Parametric Instabilities

Illumination of the ionosphere using high-power EM waves can result in the excitation of a wide variety of plasma instabilities, many of which can lead to significant modification of the plasma medium. One of the most important and commonly identified instabilities is the class of nonlinear wave-wave interactions known asparametric instabilities, named after their theoretical similarities to the coupled-oscillator parametric amplifiers used in electrical engineering. Detailed analysis of parametric processes in the ionosphere can be found in, for example, [Fejer, 1979] or [Thid´e, 1990]. In a parametric process, an initial

“parent” or“pump” wave with parameters (ω0,k0) decays into two or more daughter waves:

(ω0,k0)→(ω1,k1) + (ω2,k2) +. . . (1.114) In the ionospheric-heating context the parent wave is often the initially-transmitted EM pump wave, however it could also be a high-frequency plasma wave excited by a previous interaction. In a parametric decay interaction, the following frequency and wave matching conditions must be met for the process to be viable:

ω0 =ω1±ω2±. . . k0 =k1±k2±. . . (1.115)

Examples of several parametric decay processes are shown schematically inω−k space in Figure 1.16.

Due to the diverse range of plasma waves that may exist in the F-region, there are often several combinations of waves that allow the matching conditions (1.115) to be satisfied; one of the combinations most frequently identified during heating experiments is referred to as the parametric decay instability (PDI). The PDI involves decay of an incident electromagnetic pump wave to a high-frequency Langmuir electron plasma wave and an ion acoustic wave, as depicted by Figure 1.16 (B). Physically, the electron oscillations generated by the EM pump wave field couple with an acoustic disturbance in the ion density to produce an electric field (induced by the charge difference between the fast displaced electrons and the slow ions). This plasma wave field beats with the

This image has been removed by the author

for copyright reasons.

For the original image, please see [Chen,

1984], Figure 8-14.

Figure 1.16: Parametric wave-matching conditions for the following instabilities: (A)

decay of a Langmuir electron plasma wave to an ion-acoustic wave plus a frequency- downshifted Langmuir wave (EDI / LDI); (B) decay of an EM pump wave to a Langmuir wave and an ion-acoustic wave (PDI); (C) decay of an EM pump wave to a frequency- downshifted EM wave plus an ion-acoustic wave (SBS); (D) decay of an EM pump wave

to a pair of plasma waves propagating in opposite directions (TPD). Image credit: [Chen, 1984]

ion density variation, leading to a non-uniform distribution of the E-field amplitude that enhances the ion irregularity via the ponderomotive force. Under the correct conditions, this feedback loop leads to an instability via which the EM pump wave is efficiently converted to an electron plasma wave and a travelling ion density disturbance (ion- acoustic wave). As the ion-acoustic frequency is small compared to the electron plasma frequency, the daughter Langmuir wave is only slightly downshifted in frequency with respect to the parent wave; as such this process occurs most favourably close to the O-mode reflection height, where the pump wave frequency comes close to matching the local electron frequency. In the F-region of the ionosphere, the threshold for this instability is around ∼0.1V /m [Stubbe and Kopka, 1981] and can be easily exceeded in the swollen-amplitude region below the O-mode reflection height. The timescale over which the instability develops is of the order∼10−3sin this region. The Langmuir wave dissipates its energy into the local plasma with an attenuation distance ∼ 1000 times

shorter than that for an O-mode pump wave in the F-region [Rietveld et al., 1993], hence the plasma wave decay component from the PDI process can be completely absorbed in a very localised region of the heated volume; this form of plasma-wave-driven anomalous absorption is understood to be one of the primary drivers of the large-scale electron temperature enhancements observed in O-mode heating experiments and is an effective mechanism for transferring the EM pump wave energy to the plasma.

Further parametric decay of the Langmuir plasma wave can occur via theelectron/Lang- muir decay instability (EDI / LDI) illustrated in Figure 1.16 (A), in which the initial pump Langmuir wave decays to an acoustic wave and a daughter Langmuir wave with a frequency slightly downshifted with respect to the parent wave (by a factor of the acous- tic wave frequency). This process can occur multiple times in succession resulting in a cascade of excited plasma waves with frequencies offset from the initial heater frequency by multiples of the acoustic frequency and the formation of aweak Langmuir turbulence

region.

A variation of the PDI process in which the low-frequency decay product is a non- propagating periodic ion density variation rather than the travelling ion-acoustic wave is known as the oscillating two-stream instability (OTSI). Under F-region conditions the OTSI has a higher threshold than the PDI by a factor of ∼2, however this is still sufficiently low that the instability is frequently observed close to the O-mode reflection region during heating experiments.

Analysis of stimulated electromagnetic emission spectra has been used to infer the exis- tence of several other parametric decay processes, in which excited plasma wave modes decay to low frequency components plus EM radiation that can be detected by ground- based spectral analysers. For example, the downshifted maximum (DM) sideband is attributed to the decay of an upper-hybrid mode to an O-mode wave and a lower- hybrid mode [Stubbe et al., 1994], while the broad upshifted maximum (BUM) feature is thought to be the result of the four-body decay of the second harmonic of either the EM pump or upper-hybrid mode to a daughter mode close to an electron gyrohar- monic frequency (either an upper-hybrid or electron Bernstein mode) and an O-mode

EM wave [Leyser et al., 1989].

Further parametric instabilities may include: decay of the EM pump wave to a high- frequency upper-hybrid or electron Bernstein wave and a low frequency acoustic or lower-hybrid wave; the stimulated Brillouin scattering instability (SBS), by which an EM wave decays to a frequency-downshifted EM wave plus an acoustic wave as shown in Figure 1.16 (C); and the two-plasmon decay (TPD) process by which an EM wave decays to two daughter plasma waves, as shown in Figure 1.16 (D).