A review of the dense Z-pinch

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
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