Ion temperatures as a function of source frequency and magnetic field strength measured by laser induced fluorescence in HELIX for a neutral pressure of 6.7 mTorr and an rf power of 750 W. The white line denotes where the source frequency matches the calculated lower hybrid frequency along the axis of the source. At the plasma edge, the lower hybrid frequency curve shifts towards the lower right corner of the figure. The maximum ion temperature occurs for those source frequencies and magnetic fields at which the lower hybrid frequency matches the source frequency in the plasma edge. Reprinted with permission from J. L. Kline et al., Phys. Rev. Lett. 88, 195002 (2002). Copyright 2002 American Physical Society.
Schematic of HELIX-expansion chamber apparatus (only a portion of the end of the expansion chamber is shown at the right of this figure). The 19 cm long m = 1 antenna surrounds the glass portion of the chamber at z = 0 cm. Ten electromagnets, aligned as shown, provide the magnetic field in the source region. The ports at 70, 85, and 100 cm were used for the mm-wave and the electrostatic fluctuation measurements.
Schematic of the mm-wave system and the optical path through a cross section of the helicon source (at z = 85 cm): (S) is the mm-wave source, (D) is the detector, (M) are mirrors, (VM) is the adjustable vacuum mirror, (BS1) and (BS2) are the beam splitters. The cross sectional view includes the source chamber and additional structures that house the injection lens and collection mirror assembly.
Solutions of the cold plasma dispersion relation for k ⊥ with n = 5 × 1012 cm−3, k∥ = 0.3 rad/cm, f = 9 MHz, and no collisions. (a) The absolute value of the real k ⊥ for the slow wave, (b) the negative of the value of the imaginary k ⊥ for the slow wave, (c) the absolute value of the real k ⊥ for the fast wave, and (d) the negative of the value of the imaginary k ⊥ for the fast wave.
Normalized perpendicular wave numbers for the slow wave calculated as a function of driving frequency and magnetic field strength for a neutral pressure of 8 mTorr and an ion temperature of 0.2 eV. From left to right, the solid lines indicate for what frequency and magnetic field strength combinations the source frequency matches the lower hybrid frequency at r = 0 cm and at r = 5.5 cm (for typical helicon source density profiles). The black diamonds indicate the particular driving frequency and magnetic field strength combinations that were investigated in this work.
Radial profiles of the ratio of the driving frequency relative to the lower hybrid frequency (f/f LH), based on the measured density profiles, for driving frequencies of (a) 9.5 MHz, (b) 11.5 MHz, (c) 13.5 MHz at magnetic field strengths of (▼) 650 G, (●) 800 G, (▪) 950 G, and (♦) 1100 G. The solid line at f/f LH = 1 highlights the resonance condition. Electron temperature radial profiles for driving frequencies of (d) 9.5 MHz, (e) 11.5 MHz, and (f) 13.5 MHz at the same magnetic fields.
Spectral density from the electrostatic double probe oriented perpendicular to the magnetic field at r = 4.5 cm for a magnetic field of 800 G, neutral pressure of 8 mTorr, and driving frequency of 9.5 MHz. A suppression window at 9.5 ± 0.1 MHz is applied to assist in identification of the fluctuations.
Spectral density from the electrostatic double probe oriented parallel to the magnetic field at r = 4.5 cm for a magnetic field of 800 G, neutral pressure of 8 mTorr, and rf driving frequency of 9.5 MHz. A suppression window at 9.5 ± 0.1 MHz is applied to enhance the appearance of the fluctuations.
Spectral density from the electrostatic double probe oriented 45° to the magnetic field at r = 4.5 cm for a magnetic field of 800 G, neutral pressure of 8 mTorr, and driving frequency of 9.5 MHz.
Radial profiles of the average spectral density integrated over a 55 kHz window centered at 340 kHz and over the wave number range of 10 to 40 rad/cm for driving frequencies of (a) 9.5 MHz, (b) 11.5 MHz, and (c) 13.5 MHz at magnetic fields of (▼) 650 G, (●) 800 G, (▪) 950 G, and (♦) 1100 G.
Radial profiles of the integrated spectral power for the electrostatic double probe (squares) and the CTS diagnostic (circles) for a driving frequency of 9.5 MHz, a magnetic field strength of 800 G, and a neutral pressure of 8 mTorr. The electrostatic spectral power is integrated over 55 kHz centered at 340 kHz and the CTS spectral power is integrated over the range of 80–150 kHz.
(a) Radial profile versus time of the ion temperature during a 100 ms helicon source pulse. The first 20 ms of the discharge are shown. (b) Individual ion temperature profile measurements obtained at 2.7 ms (circles) and 14 ms (squares).
(a) Continuous wavelet transform of the first 5 ms of the electrostatic fluctuations measured at a radial location of 3.5 cm. The narrow spectral feature at 9.5 MHz is the primary rf wave for the source. (b) Expanded view of the lower frequency portion of the spectrum shown in (a). The amplitude of the peak at ∼ 245 kHz increases rapidly over the first 2 ms of the discharge. (c) The amplitude of the wavelet power spectrum at 245 kHz for radial locations of 0 cm (light gray) and 3.5 cm (black).
Spectral power versus frequency acquired during a 5 ms wide sampling window 12.5 ms into the 100 ms pulsed discharge. The peak of the driving frequency has been cut off to highlight the sideband wave at 9.745 MHz.
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