A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 81. Optical radial streak photograph of a 25 µm diameter and 2 cm length fibre taken 5 mm from the cathode [254, figure 3]. Figure 82. Schlieren images and numerical simulations of single 33 µm diameter carbon fibre on MAGPIE rising to 1.4 MA in 200 ns. Reprinted with permission from [197, figure 7]. Copyright 1997, American Institute of Physics. et al [198] have shown in simulations that m = 0 MHD instabilities lead to bifurcation of bright spots as seen in experiments [254]. The x-ray yield from these short-lived, localized regions can exceed the total yield from the background plasma by orders of magnitude. The axial velocity at which the bifurcating bright spots move is (1–3) × 10 5 ms −1 , which is an order of magnitude greater than the radial expansion velocity of 2 × 10 4 ms −1 . Figure 83 is an x-ray streak photograph of a 33 µm diameter carbon fibre showing typical m = 0 bifurcating bright spots. This behaviour is also observed in optical streak photography. Only 1% of the fibre is ionized at this time and the current is flowing in the low density (n e ∼ 10 24 m −3 ) corona, leading to sound and Alfvén speeds comparable to the axial velocity. Early radial expansion of coronal plasma and instabilities was identified also by Lindemuth and Sheehey [162] in the modelling of the deuterium fibre experiments at Los Alamos under Jay Hammel. However in this modelling the thermal neutron yield was below what was expected. This was hypothesized by Lovberg et al [329] to be due to a faster expansion associated with magnetic bubbles, and subsequent turbulent heating as they are ingested. Here the increased expansion dominates over the heating thus reducing the number density and the neutron yield. This model was also later put forward in a different context by others [331, 332] but, as argued in section 5.8 and 7.2 it is physically unlikely to occur at higher currents compared with viscous heating by saturated short wavelength m = 0 MHD instabilities [130]. A completely different hypothesis was put forward by Sethian et al [152] in explaining the neutron yield on the NRL deuterium fibre experiment. In this experiment it appeared 123
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 83. An axial x-ray streak photograph of the first 50 ns of the discharge in a 33 µm diameter carbon fibre. A 10 µm beryllium filter was employed, the spatial resolution was 640 µm and the temporal resolution 1.5 ns. Reprinted with permission from [198, figure 4]. Copyright 1997, American Institute of Physics. that the plasma was stable so long as the current was rising, and the neutrons and hard x-rays appeared when the current abruptly stopped rising. However, it could possibly be that when the m = 0 instability became fully developed and the line density of ions in the necks dropped to the critical value (equation (3.58), the increasing inductance and anomalous resistivity caused the current rise to be interrupted, and ion beams to be generated (see section 3.14). Images of the dense fibre will show little instability compared with the surrounding plasma. The results from the Imperial College deuterium fibre experiment [47] would be consistent with this interpretation. Indeed it was shown by Lebedev et al [47] that yet again the neutrons were anisotropic, consistent with beam–target nuclear reactions. A time-resolved study of the associated electron and ion beams in mega-Ampère fibre pinches was reported by Robledo et al [559] and Mitchell et al [247]. In [559] it was found that hard x-ray emission associated with energetic electrons occurred from the time of a disruption and lasted between 20 and 100 ns, indicating electrons of around 2 MeV energy in both 33 µm diameter carbon fibres and 25 µm aluminium fibres. The long time of MeV x-ray emission suggests that either the electrons are accelerated at the disruption itself and then most are confined off-axis in guiding-centre orbits, or there is a continuous heating of electrons to this energy in the low density gaps by anomalous resistivity between the plasma islands. In this region the driving voltage is due to the v r B θ electric field associated with the outward flow of under-confined plasma where the line density is less than critical. Both theories appear at first plausible. Confinement of energetic electrons off-axis requires a low guiding-centre velocity v d such that l/v d = t confinement is ∼100 ns. If the accelerated electrons have an isotropic distribution due to electron–electron collisions, the curvature and grad B drifts cancel on average, and in the dense plasma island region the E/B drift will be small and dependent on the ion temperature. The confinement time will be lµ 0 I/4πT i (eV). For a length l of 25 mm, a current of 1.4 MA and an ion temperature of 1 keV the time is 2.5 µs. However the individual hot electrons will have higher individual drift velocities, and at T = 2 MeV could traverse the length of the pinch in a few nanoseconds. In the theory of electron heating by anomalous resistivity when the local line density in the m = 0 neck is below the critical ion line density N criti given by equation (3.58), the current I will be ZN criti ec s , leading to an electron temperature at pressure balance given by T e = ( µ0 I 8π ) 2 Ze m i (7.16) For fully ionized carbon and a current of 1.4 MA, this gives a hot electron temperature of 25 keV. This is much less than the 2 MeV electron energies measured, but if the line density 124
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A review of the dense Z-pinch

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