摘要:

The stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity. The effect of a small layer curvature is simulated by a gravitational field. In an incompressible fluid, there can be three basic types of ``resistive'' instability: a long‐wave ``tearing'' mode, corresponding to breakup of the layer along current‐flow lines; a short‐wave ``rippling'' mode, due to the flow of current across the resistivity gradients of the layer; and a low‐ggravitational interchange mode that grows in spite of finite magnetic shear. The time scale is set by the resistive diffusion time &tgr;Rand the hydromagnetic transit time &tgr;Hof the layer. For largeS= &tgr;R/&tgr;H, the growth rate of the ``tearing'' and ``rippling'' modes is of order &tgr;R−3/5&tgr;H−2/5, and that of the gravitational mode is of order &tgr;R−1/3&tgr;H−2/3. AsS→ ∞, the gravitational effect dominates and may be used to stabilize the two nongravitational modes. If the zero‐order configuration is in equilibrium, there are no overstable modes in the incompressible case. Allowance for plasma compressibility somewhat modifies the ``rippling'' and gravitational modes, and may permit overstable modes to appear. The existence of overstable modes depends also on increasingly largezero‐orderresistivity gradients asS→ ∞. The three unstable modes merely require increasingly large gradients of thefirst‐orderfluid velocity; but even so, the hydromagnetic approximation breaks down asS→ ∞. Allowance for isotropic viscosity increases the effective mass density of the fluid, and the growth rates of the ``tearing'' and ``rippling'' modes then scale as &tgr;R−2/3&tgr;H−1/3. In plasmas, allowance for thermal conductivity suppresses the ``rippling'' mode at moderately high values ofS. The ``tearing'' mode can be stabilized by conducting walls. The transition from the low‐g``resistive'' gravitational mode to the familiar high‐ginfinite conductivity mode is examined. The extension of the stability analysis to cylindrical geometry is discussed. The relevance of the theory to the results of various plasma experiments is pointed out. A nonhydromagnetic treatment will be needed to achieve rigorous correspondence to the experimental conditions.

ISSN:0031-9171    

DOI:10.1063/1.1706761

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

An integral representation is obtained for the Green's function for the linearized one‐dimensional Krook equation with the induced electric field of the medium included. Various asymptotic expansions in time are then obtained. When the plasma frequency is set to zero, slightly modified hydrodynamic modes appear. For nonzero plasma frequency, only plasma oscillations unaffected by the collisions are present. Finally, the initial value problem corresponding to an initial wave packet of approximate wavenumberkis considered. For times long, but not too long, plasma oscillations are present for which the frequency and wavenumber satisfy the usual Landau dispersion relation for small wavenumber. After a sufficiently long time, the solution behaves like the Green's function itself and exhibits Landau damping.

ISSN:0031-9171    

DOI:10.1063/1.1706762

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The space—time behavior of initial density perturbations (acoustic mode) in hot plasmas is analyzed, including second‐order effects, using a one‐dimensional Cauchy velocity distribution of the form (v2+a2)−2for the equilibrium distribution. The initial density perturbation is assumed to be sinusoidal in space and to have the same Cauchy velocity distribution. The first‐order solution has an exact analytic form which gives damped oscillations at a thermally shifted plasma frequency. The nonlinear interference between the density wave and its electric field produces second harmonics in both space and time which appear in the analytic second‐order solution. The harmonic structure suggests a ``spectral decay'' of the initial perturbation energy. In general, the oscillation frequency and damping decrement increase with temperature so that at sufficiently high temperatures, all forms of ordered motion are destroyed by the random thermal motion.

ISSN:0031-9171    

DOI:10.1063/1.1706763

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The ion cyclotron resonance interaction of plasma with a rotating transverse magnetic perturbation on a longitudinal magnetic field is investigated experimentally and theoretically. The plasma is injected axially from a coaxial hydromagnetic gun along a longitudinal magnetic field on which there is superimposed a transverse spatially rotating perturbation field. A resonance transfer of ion energy from the longitudinal to the transverse direction is observed when the spatial period or wavelength of the perturbation field and the plasma velocity and ion cyclotron frequency satisfy the relation &lgr;z= 2&pgr;vz/&OHgr;B. Measurements of plasma diamagnetism and transit time show an increase of up to a factor of two in diamagnetism coupled with a decrease in axial velocity corresponding to a reduction to half the initial longitudinal energy. Resonance may be observed over a range of longitudinal energies by varying the parameters of the system. For the plasma gun and perturbation field helix used in the experiment, optimum resonance was obtained with plasmas of longitudinal energy of ∼ 2.5 keV and particle densities of ∼ 1015cm−3(&bgr; ≳ 0.8). A theoretical account of the effect is given which considers the excitation by the perturbation field of circularly polarized electromagnetic waves in the plasma at ion cyclotron frequency and the transfer of longitudinal ion energy into transverse motion through the intermediate action of the waves.

