A review of the dense Z-pinch

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Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 91. Hall acceleration and force found experimentally from the magnetic stress tensor [669]. The upper figure shows the schematic of the Z-pinch with a short coil added, including the closed path abcd along which the components of B r and B z are measured (middle figure) leading to the components of the magnetic stress tensor (bottom figure). Reprinted figure with permission from [669]. Copyright 1965 by the American Physical Society. force towards the cathode. Correspondingly on the cathode side there is a repulsive force again accelerating the plasma (ions) towards the cathode. The magnetic field lines associated with the coil are in fact pulled towards the anode, and the tension in these field lines acts like a catapult to accelerate the plasma towards the cathode. It can be thought that the magnetic field is almost frozen to the electrons which are moving axially towards the anode. Etherington 139
Plasma Phys. Control. Fusion 53 (2011) 093001 Topical Review Figure 91. (Continued) and Haines [669] measured the force on the coil as a function of time by measuring the components of the magnetic field on a surface outside the Z-pinch enclosing the coil, shown in figure 91(b); then via the stress tensor and a surface integral the force was measured as illustrated in figure 91(c). The limiting axial velocity is v z = J z /n e e, at which v × B field balances the J z B r /n e e Hall term and no further acceleration will occur. That is, the ions are carrying the Z-current. One application of this phenomenon is the development of the Hall thruster, which has been employed especially in Russian and more recently European space missions. In order to maximize the volume where the radial magnetic field exists the device has developed into a coaxial system, schematically shown in figure 92 from [670]. These are quasi-steady-state thrusters which can accelerate ions from 100 to 1000 eV. Whilst the instantaneous force is small, typically 0.04 to 1 N in a plasma of electron temperature of order 10 eV, these devices have a high specific impulse, e.g. in Xe, 1500 s or 15 kN s kg −1 . These thrusters have been used mainly for attitude control, consume some kilowatts of power with an efficiency of about 60%. Their thrust is an order of magnitude higher than electrostatic ion thrusters which are limited in current by the Child–Langmuir law. Another application of Hall acceleration is in industrial plasma processing. At Imperial College a toroidal Z-pinch was surrounded by 36 coils of spatially alternating currents, these coils producing a series of cusp-shaped magnetic fields which dominated the configuration (figure 93). The applied induced toroidal electric field led to ion acceleration through multiple coils; hence the device was named the Polytron [66, 67, 666]. The coil separation has to be less than the accelerated ion’s Larmor radius. To achieve this condition it was easier to use an argon plasma, in which it was found that a Mach number of over 2 was obtained. The equilibrium position could be controlled by an additional vertical magnetic field, thus reducing plasma–wall interactions and losses through the ring cusps. Indeed a double electrostatic sheath develops at each ring cusp. There is not only Hall acceleration of ions, but also ion-viscous heating to 100 eV, i.e. much higher than the electron temperature of 10–25 eV. In considering how this stable configuration could be improved it was proposed to have elongated cusp coils, confining the radial magnetic field to narrow regions, thus reducing ion losses and concomitant electron thermal conduction losses through the ring cusps. Furthermore, by increasing the Mach number to 5 or 7 the confinement time could be increased to satisfy Lawson’s condition. 2D, two-fluid simulations by Watkins et al [671] followed the fast radially inward diffusion of the axial current, the computational time-step now being determined by the whistler wave. Hall acceleration, ion compressional heating 140
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A review of the dense Z-pinch

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