Independent Temperature Measurements Research Articles

Plasma broadened line shapes and oscillator strengths of cesium

Theoretical line shapes and oscillator strengths for cesium are presented in this paper. These enable independent measurements of density and temperature for cesium plasma. The oscillator strengths have been determined from one electron wave functions that have been obtained by numerical solution of the Schrodinger equation with the spin-orbit term. A potential constructed by a semi-systematic improvement of the Hartree potential for Cs + was used. This single potential gives binding energies accurate to less than 1 per cent for all but the lower levels; the lower levels agree within 3 per cent. The validity of the wave functions is demonstrated by comparing with experiment calculated values of fine structure splitting, ground state hyperfine splitting, and principal series oscillator strengths. These wave functions are used to calculate oscillator strengths for over 100 transitions in or near the visible region. Definite improvements over other theoretical oscillator strengths are observed. Under equilibrium conditions these oscillator strengths in conjunction with measured line intensities enable a determination of plasma temperature. Plasma broadened line shapes of the fundamental series of cesium have also been calculated and compared with experiment (see preceding paper). Plasma conditions included in the calculations range from 10 3 to 10 4K and 10 13 to 10 16 ions/cm 3. The impact limit with the classical path approximation is used to calculate the electron contribution to broadening, while the ions are treated in the usual static limit. Only isolated lines have been considered. Graphs of the calculated width and shift versus ion density are presented. In view of the good agreement between calculated and experimental widths these plots can be used henceforth to determine ion density. Densities obtained in this manner are insensitive to temperature and accuracies of 20 per cent are possible.

Experimental cesium line shapes

The widths of some of the spectral lines emitted from a dense plasma are sensitive to the ion density but insensitive to the electron temperature. In partially-ionized cesium plasmas with number densities greater than 10 13 ions-cm −3 these plasma-broadened lines are easily measured and can be used as a simple diagnostic method for the determination of ion density, once the width versus ion density relationship is established either theoretically or experimentally. Here we present measured line widths and compare results with theoretical widths. The profiles of various lines of the sharp, diffuse, and fundamental series lines of cesium were measured at known ion densities with a scanning monochromator. The plasma was generated in a hot-cathode parallel-geometry cesium diode. For each case the ion density and the electron temperature were determined by measuring the intensity of the radiative recombination continuum. Line intensities gave independent measurements of temperature that were in agreement with the electron temperatures, showing the existence of local thermodynamic equilibrium and providing a confirmation of ion density through the application of the Saha equation. Detailed results of line width measurements are presented for a range of plasma density from 3·2 × 10 13 to 1·6 × 10 15 ions-cm −3 and for electron temperatures between 2000° and 6000°K. The results, valid in the vicinity of N ϵ = 10 15 ions-cm −3, are summarized in the following table: Series Transition Electron temp. Line width (°K) ω( A ̊ ) Sharp 6P-nS, 9 ≤ n ≤ 11 6000 w = 2 ( n-9) × 0·30 N ϵ × 10 −15 Diffuse 6P-nD, 7 ≤ n ≤ 10 6000 ω = 2 ( n-7) × 0·35 N ϵ × 10 −15 Fundamental 5D-nF, 5 ≤ n ≤ 8 2000 ≤ T ϵ ≤ 10, 000 ω = 2 ( n-5) × 1·5 N ϵ × 10 −15 In the table w is the full width at half maximum and has an accuracy of 20 per cent. The widths of the fundamental series lines are essentially independent of electron temperature, but temperature independence can not be claimed for the sharp and diffuse series lines.