摘要:

The complete Maxwell‐Vlasov equations together with feedback are analyzed in the quasi‐homogeneous case, using the Nyquist criterion. A class of feedback loops, satisfying sufficient conditions for stability but depending on the wave number k, is found. If the instability satisfies certain properties, a subclass of feedback loops, independent of the wave number, can be constructed. The classical amplification‐delay feedback, generally used in experiments, does not belong to the subclass; and therefore designing an adapted feedback loop is of importance. Applications of the general theory to the low‐frequency electrostatic microinstability and the double beam instability are given.

ISSN:0094-243X    

DOI:10.1063/1.2948494

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The problem of confining a plasma in a specified bounded spatial domain by feedback‐control forces applied over an outer shell of the domain is considered. Using a two‐component fluid model for the plasma, various forms of feedback controls are derived by minimizing an instantaneous weighted mean outflow rate over a subregion of the shell. Effects of some of the derived feedback controls on plasma confinement are determined by experiments performed on a two‐dimensional computer‐simulated plasma.

ISSN:0094-243X    

DOI:10.1063/1.2948521

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Based on the dispersion relation of the individual mode, a stability criterion accounting for the geometrical effects which inherently limit detection and enforcing processes of feedback systems while neglecting the nonlinear mode coupling effects, is formulated. If the criterion predicts instability, the plasma should be considered unstable. If the criterion predicts stability below a certain value of feedback gain, however, the plasma may in fact be unstable under those conditions; but a reduction in gain will always lead to stability. The agreement between stable operating regions predicted by this criterion and by earlier exact analysis shows acceptable agreement for design purposes.

ISSN:0094-243X    

DOI:10.1063/1.2948482

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

General boundary conditions of plasma‐feedback systems using electrodes as both sensor and suppressor at plasma boundaries simultaneously are discussed. Difference equations describing the electrical properties of the boundary are derived and converted to differential equations which lead to a boundary dispersion relation describing the boundary modes and their interaction with the plasma. Application to Kelvin‐Helmholtz instability is given.

ISSN:0094-243X    

DOI:10.1063/1.2948490

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

A simple model is discussed which illustrates the general features of plasma stabilization by an external feedback system. This indicates that different phase relations in the feedback loop are needed to stabilize differing classes of electrostatic instability.

ISSN:0094-243X    

DOI:10.1063/1.2948502

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Stabilization of an electrostatic flute‐type instability occurring in a simple magnetic mirror by feedback techniques is discussed. In the first part of the paper a diffuse plasma is considered. The effect of varying the locations of the sensing and suppressing systems is found to alter the stability threshold significantly. In the second part a sharp‐boundary plasma is considered and phase shift and frequency response are included in the feedback terms.

ISSN:0094-243X    

DOI:10.1063/1.2948510

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

An extraordinary electromagnetic wave of large amplitude will produce a quasilinear dc drift of electrons relative to ions, which can be modulated for feedback stabilization of low‐frequency waves. The effect occurs at the upper hybrid resonance. A promising way to penetrate the cut‐off in a fusion plasma is to use the nonlinear interaction of twoCO2laser beams to produce a difference frequency near &ohgr;h. We have extended the cold plasma analysis for this process and find that the intensities required are not unreasonable even when thermal effects are taken into account.

ISSN:0094-243X    

DOI:10.1063/1.2948516

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Three types of analytical models for determining adequate feedback spatial and temporal resolution are distinguished for representing dynamics with finite sampling: piecewise continuous, (‘spliced’) discrete coupled modes, and coupled wavetrains. The stabilization of the z‐&thgr; pinch is used for comparing the various representations, particularly as they represent a quasi‐one‐dimensional model for them = 1modes, and specific stability regimes are given. The advantages of the modal and wavetrain approaches in describing three‐dimensional effects are illustrated, with the wavetrain approach shown as particularly convenient for systems having many potentially unstable wavelengths within the system boundaries, hence necessitating many sampling stations. A discussion of difficulties in stabilizing interchange modes is given, and nonlinear forms of ‘bang‐bang’ feedback obviating these difficulties suggested.

ISSN:0094-243X    

DOI:10.1063/1.2948517

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

Nonlinear, or “bang‐bang, ” feedback, in which a constant corrective force of arbitrary strength is applied to the plasma for as long a time as the local average of the surface displacement is positive, is discussed for the stabilization of MHD modes. It is shown that, in addition to obvious bandwidth and impedance‐level problems, linear feedback cannot stabilize modes for which the perturbation amplitude is constant along the lines of the external magnetic field. Plasma stability with “bang‐bang” feedback scheme is studied using an energy principle (Liapunov function). Although we focus attention on modes whose amplitude is constant along Bo, the proposed scheme can be applied to stabilize all other modes as well.

ISSN:0094-243X    

DOI:10.1063/1.2948518

出版商:AIP    

年代:1970

数据来源: AIP

摘要:

The feedback control of hydromagnetically contained plasmas with dimensions large compared to potentially unstable wavelengths requires a large number of spatially distributed feedback sensors and drivers. The multiplicity of signals to be amplified and processed suggests the use of computers or other discrete‐time devices which handle signals on a ‘time‐sharing’ basis. Typically, scanning techniques are envisioned to sense and drive, thus introducing to an analytical representation discreteness in both time and space. A general method, based on the Fourier superposition of wavetrains, is developed to describe infinite continuum systems with discrete spatial and temporal feedback. Dynamics are represented by a generalization of the dispersion equation, with Z transforms used to provide closed‐form expressions if the discreteness is in space or in time only. The Bers‐Briggs criterion is generalized to differentiate between absolute instabilities and amplifying waves with the discrete feedback. A quasi‐one‐dimensional model for them = 1mode of the z‐&thgr; pinch is studied to delineate effects of spatial and temporal sampling rates on stability regimes.

ISSN:0094-243X    

DOI:10.1063/1.2948519

出版商:AIP    

年代:1970

数据来源: AIP