A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review for a fusion reactor such losses would be unacceptable except for a pulsed system. Cheng and Wang [618] indeed criticized Morozov for neglecting the energy dissipation at the electrodes and for assuming adiabatic behaviour. Winterberg, in a series of papers, has put forward several eclectic reactor concepts, but only with rudimentary theoretical backing. In 1978 he proposed the adiabatic compression of a ‘super-pinch’ at a current much higher than the Pease–Braginskii current [619], similar to Potter [261]. To obtain shear-flow stabilization he proposed shooting a moving rod or metal jet along the axis [620] later adding a laser fast ignition pulse and D–T fibre instead of a rod plus radiative collapse [621]. To take advantage of ion beam formation at a disruption and subsequent nuclear reactions to drive a detonation wave Winterberg proposed cutting a Z-pinch with a laser [622]. Magnetized target fusion could be achieved using the high magnetic field of the pinch by shooting DT pellets from several sides of the pinch of a plasma focus [623], followed by laser-driven fast ignition. With a helical sawtooth-shaped capillary tube and a solid DT core, he envisaged sheared flow to stabilize MHD, and rotation to prevent RT with a current compressed DT core, plus a laser-driven fast-ignition detonation wave [624]. This is a development of a two-part paper on thermonuclear detonation waves in one or two stages plus catalysed or auto-catalysed burn [625, 626]. A combination of axial shear flow and rotation could lead to vortex line confinement with stable spherical regions [627]. With a sheared flow Z-pinch Winterberg proposed using a non-neutronic fusion chain reaction for propulsion [628]. Employing two MITLs he proposed ignition at their focus [629, 630] and an auto-catalytic fusion–fission burn [631]. Winterberg proposed using one Marx generator at high current to compress the fuel and a faster, high voltage, low current Marx generator to act as an ignitor [632]. Lastly he proposed using the Nernst effect in the corona of a D–T pinch to confine it. Zakharov in the 1950s first considered using the Nernst effect for steady confinement. Both found T 1/4 n is a constant. Here Winterberg [633] requires the neutrons emitted from the pinch on axis to heat the corona by nuclear reactions. More realistically Hagenson et al [634] considered a gas-embedded pinch with a gain of 30. This was a level III reactor study with no engineering issues studied. The concept of using a vortex of liquid lithium was studied by Robson [635] following ideas of McCorkle [636]. At Imperial College a series of concepts based on using liquid lithium as a return conductor and blanket were studied. Bolton et al [637] considered the gas-embedded pinch at high pressure. This followed earlier proposals by Haines [638] which included employing a matrix of Z-pinches immersed in liquid lithium, and using the injection of DT gas bubbles and laser initiation. Haines and Walker [639] considered the serendipitous employment of a pressure vessel of similar design to pressurized water reactors (PWRs). This was followed up by Walker and Javadi [640]. Many of these concepts are contained in a later paper by Bolton et al [641]. During the era of frozen deuterium fibre Z-pinches, Robson [642] ingeniously proposed the injection of fibres to intersect with two lithium jets which were the anode and cathode, respectively. In addition to these concepts, Baronova and Vikhrev [643] have studied employing the m = 0 neck as a trigger for fusion reactions. This is entwined with the controversy over the origin of the neutrons during a disruption, captured by the consecutive papers by Vikhrev [246] and Trubnikov [241]. The mechanisms of beam formation have been clarified in [243, 253], as discussed in section 7.3. An important point here is overall conservation of axial momentum. In order that the m = 0 instability leads to a high density and temperature in the necked region, the initial perturbation must be of a particular form [248]. This has yet to be demonstrated experimentally. In section 7.2 the deuterium gas puff experiment was extended on Z to 17 MA, producing a record 3.9 × 10 13 neutrons. Furthermore it is likely that the ion temperature is achieved in 133
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 134
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A review of the dense Z-pinch

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