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Continuous and Discrete Spectra of LF and HF Waves in a Helicon Plasma

V. F. Virko, K. P. Shamrai, Yu. V. Virko and G. S. Kirichenko
Institute for Nuclear Research NAS of Ukraine, 47 Prospect Nauki, 03680 Kiev, Ukraine
Abstract. The results of probe measurements of low-frequency (LF) and high-frequency (HF) pump sideband waves in a helicon discharge, which were made in order to reveal the origin of turbulence arising in plasma, are presented. Both LF and HF spectra are shown to include continuous noise component and equidistant discrete spikes. LF oscillations were identified with ion-acoustic waves propagating azimuthally. Correlative measurements of wave characteristics, stationary plasma parameters, and diamagnetic signal show the excitation of continuous spectrum to result from electron drift current driven instability, while spiky spectrum from parametric instability.
Keywords: Helicon discharge, ion acoustic waves, electron drift current, parametric instabilities.
PACS: 52.35.Hr, 52.40.Fd, 52.50.Dg.
Experiments on various helicon plasmas have revealed excitation of turbulence in the megahertz range of frequencies [1-5], well below the driving frequency. Turbulence components were identified with ion-acoustic (IA) waves by using both microwave [1,5] and probe [2-5] diagnostics. Evidences have been presented that wave excitation can result from parametric instabilities of helicon pump wave [2,3,5] and provide an efficient channel of the rf power absorption. One more probable origin for the IA waves is the instability driven by electron drift across the magnetic field [4]. We report the results of probe measurements of low-frequency (LF) waves and high-frequency (HF) waves in sidebands of the driving frequency, which were performed in a helicon plasma along with measurements of diamagnetic signal and stationary plasma parameters, in order to reveal the origin of IA turbulence.
The discharge chamber is a 14-cm-diameter, 23-cm-long quartz tube with attached 14-cm-long metal section of the same diameter; it is limited by an aluminum flange, at z = 0, and by a copper grid, at z = 36 см (Fig. 1). Magnetic field was produced by two coils with separate current control and could be either uniform, at equal coil currents, or nonuniform, at zero left coil current (Fig. 2). The discharge was excited in Ar by a double-turn (m = 0) antenna that was positioned at z = 6 cm, shielded by a grounded Faraday shield, and supplied from a 13.56 MHz, 1 kW rf generator. Experiments were normally performed at the following standard conditions: absorbed power Pin = 1 kW, argon pressure pAr = 5 mTorr, right coil current Iright = 10 A, and left coil current Ileft = 0 or 10 A.
The line-averaged density was measured with the 8-mm interferometer. Spatial distributions of plasma parameters and wave characteristics were measured by the Langmuir probe; multi-purpose single-loop probe that could work as electric, magnetic, or emissive probe; and the rotatable double probe, for wave interferometry (see Fig. 1). We used also a 100-turn diamagnetic belt overlapping the quartz chamber at z = 18 см.
In uniform magnetic field, LF oscillations demonstrate continuous, noise spectrum that grows in intensity and broadens, up to 1 MHz, when moving away from the axis (Fig. 3); spectrum also broadens with increasing magnetic.

field. In some regimes, the spectrum measured closer to the periphery includes a single, intense discrete spike in the range of 0.1 MHz. In the nonuniform field, the spectrum has also a continuous, noise component and includes, in the range of 0.2 MHz, a set of spikes separated by 12.5 kHz (Fig. 4). Closer to the center, spiky spectrum disappears and only a noise spectrum exists; it has maximum around 300 kHz and is more intense in the uniform field.
At any magnetic field, noise oscillations are identified as the waves propagating obliquely (both azimuthally, along electron gyration, and radially, to plasma periphery), with inclination to radius 45−60°. Phase velocities are of the order of the IA velocity, 3×105 cm⋅s−1, independently of frequency. Density variation caused by these waves was estimated from ac-to-dc ion current ratio and found to be δn/n ≈ 1% at the spectral maximum. Note that we also measured LF waves in a helium discharge and found them to behave similarly, considering Ar/He mass ratio.
LF waves related to spikes are localized at the periphery, propagate azimuthally with IA velocity, independently of frequency, and have excitation threshold on the rf power. Correlation measurements show that they are global IA eigenmodes, with integer number of wavelengths along the azimuthal turn. Only quite high harmonics of 12.5 kHz with azimuthal numbers m =10–17 are excited. Propagation directions of these waves are opposite in the uniform and nonuniform magnetic field and are along electron drift streams detected with the diamagnetic loop.
HF sideband spectra around 13.56 MHz measured with capacitive and magnetic probes were found to reproduce the structure of LF spectra; i.e., to include both continuous, noise component and spiky component. Figure 5 shows the HF spectra taken with the capacitive probe in the nonuniform magnetic field. Two sideband peaks arising closer to the periphery, at r = 4.4 cm, are actually the sets of intense spikes (unresolved in the figure scale) that are spaced by 13.5 MHz, the same as the LF spikes measured at r = 5 cm (cf. Fig. 3). Closer to the center, at r = 3.5 cm, sideband spectrum is continuous and reproduce the shape of the LF spectrum measured at r = 3 cm (Fig. 3).
Noise component measured with the capacitive probe is fairly symmetric relative to the driving frequency. We examined interference of these oscillations by using a delay line in one of the arms of the double probe and found the interference pattern to be similar to that measured for the LF noise oscillations. Considering also mirror symmetry of sideband noise components, we concluded that these components do not relate to any potential waves and arise, most probably, from modulation of the probe signal at the driving frequency by the IA waves. Indeed, variation of plasma density caused by the LF waves alters the width of the near-probe sheath and, therefore, the probe capacitance relative to plasma. Analysis shows that under the LF modulation the phase difference between signals measured by two probes at the sideband frequency is equal to the phase difference between LF signals.

