The Effect of Neutral Atoms on Capillary Discharge Z-Pinch

Z-pinch collapse has been extensively studied since the late 50s, being a simple and effective way of producing hot and dense plasma. In this process, an electric current flowing through a plasma column, interacts with its self magnetic field, and the resulting force contracts the plasma column in the radial direction. Today Z-pinch plasma is widely used for various applications such as high power radiation sources and neutron sources [1,2]. An exciting new application of Z-pinch plasma was recently demonstrated by Rocca et. al. [3–5]. In this work, large amplification of soft-x-ray light was obtained in Nelike Ar and S plasma, created by a fast (∼ 40 ns) Z-pinch discharge inside a capillary. Compared with the alternative approach of laser driven excitation [6,7], the capillary discharge has the advantage of allowing for compact (table-top), efficient and simpler soft-x-ray lasers. In this paper we study the role of neutral atoms in the dynamics of a capillary discharge Z-pinch, in the regime for which soft-x-ray amplification was demonstrated. The commonly used one-fluid magneto-hydrodynamics (MHD) model assumes that all the particles in the plasma are charged, and drift together. We, however, show that for the case discussed here, large portions of the plasma contain an appreciable amount of neutral atoms. Since these are not affected by the electro-magnetic forces, but only by the much weaker mechanical forces, they flow with much smaller velocities than the ions and the electrons. To account for this effect, we extend the onefluid MHD model by introducing a separate fluid for the neutral atoms (in addition to the standard electrons-ions fluid). Results of calculations using this extended model give new predictions for the dynamics of the pinch collapse, with some features in better resemblance with the measured data. This confirms our previously reported estimates [8]. We start with the standard one-fluid two-temperature MHD model, commonly used for numerical calculations of Z-pinch processes [9–13]. It considers hydrodynamic flow including shock waves, heat conduction, heat exchange (between ions and electrons), magnetic field dynamics, magnetic forces, Ohmic heating, radiative cooling and ionization. We use a simple ionization model, and assume a quasi steady state, taking into account collisional ionization, and 2-Body and 3-Body recombination. Since the plasma is assumed to be optically thin, ionization and excitation by radiation are neglected. The latter assumption should hold at least to the end of the collapse. This model is incorporated into our numerical code, SIMBA, where the equations of motion of the system (see [9–14]) are solved in a Lagrangean mesh [15], assuming one-dimensional axial symmetry. Shown to be remarkably stable [16], and having a high length-to-diameter ratio (of 50-500), the capillary discharge Z-pinch experiment is naturally described in the framework of this 1-D MHD model. Previously reported works [10], have indicated that taking into account ablation of the plastic capillary wall is necessary for the correct description of the pinch dynamics. According to this the calculation should thus be extended to include a narrow region of the plastic capillary wall. However, it was also shown in [10] that even with this effect taken into account, good agreement with the measured data still requires some major artificial adjustments of the plasma transport coefficients. We have repeated these calculations using the same one-fluid MHD model, and found them to agree with the reported results. In particular, we also find that the measured data is reproduced by onefluid MHD calculations only when artificial adjustments are introduced, as demonstrated in Fig. (1). The figure displays the calculated radius of the collapsing Ar plasma as a function of time in a capillary discharge Z-pinch. The parameters of the calculations are those used for soft-xray amplification experiments [3,4,10]: initial Ar density of ρ0 = 1.7·10−6g./cm3 or n0 ≈ 2.5·1016atoms/cm3, initial temperature of T0 ≈ 0.5eV, and a maximum current of 39kA, with its peak at t=32ns [17]. The figure also presents some measured data, of the radius of soft-x-ray source, as a function of time, taken from [10]. Since the radii of the soft-x-ray source and that of the collapsing Ar plasma are related, it is clear that there are disagreements between the calculated and measured data: For example, the calculated pinch peak is about 10ns earlier than the measured one. It is shown in Fig. (1) that multiplying the classical electrical conductivity [18] by a factor of 15, results in a good agreement with the measured instant of the pinch peak, however at the same time it also spoils