A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
magnetic field to ∼5 T, unless further compressed. Indeed the azimuthal magnetic field for
20 MA in 1 mm radius is as high as ∼4000 T, the local β is of order 1 and the plasma density
at fusion temperatures (∼10 keV) is some 10 7 times that of a tokamak. The nuclear reaction
rate depends on the square of the ion density, and so the confinement time becomes a critical
factor, together with the instantaneous fusion power. If the confinement time is less than an ion
transit time along its length, there will be no problems with impurities unlike in other magnetic
confinement devices unless the plasma forms at first on an insulating wall. Wire-array and
gas-puff Z-pinches do not interact with a wall, as, unlike other magnetic confinement devices,
the currents for equilibria are not driven by outward diffusion of the plasma. For example the
tokamak has radially outward Pfirsch–Schluter diffusion to generate the equilibrium currents.
Thus in considering reactor configurations the ‘first wall’ can be far away, and indeed could be
a liquid not limited in energy flux to 10 MW m −2 , and could also carry the return current [10].
The disadvantages of the Z-pinch for fusion are well documented in papers extolling the
virtues of tokamaks, stellarators and other low density quasi-steady-state devices. The first is
its instability to m = 0 (sausage) and m = 1 (kink) instabilities. The second is the heat loss to
the two electrodes. In section 2.3 it was shown that the power loss is mainly to the anode and
is of order 5 2 IT.ForI = 2 × 107 A and T = 10 4 eV this amounts to 0.5 TW. Clearly for this
to be negligible a fusion power in the tens of TW at least must be considered and therefore for
a reasonable size power station the Z-pinch must be pulsed.
This indeed fits in with current knowledge of dynamic Z-pinches in which, for example
the intense soft x-ray power occurs over 1 or 2 radial Alfvén transit times. For high Z
radiating loads this is sufficient time to radiate a significant fraction of the stored energy,
especially if the viscous heating mechanism (section 5.8) applies. Indeed this mechanism takes
advantage of MHD instabilities and in this context instabilities are excellent for Z-pinches.
The dynamic ‘bounce’ of the pinch is very non-adiabatic, and is accompanied by the onset of
longer wavelength modes, and later, probably a disruption (section 3.14). The disruption is
characterized by the creation of electron and ion beams, the latter which for deuterium will
produce neutrons from a beam–target mechanism.
To provide a longer confinement time various ideas have been employed. (a) The
preparation of Kadomtsev current density profile (section 3.2) as in a gas-embedded pinch
(section 7.4) can eliminate the m = 0 instability, or at least, for a plasma–vacuum boundary
condition, reduce the growth rate. Instead the m = 1 instability dominates and indeed
endeavours to form a helical minimum energy configuration, i.e. an axial magnetic field is
spontaneously generated (presumably of arbitrary sign). (b) Sheared axial flow can also extend
the stability time (sections 3.9 and 7.7) and further work at high currents is needed to explore
this concept. (c) Large ion Larmor radius effects have been shown both experimentally [14]
and theoretically to reduce the growth rate of the m = 0 instability (section 3.8). (d) An axial
magnetic field could be applied and compressed by means of a liner to provide a more stable
configuration (see section 7.10). Early ideas and concepts for a Z-pinch fusion reactor were
summarized by Sethian [613], before some of the recent advances were known, and when it was
considered that radiative collapse would limit the current dynamically to a few megampéres.
Hartmann [614] envisaged a gas-puff or a gas-embedded Z-pinch (which with presentday
knowledge is, in its hollow form, a strong candidate). Later he extended this to the
continuous flow pinch [615] which had earlier been proposed by Morozov [616]. This relied
on sheared axial flow to stabilize the pinch. Indeed Newton et al [617] did find in an experiment
conducted in 1967 that a continuous flow pinch could form at the end of a Marshall gun’s central
electrode at 0.5 MA. The pinch lasted 100 µs at several ×10 17 cm −3 electron density at 100–
200 eV. However reference to section 2.3 and [97] would indicate a heat loss of 2.5TI, equal
to 0.25 GW to the electrodes even at this low power. At the temperature and current required
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