper, +20 A for carbon, and t 10 A for plexiglass). As in [ 51 the double-line character is no longer clearly resolved with a solid deuterium target; the two lines seem to merge together as their spacing becomes small. The spectrograms also showed two broad (width ==200 8) lines, about symmetric around the calculated $wL frequency and separated by * 400 8. These lines (not observed previously) were not further investigated. Fig. 1 illustrates the threshold character of OWL emission for the case of a carbon target. In the incident laser energy range of 1-3 J (corresponding to intensities 2-6 X 1013 W cmH2) the intensity of iwL emission increases by nearly five orders of magnitude from the level of plasma self-luminosity. For higher intensities it increases more slowly, possibly because the instability saturates. The absolute conversion efficiency is of the order of 1 OP5. The finite width of the transition may be attributed to the fact that an incident laser pulse is composed of a large number of spikes of unequal intensity [ 121. Only if the time-averaged intensity exceeds the threshold to some extent, all of

_I

1 INCIDENT

IO

10 ENERGY IIN

JOULES)

Fig. 1. Intensity dependence of $WI_ emission laser energy. Plane carbon target.

on the incident

them will excite the instability and contribute to $wL emission. Radiation with frequency $wL can be produced by scattering of laser radiation from plasmons with frequency iuL. Instabilities which generate plasmons with this frequency are stimulated Raman scattering and the 2wpe instability [ 1,2]. Recent computer simulations [ 1 l] have shown that $wL emission as observed here and in other experiments [3-81 should be attributed to the latter instability. Besides the rather narrow line-width observed and the low intensity of 40~ emission [ 5,8], the main argument comes from the low threshold expected for the 2ape instability as compared with stimulated Raman scattering. The threshold intensity for the 2upe instability has been calculated by Jackson [l] and for an inhomogeneous plasma by Rosenbluth [2]. For typical plasma parameters, i.e. an electron temperature kT, = 0.5 keV and an inhomogeneity scale length L = 0.1 mm as measured by X-ray spectroscopy [ 151 and pin-hole photography [ 161 respectively, the influence of the inhomogeneity of the plasma on the threshold is weak and one finds from both papers a threshold intensity 397

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of = 1013 W cmM2. Taking into account the well known uncertainties in the experimental intensity. this value is in good agreement with the observed threshold of 2 X 1013 W cm --2. The theoretical treatment [ 1,2] does not take into account effects such as steepening of the plasma density profile due to light pressure [ 11,171, the presence of ion sound waves and a standing wave field generated by collimated (Brillouin) backscatter and supersonic streaming of the plasma. The agreement between experiment and theory suggests that these effects have no strong influence on the threshold. They may, however, be important in understanding details of the experimental observations such as, in particular, the spectral structure observed. Finally, we may note that excitation of the 2ape instability does not lead to a noticeable increase of absorption in our experiment. As measured previously under identical experimental conditions, the reflection coefficient of the plasma increases steadily in the incident laser energy range of 0.1-20 J up to values of 30% [ 121. No anomaly is observed in the measured reflection curve at the onset of $q_ emission. It should also be noted that in [7] maximum zwL emission coincides with maximum reflection from the target of 50%‘. Thus the 2wpe instability may be inefficient for strong light absorption in laser-heated plasmas The laboratory assistance of H. Brandlein and E. Wanka is gratefully acknowledged. This work was performed under the terms of the agreement on association between Max-Planck-Institut fiir Plasmaphysik and Euratom.

References

[l] E.A. Jackson, Phys. Rev. 153 (1967) 235. [2] M.N. Rosenbluth, Phys. Rev. Lett. 29 (1972)

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and C. Patou, Opt. C‘ommun. I31 A. Saleres, M. Decroisette 13 (1975) 321. and E. Goldman, Report No. 30, I41 S. Jackel, J. Albritton Lab. for Laser Energetics, Univ. of Rochester, N.Y., June 1975; W.W. Alexandrov et al., at the 8th Int. Conf. on Laser Plasma Fusion, Warsaw (May 1975). B. Meyer and Y. Vitel, Phys. [Sl J.L. Bobin, M. Decroisette, Rev. Lett. 30 (1973) 594. B. Meyer and Y. Vitel, Phys. Lett. 45A [61 M. Decroisette, (1973) 443. A. Saleres, F. Floux, D. Cognard and J.L. Bobin, Phys. Lett. 45A (1973) 451. [81 Ping Lee, D.V. Ciovanelli, R.P. Godwin and G.H. McCall, Appl. Phys. Lett. 24 (1974) 406. T. Yamanaka. T. Sasaki, J. Mizui and H.B. 191 C. Yamanaka, Kang, Phys. Rev. Lett. 32 (1974) 1038. B.H. Ripin, J.M. McMahon, F<.A. McLean, W.M. Mann[lOI heimer and J.A. Stamper, Phys. Rev. Lett. 33 (1974) 634; R. Sigel, K. Eidmann, H.C. Pant and P. Sachsenmaier. to be published. 1). Biskamp and H. Welter. Phys. Rev. Lett. 34 (1975) 1111 312. and Re117.1 K. Eidmann and R. Sigel, in: Laser Interaction lated Plasma Phenomena, ed. by H.J. Schwarz and H. Hora, (Plenum Press, New York, 1974), Vol. 3, p. 667. K. Eidmann and R. Sigel, Phys. Rev. Lett. 34 (1975) 1131 799. H.C. Pant, K. Eidmann, P. Sachsenmaier, and R. Sigel, iI41 Max-Planck-Inst. fiir Plasmaphysik, Lab. Rep. No. lV/85. 1975 (unpublished). K. Eidmann and R. Sigel, in Proc. Sixth Europ. Conf. (‘ontrolled Fusion and Plasma Physics, Moscow, USSR, Academy of Sciences, Moscow, USSR, 1973). Vol. I. p. 435. M.H. Key, K. Eidmann, C. Darn and R. Sigel, Phys. Lett. 1161 48A (1974) 121. [ 171 D.W. Forslund, J.M. Kindel, K. Lee and E.L. Lindmann, LASL Report No. LA-UR 74-1636, 1974 (to be published); K.G. Estabrook, E. Valeo and W.L. Kruer. Phys. Lett. 49A (1974) 109. 171