R.P. Golingo

Sheared flow stabilization experiments in the ZaP flow Z pinch

The stabilizing effect of a sheared axial flow on the m=1 kink instability in Z pinches has been studied numerically with a linearized ideal magnetohydrodynamic model to reveal that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold. The sheared flow stabilizing effect is investigated with the ZaP (Z-Pinch) Flow Z-pinch experiment at the University of Washington. An axially flowing Z pinch is generated with a 1 m coaxial accelerator coupled to a pinch assembly chamber. The plasma assembles into a pinch 50 cm long with a radius of approximately 1 cm. An azimuthal array of surface mounted magnetic probes located at the midplane of the pinch measures the fluctuation levels of the azimuthal modes m=1, 2, and 3. After the pinch assembles a quiescent period is found where the mode activity is significantly reduced. Optical images from a fast framing camera and a ruby holographic interferometer indicate a stable, discrete pinch plasma during this time. Multichord Doppler shift measu...

Formation of a sheared flow Z pinch

The ZaP Flow Z-Pinch project is experimentally studying the effect of sheared flows on Z-pinch stability. It has been shown theoretically that when dVz∕dr exceeds 0.1kVA the kink (m=1) mode is stabilized. [U. Shumlak and C. W. Hartman, Phys. Rev. Lett. 75, 3285 (1995).] Z pinches with an embedded axial flow are formed in ZaP with a coaxial accelerator coupled with a 1m assembly region. Long-lived, quiescent Z pinches are generated throughout the first half cycle of the current. During the initial plasma acceleration phase, the axial motion of the current sheet is consistent with snowplow models. Magnetic probes in the assembly region measure the azimuthal modes of the magnetic field. The amplitude of the m=1 mode is proportional to the radial displacement of the Z-pinch plasma current. The magnetic mode levels show a quiescent period which is over 2000 times the growth time of a static Z pinch. The axial velocity is measured along 20 chords through the plasma and deconvolved to provide a radial profile. U...

Equilibrium, flow shear and stability measurements in the Z-pinch

The stabilizing effect of a sheared axial flow is investigated in the ZaP flow Z-pinch experiment at the University of Washington. Long-lived, hydrogen Z-pinch plasmas are generated that are 1 m long with an approximately 10 mm radius and exhibit gross stability for many Alfven transit times. Large magnetic fluctuations occur during pinch assembly, after which the amplitude and frequency of the fluctuations diminish. This stable behaviour continues for an extended quiescent period. At the end of the quiescent period, fluctuation levels increase in magnitude and frequency. Axial flow profiles are determined by measuring the Doppler shift of plasma impurity lines using a 20-chord spectrometer. Experimental measurements show a sheared flow that is coincident with low magnetic fluctuations during the quiescent period. The experimental flow shear exceeds the theoretical threshold during the quiescent period, and the flow shear is lower than the theoretical threshold at other times. The observed plasma behaviour and correlation between the sheared flow and stability persists as the amount of injected neutral gas and experimental geometry are varied. Computer simulations using experimentally observed plasma profiles show a consistent sheared flow stabilization effect. Plasma pinch parameters are measured independently to demonstrate an equilibrium consistent with radial force balance.

Spatial deconvolution technique to obtain velocity profiles from chord integrated spectra

Passive spectroscopy is used to measure the plasma parameters on the ZaP experiment at the University of Washington. Twenty spectral intensities, which are functions of the plasma’s density, velocity, and temperature along the viewing chord, are recorded on a charged coupled device. The instrument function is different for each viewing chord. A deconvolution technique based on a shell model, which includes the effects of the instrument function, is developed to deduce the local plasma parameters. The error analysis for this technique is also developed. The technique is able to model complicated plasma parameter profiles and is able to deduce the local plasma parameters and position of the plasma.

Telecentric viewing system for light collection from a z-pinch plasma

As part of a Doppler spectroscopy system to measure the radial variation of ion flow and temperature, a pair of telecentric viewing telescopes has been installed on the ZaP z-pinch plasma device. Each telescope simultaneously collects 20 chords of light (200–1200 nm) emitted by impurities in the plasma, and images the chords on a fiber optic bundle for transport to a spectrometer. The center-to-center spacing of adjacent chords in the plasma is 1.24 mm, thus radial variation across the r=10–15 mm ZaP plasma is completely recorded. In this telecentric imaging system, all object chords and image points, including those laterally displaced from the optical axis, are formed by ray bundles whose chief ray is parallel to the optical axis. Thus all 20 light collection chords passing through the ZaP plasma are parallel, and all 20 image points fill the optical fibers with an identical cone. This maximizes system efficiency and measurement precision, and simplifies calibration and data analysis.

