摘要:

A systematic account of the infinitely many solutions of Landau's dispersion relation verifies that there is always a least‐damped wave provided the wavenumber is real and not zero. This no longer holds when the frequency is real; yet, the mode originally considered by Landau predominates in a limited range. Strong “coupling” is found between this wave and higher‐order modes at complex frequencies, or when collisions are taken into account. However this coupling does not give rise to resonances other than at the plasma frequency. Short tables of Landau poles and singular points of the dispersion relation conclude this account.

ISSN:0031-9171    

DOI:10.1063/1.1692477

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The linearized Vlasov equation is used to describe the coupling to plasma waves in bounded plasmas of externally driven quasistatic electric fields of frequency&ohgr;, treating as an example a cylindrically symmetric equilibrium. The coupling takes place at the plasma resonance, where&ohgr;equals the local plasma frequency. It is described by an asymptotic theory based upon the small parameter&ngr;T/&ohgr;L < < 1, where&ngr;T, where is the electron thermal velocity andLthe equilibrium scale length. A previously suggested mechanism based on a WKB solution of the Vlasov equation is then developed to provide trapping of the plasma waves between the plasma resonance and the wall sheath, including the effects of Landau damping. The effect of these internal resonances on the external admittance of the plasma is shown, and a numerical example containing typical experimental parameters is given. A comparision is made with previous theories which utilized a fluid model of the plasma.

ISSN:0031-9171    

DOI:10.1063/1.1692478

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The interactions of an electron beam with a bounded, uniform, equilibrium plasma have been studied experimentally by varying several of the physical parameters that appear in the dispersion equation. This equation (which takes into account the geometry, the magnetic field, and collisions, but which neglects temperature), is solved for complex wavenumber roots in order to compare the wave variables&ohgr;,kr, andkiwith their experimental counterparts. The only instability that has been observed with certainty is a convective one having a frequencyfbelow bothfpeandfce, all of which are in the neighborhood of 1 GHz. This frequency, and the associated wavelength and axial growth rate as well, are in reasonable agreement with the calculated values, if the absolute values of the effective plasma frequency as obtained from probe measurements are correct. Data are presented on the behavior of the wave properties with time, distance, beam voltage, frequency, and plasma and cyclotron frequencies; and the existence of several nonlinear effects is noted.

ISSN:0031-9171    

DOI:10.1063/1.1692479

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An analysis is presented for the normal modes of low‐frequency wave propagation on the positive column in an axial magnetic field. Dispersion characteristics are obtained from a hydrodynamic treatment by perturbing a steady‐state discharge model which includes generation and ion inertia, and is valid for arbitrary pressure. The resulting complex eigenvalue problem is solved numerically by use of a Fourier‐Bessel expansion. In general, two types of waves are found for a given frequency: ion‐acoustic waves and electron waves. For the regions of parameter space appropriate to laboratory discharges, the ion‐acoustic wave branches are predicted to be heavily damped, expect at low pressures where the computer solutions are in general agreement with available experimental data. The electron wave branches do not show instability for axisymmetric modes(m = 0), but can be unstable for asymmetric modes(m ≠ 0). Stable modes only are considered and it is shown that some hitherto unexplained damped waves, observed experimentally, are identifiable as symmetric electron‐wave modes(m = 0).

ISSN:0031-9171    

DOI:10.1063/1.1692480

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An analysis was presented previously [H. N. Ewald, F. W. Crawford, and S. A. Self, Phys. Fluids 12, 305 (1969)] for the normal modes of low‐frequency wave propagation on the positive column in an axial magnetic field, and dispersion characteristics were discussed for axisymmetric(m = 0)ion‐acoustic and electron wave modes. These studies are complemented with an examination of asymmetric modes(m ≠ 0). First, the stability of a low‐pressure positive column without axial drift has been investigated. It is found that with increasing magnetic field, instability first occurs in high‐order modes. Next, the theory has been applied to the positive column over a wide pressure range. The computed results are compared with previous approximate analyses of the current‐convective instability. Finally, the specific prediction of the theory that asymmetric electron wave modes, rotating in the sense of the electron diamagnetic drift(m ≥ 1), should grow convectively for sufficiently large magnetic field has been checked experimentally. Measurements on the propagation of them = 1wave on a low‐pressure mercury‐vapor positive column are presented which support this prediction.

ISSN:0031-9171    

DOI:10.1063/1.1692481

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

It is shown that there exists a large family of global quadratic constants of motion for perturbations around the steady large‐amplitude electrostatic waves of Bernstein, Greene, and Kruskal.

ISSN:0031-9171    

DOI:10.1063/1.1692482

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Analysis of “exact” numerical solutions of the Vlasov equation for longitudinal perturbations of a realistic inhomogeneous plasma shows that the responseEp(x)eiwtto an externally supplied driving fieldEd(x)eiwtis well described by a normal mode representationEp(x) = n=1N En(x)&ohgr;2 − &ohgr;n2 0L En(x′) dx′. The free oscillation frequencies&ohgr;nand the normal modesEn(x)are determined from solutions of the Vlasov equation for a&dgr;‐function driving field. The normal mode representation is then used to obtain the solution of the Vlasov equation for a uniform driving field, and the results compare well with “exact” solutions.

ISSN:0031-9171    

DOI:10.1063/1.1692483

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The bounce model has been used to calculate the growth rate of them = 1mode of a linear&thgr;pinch having an isotropic Maxwellian ion distribution function rotating with angular velocity&ohgr;. For short wavelength, the perturbation rotates with the ions; for longer wavelength it rotates more slowly. The plasma is unstable above a critical wavelength, with growth times&tgr; ≈ 25 &mgr;secfor typical values of&ohgr;. This result falls between the magnetohydrodynamic result of&tgr; = ∞(stable) and the rigid body limit of&tgr; ≈ &ohgr;−1. Consideration of them = 2mode is also included.

ISSN:0031-9171    

DOI:10.1063/1.1692484

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Some numerical results for the high‐frequency nonlinear conductivity of a fully ionized plasma are presented. Special attention has been given to the case when the frequency&ohgr;of the applied electromagnetic field is close to the electron plasma frequency&ohgr;p. Apart from its intrinsic theoretical interest, this frequency range is of relevance to the problem of production and heating of plasmas by laser irradiation.

ISSN:0031-9171    

DOI:10.1063/1.1692485

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

For a high negative voltageV0placed impulsively at the edge of a plasma, a sheath is formed of thicknessX = (2eV0)1/2(4&pgr;nie2)−1/2This sheath is observed by extrapolating the position of the leading edge of an ionic sound‐wave pulse back to zero time. The ion number density can be obtained from this sheath.

ISSN:0031-9171    

DOI:10.1063/1.1692486

出版商:AIP    

年代:1969

数据来源: AIP