Index of content:
Volume 25, Issue 2, February 1982

A finite element analysis of isothermal fiber formation
View Description Hide DescriptionThe formation of isothermal fibers composed of an incompressible Newtonian liquid is investigated. The fully two‐dimensional axisymmetric Navier–Stokes equations are solved in the exit region of the spinneret using the Galerkin finite element method and are matched to an asymptotic one‐dimensional equation downstream. The importance of boundary conditions and the manner in which they are imposed are discussed. Inertial, surface tension, and gravitational, as well as viscous effects, are retained in the formulation. Numerical results showing the effect of winder speed on fiber profiles are presented for some sample cases.

Marginal stability of impulsively initiated Couette flow and spin‐decay
View Description Hide DescriptionA viscous, incompressible fluid is contained within an infinitely long circular cylinder or between a pair of infinitely long concentric cylinders. In both cases, the entire system is in a state of rigid‐body rotation. At time t = 0 the outer flow boundary is impulsively brought to rest, giving rise to a potentially unstable, unsteady swirl flow. The stability of these flows is examined by employing energy theory with a marginal stability criterion to obtain lower bounds on the onset times for instability. In some cases, the asymptotic steady‐state flow will be stable, with any instability merely a transient, while in other cases, stability of the asymptotic state is not guaranteed.

Long‐wave energy trapping
View Description Hide DescriptionLow‐wave energy trapping by refraction on a curved coastline is considered. The parameters controlling energy trapping are developed and defined. Solutions are developed for defining the periods of trapped waves for a given physical geometry.

Shock wave interactions with the ocean surface
View Description Hide DescriptionThe interaction of plane shock waves with the air–ocean surface is investigated in detail. Interaction patterns for incident waves originating in both air and water are considered and the range of angles of incidence extends from normal to critical, and beyond. For shocks originating above the ocean surface, the interaction is irregular when the critical angle of incidence is exceeded and the transmitted shock is then diffracted about the disturbed ocean surface. For shocks arriving from an underwater source, the interaction is always regular and the reflected wave is always an expansion wave.

Single and multiple waves induced by power absorption
View Description Hide DescriptionSub‐ and supersonic wave fronts produced by heat input have been generated in a shock tube driven by a step current pulse of variable magnitude (4–50 kA, duration up to 160 μsec). At high current and low fill gas densities, the supersonic mode appears and no substantial compression is possible. The limiting current I _{ c } to reach this supersonic mode is determined as a function of the fill gas pressure. Front velocities, pressures, and electron densities are measured, and the heating characteristic (maximum enthalpy as function of the net absorbed energy flux) is derived. Scaling laws are obtained for the fluid parameters as a function of fill gas density and current. The measurements are interpreted in terms of one‐dimensional wave model calculations. Studies with two stepped power pulse reveal that multiple shocks with a region of substantially increased density can be obtained only if the total current I _{ t } remains below the critical value I _{ c }. For I _{ t }≳I _{ c }, a supersonic heat wave is created after the transient phase, and multiple shocks with increased density can no longer be achieved.

Development of two‐dimensional structure in cavitons
View Description Hide DescriptionExperimental observations of the time and space evolution of resonantly enhanced electric fields and plasma density in cylindrical geometry demonstrate the development of caviton structure in the direction perpendicular to the driving electric field. Electrostatic fields in this perpendicular direction are observed to have growth times on the ion time scale and to develop concurrently with two‐dimensional density profile modification near the critical surface.

Reversed‐field flux‐trapping in a low‐compression theta pinch
View Description Hide DescriptionRapid field reversal is employed to trap an initial negative‐magnetic‐field bias flux in a 300‐cm long theta pinch having an inner radius of 10 cm. A large fraction (40%–75%, depending on filling pressure) of the initial bias flux is trapped after the implosion (∼1 μsec); this fraction then diminishes to a plateau value of 25% to 35% in approximately 2 μsec. During this decay, magnetic probe measurements indicate an average anomalous resistivity one order of magnitude greater than classical. The open‐line configurations obtained have large separatrix (zero enclosed flux) radii and are present for the duration of the applied magnetic field. The presence of the reversed bias field lowers the plasma temperature by a factor of two.

Application of explosive‐driven implosions to fusion
View Description Hide DescriptionOur explosive‐driven implosion facility was used to produce hemispherical implosions in a stoichiometric mixture of deuterium‐oxygen. A high‐resolution scintillator detection system measured neutrons and γ rays resulting most likely from the fusion of deuterium.

Expulsion of a plasmoid from a spatially nonuniform magnetic field
View Description Hide DescriptionThe spatial evolution of an isolated plasma released from a region of large magnetic field has been investigated using a two‐dimensional electrostatic particle code with a fixed nonuniform magnetic field. In general, the plasmoid is seen to accelerate and cool in accordance with the predictions of magnetohydrodynamic theory for a low‐β plasma. However, it is found that two trailing plasma edges with their associated polarization charges are gradually shed leaving wakes of oppositely rotating vortices several Larmor radii in diameter.

Theory of phase‐space density holes
View Description Hide DescriptionA Bernstein–Green–Kruskal mode consisting of a depression or ’’hole’’ in the phase‐space density is shown to be a state of maximum entropy subject to constant mass, momentum, and energy. The parameter space of such holes is studied. The maximum entropy property is used to develop a simplified approximate analytic method as well as to infer the results of hole collisions including coalescing and decay. The maximum entropy property suggests that random, turbulent fluctuations tend to form into such self‐trapped structures and this nonperturbative concept is related to the physics of ’’clumps’’ which occur in a renormalized perturbative theory of turbulence.

