Bright Spot Characterization of Low dI/dt X-pinch Plasmas using Soft X-ray Spectroscopy with Bennett Relation

Abstract

This study investigates the characteristics of X-pinch plasmas driven under low current rise rate ($dI/dt$) conditions using soft x-ray spectroscopy combined with the Bennett relation. X-pinch experiments were conducted on the SNU X-pinch device using copper wires at a low $dI/dt$ of 0.2-0.3 kA/ns. The resulting 1-10 keV soft x-ray signals, measured by an x-ray filtered AXUV photodiode array (XFPA), exhibit significant nonlinear effects due to the high intensity of the soft x-ray pulses. This work characterizes the nonlinear behavior of the AXUV-HS5 Si PIN photodiodes under intense pulsed radiation using a pulsed laser. We identified a charge conservation property that the total collected charge remains proportional to the incident pulse energy despite temporal profile distortion. Based on this diagnostic finding, we developed and applied a new framework for plasma parameter estimation. By combining a spherical emission model with the Bennett equilibrium, this approach determines that the soft x-ray source plasma is a 'bright spot', characterized by a plasma density $n_e \sim 10^{21} \text{ cm}^{-3}$, size $d \sim 30-40\ \mu\text{m}$, electron temperature $T_e \sim 1 \text{ keV}$, and an emission duration $t_B \sim 1 \text{ ns}$, rather than an extremely compressed 'hot spot'.