Volume 24, Issue 5, May 1981
Index of content:

Molecular diffusion in oscillating laminar flow in a pipe
View Description Hide DescriptionThe effect of flow oscillations on the axial diffusion of a solute in a pipe is analyzed theoretically by a perturbation method for small oscillation Reynolds numbers. The specific case of an initial step disribution in concentration is solved to second order. Numerical results of diffusion enhancement are given for several values of the parameter involved and are found to be conveniently summarized in terms of an equivalent diffusion parameter.

Round buoyant laminar and turbulent plumes
View Description Hide DescriptionTwo approximate solutions, which become exact for Prandtl numbers 1 and 2, are given for laminar round plumes for arbitrary Prandtl number σ. The first of these gives a very accurate solution for laminar found plumes in air, for which σ = 0.73, and the second provides a good solution for laminar round plumes in water, for which σ = 6.7. Two approximate solutions, which become exact for turbulent Prandtl numbers 1.1 and 2, respectively, are given for turbulent round plumes. The one which becomes exact at σ = 1.1 is used to give a highly accurate solution for σ = 1, which, for an eddy‐viscosity coefficient λ equal to 0.0156, provides a remarkably good agreement with the experimental data of Beuther, Capp, and George, Jr.

Turbulent boundary layer at low Reynolds number
View Description Hide DescriptionThe results of an experimental investigation of a turbulent boundary layer with zero‐pressure gradient directed toward extending the data base at low Reynolds numbers are presented. The data obtained are concerned primarily with mean‐velocity distributions, skin‐friction coefficients, and distributions of intensity of the longitudinal‐component of the turbulent‐velocity fluctuations for Reynolds numbers based on momentum thickness as low as 465. The validity, at low Reynolds numbers, of the semi‐empirical laws characterizing the inner and outer regions of the boundary layer is examined.

Numerical calculation of standing waves in water of arbitrary uniform depth
View Description Hide DescriptionA numerical scheme is presented for the computation of time and space periodic standing waves of finite amplitude in water of arbitrary uniform depth. The dynamic and kinematic boundary conditions are used in their exact nonlinear form. The numerical procedure involves series truncation. Accurate solutions are presented for various values of the amplitude and of the depth. It is found that for some values of the depth, the frequency is not a monotonic function of the amplitude.

Numerical solutions to water waves generated by shallow underwater explosions
View Description Hide DescriptionNumerical solutions are given for surface waves generated by underwater explosions. The shallow water approximation is used for the governing equations. An axisymmetric initial impulse is applied to the surface of the water. The initial impulse distribution is taken from the results obtained by Falade and Holt. Due to the unavailability of the initial displacement distribution, the latter is assumed to be zero, but the method can work for the case when both initial impulse and displacement are presented. Glimm’s scheme is used to obtain the solution for the shallow water equations. The scheme was developed to solve one‐dimensional gas dynamic problems. With slight modification, the scheme can be used for the shallow water equations. It is tested successfully on the dam break problems. The calculations confirm the existence of the upper critical depth effect, namely, that for near surface explosions, the maximum amplitude surface wave is that generated by an explosion just below the surface.

Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field
View Description Hide DescriptionA strong external dc magnetic field introduces a basic anisotropy into incompressible magnetohydrodynamic turbulence. The modifications that this is likely to produce in the properties of the turbulence are explored for the high Reynolds number case. The conclusion is reached that the turbulent spectrum splits into two parts: an essentially two‐dimensional spectrum with both the velocity field and magnetic fluctuations perpendicular to the dc magnetic field, and a generally weaker and more nearly isotropic spectrum of Alfvén waves. A minimal characterization of the spectral density tensors is given. Similarities to measurements from the Culham–Harwell Zeta pinch device and the University of California, Los Angeles Macrotor tokamak are remarked upon, as are certain implications for the Belcher and Davis measurements of magnetohydrodynamic turbulence in the solar wind.

One‐dimensional direct current resistivity due to strong turbulence
View Description Hide DescriptionStrong Langmuir turbulence acts to generate localized spiky fields and ion cavities. It is shown that these cavities generate potential barriers that can trap a significant fraction of the electrons. For example, a 20% cavity traps 50% of the electrons. This can seriously change the direct current properties of a collisionless plasma and lead to the appearance of anomalous dc resistivity.

Observation of bumps on the electron distribution function during ionization
View Description Hide DescriptionDuring the implosion of weakly ionized plasmas in a theta pinch, monoenergetic electron beams in the direction of the magnetic field lines are observed, the energy of the beam corresponding to the ionization energy in each case. The distribution function has been measured by incoherent Thomson scattering.

Kinetic‐theory description of electron heat transfer in a plasma
View Description Hide DescriptionElectron heat flux in a fully ionized gas between two parallel boundaries is studied. The moment method is employed to analyze the relation between the electron heat flux and the plasma collisionality parameter L/λ_{ e }, both with and without electron‐electron collisions (λ_{ e } is the electron mean‐free‐path). The electron heat flux is determined as a function of L/λ_{ e } over the entire range from free flow of collisional regimes. These calculations employ various combinations of trial distribution function and collision operator. Comparisons are made between the various models and with the known result in the collisional limit. Discrepancies between the present model and the known collisional behavior are discussed, and an approximate heat flux expression is presented.

Monte Carlo evaluation of transport coefficients
View Description Hide DescriptionA method is developed for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method. The method is applied to the stellarator.

