A review of the dense Z-pinch

More documents

Recommendations

Info

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
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review discharge in which a 40 TW peak-power 1 µm wavelength 38 ps laser pulse was axially propagated. Without guiding by a profiled dielectric constant or thermal self-focusing the laser–plasma interaction length would be limited to the order of a Rayleigh length which is proportional to the spot size. Relativistic self-focusing extends the propagation distance but the effective dielectric constant is a function of laser intensity itself. Thus the leading edge of the laser pulse will be eroded. The self-focusing is a result of balancing the focusing effect of the dielectric profile resulting from the relativistic mass increase on axis with the centrifugal effect on the photons due to their spin [82]. The use of a channel allows a smaller spot size and hence a more efficient use of the laser energy. Much narrower capillaries of 150 and 310 diameter were used. The time delay between the peak discharge current and the laser was varied to give the optimal electron density profile at (2.7–3.2) × 10 18 cm −3 . In this experiment the input intensity was ∼10 18 Wcm −2 and the spot radii were 25–27 µm at the entrance and 31–34 µm at the exit. The plasma channel here was preformed by a laser. Further insights into the physics, especially the key process of injection of electrons into the laser wakefield, were found by Rowland-Rees et al [704]. In particular they concluded that it is beneficial if the plasma is only partially ionized near the axis: It was noted that the generation of electrons within the wakefield reduced the threshold for trapping because these electrons are born with ∼zero velocity while those of the background plasma have backwards momentum. The length of the channel (10 mm) here was of order of the dephasing length associated with the velocity difference between the accelerated bunch of electrons and the propagating bubble shaped vacuum generated by the ponderomotive force in the wakefield. In summary, two important branches of physics have developed out of the capillary Z-pinch, the capillary x-ray laser and the monoenergetic acceleration to GeV energy of electron bunches by a short-pulse intense laser. 8.9. Conical and radial arrays; plasma jets Conical arrays have been explored in depth by Ampleford et al [705] using both the MAGPIE generator at Imperial College and the ZEBRA generator at the University of Nevada at Reno. Figure 94 shows the schematic idea, and there is now an angle α at which the wires are inclined to the Z-axis. As can be deduced from this, even though the global magnetic field is purely azimuthal the currents have a radial component. The J ×B force now has an axial component, and the resulting precursor velocity and final implosion velocity will have axial components leading to a flow of plasma through a hole in the anode, usually in the form of a narrow, radiatively cooled jet of high Mach number (see section 8.10). Two types of experiment should be distinguished; (a) the overmassed, non-imploding wire array to study the precursor jet which is to a good approximation free of magnetic field and (b) the optimally massed array for implosion studies with a strong azimuthal magnetic field. In both cases there is zippering. This is because the global magnetic field at the array is larger nearer the cathode due to the smaller array radius there, and there is a shorter distance for the plasma to reach the axis. Interestingly during the precursor phase both the wavelength of the perturbations along the length of the wires and the ablation velocity V abl are constant, despite the large variation in the global magnetic field. In the case of the early stage of the instability it is more consistent with a primary role for the heat-flow-driven electrothermal instability, which is essentially only material dependent (see section 5.4). With a constant V abl it is the mass ablation rate per unit length, ṁ l that responds to the larger J × B force, and is given approximately by [705], 146 ṁ l (z) = µ 0 I 2 (t) 4πV abl (R c + z tan α) , (8.9)
Page 1 and 2:
Home Search Collections Journals Ab
Page 3 and 4:
Plasma Phys. Control. Fusion 53 (20
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96: Plasma Phys. Control. Fusion 53 (20
Page 145: Plasma Phys. Control. Fusion 53 (20
Page 169: Plasma Phys. Control. Fusion 53 (20
show all

A review of the dense Z-pinch

Create successful ePaper yourself

Delete template?

Save as template?