P.-A. Gourdain

A multichannel, frequency-modulated, tunable Doppler backscattering and reflectometry system

A novel multichannel Doppler backscattering system has been designed and tested for application on the DIII-D [J. L. Luxon, Fusion Sci. Technol. 48, 828 (2005)] and National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] fusion plasma devices. Doppler backscattering measures localized intermediate wavenumber (k(perpendicular)rho(i) approximately 1-4,k(perpendicular) approximately 2-15 cm(-1)) density fluctuations and the propagation velocity of turbulent structures. Microwave radiation is launched at a frequency that approaches a cutoff layer in the plasma and at an angle that is oblique to the cutoff layer. Bragg backscattering occurs near the cutoff layer for fluctuations with k(perpendicular) approximately -2k(i), where k(i) is the incident probe wave vector at the scattering location. The turbulence propagation velocity can be determined from the Doppler shift in the return signal together with knowledge of the scattering wavenumber. Ray tracing simulations are used to determine k(perpendicular) and the scattering location. Frequency modulation of a voltage-controlled solid state microwave source followed by frequency multiplication is used to create an array of finely spaced (Delta f=350 MHz) frequencies spanning 1.4 GHz. The center of the array bandwidth is tunable within the range of approximately 53-78 GHz. This article details the system design, laboratory tests, and presents initial data from DIII-D plasmas.

Initial experiments using radial foils on the Cornell Beam Research Accelerator pulsed power generator

A novel technique involving radial foil explosions can produce high energy density plasmas. A current flows radially inward in a 5 μm thin aluminum foil from a circular anode, which contacts the foil on its outer rim, to the cathode, which connects to the foil at its geometrical center. When using small “pin” cathodes (∼1 mm in diameter) on a medium size pulsed-current generator such as the Cornell Beam Research Accelerator, the central magnetic field approaches 400 T, yielding magnetic pressures larger than 0.5 Mbar. While the dynamics is similar to radial wire arrays, radial foil discharges have very distinct characteristics. First a plasma jet forms, with densities near 5×1018 cm−3. J×B forces lift the foil upward with velocities of ∼200 km/s. A plasma bubble with electron densities superior to 5×1019 cm−3 then develops, surrounding a central plasma column, carrying most of the cathode current. X-ray bursts coming from the center of this column were recorded at 1 keV photon energy. As the magnetic bubb...

Growth and saturation of the axial instability in low wire number wire array Z pinches

The growth of the axial instability in low wire number wire array Z pinches using a 100 ns rise time, 1 MA pulsed power accelerator is examined. The axial instability manifests itself as a quasiperiodic variation of the radius of the coronal plasma along each wire and a consequent modulation of the rate of ablation of material from the dense wire core. The dominant wavelength of the modulation becomes constant late in time. In this work laser shadowgraphy is used to measure the growth of the wavelength and amplitude of the instability as well as the size of the coronal plasma in aluminum wire arrays from the time of plasma formation to the time the wavelength seen late in time is reached. Using magnetic probes, the distribution of current and magnetic topology are also investigated. It is found that a distinct change in magnetic field topology associated with the onset of advection of current to the array axis by the streaming wire-ablation plasma appears to be responsible for ending the growth of the axi...

Radial electric field required to suppress ion temperature gradient modes in the Electric Tokamak

The Electric Tokamak (ET), currently under construction at the University of California–Los Angeles, is designed to rotate poloidally via a radial current induced by fast wave rf heating fast enough to bifurcate the plasma into a global “H mode” (“high confinement mode”). A global gyrokinetic code is used to explore and illustrate some of the effects on ion temperature gradient turbulence. The realistic radial electric field required to completely suppress these modes for ET parameters is demonstrated to be <−30 V/cm at its maximum near the half radius. The effects of both a poloidally supersonic bulk rotation threshold and the shear in this rotation near that supersonic threshold were shown to be important in reducing these modes.

Impact of the Hall effect on high-energy-density plasma jets.

