Historical research guide · 0516 · 2004
Equilibrium flow structures and scaling of implosion trajectories in wire array Z pinches
J. P. Chittenden · S. V. Lebedev · B. V. Oliver · E. P. Yu · M. E. Cuneo
In one minute
Take the picture Lebedev’s team measured — wires that stay put and boil plasma inward — and ask what follows if the whole array is treated as an ablating mass source sitting inside a magnetic force field. That is what Jeremy Chittenden and colleagues at Imperial College and Sandia National Laboratories do here, with two-dimensional simulations of the wire cores and of the array cross-section. They find the rate at which a core gives up plasma is fixed by a force balance right at its surface, which leaves the resulting inward speed almost indifferent to the machine’s current, the array’s radius or its mass. Run that steady source and the flow between the wires and the axis settles into a fixed radial shape: a time-independent equilibrium that is the single solution the ideal magnetohydrodynamic equations allow for flow faster than the local Alfvén speed in a cylinder. Checked against streak photographs of real implosions, the simple version bends — the number of wires matters, and it sets the trajectory, the symmetry and the x-ray pulse.
Connection
Chapter 9 is about plasma that organises itself, and this is the sharpest statement of it in the wire-array literature: the flow does not merely settle down, it converges on one profile that the equations single out. Chapter 12 gets the engineering consequence — ablation rate, and therefore wire number, is what sets the implosion trajectory and the shape and peak power of the radiation pulse a machine like this delivers.
From the source
A wire array Z-pinch radiation source can be represented as an ablating mass source embedded within a Lorentz force field, and that representation is enough to predict the trajectory and the spatial structure of the implosion that follows.Abstract, opening statement of the hypothesis
Two-dimensional resistive magnetohydrodynamic simulations of the ablating core regions and of the array cross-section indicate that the core ablation rate is determined by force balance at the ablation surface — a local condition at the surface of each wire, not a property of the machine as a whole.Abstract, simulation result
That force balance implies a weak dependence of the ablation velocity — the ratio of the magnitude of the Lorentz force to the mass ablation rate — on the array parameters, meaning current, radius and mass. The inward speed of the ablated plasma is close to an invariant of the design.Abstract, statement on ablation velocity
For a constant ablation rate, the radial profiles in the flow region between the wires and the axis converge to a set of time-independent equilibria, and these profiles are a unique solution to the ideal magnetohydrodynamic equations for flow faster than the local Alfvén speed in cylindrical geometry.Abstract, equilibrium result
Compared against experimental optical streak photography as a code validation exercise, simulated implosion trajectories show important deviations from the scenario of an invariant ablation velocity — the measurement, not the model, sets the terms of the comparison.Abstract, code validation against streak photography
The number of wires in the array is what determines the ablation rate, and through it the trajectory and structure of the implosion — which carries straight through to the inferred implosion symmetry and to the shape and peak power of the x-ray pulse. Wire count is a first-order design variable for the larger machines.Abstract, closing discussion of wire number, symmetry and pulse shape
The way in
https://doi.org/10.1063/1.1643756How to cite it
J. P. Chittenden, S. V. Lebedev, B. V. Oliver, E. P. Yu, M. E. Cuneo (2004) Equilibrium flow structures and scaling of implosion trajectories in wire array Z pinches doi:10.1063/1.1643756