Measurement of Radiative Collapse in 2.2 kJ PF: Achieving High Energy Density (HED) Conditions in a Small Plasma Focus

Abstract

Radiative collapse in the plasma focus (PF) pinch creates extreme high energy density (HED) in the laboratory. The Pease–Braginskii current is that current flowing in a hydrogen pinch which is just large enough for bremsstrahlung to balance Joule heating; this threshold value being 1.4 MA. For high-Z gases undergoing strong line-radiation the radiation-cooled threshold current is considerably lowered. Recent work applied to a MJ PF has revealed that even if a threshold current is exceeded there is a condition that the characteristic depletion time of the pinch energy by radiation should be of the order of the pinch time in order for strong radiative collapse to be observed, thus explaining why no radiative collapse may be expected in deuterium; and also in helium; even in multi-MA PF devices. This paper extends the computation of depletion times to a kJ PF, the INTI PF showing that in the INTI PF only a small reduction in radius ratio may be anticipated in Ne whilst in Ar, Kr and Xe strong radiative collapse is expected. Two useful Tables are obtained applicable to kJ PF devices, one of reduced Pease–Braginskii currents in various high-Z gases and the other of corresponding characteristic depletion times. Two earlier papers using the Lee code had already demonstrated that radiative collapse occurs in plasma focus operated in high-Z gases. However in those papers computation could only be carried out up to a cut-off radius set at 0.01 of anode radius. Thus as shown in this paper most of the radiative compression was not computed or measured. This paper reports the measurement of the pinch trajectory in Kr by the fitting of a measured current waveform using the code with the cut-off radius successfully removed, so that the fitting fully follows the compression to its minimum radius and beyond to the rebound of the trajectory. The measured current waveform shows radiative collapse to a minimum radius ratio of 0.0014 or 0.0013 cm. Ion density reached 3.7 × 1026 m−3; and an immense burst of radiation is emitted with peak power of 1012 W, radiating 30 J in 50 ps, during the time of peak radiative compression. The energy density at peak compression is 4 × 1013 J m−3 or 40 kJ mm−3. This is the first time such a measurement has been made; and indicates that even in a kJ plasma focus, such a HED state is achieved.