Detailed experimental investigations of Brillouin-enhanced four-wave
mixing(BEFWM) and phase conjugation of microwaves in an unmagnetized
plasma have been performed. Through the use of plasma probes
and energy analyzers together with a millimeter-wave interferometer/scattering
system, both the transient and steady-state responses of the plasma
and the phase conjugate wave have been investigated. Low power,
low density operation is shown to agree well with two-fluid plasma
theory. Strong suppression of the BEFWM interaction is observed
at an electron density ne=nc/4, indicative
of the 2wpe instability. High power,
high density operation is seen to deviate from simple theoretical
predictions; slight amounts of plasma pushed out of the interaction
region by the ponderomotive force of the high power pump waves
are observed to disrupt the relative phases of the electromagnetic
waves involved in the BEFWM interaction.
Four-wave mixing (FWM ), in its simplest form, can be modeled
as a pair of simultaneous three-wave mixing processes. In the
first(optical mixing) process, a strong pump wave mixes with a
weak signal wave in a nonlinear medium (such as a plasma) to generate
a density modulation or "grating" in the medium. In
the second (scattering) process, another strong pump wave scatters
off this grating to generate a fourth wave. If the two pump waves
are antiparallel, the fourth wave is then phase conjugate to the
signal wave, i.e. its wavefronts coincide everywhere with the
signal wave and are counterpropagating.
A 200cm long, 75cm diameter stainless steel vacuum vessel in which low density unmagnetized H3+ ion filament discharge plasmas are produced, is employed for experimental BEFWM studies. Due to the 38 degree tilt angle between the pump and signal waves, both a large-k and a small-k grating
are formed in the plasma. The conjugate wave thus results from the scattering of E2 off the large-k grating and of E1 off the small-k grating. And due to the rather large wavelengths utilized, considerable diffraction and beam spreading occurs within the chamber. A forth-order high pass filter section was employed to filter out the undesired pump and signal wave power in order to accurately measure the conjugate power collected by the signal horn.
Phase measurements, in which calibrated phase delays were placed along various points in the signal and conjugate wave paths, show that out put wave is indeed phase conjugate to the input signal wave.
Figure 4 displays the scaling of the conjugate wave signal with plasma density, taken with power levels of P1=10 kW, P2=7.5 kW, and Ps=1.2 kW. at low densities, the signal is observed to indeed grow linearly with increasing plasma density. The conjugate wave amplitude is seen to drop sharply near the quarter-critical layer, disrupted possibly by the large amplitude ion fluctuations often observed in presence of the 2wpe instability.
Figure 5 illustrates the effect that increasing pump power has upon the conjugate wave. The "oscillations" have been observed to grow in size and frequency as the pump and plasma density are increased.
Independent evidence of ponderomotive whole-beam self-focusing is found through the use of the millimeter-wave interferometer system. In Fig. 6 are line-integrated plasma density waveforms, first of a low density plasma discharge followed by a higher density plasma discharge. Simultaneous measurements using a planar Langmuir probe, moveable along the chamber axis, confirm the interferometer results.
Measurements of the conjugate wave power Pc as a function of signal wave power Ps provides further proof that the temporal distortions observed at high power levels arise from the ponderomotive whole-beam self-focusing instability, and not from, say, ion wave saturation which is dependent upon both the pump wave and signal wave power levels.
Brillouin-enhanced four-wave mixing in an unmagnetized plasma has been clearly demonstrated. The detailed measurements have proven the validity, under low gain(i.e. low power and low density) conditions, of two fluid plasma theory. High power, high density operation is seen to deviate strongly from theory; evidence has been gathered to support the hypothesis that much of the deviation can be attributed to ponderomotive whole-beam self focusing of the high power pump waves.