ISSN:0031-9171    

DOI:10.1063/1.1706764

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The problem of hydromagnetic reflection and refraction at a fluid velocity discontinuity is solved. Expressions for the propagation vector of the refracted wave and for the reflection coefficient are derived. It is found that the reflected and refracted waves are pure characteristic waves if the incident wave is a pure characteristic wave.

ISSN:0031-9171    

DOI:10.1063/1.1706765

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

If inertial waves in a uniformly rotating fluid reflect from a rigid plane surface, it is shown that the magnitudes of the incident and reflected wavenumbers are generally unequal. The reflection process thus provides an interchange of energy among different scalar wavenumbersk. In an inviscid fluid, the ratio &agr;(k)/kis conserved on reflection, where &agr; is the particle orbit speed associated with the wavenumberk. In a viscous fluid the reflection coefficient is generally 1 ‐O(R1/2), whereRis the wave Reynolds number 2&OHgr;/&ngr;k2, though there is an exceptional case in which the incident energy flux is totally absorbed. When the fluid is contained in a large rotating box of general shape, the energy interchanges from repeated reflections can result in a statistical radiative equilibrium over the high wavenumbers. A dynamical equation is derived that specifiesE&Vthgr;(k), the energy distribution among wavenumbers inclined at an angle &Vthgr; to the rotation vector. An approximate solution shows thatE&Vthgr;(k) is constant whenk«k&ngr;= (&OHgr;/&ngr;L)1/3, whereLis the size of the domain. Whenk»k&ngr;, the spectrum decreases exponentially.

ISSN:0031-9171    

DOI:10.1063/1.1706766

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The collapse of an empty cavity in water has been treated by Hunter, using a similarity solution. Conditions for similarity require that the value of the density of water at the cavity boundary is zero, although the value corresponding to zero pressure given by the Tait equation of state is nonzero. To satisfy the correct boundary conditions on the cavity surface, Hunter's similarity solution is perturbed to take account of first‐order changes in the wall density. The perturbation equations have critical points coinciding with or close to the corresponding singularities of the similarity equations. Regular integral curves passing through all these points can be determined uniquely. Near the cavity wall these can be represented by expansions in powers of the similarity variable. Near the singular characteristic, however, the corresponding expansions must be found in terms of a modified variable, determined by Lighthill's technique. The corrected velocity of the cavity wall can be determined solely in terms of series expansions there.

ISSN:0031-9171    

DOI:10.1063/1.1706767

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

When a straight two‐dimensional vortex filament, which is laid on thexaxis, is perturbed by a three‐dimensional distortion, it deforms progressively by its own induction. The progressive deformation is numerically obtained in this paper for a localized distortiony=aexp(−x2) and for a periodic distortiony= 2acos[¼(&pgr;x)],abeing the amplitude relative to the lateral extent of the distortion. Whenais small, the Gaussian distortion causes a helical deformation which first moves in and then moves away toward far ends along the vortex filament, whereas the central portion where the disturbance was originally located, subsides and straightens. The plane of the sinusoidal distortion simply rotates in the direction opposite to that of the translation of fluid in the undisturbed vortex. The retrograde rotation is the same as that formulated by Kelvin. For these cases of small amplitude, a linearlized theory is also put forward. Whena2is large compared with unity, on the contrary, a nonlinear effect comes in, causing higher‐order deformations to take place in both cases near the tip of the distorted pattern. This substantiates in part the author's experimental observation of the progressive deformation of a vortex loop in the final stage of boundary‐layer transition. A possible mechanism of three‐dimensional amplification of initially small perturbation in a shear flow is also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706768

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A theory is developed concerning the onset of interfacial instabilities at the liquid—liquid interface between two solvents when they are mutually immiscible and when a third species, the solute, is diffusing across the interface. The analysis made involves solving the linearized hydrodynamic equations of motion for an idealized model with appropriate boundary conditions at the interface. The interface becomes unstable and turbulence at the interface develops under certain conditions which depend upon the densities of the solutions, the strength of the frictional forces between solute and solvents, concentration gradients, and the direction and rate of diffusion of the solute. The effects of surface tension and viscosity are considered. Some experimental results pertaining to the instability are cited.

ISSN:0031-9171    

DOI:10.1063/1.1706769

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

An explicit solution is given to the one‐dimensional hydrodynamic shock tube problem. The dynamic and thermodynamic quantities in the quasisteady states and the properties of the resulting waves are derived from the diaphragm pressure ratio and the initial conditions of the driver gas and the driven liquid. The planar flow results also apply, at the instant of diaphragm rupture, to the equivalent problem in a cylindrical or a spherical geometry, such as an underwater blast for example, and are therefore useful for establishing the initial blast properties. For this reason, some preliminary experimental data on low‐energy, spherical underwater explosions are included.

ISSN:0031-9171    

DOI:10.1063/1.1706770

出版商:AIP    

年代:1963

数据来源: AIP