The Sheared-Flow Stabilized Z-Pinch

The stabilizing effect of a sheared axial flow is investigated in the ZaP Flow Z-pinch experiment at the University of Washington. Long-lived, Z-pinch plasmas are generated that are 100 cm long with a 1 cm radius and exhibit gross stability for many Alfvén transit times. Experimental measurements show a sheared flow profile that is coincident with the quiescent period during which magnetic fluctuations are diminished. The flow shear is generated with flow speeds less than the Alfvén speed. While the electrodes contact the ends of the Z-pinch, the surrounding wall is far enough from the plasma that the wall does not affect stability, as is investigated experimentally and computationally. Relations are derived for scaling the plasma to high energy density and to a fusion reactor. The sheared flow stabilized Z-pinch concept provides a compact linear system.

Note: Zeeman splitting measurements in a high-temperature plasma

The Zeeman effect has been used for measurement of magnetic fields in low-temperature plasma, but the diagnostic technique is difficult to implement in a high-temperature plasma. This paper describes new instrumentation and methodology for simultaneous measurement of the entire Doppler-broadened left and right circularly polarized Zeeman spectra in high-temperature plasmas. Measurements are made using spectra emitted parallel to the magnetic field by carbon impurities in high-temperature plasma. The Doppler-broadened width is much larger than the magnitude of the Zeeman splitting, thus simultaneous recording of the two circularly polarized Zeeman line profiles is key to accurate measurement of the magnetic field in the ZaP Z-pinch plasma device. Spectral data are collected along multiple chords on both sides of the symmetry axis of the plasma. This enables determination of the location of the current axis of the Z-pinch and of lower-bound estimates of the local magnetic field at specific radial locations in the plasma.

Increasing plasma parameters using sheared flow stabilization of a Z-pinch

The ZaP and ZaP-HD Flow Z-pinch experiments at the University of Washington have successfully demonstrated that sheared plasma flows can be used as a stabilization mechanism over a range of parameters that has not previously been accessible to long-lived Z-pinch configurations. The stabilization is effective even when the plasma column is compressed to small radii, producing predicted increases in magnetic field and electron temperature. The flow shear value, extent, and duration are shown to be consistent with theoretical models of the plasma viscosity, which places a design constraint on the maximum axial length of a sheared flow stabilized Z-pinch. Measurements of the magnetic field topology indicate simultaneous azimuthal symmetry and axial uniformity along the entire 100 cm length of the Z-pinch plasma. Separate control of plasma acceleration and compression has increased the accessible plasma parameters and has generated stable plasmas with radii of 0.3 cm, as measured with a high resolution digital...

Calculation of the Equilibrium Evolution of the ZaP Flow

A four-chord interferometer and measurements from an array of surface-mounted magnetic probes were used in conjunction with equations of radial heat conduction and radial force balance to calculate the equilibrium evolution of a pinch plasma in the ZaP flow Z-pinch. A multiple shooting method was used to solve the nonlinear coupled differential equation system, with ohmic heating and bremsstrahlung radiation as sources and sinks, respectively. Data from a single ZaP pulse are reported including profiles of magnetic field and temperature and their evolution. Profiles are dominated by high thermal conductivity near the axis which quickly decreases with radius. This is due to the plasma being weakly magnetized near the axis which increases thermal conductivity and flattens the temperature profile, but strongly magnetized near the characteristic radius, significantly reducing thermal conductivity and resulting in a large temperature gradient. The equilibrium evolution indicates that plasmas in ZaP heat and compress with increasing current as a result of magnetic compression during the quiescent period.

Z

Calculating magnetic fields at the surface of a flux conserver, perfect conductor, for displaced plasma currents is useful for understanding modes of a Z-pinch. The magnetic fields measured at the flux conserver are a sum of the magnetic fields from the plasma current and the eddy currents which form in the walls to keep the flux constant. While the magnetic field at the wall from the plasma current alone is easily calculated using the Biot-Savart law, finding the eddy currents in the flux conserver which satisfy the boundary conditions can be a tedious process. A simple method of calculating the surface magnetic field for a given Z-pinch displacement off-axis is derived for a cylindrical flux conserver. This relationship does not require the explicit calculation of the eddy currents, saving time when analyzing surface magnetic probe measurements. Analytic expressions can be used to describe the surface magnetic field which increase the understanding of the magnetic probe measurements.