A review of the dense Z-pinch

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
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