On shear flow stabilization concepts for the dense z – pinch by Winterberg (17 page pdf)
Different ways to achieve the stabilization of a linear z-pinch by a superimposed shear flow are analyzed. They are:
1) Axial shear flow proposed by Arber and Howell with the pinch discharge in its center, and experimentally tested by Shumlak et al.
2) Spiral flow of a dense low temperature plasma surrounding a dense pinch discharge.
3) A thin metallic projectile shot at a high velocity through the center of the pinch discharge.
4) The replacement of the high velocity projectile by the shape charge effect jet in a conical implosion.
5) The replacement of the jet by a stationary wire inside the conical implosion
The linear z-pinch effect is the oldest and most simple magnetic plasma configuration. But because of its instability it was abandoned a long time ago as a useful configuration for the release of energy by nuclear fusion. Even if stabilized, a pinch discharge as steady state magnetic confinement device would require that the discharge channel must be rather long to keep the end losses low. This requirement is greatly relaxed if it is the goal to ignite a thermonuclear detonation wave propagating at supersonic velocities along the pinch discharge channel. There the time needed to keep the pinch stable is short. The ignition of the detonation wave could be done with a pulsed laser, for example. But for the ignition of the thermonuclear detonation wave, the pinch current must be of the order 10^7 Ampere to keep the fusion α-particles entrapped in the pinch, and the pinch must have a high density.
At low pinch densities the modified Shumlak et al. configuration, separating the dense pinch plasma from the spiraling high density shear flow, has a distinct advantage because it does not require a supersonic shear flow. It also permits to reach a higher z-pinch density, because there no electric field is set up by the v×B term. But for a non-pulsed steady state configuration it still would require a rather large pinch column to reduce the end losses. Against the modified Shumlak et al. configuration, stands the unavoidable mixing of the high A-number spiraling shear flow with the non-flowing z-pinch plasma. It is for this reason, that the steady state configuration proposed by Hassam and Huang has to be preferred.
Comparing the stationary central wire surrounded by fast axially moving pinch discharge, configuration, with the complementary fast moving central wire through a stationary pinch configuration, the fast moving central wire configuration is the clear winner, because it only requires a subsonic velocity of the wire in the >10km/s range, instead of the more than 10^3km/s dense plasma flow required for the stationary wire configuration.
This result is surprising only if one incorrectly thinks that it should make no difference if the wire is at rest with the plasma flowing, or if the plasma is at rest with the wire moving. In reality the wire at rest is attached to the large mass of the earth, and vice verse the pinch plasma at rest is part of an apparatus attached to earth. In each case this is a two body problem, where one of the masses is very large. Therefore, in the first case it is the momentum flux density ρv2 of the moving plasma against the earth, and in the second case the momentum flux density ρ0v02 of the moving wire against the earth.
For a dense z-pinch at thermonuclear temperatures the density is ρ~10^-3 g/cm3, and the velocity of sound a~108 cm/s. For MA≃1, one there has ρv2~10^13 erg/cm3. This can be reached with a metallic wire of density ρ0~10 g/cm3 moving with 10km/s=10^6 cm/s. But it much easier to accelerate a wire to 10km/s, by a travelling magnetic wave accelerator, for example, than a dense plasma to more than 1000 km/s, requiring to heat an expanding plasma to more than 10^8 °K