A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
the cold liner, and also to magnetize alpha particles so as to deposit their energy in the plasma,
but its pressure is much less than the plasma pressure. Spherical and cylindrical configurations
have been considered, while the most favoured is the magnetic theta pinch or field-reversed
configuration (FRC). In Russia the subject is called MAGO [601] and the subject is intermediate
in density and confinement times to magnetic and inertial fusion. Essentially the inertia is
greatly increased by the relatively massive liner which usually is considered to compress
adiabatically with a velocity of 10 4 to 10 5 ms −1 . The parameter space for MTF is discussed
by Lindemuth and Kirkpatrick [602]. A useful summary of the field is given by Dahlin [603].
It is important to remember that this is still inertial confinement. An important feature of
this is that the energy E to be provided to an inertially confined sphere is proportional to n −2
i
where n i is the ion density. This can be seen as follows
E = 4 3 πR3 · 3n i eT i (7.19)
and the Lawson product n i τ for inertial confinement is n i R/c s , but now multiplied by
(M L /M) 1/2 where M L is the sum of the liner and plasma mass M and c s is the ion sound
speed. Thus E is given by
E = 4π (n iτc s ) 3 ( ) 3/2 ML
n 2 eT i . (7.20)
i
M
The final, compressed plasma is considered to be 10 26 m −3 at 10 keV which is a density some
10 5 smaller than that usually considered for ICF. Thus the driver can be much weaker, but
the energy required for the plasma is greatly increased. Furthermore the energy that has to be
employed for the driver would have to be recycled with a very high efficiency of over 90%.
A reactor would be a pulsed system, which, for example, at 4 pulses a second would give
an output of 160 MWe. But because of the comparatively low fuel density there would only
be a fractional burn-up of ∼1%. It would appear that the higher the initial plasma density the
more efficient the reactor would be for a given volume contraction.
A Z-pinch, rather than a FRC, might be one answer, as unlike the FRC there is no limitation
of magnetic field or plasma density for a Z-pinch since no magnetic coils are employed. Such
a scheme, the staged Z-pinch, was proposed by Rahman et al [604] in which a Z-pinch liner
collapses on to a DT-fibre Z-pinch. However in this paper an axial magnetic field is also added
to ensure magnetization of alpha particles, and also to provide some stabilization. Diffusion of
this field will occur, especially if the plasma is turbulent, but the main flux compression is of the
azimuthal magnetic field. An experiment by Klir et al [605] was conducted on the S-300 device
in Moscow with an aluminium wire array imploding on to a CD 2 fibre. The x-ray pulse was
almost the same with and without the central fibre, while the peak neutron yield of 2×10 8 with
a fibre was not associated with a dominant x-ray pulse, and indeed was of beam–target origin.
Magnetically insulated inertial fusion applied to laser-driven ICF was proposed in 1986
by Hasegawa et al [606].
Simulations have been undertaken by Sheehey et al [607] where the DT fibre pinch is
allowed to develop into a Kadomtsev (m = 0 stable) profile as it meets the liner wall followed
by liner compression. Joint studies by Los Alamos and the Air Force Research Laboratory are
concentrating on the compression by liners of field-reversed configurations [608].
7.11. Inverse Z-pinch
The inverse Z-pinch consists of a hard-core insulated cylindrical conductor on the axis, and
a return current in a plasma shell around it [609]. This shell will be accelerated radially
outwards, but there is an axial magnetic field applied which will then be compressed. The
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