Z-Pinch

A wide variety of plasma diagnostic applications is available from the measurement of the relatively simple X-ray spectra of He-like ions [1] and references therein. The n = 2 and n = 3 X-ray spectra from many mid- and high-Z He-like ions have been studied in tokamak plasmas [2-4] and in solar flares [5,6]. The high n Rydberg series of medium Z helium-like ions have been observed from Z-pinches [7,8], laser-produced plasmas [9], exploding wires [8], the solar corona [10], tokamaks [11-13] and ion traps [14]. Always associated with X-ray emission from these two electron systems are satellite lines from lithium-like ions. Comparison of observed X-ray spectra with calculated transitions can provide tests of atomic kinetics models and structure calculations for helium- and lithium-like ions. From wavelength measurements, a systematic study of the n and Z dependence of atomic potentials may be undertaken. From the satellite line intensities, the dynamics of level population by dielectronic recombination and inner-shell excitation may be addressed. 

Figure 3-20. Pinch effect, plasma bent Z-pinch instability.

The pinch effect can be presented as an example of magneto-hydrodynamic effects in plasma. The effect consists of the self-compression of plasma in its own magnetic field. Consider the pinch effect in a long cylindrical discharge plasma with an electric current along the axis of the cylinder (Fig. 3-20), which is the so-called Z-pinch (Allis, 1960). The equilibrium of the Z-pinch is determined by the Bennett relation (1934) ... 

C. W. Hartman, Finite Larmor Radius Stabilized Z-Pinches, UCID-17118, April 1976. 

The "Extrap" (External Ring Trap) scheme consists of a toroidal Z-pinch immersed in a transverse (poloidal) magnetic field which is produced by currents in a set of external ring-shaped conductors . This scheme has two characteristic features. First, a purely transverse confinement field = JBp + is obtained by generating... 

There are in particular two linear versions of the Z-pinch for which Extrap could lead to schemes of fusion technological interest. First, the parameter ranges of stable operation of the pulsed high--density Z-pinch should become substantially extended in presence of Extrap conductors. Second, in a quasi Steady Z pinch stabilized by such conductors, the reduction of axial heat transport by the purely transverse magnetic field should make ignition possible in a pure plasma at technically realistic pinch lengths. ... 

Fig.4. Behaviour of straight Z-pinch in a stabilized case with the external rod current Jv==36 kA (Fig.4.1.), and in an unstabilized case with Jv=0 (Fig.4.2) (a) Pinch current Jp, (b) Side-on streak picture, (c) Loop signal, (d) Framing pictures. Shaded markings in (b) and (d) indicate limits of visibility.

The name Plasma Focus (PF) has been bestowed upon a development of the fast dynamic Z-pinch characterized by a new type of electrode configuration which lends itself to the production of a non-cylindrical implosion of the current sheath. It produces a short lived, rather dense plasma, whose properties are dominated by the occurrence of macroscopic and microscopic instabilities. The fame of the PF has long been based essentially on the fact that it was the most intense neutron producing device in the field of controlled thermonuclear research. Moreover, the neutron yield has the remarkable property of scaling as the second power of the energy IVo stored in the capacitor bank. The question of the character of the neutron spectra of the PF correlated to the neutron production mechanism, has long cast fundamental doubts on the relevance and interest of developing further this line of research for applications in the field of controlled fusion. 

Plasma Focus was discovered by N. V. Filippov in the USSR in the 1950s when studying the Z-pinches in a metal-wall chamber / /. A similar phenomenon was later observed by J. Mather in the USA when studying coaxial plasma guns /2/. Many laboratories are now studying the Plasma Focus phenomenon throughout the world, but in spite of this no clear ideas of the principles of Plasma Focus dynamics have yet been found, i.e. the mechanisms of neutron emission and the life-time of Plasma Focus. This... 

In the first experiments with Z-pinches, when the currents were about 10 MA, neutron emission was produced by accelerating (turbulent) mechanisms. In the present experiments with Plasma Focus, when the currents are about 10 A, neutron emission is produced by the joint thermal and turbulent mechanisms. We can hope that, if the currents are 10 A, neutron emission will be purely thermal and the contribution of turbulent mechanism will be comparatively small. There are no great technical problems in producing the 10 MA current, but great efforts will be needed to find the conditions for the cumulation of the whole discharge current near the axis of the system. This problem appears to be very important even in the present-day experiment. 

This term has also been applied to linear plasma columns where the field has azimuthal components in addition, such as linear stabilized Z pinches. 

An extensive review of linear systems, including several topics (Z-pinches, liners, fusion burners...) not discussed in this paper, was given by Krakowski. In addition, the reader is referred to proceedings of two conferences on linear systems held in the United States in 1977. 

The effect was first observed in the MAFINA experiments where in some shots the peak compression of an axial magnetic field occurred significantly before the time predicted by the dynamics of a Z-pinch driven cylindrical foil. (See Exploding, Imploding Metal Foils in /13/). 

One would envisage about 1 GJ coming from Fima alone and perhaps 30 GJ from the remaining nuclear reactions. The initial energy in the SL would have to be about 10 MJ which implies the Z-pinch energy of at least 100 MJ. Repetition frequency could be 0.1 c/sec. 

As you see the Z-pinch vessel becomes very large here, but so did the synchrotrons of 1950, as well as the projects of the tokomak reactors of today. 

Recent experimental results on a compressional Z-pinch and on a laser-initiated gas-embedded Z-pinch show considerable enhancement of MHD stability over conventional theory. It is thought that this could be due to finite ion Larmor radius effects. Several theoretical models of energy and pressure balance of a linear Z-pinch with end-losses have been made electron thermal conduction with (jot = 0, with ojT = oo, and singular thermal ion transit time loss. 

All yield the same essential scaling laws showing that Z-pinch will satisfy Lawson conditions with a current of 10 A, a line density of 10 and a ratio of ion Larmor radius to pinch radius of about... 

W, and burn time 10 s discharge frequencies of 10 s will be required for a 1000 MW plant. The merits of the system are simplicity, scalability to small power stations since the discharges can be arranged in modular form, and no impurity or first wall problems. Further experimental work on compression and laser-initiated gas embedded Z-pinches extending studies to higher currents of 10 A is required, with particular emphasis on large ion Larmor radius stabilisation. 

In this paper we are going to consider the dense and compact Z-pinch as a very interesting candidate for a controlled fusion reactor. By dense and compact we mean a density of about 4 x 10 cm, a length of say 10 cm and a pinch radius of 20 pm. To... 

Lastly we will consider the reactor advantages of the Z-pinch, especially the gas embedded pinch if it is formed in a high pressure ( 100 Atmos.) D-T gas bubble immersed in a vessel of liquid lithium. The liquid lithium will act as one or possibly both electrodes, return conductor, first wall, moderator, breeder, and coolant, and so relax the conditions on wall loading and blanket thickness which restrict the economic operation of other magnetic fusion systems. 

Taking the axisymmetric geometry of an unstabilised Z-pinch in which the only magnetic field component is B0, we can form the exact... 

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