Z-Pinch Configuration

The Z-pinch configuration consists of a column of plasma with an axial current flowing through it. This axial current generates an azimuthal magnetic field, which results in an inward pressure exerted on the plasma. This inward magnetic pressure is balanced by the outward plasma pressure.

This radial force balance is described by the Bennett relation. This configuration is inherently unstable in the m = 0 (“sausage”) and m = 1 (“kink”) modes. The ZaP Experiment studies the stabilization of the pinch through sheared axial flow.

Z-Pinch Instabilities

m = 0 “sausage” instability
If a slight perturbation causes a local decrease in radius, this increases the strength of the local magnetic field. The result is an increase in the inward magnetic pressure, which further accentuates the perturbation.

m = 1 “kink” instability
If a slight perturbation causes a local displacement of the pinch, this increases the strength of the local magnetic field on the side closest to the centerline and decreases the strength of the magnetic field on the side farthest from the centerline. The result is a net outward force which accentuates the perturbation.

Sheared Flow

Sheared flow refers to the differential velocity along the plasma radius. That is to say, the velocity of the plasma varies with radius. It is thought that this may have a tendency to “smooth out” the instabilities.

ZaP Geometry

Below is a schematic of the ZaP Flow Z-Pinch experimental apparatus. The horizontal centerline defines the z-axis of the apparatus. The location of z = 0 is marked on the image, with z increasing to the right and the coordinate units in cm. (y is up and x is into the page.) The pinch forms on axis in the assembly region between the end wall and the tip of the inner electrode. 

ZaP Specifications

Pinch Properties
Diameter: 0.5 cm
Length: 50 cm
Peak Current: 200 kA
Density: 1e23 – 1e24 m^-3
Electron/Ion Temperature: 200 – 1000 eV
Magnetic Field Strength: 1 – 9 T
Pinch Duration: 20 – 40 μs