Determination of plasma temperature by a semi-empirical method

Abstract

Doppler or Stark line broadening effects are generally used to determinate plasma temperature. These methods are difficult to apply to spectra of highly ionized atoms due to the short wavelengths involved. It is not at all easy to achieve sufficient wavelength resolution in this spectral range. In this case, a spectroscopic technique based on the relative intensities of lines must be used to measure the electron temperature in a plasma. However the relation of the measure of relative line intensity and the plasma electron temperature is complex and a number of issues must be examined for the diagnostic. In simple cases, only a two levels system need be considered. Here we introduce a semi-empirical method to determine the plasma temperature that takes into account multiple levels structure. In the theoretical model we consider a local thermodynamic equilibrium (LTE). The greatest difficult in the determination of plasma temperature using a multiple levels approach is overcome by calculating the transition probabilities in terms of the oscillator strength parameters. To check the method we calculated the oscillator strengths for the Cu I using a multi-configurational Hartree-Fock relativistic (HFR) approach. The electrostatic parameters were optimized by a least-squares procedure, in order to obtain the best fitting to the experimental energy levels. This method produces gf-values that are in better agreement with their experimental values than the produced by the ab initio calculation. The temperature obtained was 5739.3 K, what is compatible with direct measurements made for cupper DC discharge. Determination of plasma temperatureThe plasma temperature may be estimated through the relative emission intensities of spectral lines. From the theory of atomic structure and spectra [1], the relative intensities of the spectral lines, considering a Boltzmann distribution, are given by the equation ln Iλwhere I, λ and f are the relative intensity, wavelength, and oscillator strength respectively. E u is the energy of the upper level and g is the statistic weight of the lower level; k B is the Boltzmann constant, T is the temperature and b a constant parameter for all ion lines considered. In a few cases, g, f and E u can be obtained from the handbook of the spectroscopic constants, chemistry and physics. The equation (1) gives the plasma temperature in the case of LTE approximation. To increase the precision a large number of spectral lines must be used to determine plasma temperature. For a given spectrum, a plot of the logarithmic term in the right hand of equation (1) versus E u yields a straight line whose slope is equal to 1/k B T . Thus we can obtain the plasma temperature from the slope a. UsingWe apply the above mentioned method to some copper lines which spectroscopic constants are listed in Table 2.The major difficult here, is to obtain the oscillator strengths for the observed lines which are absent in the literature. Therefore to obtain the plasma temperature and overcome this diffcult it is necessary to ob...

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