Plasma dynamics at the preionization stage in discharge-based EUV lasers

Abstract

In this paper we present the results of a detailed numerical investigation of plasma formed at the preionization stage of extreme ultraviolet (EUV) lasers based on nanosecond capillary discharges. Despite the general consensus that preliminary ionization is one of the features that have originally allowed creating stable and efficient lasers operated in argon-filled capillaries, little attention has been paid to the observed sensitivity of their performance to the properties of the preionizing current pulse. The goal of present studies was to obtain basic description of preliminary plasma state that could be used for interpretation of available experimental data on the subject. The numerical model was based on the hydrodynamic ‘fluid’ approach coupled with the heat transfer, the continuity and the Navier–Stokes equations. Preliminary discharge dynamics for conditions typical of an argon EUV laser is illustrated in detail, starting from the initial breakdown, taking the form of a fast ionization wave, to formation of a self-sustaining nonequilibrium plasma column. It is shown that a few microseconds after application of the prepulse a concave gas density profile is formed that can potentially be a factor influencing plasma compression and emission during the main stage of a capillary discharge.

On the mechanisms of the influence of preliminary ionization on the plasma dynamics of nanosecond capillary discharges and the properties of discharge-based EUV lasers

“…The concave shape is due to plasma pressure being almost constant along the capillary radius, while plasma itself is hotter on the axis and cooler at the periphery as a result of contact with the capillary wall. This also explains the greater overall degree of inhomogeneity of a profile for higher prepulse current amplitudes (for a detailed discussion of plasma properties at this stage and their dependence on prepulse parameters see [19]). In figure 4 presented are the calculated temporal dependencies of electron density (figure 4(a)) and electron temperature (figure 4(b)) at the capillary axis for cases of different prepulse current amplitudes together with the case of uniform initial density distribution.…”

“…In the present work, we considered both the preliminary and the main current pulses within a single MHD simulation. The MHD model does not take into account ambipolar diffusion, which for cases of discharge plasma created by current pulses with low amplitude can be a major particle loss mechanism leading to a great deviation from equilibrium [19]. However, it can still be used to obtain and parameterize a nonuniform initial radial density profile that takes place during the prepulse stage in EUV lasers [26] and whose influence on the compression stage of a capillary discharge is to be established.…”

“…While these factors may indeed take place, they do not seem to provide an unequivocal interpretation for the different experimental data available on the subject. We have previously investigated the parameters of low-temperature nonequilibrium plasma formed in the capillary during the preionization stage and have found that even at modest prepulse currents a considerable radial inhomogeneity of plasma density takes place, which could be a factor influencing plasma dynamics at the compression stage of the discharge [19]. In this work, we undertook magnetohydrodynamic (MHD) simulations to test this hypothesis and investigated the intrinsic mechanisms in which the initial state of plasma inside the capillary can influence the main discharge properties and EUV laser operation.…”

Effect of delay time between pre-pulse and main pulse on single-pass and double-pass amplification of 46.9 nm laser

“…We attribute the variation of the plasma column state with the delay time to the radial inhomogeneity of the initial plasma column introduced in Ref. [11]. In Ref.…”

“…In Ref. [11], it is found that the initial plasma generated by the pre-pulse is radially inhomogeneous and changes with time. Therefore, when the main pulse flows through the initial plasma at different delay times, the state of the plasma column generated by the main pulse will be different.…”