Effect of magnetic field errors on low‐frequency waves in a pure electron plasma
View Description Hide DescriptionIt is demonstrated how static magnetic field errors can resonantly drive low‐frequency electrostatic waves in a pure electron plasma column. The driving mechanism is identified as a charge bunching that results from the field error. It is found that the wave amplitude increases linearly with time.

Magnetohydrodynamic stability of high‐beta closed‐line systems
View Description Hide DescriptionThe ideal magnetohydrodynamic stability of high‐beta model equilibria in slab geometry with B _{ z } = 0 and containing elongated regions of closed field lines is investigated as an initial‐value problem and in terms of the energy principle. For moderate or larger elongations, flute (interchange) modes are found to be stable throughout the closed region. Co‐interchange modes with the character of an m = 1 kink mode, however, are found to be unstable. The growth rate of these modes initially increases rapidly with k _{ z } and then approaches a finite limit as k _{ z }→∞. As the elongation of the closed region is increased, the growth rate decreases rapidly. Possible implications of these results for field‐reversed theta pinches are discussed.

Warm plasma axial flow through a magnetic mirror
View Description Hide DescriptionSolutions are given for the characteristics of a warm plasma flowing axially through a magnetic mirror in the presence of a confined hot‐ion species. The warm plasma is assumed to have negligible effect on the magnetic field. The plasma is described by four moment equations for the density, velocity, parallel temperature, and perpendicular temperature of the ions, that are solved by a time‐dependent finite‐difference computer code. Two basic types of solutions occur corresponding to the warm‐ion density (n _{ w }) being less than the hot‐ion density (n _{ h }), and n _{ w }≳n _{ h }. In the first case, the flow is nearly stagnant between the warm‐ion source and the midplane, but the flow rapidly accelerates to a supersonic velocity just beyond the midplane. In the second case, the flow velocity profile is more symmetric about the midplane, and the sonic transition occurs at the mirror throat. Specific calculations are given for gas box and stream gun sources used to stabilize microstabilities and for a collisional tandem mirror.

Electron plasma wave breaking with ion flow
View Description Hide DescriptionThe effects of ion flow on the nonlinear development of resonantly driven electron plasma oscillations in a nonuniform plasma are investigated. The Lagrangian oscillator equation is generalized to include ion flow. A solution of the oscillator equation is obtained and is examined in detail for a model profile. Plasma flow through the critical surface is found to substantially reduce the energy of electrons at wave breaking when the flow velocity exceeds the oscillating velocity of electrons in the driver field.

Nonlinear frequency shift induced by the lower‐hybrid drift instability
View Description Hide DescriptionIt is found that a finite perturbations of the ion orbits leads to a nonlinear frequency shift that reduces the mode frequency and has a weak stabilizing effect on the lower‐hybrid drift instability. This result is obtained from a self‐consistent solution of the Vlasov–Poisson equations using perturbation theory in which the nonlinear dielectric function and the nonlinear temporal evolution of a single unstable mode in the low drift velocity regime are calculated analytically. The nonlinear frequency shift does not seem to be a potent saturation mechanism in a collisionless plasma, but may be more relevant when there are ion‐ion collisions.

Incomplete relaxation of pinch discharges
View Description Hide DescriptionSolenoidal field linkage is explained and its application to magnetic helicity is discussed. A Green’s tensor function for the magnetic vector potential of a plasma current distribution bounded by a perfect conductor is derived. A hypothesis of incomplete relaxation of a turbulent discharge is then used to establish reversed‐field pinch configurations with finite beta.

Absolute and convective instabilities in two‐dimensional free‐electron lasers
View Description Hide DescriptionComputer simulations of the free‐electron laser have been carried out using a two‐and‐one‐half dimensional fully electromagnetic relativistic particle code. It has been found that waves propagating obliquely with respect to the electron beam are always unstable with appreciable growth rates and, therefore, mode competition is an important consideration in the design of free‐electron lasers. Furthermore, electromagnetic waves with group velocities opposite to the direction of electron beam propagation can be absolutely unstable. It is shown that the absolutely unstable waves can completely disrupt the electron beam and any laser oscillaton; therefore, they are extremely detrimental to the operation of free electron lasers. However, it has been found that one can stabilize the absolute instability by taking particular precautions in the design of free‐electron lasers.

Oscillating two‐stream instability with pump of finite extent
View Description Hide DescriptionIn one spatial dimension, the effects of finite pump length L on the oscillating two‐stream instability are considered. In the absence of damping, a purely growing instability for very small pump extent is found. Under certain conditions, the finite system exhibits faster growth rates than the corresponding infinite system.

Parametric excitation of electrostatic drift waves by a low frequency oscillating magnetic field
View Description Hide DescriptionParametric excitation of drift waves and suppression of drift instabilities in a plasma by an oscillating field of low frequency has been studied. The role of such an oscillating field of frequency, much higher than the drift frequency in determining the stability properties of the waves, has been investigated.

Growth of laser ripple in a plasma and its effect on plasma wave excitation
View Description Hide DescriptionAn investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian laser beam in a collisionless unmagnetized plasma is presented. The effect of the position and the width of the ripple on its growth has been studied in some detail. In a special case, the growth rate of the ripple is seen to be comparable to the growth rate of filamentation instability. In addition to the growth of the ripple, the effect of the presence of the ripple on the excitation of an electron plasma wave has also been studied.