A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
part by ion-viscous heating. The extension of this to DT and to higher currents for at least a
neutron source [494], if not yet a reactor, is very promising. The important point is that viscous
heating not only raises the temperature but also removes any limiting current associated with
radiative collapse. Alpha particle heating will continue to heat primarily the electrons.
The addition of an axial magnetic field is considered in sections 3.10 and 8.7.
Lastly it is interesting to examine the scaling of the vector triple product n i τT i which
should exceed 10 24 m −3 s (eV) for fusion break-even. If the pinch can be confined for 10τ A
at 10 keV and at a radius of 1 mm, a current of 35 MA is required, and n i τT i scales as I 2 .
Perhaps future experiments will explore this, perhaps extending the confinement time with
axial velocity shear.
8.2. X-ray sources
The use of pulsed-power generators to power Z-pinches as x-ray sources was reviewed over
20 years’ ago by Pereira and Davis [51]. Since then the generation of soft x-rays using wire
arrays has reached high powers of 280 TW for a FWHM pulse of 5 ns with a 17% conversion
efficiency from the wall-plug [1, 2].
Early work on soft x-ray emission from imploding aluminized plastic cylindrical liners
using the SHIVA capacitor bank by Degnan et al [644] gave up to 240 kJ in an x-ray pulse of
130 ns FWHM. Deeney et al [645] as early as 1991 found that there appeared to be an extra
heating mechanism during stagnation when using low mass aluminium arrays of large array
diameter to study keV x-rays. Increased x-ray yield was found by mixing elements of similar
atomic numbers [646]. Later at 20 MA on Z up to 125 kJ of K-shell x-rays from titanium wire
arrays was obtained with electron temperatures up to 3.2 keV [647].
Zakharov et al [648] employed the collision of an accelerated gaseous liner with an inside
shell on the Angara 5 generator producing 9 TW in a 90 ns pulse. Sharpening the x-ray pulse
was the main purpose of this early work. Instabilities in liners, involving azimuthal and axial
inhomogeneities, were found by Branitsky et al [649], and they could reduce their effect by
using thin foam (50–100 µm) liners rather than gas puffs. For further discussion on gas puffs
see section 7.2.
If x-ray energies greater than 1 keV are needed, Whitney et al [650] have developed a 1D
model to give scaling laws. They define a parameter
η = K i /E min , (8.1)
where K i is the kinetic energy per ion before stagnation and E min is the minimum energy to
promote K-shell excitation and not allow recombination back into the L shell. For aluminium
this energy is about 12 keV/ion. For a small mass of 6 µgcm −1 figure 88 shows that there is
an optimum value of η for maximum yield per unit length of x-rays above 1 keV. Here η was
varied by varying the implosion time and hence the peak current. For low η there is little energy
to radiate while at high η the plasma overheats and hence becomes an inefficient radiator. As
the mass of the array is increased in these calculations, which are based on 1D calculations
of the stagnation itself in the absence of current, the optimum value of η increases such that
at 200 µgcm −1 η was equal to 27.5. Because at low mass the plasma is optically thin and the
radiated power scales as the square of the density, it follows that the x-ray yield would scale as
mass squared. At high mass the radiated energy is limited by the thermal energy at stagnation.
The yield therefore is proportional to mass. This transition is clearly seen in figure 89 for
two cases in each of which the kinetic energy per ion and η are fixed. Below the transition
in scaling the regime is termed inefficient because the energy radiated is a small fraction of
that available, while above the regime is termed efficient. As one considers other elements the
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