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Chapter 9:
HEIGHTS-EUV Package for DPP Source Modeling
This chapter presents an integrated model that is being developed to describe the hydrodynamic and optical processes that occur in DPP devices for EUVL applications. The developed model will eventually address the following subjects: plasma evolution and magnetohydrodynamic (MHD) processes, atomic data and plasma properties, detailed photon radiation transport, and interaction between plasma∕radiation and material. Regions with differing propagation speeds of perturbation require accurate numerical solutions of the MHD equations. The total variation diminishing (TVD) scheme in the Lax-Friedrich formulation for the description of magnetic compression and diffusion in a cylindrical multidimensional geometry is the most suitable and is used in our model. Depending on the complexity of the problem and the availability of computer time, a combination of various atomic and plasma models is being developed for populations of atomic levels, ion concentrations, plasma properties, and opacities. These include a collisional radiation equilibrium plasma model, a Hartree-Fock (HF) self-consistent-field atomic model, and a Hartree-Fock-Slater (HFS) method with splitting of atomic levels. Because of its influence on the whole dynamics of the discharge, radiation transport for both continuum and lines with detailed spectral profiles is modeled by various discrete-ordinate and Monte Carlo methods. The developed models have been integrated into the HEIGHTS-EUV computer simulation package. The features of the package allow one to study the hydrodynamics and radiation of two-gas mixtures in dense plasma focus (DPF) devices in the presence of impurities and erosion products that can affect radiation output. The goal of this chapter is to provide an overview of methods and techniques we use to simulate MHD and optical processes that occur in DPP devices of various electrode constructions. The general types of DPP devices that can be simulated within the HEIGHTS-EUV package are schematically shown in Fig. 9.1: (a) the DPF device, (b) the Z-pinch device, and (c) the hollow-cathode triggered pinch plasma source. The electrodes are drawn solid and shown in gray. The device is filled with xenon gas under an initial pressure in the range of several tens of millitorr at room temperature, corresponding to an initial density of the gas in the range of 1014–1015 cm−3. It is also assumed that a preionization step heats the gas to a temperature of near 1 eV and initiates the discharge. Typical representatives of the DPP devices are the conduction-type devices. The plasma is an element of the electric circuit, which gets its discharge current from the feeding capacitor C0. The simulation of the discharge by using the external (experimentally recorded) current may lead to the violation of the self-consistency principle, because the energy balance is not conserved and the plasma dynamics can be distorted. The physical processes that take place in these DPP devices are identical and can be described within the same mathematical model.
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