A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review and Mamada return to the plasma diode model with anomalous resisitivity after disruption by a m = 0 mode. There is no conservation of axial momentum in this model, in contrast to the earlier work of Haines [243]. Vikhrev [246] and Trubnikov [241] published their two papers in 1986 to celebrate Filippov’s 70th birthday. Disagreeing as to the origin of the neutrons, Vikhrev, backed by 2D MHD simulations, considered the neutrons as thermonuclear arising in the high temperature m = 0 necks of the Z-pinch. Trubnikov developed his earlier model further in which the ions are accelerated by a large induced electric field resulting from the redistribution of current. Again there is a problem of momentum conservation. Schmidt [542, 543] assumes in his ‘gyrating particle model’ deuterium ions originating at r = 0, z = 0 already with high energy. He follows their orbits with electron collisions and D–D fusion reactions in the surrounding gas in an attempt to match their energy and orientations with experimentally measured time-integrated and spectrally resolved distributions of fusion protons and neutrons. A similar method was applied by Rhee and Weidman [544] in which the acceleration process was consistent with a diode action. Hora et al [545] considered a double layer model for a fast decaying current, but implied that in their model the ion current would be orders of magnitude lower than the electron beam current. In conclusion, the origin of the ion and electron beams whilst perhaps still controversial could be best explained by the breaking of symmetry each side of a m = 0 neck by the Hall and FLR terms. This evolves during the redistribution of current density in the neck, like Trubnikov’s model, into a disruption with anomalous resistivity when the line density in the neck drops below the critical value given by equation (3.58). This leads to energetic singular ion beams and off-axis reversed ion flow (conserving momentum) [243] of lower energy deuterons as measured by Tisaneau and Mandache [250]. Electron beams which impact a solid anode typically have energies greater than 100 keV to 1 MeV. 7.4. Gas-embedded pinch It could be said that the origin of the gas-embedded Z-pinch dates back to 1947 with the investigation in Russia of the development of a spark channel under high pressure with moderate currents. This is discussed by Braginskii [546] who developed a theory of Joule heating and expansion of a channel with classical resistivity and thermal conductivity with bremsstrahlung radiation loss, neglecting the effect of magnetic forces. For Alfvén and Smårs [547] the magnetic pressure was important for confinement, and the surrounding gas was considered as high density gas-insulation. Fälthammar [108] investigated the steady-state cross-field thermal conduction losses of such a Z-pinch, as discussed in section 2.3. Smårs [548] reported experimental results in hydrogen, helium, and nitrogen. Kerr cell photographs showed the familiar m = 1 kink instability at currents of 100 kA. Skowronek et al [549] described the production of an exploding plasma filament which generated a Mach 12 shock in atmospheric air. First a filament is produced between two needles 3 cm apart and 0.5 µm radius, stabilized by two rings at intermediate potentials and a current of 100 µA, stable for 10 min. A 90 kV capacitor bank is then discharged rising to 200 kA in 1 µs. The aim of this experiment was to study dense, low temperature plasmas in the regime between degenerate and non-degenerate plasmas and also when the distance between ions n −1/3 i , the Debye length and the Landau lengths are almost equal, i.e. strong coupling. Over a large spectral region the plasma column radiates as a black body at 44 000 K, and is stable. In a later paper [550] they identified the onset of anomalous resistivity. Benage et al [551] extended this to 240 kA in 220 ns. The pinch always expanded reaching a radius of 8 mm with a velocity of 30 km s −1 with accretion of the surrounding gas. A helical instability occurred within the expanding cylindrical envelope. 119
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 78. Imperial College gas-embedded pinch; number density profile of electrons and neutrals during preheating phase at a filling pressure of 0.3 bar [182, figure 3]. Reprinted with permission from the IAEA. In their conceptual fusion reactor based on the high plasma density Z-pinch Hartman et al [552] considered that one means of isolating the Z-pinch is by a dense blanket of cold neutral gas. Two pinch cycles were considered, one where the pinch was sufficiently long to minimize plasma flow out of the ends and the other where refuelling occurred by plasma flow, e.g. using axial flow as proposed by Morozov [553] with FLR stabilization This has developed further to include sheared axial flow, considered in sections 3.5 and 7.7. Jones et al’s [554] laser-initiated, gas-embedded Z-pinch experiment with a 2D MHD model indicated a 200 eV electron temperature at a density of 10 20 cm −3 . The pinch was powered by a 600 kV Marx generator and (water) transmission line into 3 atm H 2 gas with 260 kA, rising in 200 ns. In his thesis [555] Shlachter presented schlieren images showing the growth of helical structures inside the cylindrical, expanding envelope of the current-carrying plasma. This illustrated the dominance of m = 1inaZ-pinch with a centrally peaked current density (see section 3.2). Dangor et al [556] found that their laser initiated, gas-embedded pinch with a preheat current to raise the initial temperature and lower the density, did not expand but maintained a constant radius during the time of the main current rise. This is because the current rise approximately satisfied the Haines–Hammel [103, 104] curve. After this time the pinch transformed into an expanding helical structure similar to that reported by Smårs [548]. No disruptive break-up occurred. Scudder [109] undertook a more complete 1D steady-state calculation of radial heat loss and bremsstrahlung losses. Problems arise when the Pease–Braginskii current is approached. Indeed at 1.8 MA both the pressure and radial heat flux go to zero at the plasma boundary. (However we should note that radiative collapse is probably precluded by ion-viscous heating associated with short wavelength m = 0 MHD instabilities, section 5.8.) The Imperial College gas-embedded pinch [53] was upgraded in current to 150 kA and in the use of laser interferometry to show that three phases could be distinguished. In the preheating phase the plasma column expanded from an initial radius of 100 µm with a radial velocity of 1.7×10 4 ms −1 driving a shock wave in the neutral gas. The Abel inversion of an interferogram gives the electron and neutral densities in figure 78. The equilibrium phase followed when 120
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A review of the dense Z-pinch

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