A review of the dense Z-pinch

Plasma Phys. Control. Fusion 53 (2011) 093001
Topical Review
J = 0–1 line of neon-like Ar 8+ . With gain G of 0.6 cm −1 at a wavelength of 46.9 nm, three
lengths of discharge were tried; 3, 6 and 12 cm. The longest gave a gain–length product, Gl,
of 7.2. At this time the pinch radius was 100–150 µm. A buffer gas of hydrogen was added
in a 1 : 2 mixture to reduce radiative trapping on the lower laser level; this level must quickly
decay to the ground state. Neon was also explored as a buffer gas, but pure argon also lased
well at a full pressure optimized at 700 mTorr. To obtain successful lasing action required hot,
dense and axially uniform plasma (i.e. no instabilities), and sufficiently fast current rise to give
collisional excitation.
It took some years for other researchers to master the black art. Among these should be
mentioned Ben-Kish et al [694] and Kwek and Tan [695]. The former used an initial spark
followed by a prepulse in the current range 10 to 50 A. In a capillary of 4.2 mm diameter and
80 mm length with argon pressure of 500 mTorr, the main discharge was a peak current of
40 kA in 51 ns. There was shock heating, and a pinched, uniform column of 150 µm diameter
formed at the time of the lasing. The electron density was ∼10 19 cm −3 and electron temperature
∼60 eV. The reflected shock led to an increase in radius; and it is at this time of 45 ns that for
1–2 ns lasing action occurs. It is inferred that at the time of lasing a concave electron density
profile in the radial direction occurs to give beam guiding, and a thin plasma diameter avoids
self-absorption of the Ne-like Ar 2p-3s line. A gain G of 0.75 cm −1 similar to that of Rocca
et al was found, and the angular divergence of the laser beam was less than 5 mrad. Kwek and
Tan found that lasing action could occur at discharge currents as low as 9 kA, and that timing
of the prepulse relative to the main discharge is crucial, being 2–4 µs delay. Fill-pressures
from 0.15 to 0.35 mbar showed an optimum pressure increasing with current and 0.24 mbar at
19 kA. The prepulse current amplitude was varied and 23 A was optimal.
In the light of the work on stability regimes [136] and section 3.1, it is instructive to
ascertain in what regime are the above capillary Z-pinches. At peak compression followed by
expansion at a peak current of 40 kA the Bennett relation must momentarily hold. This gives an
ion temperature of 1.56 keV for T e = 60 eV and N i = 2.45 × 10 17 m −1 . From this we find that
i τ i = 0.02 and e τ ei = 0.50, i.e. the plasma is hardly magnetized, but the radially inward
Ettingshausen heat flux is a maximum, and this with the Nernst term ensures that the current
flows on axis. This could be assisted by the current-driven electrothermal instability [158]
which would occur earlier at T e below 48 eV with a radial wavelength close to the pinch radius
to give a single filament. The higher temperature on axis can lead to a local drop in density, as
required for focusing or optical guidance. With regard to MHD stability the Lundqvist number
is 0.78, showing that the pinch is extremely resistive and more dependent on Joule heating
than MHD effects. The magnetic Prandtl number is 0.016 showing that viscous effects are
negligible. With this knowledge, scaling to higher or lower parameters should be possible. A
fully time-dependent collisional–radiative model has been developed by Pöckl et al [696]ina
recombining carbon/hydrogen plasma formed from the walls of a capillary Z-pinch. A useful
review by Suckewer and Skinner [697] reports progress in table-top soft x-ray lasers.
Another and perhaps even more important application of the capillary Z-pinch is its use in
forming a straight channel of axially uniform plasma with a radial minimum density on axis,
for guiding an intense short pulse. It has been established by several research groups [698–700]
that laser-driven acceleration of electrons to 200 MeV energy can be achieved in a medium of
a mm-scale helium gas jet. Pukhov and Meyer ter Vehn [701] had earlier in simulations shown
how a monoenergetic beam of electrons could be accelerated in the wakefield scheme proposed
by Tajima and Dawson [702]. Here the electric fields, caused by charge separation, can be
of order 10–100 GV m −1 . By using instead a capillary Z-pinch a much longer acceleration
length can be achieved in principle. Leemans et al [703] demonstrated the production of a
monoenergetic electron beam of 1 GeV energy in a 3.3 cm long hydrogen gas-filled capillary
145