The use of geometric effects in diagnosing ion density in ICF-related dot spectroscopy experiments

Abstract

We describe a method to calculate the ion density of High Energy Density (HED) cylindrical plasmas used in Dot Spectroscopy experiments. This method requires only spectroscopic measurements of the Heα region obtained from two views (Face-on and Side-on). We make use of the fact that the geometry of the plasma affects the observed flux of optically thick lines. The ion density can be derived from the aspect ratio (height-to-radius) of the cylinder and the optical depth of the Heα-y line (1s2p 3 P 1 → 1s 2 1 S 0 ). The aspect ratio and the optical depth of the y line are obtained from the spectra using ratios measured from the two directions of emission of the optically thick Heα-w line (1s2p 1 P 1 → 1s 2 1 S 0 ) and the ratio of the optically thick to thin lines. The method can be applied to mid-Z elements at ion densities of 10 19 − 10 20 cm −3 and temperatures of a the order of keV, which is a relevant regime for Inertial Confinement Fusion (ICF) experiments.

Laboratory measurements of geometrical effects in the x-ray emission of optically thick lines for ICF diagnostics

“…We have also presented the first results of ion density calculations using the He-α spectra of cylindrical HED plasmas 53 . These results agree with the measured density from the imaging data and show the capabilities of the method in Pérez-Callejo et al as a spectroscopic diagnostic.…”

“…These results are indicated in figure 11b as green circles. As a double check, the ion density was also obtained from the w/y ratios for Face-on and Side-on view, using the method by Pérez-Callejo et al 53 . This method assumes a perfectly uniform plasma cylinder and calculates the ion density from the differences in the w/y ratio in the Face-on and Side-on spectra.…”

Spectroscopic characterisation of the effects of plasma geometry on the angular distribution of X-Ray emission in HED plasmas

“…First, the simple case of a uniform plasma cylinder, which is discussed in depth in reference [55], is considered. Figure 2.3 shows a schematic drawing of this geometry.…”

“…Working with Equation 2.26 is not computationally (or analytically) easy, given the complicated functions inside the brackets. One possible approach is to approximate the exact solution by a function of the form (1 − exp[−aκR]), by choosing a value of a such that it minimises the differences with the exact solution over a wide range of κR values [55,80]. In this case, a maximum value for κR of 10 was chosen to ensure convergence of the calculations, and the optimal value of a was found to be 1.45.…”

“…The face-on emission (in the direction of the axis) can be considered as the side-on emission of a series of differential cylinders with thickness Rdθ. This was described in Section 2.3.1, and has the form [55]…”