Low-frequency modes that develop as a result of an instability in a dusty rf discharge plasma were studied experimentally, leading to an empirical explanation for the instability. In the experiment, particle diameter grew with time. Two instability modes appeared after growth to a sufficient size. A filamentary mode appeared abruptly, and later a great void mode developed as a dust-free region with an intense glow inside and a sharp boundary outside. These modes were characterized by two-dimensional laser light scattering, video imaging, optical emission spectroscopy, Langmuir probe measurements, and Fourier analysis of the fluctuation spectrum. Dust growth was measured by electron microscopy and optical extinction, yielding the dust particle size and dust number density. The electron density was found to be enhanced inside the great void, due to an absence of electron depletion on the dust grains. The great void was explained by the ion drag force, which becomes stronger than the opposing Coulomb force once the particle size reaches a critical diameter. When a dust-free region develops, its electron density is enhanced, the ionization rate increases, and the ion flow that pushes particles outward is further augmented. The plasma used in the experiment grew particles by sputtering of the electrodes, although the same instabilities are expected to occur in other types of dusty plasma discharges as well. ͓S1063-651X͑99͒00801-6͔

Mach cones, or V-shaped disturbances created by supersonic objects, have been detected in a twodimensional Coulomb crystal. Electrically charged microspheres levitated in a glow-discharge plasma formed a dusty plasma, with particles arranged in a hexagonal lattice in a horizontal plane. Beneath this lattice plane, a sphere moved faster than the lattice sound speed. Mach cones were double, first compressive then rarefactive, due to the strongly coupled crystalline state. Molecular dynamics simulations using a Yukawa potential also show multiple Mach cones.

Experimental studies of the formation and structure of Mach cones in a plasma crystal are presented. Plasma crystals are ordered structures of charged microspheres trapped in the sheath of an rf discharge plasma. Using a monolayer crystal with a hexagonal lattice, Mach cones were excited by the radiation pressure of a focused laser beam. The beam was swept at a supersonic speed through the crystal, in a controlled and repeatable manner. A multiple Mach cone structure was observed, with at least three distinct Mach cones. The Mach angle relation was verified over a wide range of Mach numbers, for both the first and second cones. The sound speed, measured from the first Mach angle, was found to increase with the particle number density. Two methods of determining the particle charge and screening distance are developed, making use of the sound speed and an assumption of a Yukawa interparticle potential. Molecular-dynamics simulations of the experiment were carried out, using a monolayer of particles interacting through a Yukawa potential, and these show close agreement with the experiment.

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.

Based on the structure of the original helical FDK algorithm, a three-dimensional (3D)-weighted cone beam filtered backprojection (CB-FBP) algorithm is proposed for image reconstruction in volumetric CT under helical source trajectory. In addition to its dependence on view and fan angles, the 3D weighting utilizes the cone angle dependency of a ray to improve reconstruction accuracy. The 3D weighting is ray-dependent and the underlying mechanism is to give a favourable weight to the ray with the smaller cone angle out of a pair of conjugate rays but an unfavourable weight to the ray with the larger cone angle out of the conjugate ray pair. The proposed 3D-weighted helical CB-FBP reconstruction algorithm is implemented in the cone-parallel geometry that can improve noise uniformity and image generation speed significantly. Under the cone-parallel geometry, the filtering is naturally carried out along the tangential direction of the helical source trajectory. By exploring the 3D weighting's dependence on cone angle, the proposed helical 3D-weighted CB-FBP reconstruction algorithm can provide significantly improved reconstruction accuracy at moderate cone angle and high helical pitches. The 3D-weighted CB-FBP algorithm is experimentally evaluated by computer-simulated phantoms and phantoms scanned by a diagnostic volumetric CT system with a detector dimension of 64 x 0.625 mm over various helical pitches. The computer simulation study shows that the 3D weighting enables the proposed algorithm to reach reconstruction accuracy comparable to that of exact CB reconstruction algorithms, such as the Katsevich algorithm, under a moderate cone angle (4 degrees) and various helical pitches. Meanwhile, the experimental evaluation using the phantoms scanned by a volumetric CT system shows that the spatial resolution along the z-direction and noise characteristics of the proposed 3D-weighted helical CB-FBP reconstruction algorithm are maintained very well in comparison to the FDK-type algorithms. Moreover, the experimental evaluation by clinical data verifies that the proposed 3D-weighted CB-FBP algorithm for image reconstruction in volumetric CT under helical source trajectory meets the challenges posed by diagnostic applications of volumetric CT imaging.