Sideband spectra taken with the magnetic probe are asymmetric, with dominance of the lower sideband, and also include spikes identified with the waves with azimuthal phase velocities (2.5−4.5)×107 cm⋅s−1. Propagation directions are opposite for the lower and upper sidebands and for the uniform and nonuniform magnetic field. The lower sideband waves and their LF partners have equal wavelengths but propagate oppositely. The amplitude of magnetic signal in the lower sideband can be as high as that of the pump. As for the phase of the signal at 13.56 MHz, it does not depend of azimuth, as expected for an m = 0 wave.
LF waves from continuous spectra are apparently excited by the azimuthal drift of electrons across the magnetic field, as was observed in other experiments (e.g., [6]). To detect these currents, we examined plasma diamagnetic response at the discharge breaking. Figure 6 shows the signal of the diamagnetic belt as function of before-breaking plasma density; the latter was varied by varying the rf power and measured by the 8-mm interferometer at z = 12 cm. The signal in the nonuniform (uniform) field has diamagnetic (paramagnetic) polarity; i.e., electron current attenuates (amplifies) the external magnetic field. Figure 7 shows the diamagnetic signal measured at a fixed input power of 1 kW, as a function of the left coil current, i.e., of magnetic field nonuniformity. As seen, signal polarity alters under transition from uniform to nonuniform field, and the plasma density grows with increasing field nonuniformity.
Diamagnetic signal is an integral characteristic of the azimuthal currents of different nature. To evaluate radial profiles of the drift current, we examined static plasma parameters. Figure 8 shows the radial profiles of electron temperature Te measured in the nonuniform field. As seen, Te grows when moving away from the antenna located at z = 6 cm and has local maximum at r ≈ 4 cm, in cross-section z = 18 cm. In the uniform field, Te is uniform, about 4 eV, in the plasma bulk and slightly grows, up to 5 eV, at the periphery. Radial profiles of the probe floating potential, Vf, measured by the multi-purpose single-loop probe are shown in Fig. 9. Deep minima, which arise in the nonunifrom field at r = 4 cm, are located around the zone of electron heating (cf. Fig. 8). The same multi-purpose probe was biased (up to +100 V) with a saw-tooth potential and heated by the ac current to determine plasma potential, Vs, from the merge point of cold and hot probe characteristics. Radial profiles of Vs shown in Fig. 10 are similar along the whole discharge length (z = 6 to 26 cm) and do not demonstrate substantial potential drops, in both the uniform and nonuniform fields. Note these profiles to differ cardinally from that calculated from the relation Vs = Vf + 5Te. Unfortunately, our measurements are not so accurate as to detect radial fields of the order of 1 V⋅cm−1, which would be enough to produce the electric drift compatible with the diamagnetic drift. Figure 11 shows the radial profile of electron pressure, for the nonuniform magnetic field. It is flat in the central part where density and temperature variations compensate each other. Pressure gradient is considerable only at the plasma periphery.

Helicon discharge operated at relatively low magnetic field and input power demonstrates both LF wave activity and activity in sidebands of the driving frequency, at any magnetic field shape. Spectra of LF waves have noise component, in the range of 1 MHz, and one (in the uniform magnetic field) or several (in the nonuniform field) spikes, in the range 0.1−0.2 MHz. Noise oscillations, with relative density pulsations ∼1%, are the IA waves that propagate obliquely in cross-section and are thought to arise from diamagnetic electron drift. Spiky spectrum is excited with threshold on the rf power and is formed by global IA modes with high azimuthal numbers. HF sideband spectra reproduce the structure of LF spectra. Their noise components result from modulation of the probe signal at the driving frequency by the IA waves. Spiky components are the waves with frequencies ω = ω0 ± ωS and phase velocities that fit well the relation ω/kS where ω0 is the pump frequency and ωS and kS are the frequency and wave number of the IA partner. The waves related to spikes in the upper (lower) sideband propagate azimuthally along (contrariwise) propagation of the LF partners. Thus, the waves forming spiky components of the HF and LF spectra satisfy the conditions for parametric decay of the pump wave into the IA wave and the HF satellite.
This work was supported by the Science and Technology Center in Ukraine under contract No. 3068.
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