摘要:

The linearized Vlasov equation is employed to investigate the stability of the various equilibrium solutions determined from the following model: an infinite slab of width 2Lcontains a uniform densityNof infinitely massive, singly charged, positive ions. The bounding planes (cathodes) emit fixed Maxwellian electron distributions and absorb all impinging electrons, so that the total number of electrons in the system, and their energy, need not remain constant. This model permits three types of time‐independent, equilibrium solutions for the electron distribution. One of these solutions shows a Maxwellian electron velocity distribution everywhere in the slab and is stable. The other two types of solution have regions where the electron velocity distribution is not Maxwellian. These latter solutions are shown to be unstable for a range of system parameters to a longitudinal electron collective mode with a growth rate on the order of&ohgr;p≡(4&pgr;e2N/m)12.

ISSN:0031-9171    

DOI:10.1063/1.1706897

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The quasi‐linear theory of plasma oscillations developed by Drummond and Pines, and Vedenov, Velikhov, and Sagdeev is examined in detail using the Bogoliubov‐Krylov technique of nonlinear mechanics. For the particular case treated, the mode coupling terms which were neglected in earlier work are of the same order of magnitude as those kept. The asymptotic time development of the system is also discussed in detail.

ISSN:0031-9171    

DOI:10.1063/1.1706898

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency &ohgr; in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant&kgr;=[1−&ohgr;p2/&ohgr;2(1−5KT/2mc2)], unless the driving frequency lies in the small band&ohgr;p2(1−5KT/2mc2)<&ohgr;2<&ohgr;p2(1+KT/2mc2). When the driving frequency satisfies the inequality, then the plasma also supports standing waves which satisfy the relativistic dispersion relation for longitudinal waves.

ISSN:0031-9171    

DOI:10.1063/1.1706899

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The equations of motion of a perfectly conducting, current‐carrying, plasma filament are derived from Hamilton's principle. The result is a nonlinear second order vector partial differential‐integral equation, the solution of which gives the equation of the centerline of the filament. This is extended to the dissipative case for an incompressible fluid. A stability example is worked out.

ISSN:0031-9171    

DOI:10.1063/1.1706900

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The basic magneto‐fluid‐dynamical and electromagnetic equations are applied to study the flexure of an electrically neutral plasma conductor subjected to low Mach number subsonic forced convection. The basic equations, in particular the equation of energy balance, are shown to provide a linear relation between the curvature of the conductor and the mass flux of convection. For a given mass flux the curvature is found to vary inversely with a parameter introduced as the ``flexural rigidity'' of the conductor. The flexural rigidity is proportional to the coefficient which relates to the thermal conduction and the enthalpy flux due to diffusion. The flexural rigidity also increases with radiation losses and is inversely proportional to the specific heat at constant pressure. The theory is compared favorably with the results of an experimental investigation of the deflection of an arc positive column drawn between local, collinear electrodes in argon near atmospheric pressure. The arc current was varied from 2 to 6 A for various incident convection velocities normal to the interelectrode axis up to approximately 200 cm/sec.

ISSN:0031-9171    

DOI:10.1063/1.1706901

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A simple current‐sheet model of a hydromagnetic shock is employed in an attempt to explain the origin of theB&thgr;andvpoloidalobserved previously in the hydromagnetic vortex rings produced in the conical &thgr; pinch. Although this simple model has its limitations, it nevertheless shows clearly that theB&thgr;and the vortex structure are due to Hall currents which are driven by shear in acceleration, and that the existence of any right handedness and left handedness and of the plasma vortex structure itself depends upon the fact that negative electricity (electrons) are light and positive electricity (protons) are heavy. The model also gives a plausible explanation and description of the origin of &thgr; rotation, i.e.,v&thgr;in the &thgr; pinch.

ISSN:0031-9171    

DOI:10.1063/1.1706902

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

If flux lines cannot penetrate into the conducting walls of a theta‐pinch coil, then a repulsion force arises as a diamagnetic plasma approaches the coil wall. This results from the three‐dimensional curvature of the flux lines when the plasma is near the wall. Neglecting changes in plasma shape, the stabilization energy is obtained by computing the energy needed to ``turn on'' the plasma surface currents in the presence of the coil wall. This is done accurately for spherical plasma shapes in cylindrical coils, and approximately for ellipsoidal shapes. The stabilization energy of spheres is proportional to the square of their volume, and becomes effective within a sphere diameter from the wall. It is approximately 10% of the energy needed to introduce the sphere into the coil center. Ellipsoids show roughly the same stabilization as spheres, but the force comes into play farther from the wall. By replacing the plasma with a conducting object of the same shape, an analog experiment is performed to determine the change in inductance as the object is moved about in the coil. For spheres and ellipsoids, agreement is found between the calculations and experiment. The experiment may be used to find the stabilization for complex shapes.

ISSN:0031-9171    

DOI:10.1063/1.1706903

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

An experimental study of the rotation and associated instability was made in a theta pinch with a peak field of 85 kG reached in 2.3 &mgr;sec. The starting deuterium gas pressure was in the range 50–150 &mgr; Hg, and for operation on the second half‐cycle of the sinusoidal driving field the magnetic flux trapped within the plasma varied between ±100 kMx. In most conditions the circular cross section of the plasma became perturbed along its length by the growth of two flutes which rotated at an angular velocity of up to 6 × 107rad/sec. It is deduced from measurements on the rotation that the plasma acquires its angular momentum at the start of the half‐cycle, and the results are interpreted on the basis that the angular momentum is initially in a diamagnetic (azimuthal) ion current. A model is described for establishing this current as a consequence of contact between the plasma and the walls. Results on the time of onset of the instability, and on the growth rate of the flutes, point to the existence of some damping or stabilizing process; it is found that field diffusion, or a rapid axial contraction of the plasma (due to closed reversed field loops), can lead to instability, and when these are reduced the stable time is increased. The possible influence of finite Larmor radius stabilization is discussed. The stability condition, originally derived for low &bgr; but recently shown to have more general validity, is in qualitative agreement with the results.

ISSN:0031-9171    

DOI:10.1063/1.1706904

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

It has been observed experimentally that the application of a radio‐frequency voltage (10 kc/sec–50 Mc/sec) to any one of several electrode configurations around the outside of a plasma discharge tube results in a constriction of the luminous portion of the plasma away from the inner walls of the glass tube. This investigation has established that the phenomenon is basically a radio‐frequency rectification effect, leading to the formation of thick ion sheath. The interaction is described mathematically in terms of a differential equation which has an approximate solution that fits qualitatively all the observed characteristics of the phenomenon. The differential equation, in its most general form, has also been solved numerically and the solution is shown to quantitatively fit our experimental observations for both radio‐frequency sine and square wave signals. An application of this phenomenon as a possible external diagnostic probe technique is proposed.

ISSN:0031-9171    

DOI:10.1063/1.1706905

出版商:AIP    

年代:1963

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706907

出版商:AIP    

年代:1963

数据来源: AIP