Parametric Decay Instability Control In Inhomogeneous Plasma By The Pump Frequency Modulation

Parametric Decay Instability Control In Inhomogeneous Plasma By The Pump Frequency Modulation

V.I. Arkhipenkoa, E.Z. Gusakovb, V.A. Pisareva, L.V. Simonchika, B.O. Yakovlevb
Institute of Molecular and Atomic Physics NASB, pr. Nezalezhnastsi 70, 220072 Minsk, Belarus Ioffe Institute RAS ,Polytechnicheskaya 26, 124091 St.Petersburg, Russia
Abstract. The experimental investigation of inhomogeneous plasma parametric decay instability driven by frequency modulated pump is performed. In agreement with theoretical predictions it is shown that the decay instability is stable against the modulation faster than the decay wave transient time in the interaction region. In the case of slower modulation the decay instability resonant enhancement is observed when the decay point velocity is close to the decay wave group velocity. The possibility of the decay instability suppression at harmonic pump frequency modulation is also demon­strated.
Keywords: parametric instability, frequency modulation, plasma nonlinearityPACS: 52.35.Mw
The pump phase modulation was discussed as a possible way of parametric decay instability (PDI) suppression starting from 60th. According to results of homogeneous plasma theory [1], it can serves as an effective method for parametric instability control. However the analysis carried out in inhomogeneous plasma model for very fast random pump phase modulation had revealed high stability of convective amplification coefficient, which appeared to be non-sensitive to modulation [2]. A more detailed theoretical investigation accounting for various (linear, harmonic and stochastic) frequency modulation possessing arbitrary rate was performed recently in [3]. It was carried out in the framework of coupled equations for slow varying wave amplitudes a1 and a2 of oppositely propagating plasma waves, neglecting pump wave amplitude depletion:
the decay point, occurring under the pump frequency modulation. Such suppression should take place when the ve­locity of the decay point coincides with the group velocity of a decay wave Vd = V2.
The most simplified model suitable for analytical investigation of the convective losses suppression effect is the model of a linear frequency modulated pump. In this case, the pump phase modulation can be written as 5Ф(х, t) = a(x-V0t)2, where parameter a is related to the frequency modulation rate by a = -ll(2V02)(dmldf). After the corre­sponding transformation of the equations (1) the spatial amplification coefficient expression can be written in the form

This expression describes the decay wave amplification in the presence of linear frequency modulated pump wave in the inhomogeneous plasma. The amplification should experience the resonance growth, when the decay point velocity approaches the group velocity of one of the decay waves, thus leading to sup­pression of convective losses.

It should be stressed that resonant enhancement of the convective amplification coefficient is possible not only for linear or harmonic pump frequency modulation, but also for stochastic modulation, as was shown in the numerical modelling. The pump phase modulation was taken in the form:
which in the case coj = liylT, T was taken longer then any time scale of the problem, and Uj is a random phase taken from [0, 2тг] interval. This representation provides statistically uniform, Gaussian frequency modulation possessing correlation function <5Q(t)5Q(t’)> = A2exp(-(t-t’)2/2xc2), <5Q(t)> =0, <5Q2>1/2 = Д. As it was obtained, in the case of fast phase modulation (xc = 1) amplitude growth is much slower than that associated with growth rates y0 or Yo/(jyPi)1/2, but saturates at the level prescribed by amplification coefficient ехр(тгу02^2/1 V1V21) in agreement with [2]. On the contrary, for slow modulation ( xc = 16) the fast bursts of growth are observable and the level of amplifi­cation is much higher.
The experiment was carried out in the linear plasma device “Granit” [4]. The Trivelpiece-Gould (TG) pump wave (f0~ 2500 MHz) was excited in the inhomogeneous plasma with a waveguide using the electron cyclotron discharge

in a tube 2 cm in diameter and 100 cm long. The experi­ment parameters are as follows: magnetic field H~3.5 kG, the argon gas pressure is 10-2 Torr, the plasma inhomoge-neity scale along magnetic field and across it are a~5 cm and b~0.4 cm, respectively, the maximal electron density is ne~1012 cm-3, electron temperature is Te~2 eV. The high density plasma (ne(r,z) > nc, where nc – critical electron density – creates a plasma waveguide for the TG wave, shown in figure 1. It is weakly inhomogeneous in the axial direction. Propagating toward decreasing electron density to the point of plasma resonance (focal point), where coo

