6Soltan Institute for Nuclear Studies, Warsaw, Poland

Plasma focus devices (PF) operated with admixtures of deuterium or hydrogen with heavy and medium-Z gases produce intense pulses of x-rays having a duration between a few ns and a few hundred ns, with photon energies from below 1 keV up to over 0.5 MeV. The soft x-ray emission displays two or three pulses and comes from plasma combined with the PF pinch and post-pinch phase. The hard x-rays are emitted usually in a short (from a few ns to a few tens ns) pulse, with the source being the anode surface exposed by the strong electron beams generated in the focus region. Recent experiments using argon-hydrogen mixtures performed at the Warsaw Institute of Plasma Physics and Laser Microfusion show detailed space resolved x-ray spectra for argon K-shell satellite lines from the He-like to the F-like ion and including the Ka . The radiation is produced by collisions of energetic electrons that excite and ionize the inner K-shell electrons of the argon ions present. These high-energy electrons occur because a beam is created by the constrictions of the plasma column due to the development of magnetohydrodynamic instabilities.

The Los Alamos suite of atomic physics and kinetics codes were used to simulate the observed spectra. An atomic physics data base was calculated for the Ne-like through H-like ionization stages of argon. Fine structure energy levels were calculated, including the effects of intermediate coupling and configuration interaction, for selected configurations in each ion stage. An adaptation of the Cowan atomic structure code was used. Electron configurations were chosen to provide an adequate representation of the line structure in the wavelength range of interest.

Cross sections for processes involving transitions between levels were calculated and incorporated into the data base. Plane-wave Born electron impact excitation cross sections were calculated for all possible transitions between levels of configurations within the ion stages described above. The data base was augmented with distorted wave cross sections which were calculated for the more important transitions from initial levels of configurations near the ground state of each stage of ionization considered. Cross sections for electron impact ionization, photo-ionization, and auto-ionization were calculated for transitions between levels of adjacent stages of ionization. The cross sections were all based consistently on the atomic structure described above.

The calculated data base was used to construct a collisional-radiative model for the argon plasma focus experiment. The level populations deduced from this model were used to simulate spectra for comparison with the measurements. The rate coefficients that appear in the model are cross sections integrated over a electron energy distribution function (EEDF). The EEDF function is chosen to adequately represent the actual plasma conditions. For this case, the electron energy distribution function was chosen to consist of a thermal Maxwellian component plus a high energy Gaussian component. The Gaussian component was used to represent the traversing electron beam. The two components are weighted by a factor f which is defined as the fraction of free electrons involved in the high energy component. This model for the EEDF has been used to calculate satellite structures in X-pinch and laser produced plasmas. The Gaussian was centered at 5keV with a width of 100eV. Previous calculations show that results are rather insensitive to the values of position and width but strongly sensitive to the value of the beam fraction f.

The resulting spectral simulations were compared to the spatially resolved measurements recorded at various distances from the anode. From these calculations a single value of f=.001 was chosen to represent the electron beam throughout the entire volume of interaction. This value of f was chosen because the calculations fit the observed spectrum in the cold spatial regions with a electron temperature of about 10eV. In addition, calculations with the same value of f reproduce the shape of the He-like and Li-like emissions observed in the hot spots at temperatures above 200eV.

It was necessary to use a three-temperature model to recover the emissions from all the ion stages occurring in the measured hot spots. Here the emission spectra for kT = 20, 100, and 230eV were combined in a 1.5-1-1 ratio, respectively. The results are shown in the figure below. The solid line is theory and the dashed line is the measured spectrum. The relative intensities of the spectral features are reproduced well by the model, however there is a small disagreement in the wavelengths. The results show large temperature gradients and strong electron beam effects in the PF hot spots.