The nonlinear interaction of two electromagnetic waves (E1, E2) can produce a third (plasma) wave (Ep) via the process of optical mixing. The resultant density fluctuations can become appreciable when f1-f2= fp and k1+k2= kp where fp, kp satisfy the plasma dispersion relation (fp, kp)=0. This has, for example, been demonstrated for the case of mixing of two laser beams. The current work studies the optical-mixing generated acoustic waves including their saturation via ion heating. Not only does this optical-mixing study provide insight into the saturation of SBS, it also models the actual laser interaction. Specifically, imperfect absorption of the laser light can lead to the Doppler-shifted light reflected from the moving critical layer beating with the incoming laser light. The SBS instability is thereby generated with an effectively enhance initial noise level.
In optical mixing, the beating of two EM waves with the proper frequency and wave-number differences can resonantly excite waves in plasmas. The current research has performed extensive studies of the growth and saturation of optically-excited IAWs. In Fig.1, theoretical and experimental IAW fluctuation amp-litudes are displayed as a function of input power. It should be noted that the entire time history of the IAW growth, saturation, and decay can be observed together with harmonic generation.
Fig. 1. IAW dependence on microwave power from (o) scattering, (Æ) probes, () 1-D simulations; the curves are calculated using (- · -) linear damping and (- -) ion tail formation.
In the present experiment, two electromagnetic waves with parallel polarization were propagated antiparallel to each other in a field-free plasma. The difference frequency between the two source can be accurately set (and maintained) to within +100 Hz over the range from zero to many times the ion plasma frequency. The experimental results are shown in Fig. 2. The figure 2 displays the magnitude of the observed density fluctuation level in a neon species plasma as a function of the difference frequency between the two sources. The maximum is observed when = kscs+Ksu0. The smaller, secondary peaks were associated with optical mixing of the reflected electromagnetic waves from each end of the chamber and the horns.
Fig. 2 Amplitude of ion acoustic waves in a neon plasma as a function of the difference frequency (f=f1-f2) between the two microwave sources (=50 µs, P1 = 10 kW, P2 = 20 kw).
The scaling of n/n0 with the magnitude of E1E2 was studied. Figure 3 shows the maximum density fluctuation level as a function of (P1P2)1/2 E1E2for a pure helium plasma, a pure neon plasma, and two mixed-species neon-helium plasmas.
Fig. 3 Amplitude of ion acoustic waves as a function of (P1P2)1/2 for pure and mixing helium- and neon-ion plasmas; a, pure helium, f =210 kHz (resonant); b, pure neon, f =100 kHz (resonant); c, pure neon; d, neon + 5% helium; e, neon + 10% helium. f =100 kHz in all of the last three cases ( d is near resonance).
The time history of the ion waves was also investigated. Figure 4 shows the measured temporal behavior for several power levels with dashed curves being the simple predictions of a nonlinear saturation mechanism at the higher power levels.
Fig. 4 Time evolution of the amplitude of the ion acoustic waves for several power levels. The dashed lines represent the predictions of theory while the solid lines are obtained by a self-consistent treatment of the ion tail formation.
At the low power levels employed for these studies, both density-profile modifications and electron heating (inverse bremsstrahlung absorption) are negligible. In addition, even far into saturation the ion waves were found to be extremely pure with virtually on harmonic content. To investigate the possibility of saturation via ion heating, the detailed measurements of the ion distribution function were performed with a retarding-gird energy analyzer. Figure 5 shows typical data indicating the formation of a hot-ion tail in the presence of the rf. As shown in the inset to Fig. 5, the enhanced tail is only found when the rf source difference frequency is tuned to the appropriate acoustic frequency. In addition, the fraction of hot ions was found to scale linearly with E1E2 up to (P1P2)1/2 = 50 kW.
Fig. 5 The tail of the ion distribution function for the cases of no rf with the appropriate difference frequency between sources (helium plasma, = 50 µs). Inset: Relative fraction of hot ions with E > 1.5 eV as a function of source difference frequency, with and without rf (P1 =10 kW, P2 = 20 kW).