Using a 1-MA, 100 ns-rise-time pulsed power generator, radial foil configurations can produce strongly collimated plasma jets. The resulting jets have electron densities on the order of 10(20) cm(-3), temperatures above 50 eV and plasma velocities on the order of 100 km/s, giving Reynolds numbers of the order of 10(3), magnetic Reynolds and Péclet numbers on the order of 1. While Hall physics does not dominate jet dynamics due to the large particle density and flow inside, it strongly impacts flows in the jet periphery where plasma density is low. As a result, Hall physics affects indirectly the geometrical shape of the jet and its density profile. The comparison between experiments and numerical simulations demonstrates that the Hall term enhances the jet density when the plasma current flows away from the jet compared to the case where the plasma current flows towards it.

Study of gas-puff Z-pinches on COBRA

Gas-puff Z-pinch experiments were conducted on the 1 MA, 200 ns pulse duration Cornell Beam Research Accelerator (COBRA) pulsed power generator in order to achieve an understanding of the dynamics and instability development in the imploding and stagnating plasma. The triple-nozzle gas-puff valve, pre-ionizer, and load hardware are described. Specific diagnostics for the gas-puff experiments, including a Planar Laser Induced Fluorescence system for measuring the radial neutral density profiles along with a Laser Shearing Interferometer and Laser Wavefront Analyzer for electron density measurements, are also described. The results of a series of experiments using two annular argon (Ar) and/or neon (Ne) gas shells (puff-on-puff) with or without an on- (or near-) axis wire are presented. For all of these experiments, plenum pressures were adjusted to hold the radial mass density profile as similar as possible. Initial implosion stability studies were performed using various combinations of the heavier (Ar) a...

Initial magnetic field compression studies using gas-puff Z-pinches and thin liners on COBRA

This magnetic compression of cylindrical liners filled with DT gas has promise as an efficient way to achieve fusion burn using pulsed-power machines. However, to avoid rapid cooling of the fuel by transfer of heat to the liner an axial magnetic field is required. This field has to be compressed during the implosion since the thermal insulation is more demanding as the compressed DT plasma becomes hotter and its volume smaller. This compression of the magnetic field is driven both by the imploding liner and plasma. To highlight how this magnetic field compression by the plasma and liner evolves we have separately studied Z-pinch implosions generated by gas puff and liner loads. The masses of the gas puff and liner loads were adjusted to match COBRAs current rise times. Our results have shown that Ne gas-puff implosions are well described by a snowplow model where electrical currents are predominately localized to the outer surface of the imploding plasma and the magnetic field is external to the imploding plasma. Liner implosions are dominated by the plasma ablation process on the inside surface of the liner and the electrical currents and magnetic fields are advected into the inner plasma volume; the sharp radial gradient associated with the snowplow process is not present.

High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

There is great interest in the properties of extremely high-s magnetohydrodynamic equilibria in axisymmetric toroidal geometry and the stability of such equilibria. However, few equilibrium codes maintain solid numerical behavior as beta approaches unity. The free-boundary algorithm presented herein utilizes a numerically stabilized multigrid method, current density input, position control, magnetic axis search, and dynamically adjusted simulated annealing. This approach yields numerically robust behavior in the spectrum of cases ranging from low to very high-s configurations. As the convergence time depends linearly on the total number of grid points, the production of extremely fine, low-error equilibria becomes possible. Such a code facilitates a variety of intriguing applications which include the exploration of the stability of extreme Shafranov shift equilibria.

Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria

Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times.

Dynamics of hybrid X-pinches

The dynamics of a new type of pinches—hybrid X-pinches (HXPs)—has been studied experimentally and numerically. The initial configuration of an HXP consists of a high-current diode with conical tungsten electrodes separated by a 1- to 3-mm-long gap and shunted with a 20- to 100-μm diameter wire. It was shown earlier that a hot spot (HS) with high plasma parameters also formed in the HXP, although its initial configuration is simpler than that of a standard X-pinch. Although details of the HXP dynamics still remain insufficiently studied, the main factors governing the HXP formation were investigated both experimentally and using magnetohydrodynamic simulations. The formation of a specific pressure profile in the electrode plasma after the wire explosion was investigated both experimentally and theoretically. It is shown that the effect of the pressure profile on the expanding wire plasma is similar for both standard X-pinches and HXPs, which allows one to assign them to the same class of loads of pulsed facilities. It is also established that the final stages of HS formation and the parameters of the HS plasma in standard X-pinches and HXPs are practically identical.