Ion heating due to modulated parametric decay

Abstract Under circumstances where parametric decay occurs in a plasma, a lower hybrid pump wave modulated near ion cyclotron harmonics is found to increase ion temperatures up to a factor of two over CW pump wave application.

I. Introduction. Lower hybrid waves may be used simultaneously for current drive and heating in tokamaks. The availability of microwave power and wave guide structures make it an attractive candidate for heating reactor-grade plasmas. The high powers necessary for current drive in this environment can produce ion heating via nonlinear interactions. Heating via parametric decay of lower hybrid waves could be an auxiliary heating method for tokamaks. In previous experiments ion heating has been observed along with parametric decay of lower hybrid waves (LHW) in ACT-l [l] , ATC [2], JFT [3], Doublet-IIA [4], WEGA [5], PETUAL [6], ALCATOR A [7], H-l [8,9], and the Irvine Q-machine [lo].
In this letter we present data showing enhanced ion heating due to modulation of a parametrically decaying lower hybrid pump wave. The launched lower hybrid wave decayed into a daughter LHW and an electrostatic ion cyclotron wave (EICW). Ion heating consistent with heating due to parametric decay was measured when the pump wave amplitude was constant in time. By modulating the LHW pump at frequencies near the ion cyclotron frequency the ion heating was increased up to a factor of 2 over the CW application.
2. Theory. In the regime tici, Opi < w < ape % ace, where o = apump the pump frequency or w = ad the daughter LHW frequency; the LHW disper- For w = Wicw, the EICW frequency, the dispersion relation is w = wc + (Te/Ti)rl(pLk:) for V, 9 w/k,, > Vi, where V, (V is the electron (ion) thermal speed (2T,/m,)l/* and PI(x) = e-XZ1(x). The theory of parametric decay has been applied to the LHW by several authors [12-141. In parametric decay the EICW (daughter LHW) is driven by the beat between the pump LHW and the daughter LHW (EICW). This requires plasma conditions which give the proper frequency and wavelength matching (apump = Oicw + ad and kpump = kicw + kd). When the pump LHW is modulated near Wicw its lower sideband coincides with ad and will pump the daughter LHW. The increased amplitude of the pump and the daughter LHW when coupled to the EICW will increase the amplitude of the EICW.
From kinetic theory [lo] the heating rate for parametric decay of a CW pump LHW is where JL is essentially a maxwellian integrated over weakly Landau damped resonant particles and L represents each of the ion cyclotron harmonics above which a decay wave was observed. An increase in the amplitude of the EICW, &z/n, will increase the heating rate.
Enhanced heating also arises from the higher peak values of the modulated signal over the CW signal. This was found to descrease the threshold average power level for parametric decay [15]. Thus for a given power above the threshold the amplitude of the EICW decay wave would be larger and thus the heating due to the parametric decay would be increased.
3. Experimental set up. This experiment was performed in a single ended Q-machine [16] which provided a low density (5 X 109 < n e < 2 X 1010 cm-3), low temperature (T i = T e ~, 0.2 eV) nearly completely ionized barium and cesium plasma 1.0 m long and 5 cm in diameter ( fig. 1). The confining magnetic field was 2-6 kG. The LHW were launched from a slow wave antenna consisting of eight coaxial loops [17]. The radial wavelength and resonance cone width were measured and found to be consistent with the dispersion relation. The modulated signal was created by mixing a 30 MHz CW signal with a low frequency, ~Omo d (kHz), modulating signal in a mixing circuit. Electron temperature was estimated with a Langmuir probe.
Ion temperatures were determined from velocity distributions measured with a laser induced fluorescence (LIF) diagnostic [18,19] which uses a tunable dye laser to induce transitions to an excited state in target plasma ions. Measuring the Doppler shifts of the decay transitions in the direction perpendicular to the magnetic field gave f(V J. B) ( fig. 1 ). The spatial resolution was limited only by the laser beam width (collimated to 1 mm diameter). The velocity resolution was limited only by the natural linewidth of the absorption line, corresponding to an uncertainty of 1000 cm/s or 0.03 Vth for cold ions (T i = 0.2 eV).

Results. The conditions for the CW parametric
decay of LHW into EICW [20] were created. The decay was characterized by the appearance of several sidebands below the CW pump frequency, and the appearance of several low frequency waves. The low frequency waves were identified as EICW by their B-field dependence. Each low frequency wave and sideband pair satisfied the frequency matching conditions seperately. The low frequency waves followed 6o L = L(1 + ~L)Wd, ~L =~ 5L+ 1, where L indicated the Lth harmonic. Nine waves above the harmonics were seen.
The modulated RF signal consisted of the main center frequency and several sidebands. When this signal was coupled into the plasma through the coaxial antenna at an average power level 6 dB above threshold not only were the LHW pump wave and its sideband waves driven but several low frequency waves were observed. It was found that these low frequency waves were driven even at average power levels 2 dB below the threshold level for the parametric decay of the CW pump wave. The low frequency waves and side band pairs satisfied the frequency matching conditions These low frequency waves were all harmonics of the frequency of modulation of the pump waves and followed, co L = L~mo d where L is the Lth harmonic. the CW LHW showed EICW waves at 65 kHz and 125 kHz. The peaks in heating (about a factor of 2 over the CW heating levels) suggest a resonant interaction between the low frequency harmonics of the modulated wave and the EICW of the parametric decay. This resonant interaction is consistent with the observation that these heating resonances disappeared at power levels below the parametric decay threshold. The frequencies of modulation which showed heating peaks may not match the parametric decay waves, because of frequency mismatching. Since the set of EICW waves of the parametric decay are not exactly multiples of each other they will not match the set of low frequency harmonics of the modulated wave. Any resonant heating of the ions will be the sum of the heating over all harmonics. Only some of the modulated waves harmonics will be able to interact with the EICW for a given modulation frequency.

5.
Conclusions. Ion heating enhanced by the modulation of a parametrically decaying LHW was examined. Peaks in heating at modulation frequencies near the ion cyclotron harmonics suggested resonant interactions between the EICW of the parametric decay and the low frequency wave generated by the modulated LHW. Modulation of LHW increased the ion temperatures up to a factor of 2 over that of the CW LHW.