A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
higher velocity near the cathode in the main implosion phase means that there is an increased
zipper effect.
Above a critical angle α the early implosion at the cathode end results in the creation
of a ‘magnetic bubble’. This is seen at 73 ns in the faster ZEBRA experiment illustrated in
figure 95(b). Also in figure 95(a) can be seen the axially uniform wavelength and in 95(c) the
axial zipper position of the precursor plasma. There are 3D MHD simulations in this paper
and an earlier one by Ciardi [706] which broadly agree with the dynamical phenomena.
An interesting possible application is the broadening of the x-ray pulse in time, typically
by a factor of two which would be needed by ICF. Indeed further shaping of the x-ray pulse
could probably be achieved by using a mixture of conical sections to the load.
In another proposed application, Chittenden et al [707] have proposed using two jets of
plasma as drivers for indirect inertial confinement by aiming each at a material convertor
(as in heavy-ion fusion) each end of a cylindrical hohlraum in which is placed the fuel
capsule.
The magnetic bubble is probably associated with a strong radial current connecting the
already imploded plasma at the cathode end with the remains of the conical wire array. Thus
it would be expected that a purely radial array would have a similar rising magnetic bubble
or tower as its main feature. Because of its relevance to laboratory astrophysics it will be
considered in more detail in the following section.
8.10. Laboratory astrophysics
The Z-pinch and laser-produced plasmas can be used to model on the laboratory scale certain
astrophysical phenomena, even though the length and time scales can be up to 10 24 times
greater. The reason for thinking that the basic hydrodynamic or MHD phenomena are
essentially the same is that if the corresponding dimensionless numbers such as the Reynolds’
number, R e , and Peclet number, P e , in hydrodynamics and the magnetic Reynolds’ number,
R m , in MHD are much larger than unity in both the laboratory and the astrophysical situation,
then the resulting phenomena will be similar. Such astrophysical phenomena as shocks and
jets formation and collimation could thus be modelled in the laboratory using lasers or Z-
pinches [708, 709].
The longest highly collimated jet so far found in active galactic nuclei (AGN) is estimated
as being 1.5 million light years (mly) or 1.4 ×10 22 m long [710] emanating from an extremely
massive black hole (>10 9 solar masses). More standard, Centauris has a jet 4.5 kilo-parsec
(kpc) or 1.4×10 20 m long (and a counter-jet) [711]. Young stellar objects (YSOs) have shorter
jets, often with more structure. In particular Herbig–Haro (HH) jets [712] are associated with
the birth of stars, formed from giant molecular clouds (GMCs) via accretion in a disk under
gravity. These jets are typically 0.5pc or 1.5 × 10 16 m in length, and, like the other jets, are
moving at speeds of 100–1000 km s −1 [713]. Molecular bow shocks typically occur at the
ends of the HH jets due to interaction with the surrounding cloud, and emit in the infra-red
(IR) or optical region. Knots have been observed [714], which is consistent with nonlinear
m = 1 instabilities.
A large Reynolds’ number, R e , or Peclet number, P e , implies a short mean-free path (mfp),
since they are proportional to L/λ mfp while, paradoxically the magnetic Reynolds’ number,
R m ,isproportional to the electron–ion mean-free path. A large magnetic Reynolds’ number
means that at sonic flow the mean-free path multiplied by L is much greater than the square
of the ion collisionless skin depth. Another important comparison between laboratory and
astrophysical phenomena is the radiative cooling time compared with L/v where L and v are
the characteristic length and velocity, respectively.
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