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This paper investigates the dense plasma focus (DPF) for applications in space-plasma physics. The plasma focus (a variant of Z-pinch) generates plasmas from fast high-voltage electrical discharges on coaxial electrodes suitable for very different studies: from fusion up to plasma-space modeling. In particular, the plasma sheath of the DPF is studied here and measured in some detail as a possible model for auroral observations. Deuterium gas was used in the experiments, and many helpful techniques were used, such as ultrafast photograph and neutron detection from nuclear-fusion reactions. In this paper, we show the different phases of the plasma focus correlated with discharge-current characteristics and neutron and X-ray production. Filamentary formations in the current sheath are shown, and its correlation with neutron production is done. The same number of filaments (about 60) reported in auroral observations are detected in plasma-focus discharges.