Nonlinear theory of the ∇B×B instability in weakly ionized plasmas
View Description Hide DescriptionThe instability of a weakly ionized inhomogeneous plasma in a strong nonuniform magnetic field is investigated. By a particular scaling of the harmonics of the linearly unstable modes, an explicit calculation of the finite saturation amplitudes is performed. A nonlinear analysis shows the oscillating equilibrium states to be stable only in a subinterval of the linearly unstable wavenumbers. An alternative scaling of the harmonics establishes the validity of the results well into the unstable regime. There is excellent agreement with a previous numerical analysis by Shiau.

The gyroelastic screw pinch
View Description Hide DescriptionA study is made of a scale model in three dimensions of a guiding center plasma within the purview of gyroelastic (also known as finite gyroradius‐near theta pinch) magnetohydrodynamics. The nonlinear system sustains a particular symmetry called isorrhopy which permits the decoupling of fluid modes from drift modes. Isorrhopic equilibria are analyzed within the framework of geometrical optics, resulting in local dispersion relations and ray constants. A general scheme is developed to evolve an arbitrary linear perturbation of a screw pinch equilibrium as an invertible integral transform over the complete set of generalized eigenfunctions defined naturally by the equilibrium. Details of the structure of the function space and the associated spectra are elucidated. Features of the global dispersion relation owing to the presence of gyroelastic stabilization are revealed. An energy principle is developed to study the stability of the tubular screw pinch.

Single mode saturation of the rotational instability in a low‐β, finite Larmor radius plasma
View Description Hide DescriptionThe nonlinear dynamics of the rotational instability in a low‐β, finite Larmor radius plasma is investigated. Due to the effect of finite Larmor radius and line bending it is possible to have only a single, slightly unstable mode. By means of the multiple time scale method the evolution in time of this mode is determined. As a result, recurrence in the amplitude of the unstable mode is found, whereas on the average the particle transport vanishes.

Verification of the classical theory of helical transport in stellarators
View Description Hide DescriptionThe apparent discrepancies of the classical theory of helical transport in stellarators, versus two recent numerical studies of stellarator transport, are investigated. Numerical results are presented, verifying the classical theory, when the model for the magnetic field has the simple form assumed by the classical theory. When the helical contribution to the total transport is isolated numerically, and the different energy dependence of the particle distribution is accounted for, the results of one of the numerical studies is brought into substantial agreement with theory. It is argued that the anomalously favorable low collisionality results of the second numerical study are due partially to numerical procedure, and partly to a more complicated spatial dependence of the magnetic field.

Long wavelength collisional tearing modes in a stochastic magnetic field
View Description Hide DescriptionRenormalized statistical equations which characterize a long wavelength resistive tearing mode when the magnetic field is stochastic are derived. The theory predicts a broadening of the current layer of the mode due to enhanced perpendicular electron motion. This increase in the current layer width is significant for fluctuation levels 〈(δB/B)^{2}〉 as small as 10^{−8}, where 〈(δB/B)^{2}〉 is the ratio of the energy in the magnetic fluctuations to the equilibrium magnetic energy. As a consequence of this broadening, the transition from exponential to algebraic growth is not attained until the magnetic energy density of the mode exceeds the total magnetic energy density of all the other fluctuations.

Universal instability in a plasma sheath
View Description Hide DescriptionLow‐frequency drift waves are considered in a planar sheath of neutral plasma with thickness on the order of the ion gyroradius. An integral eigenmode equation is derived and solved numerically using fast Fourier transforms. The analysis is valid for arbitrary wavenumbers and accounts for shear in the equilibrium magnetic field. It is found that unstable universal drift modes can exist in this strongly localized plasma. In contrast to what has been found previously in connection with weakly inhomogeneous plasmas, it is observed here that shear can have a destabilizing influence. The relevance of this idealized model to experiments is also discussed.

Two‐and‐a‐half‐dimensional magnetohydrodynamic turbulence
View Description Hide DescriptionIncompressible magnetohydrodynamic turbulence is considered in a geometry in which the fields are all independent of the z coordinate, e.g., but have all three components. This is a limit frequently called ’’two‐and‐a‐half‐dimensional.’’ It is conjectured that simultaneous inverse cascades of magnetic helicity and mean square z‐component of vector potential may exist. At high Reynolds numbers, selective decays to states of finite pressure gradients appear to be possible. Anti‐dynamo theorems are difficult to prove for this geometry.

Renormalization of plasma turbulence in toroidal geometry
View Description Hide DescriptionAction‐angle variables are used to renormalize the nonlinear drift‐kinetic equation in an asymmetric torus. Special cases of the result are shown to agree with previous nonlinear theories.

α‐particle ripple losses during slow down in a tokamak reactor
View Description Hide DescriptionAn investigation is made of the effect of toroidal field ripple mirrors on the confinement of α particles. It is found that the diffusion of α particles into the loss regions of the ripple mirrors during slow down gives rise to significant particle and energy losses.

Toroidal and scattering effects on lower‐hybrid wave propagation
View Description Hide DescriptionThe effects of toricity and density fluctuations on the propagation of lower‐hybrid waves are studied. These effects result mainly from changes in k _{∥} as the wave propagates (k _{∥} is the wavenumber parallel to the applied magnetic field). With respect to toroidal effects, k _{∥} changes due to the nonconstancy of the poloidal mode number in toroidal geometry. Using ray tracing techniques, an assessment of this toroidal effect has been made. It is found that waves, which on the basis of the cylindrical geometry theory would be inaccessible, may actually propagate to the plasma center and damp. The result is related to the onset of ray ergodicity. Further, it is shown that for accessible waves the optimal poloidal launch point is near the top or bottom of the torus. In order to include the effects of density fluctuations, an electromagnetic wave kinetic equation is derived and solved by a Monte Carlo technique. It is found that scattering can further enhance accessibility.