Figure 1. Schematic diagram of the Trivelpiece-Gould ~TG! mode excitation and its propagation. 1—glass tube; 2—waveguide; P0, Pr, Pt, and Ps — incident, re­flected, passed, and scattered waves.
mPe(0, z) the wave slows down and its electric field in­creases drastically. The backscattering parametric instabil­ity l0 -> l0‘ + s was observed under these conditions in previ­ous experiments [5], utilizing a monochromatic pump. The
reflected fundamental TG mode l0‘ and ion acoustic wave s,
propagating along the magnetic field in the direction of decreasing plasma density, are produced by this decay. The satellite, redshifted by 3 MHz, appears in the spectrum of the signal reflected by the plasma due to this instability.
The effect of the pump frequency modulation f= f0 + Af F(t), where F(t) – linear, harmonic or stochastic function, on the mentioned above PDI was investigated. The enhanced scattering technique was used to study the ion acoustic wave, generated due to the parametric instability of the frequency modulated pump. For this purpose a small power (Pp<5 mW) probing TG mode ( fp ~2350 MHz) was launched into the plasma by the same waveguide, which was used for pump wave excitation. The probing wave backscattering off the decay ion acoustic wave providing informa­tion on the decay wave amplitude and spectra was studied using spectral analyses and detectors.
Linear frequency modulation of the pump wave
To obtain the linear frequency modulation of pump wave the special microwave generator controlled by the saw­tooth voltage was used in the experiments. The decay point velocity was changed by the variation of the modulation period from 3 (is up to 10 (is at the frequency deviation of A/= 300 MHz, and was determined by the same relation as the velocity of the hybrid resonance point Vd = 2aAfl(rf). The first experiments have shown the possibility of decrease of the power threshold for parametrically driven ion-acoustic wave observation by a factor 1.5 – 2, compared to the nonmodulated pump case. The consequence of spectra for different modulation period is shown in figure 2a. The
a b
Figure 2. Spectra and amplitude of the parametric scattered wave at different velocities of linear frequency modulation
maximal stimulation of the parametric instability was observed at the changing frequency velocity close to 50 MHz/(is. It corresponds to the decay point velocity equal to the ion-acoustic wave velocity cs = (Te/Mi)1/2 ~ 2.2 x 105 cm/s. The temporal structure of the ion-acoustic wave was investigated with a help of the backscattering signal meas­urements using homodyne detector. The frequency modulated pump was incident on to plasma during 5 (is (Figure 2b). The burst of the scattering signal appears after 2 microsecond delay. It looks as a result of backscattering from the soliton like structure.
The effect of the harmonic pump frequency modulation f=f0Af sin(2nfmt) on the PDI was investigated in the wide modu­lation frequency region for 0.1 MHz m <10 MHz. Figure 3 shows the scattered-signal amplitude as a function of the modulation frequency for different widths of the pump-wave spectrum. The dashed line in figure 3 indicates the level of the scattering signal for a monochromatic pump wave (A/ = 0). The signal is close to this level at fm > 1.5 MHz and fm < 0.6 MHz. However, around fm= 1 MHz, within a wide range of deviation values, 10 MHz < A/ < 100 MHz, resonant suppression of the signal is observed. This is most pronounced within the range 40 MHz < A/< 80 MHz.
At smaller modulation frequencies fm <0.5 MHz there was no suppression of PDI, on the contrary, a visible enhancement of the instability was observed. The evident growth of the back-
Figure 3. Resonant suppression of the instability by the harmonic frequency modulation for different

scattered signal, shown in figure 3 for A/ = 30 MHz and fm = 0.5 MHz is associated with the effect of the decay insta­bility enhancement in the case, when the decay point velocity coincides with the ion acoustic velocity. In this case the bursts of the ion acoustic waves corresponding to each sinusoidal period are observed on the scattering signal wave­form at the homodyne detector (Figure 4a). The resonant suppression transient phenomenon is also studied using this type of measurement. As it is seen in figure 4b, at the modulation frequency of 1 MHz the suppression of parametric instability takes place only 10 (is after the modulation switching on (Figure 4b). The recovering of the scattering sig­nal after the modulation switch off takes as well around 10 ms. The possible explanation for the decay instability suppression effect may be related to a resonance of the frequency modulation period and typical time of energy cir­culation in the feed back loop leading to the absolute parametric decay instability onset [6].

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