Electric field strengths in a hollow cathode measured by Doppler-free two-photon optogalvanic spectroscopy via Stark splitting of the 2S level of deuterium

Abstract

We present, in this work, Doppler-free two-photon optogalvanic spectroscopy as a tool to measure the electric field strength in the cathode fall region of a hollow cathode discharge via the Stark splitting of the 2S level of atomic deuterium. The strong electric field strength (1 to 4 kV cm −1 ) present in the hollow cathode is determined for various discharge conditions (currents from 50 to 200 mA and pressures from 400 to 1350 Pa), which allows investigation of the corresponding variations of the cathode fall and its changes with discharge operation time.

Calculation of the spatial resolution in two-photon absorption spectroscopy applied to plasma diagnosis

“…The primary aim of the following analysis is to reveal some important characteristics of yield distributions that correspond to the experimental conditions used for the recent local electric field strength measurements. 12,13 In these experiments, and in the following calculations, a beam with a narrow beam waist is combined with a broader one, like beam 1 and beam 2 shown in Fig. 3, and both beams have equal pulse energy.…”

“…Therefore, optogalvanic detection is perfectly suited for local electric field strength measurements which reveal a strong broadening of the shifted 2S Stark components. 12,13 Under usual experimental conditions, the duration of the laser pulse (2.5 ns) is small compared to the fluorescence decay time; hence a detailed knowledge is not essential for the conclusions drawn in this study. If necessary, the rate equations can be extended to other twophoton transitions, quenching and branching rations can be included.…”

“…In almost, all these experiments, the variation of the plasma parameters to be measured was negligible compared to the spatial resolution, except for the E-field strength measurements in a HCD. In fact, in recent more accurate experimental studies in deuterium and hydrogen via optogalvanic spectroscopy in HCD 12,13 we have found that the E-field in front of the cathode increases, in a sheath of about 2 mm, up to 4 kV/cm. The spatial resolution was estimated using pinhole and geometrical optics resulting, in this case, in a length of 30 mm and a focal diameter of 200 lm in the overlap centre.…”

“…14 The laser radiation is split in two beams, a complete description of a typical experimental set-up used for plasma and flame diagnostic, can be seen elsewhere. 8,12 As this work is dedicated to study the spatial resolution in the overlap volume, we just explain the main aspects of beam preparation. The selection rule of the angular momentum for two-photon absorption for the 1S-2S hydrogen transition postulates DL ¼ 0, this means, the two-photon excitation is only possible for the absorption of one photon out of each beam opposite circularly polarized.…”

“…This particular angle comes from our experimental arrangement limitation for Dopplerfree configuration. 12,13 The beam waist measurements consisted of 60 subsequent samples taken for each of the two beams, for different apertures used for the variation of the beam waist diameter and at three positions: 30 mm before, in the centre and 30 mm behind the beam overlap.…”