Optical Mixing as a Plasma Density Probe

VOLUME PHYSICAL REVIEW LETTERS 13, NUMBER 3 20 JUL@ 1964 unstable waves are the features of most general interest. A detailed account of the work will be published shortly. Dreicer, Phys. Rev. 115, 238 (1959). 2T. Dupree, Phys. Fluids 6, 1714 (1963); Iu. Kli- montovich, Zh. Eksperim. i Teor. Fiz. 33, 982 (1957) [translation: Soviet Phys. — JETP 6, 753 (1958)]. ~N. Rostoker and M. Rosenbluth, Phys. Fluids 3, B. D. Fried and R. Gould, Phys. Fluids 4, 139 *Work supported in part by National Science Founda- tion, Air Force, and THW Space Technology Labora- 5E. C. Field and B. D. Fried, Bull. Am. Phys. Soc. 9, 329 (1964). 66. J. Culler and B. D. Fried, Thompson-Ramo- tories Independent Research Program. ~Permanent address: Hand Corporation, Monica, California. Santa ~H. Wooldridge Report No. M 19-3U3, 1963 (unpublished). OPTICAL MIXING AS A PLASMA DENSITY PROBE~ Norman M. Kroll, Amiram Ron, ~ and Norman Rostoker University of California, San Diego, I. a Jolla, California (Received 11 May 1964) It is difficult to stimulate plasma oscillations a single light wave because a light wave is transverse and plasma oscillations are longitu- dinal. Moreover, the frequencies and wave- lengths of the two kinds of waves in a plasma are usually quite different. However, if one con- siders two light beams of frequencies &» ro, and wave vectors k„k incident on a plasma, the plasma acts as a mixer and it is possible to sat- isfy the plasma dispersion relation by tuning the frequency ~2 so that cu2 - ~1 =- cop„where ~P = (4we'n/m)' , the plasma-wave frequency; in addition, it is necessary to adjust the directions of k„k2 so that Ikl-k2[ ED &1, where f. D = (k~T/ 4we'n)' is the Debye length. In this case ener- gy and momentum conservation can be satisfied, a resonance takes place, and the amplitude of the plasma wave is significant. The same light waves that produce the plasma wave will also scatter. Alternatively, it may be more con- venient to introduce a third beam and measure the scattering of it by the stimulated plasma oscillations. The purpose of this paper is to estimate the scattering and show that the mea- surement is quite feasible with modern laser techniques. The scattering cross section per unit frequency and per unit solid angle of a plasma electron is' with do' d(d Tp S K- C 1, &u'- w (1- ' sin'8), where ro =e'/rnc' is the classical electron radius and K is the wave vector at the incident light wave of frequency w =Kc. It is assumed that co the plasma frequency. The scattered wave is of frequency &' and is observed in a direction given by the unit vector T, where cos8 =I K/K. The quantity S(k, u&) is the spectral density of fluctuations of electron density, i. e. , S(k, (u) lim V, 2}n(k, &u) T-~ n(k, w) is the Fourier component of the electron density. If the energy flux of the incident beam is I the energy flux per unit frequency scattered into the direction 1 is dF /d(u'=(NF /r')da/d(u', s where N is the total number of electrons and r is the distance from the plasma to the detector. This formula applies to the case where the scattered wave is detected in the wave zone, i. e. , for r)a'/A, , where a is the diameter of the incident beam and A. is the wavelength. For a plasma in a state of thermal equilibrium, der/d&u' has sharp resonances at w'=a+up. The total contribution from one of these resonances is &ares =ra'(kl. D)'. For illustrative purposes we assume a plasma of easily attained properties: density n =10 cm ', temperature k&T=10 eV, and cup = 5. 64&10 sec Consider the scatter- ing of light from a ruby laser of wavelength A =0. 7x10 ~ cm. For the plasma resonance to be well defined we must have kLD(1, where k —X8 which implies observation at IK- +'T/c } = an angle of 8 = k/E. For the pla— sma under con- sideration, LD = 3. 16 & 10 cm, ' we assume kLD =0. 2 which implies that the scattered wave will