The Pierce diode with an external circuit. I. Oscillations about nonuniform equilibria

Lawson, William S.

doi:10.1063/1.858925

Cited by 31 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the details of calculating the nonuniform static equilibria and their stability, the reader is referred to Refs. [36,135,147,148,1611.…”

Section: A Linear Eigenmode and Stability Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The Physics of Bounded Plasma Systems (BPS's): Simulation and Interpretation

Kühn

1994

Contrib. Plasma Phys.

View full text Add to dashboard Cite

The dynamical behavior of a bounded plasma system (BPS) is, by definition, characterized by the simultaneous and self-consistent interaction of the plasma itself, its material boundaries, and whatever external circuit(s) there may be. A full theoretical description of these systems, which are of relevance in a variety of fields (e.g., plasma technology), must involve (microscopic or macroscopic) evolution equations for the plasma, Maxwell's equations for the fields, boundary conditions for the plasma and the fields, and the external-circuit equation(s). By "BPS simulation" we mean obtaining theoretical (including numerical) results from models accounting, at least conceptually, for all the basic features mentioned above.This paper is exclusively concerned with microscopic (i.e., kinetic and particle) BPS simulation. A very general system of basic equations for kinetic BPS simulation is proposed. With the PD ("plasma device") codes from U.C. Berkeley [BIRDSALL, C. K., IEEE Trans. Plasma Sci. 19 (1991) 651, particle simulations of (14 3 4 BPS's can now be routinely performed by everybody. Particular emphasis is laid on an alternative method called "trajectory simulation", which has shown great potential for kinetic BPS simulation with high accuracy and resolution. From the point of view of nonlinear dynamics, BPS's are rather complex dissipative systems exhibiting, in particular, regular and chaotic attractor states. For their proper interpretation, an advisable (if not indispensable) first step is to carefully study relatively simple, but still representative "archetypal" BPS's, such as the Pierce diode [GODFREY, B. B., Phys. Fluids 30 (1987) I5531 and the single-emitter plasma diode or "KDSI" [CRYSTAL. T. L., et al., Phys. Fluids B 3 (1991) 2441. These systems and representative results obtained therewith are surveyed, and both recent developments and future perspectives of BPS physics are addressed.

show abstract

“…For the details of calculating the nonuniform static equilibria and their stability, the reader is referred to Refs. [36,135,147,148,1611.…”

Section: A Linear Eigenmode and Stability Resultsmentioning

confidence: 99%

“…The classical Pierce diode. In the "classical Pierce diode" [2,15,36,40,89,96,97,111,114,122,127,132,135,139,[147][148][149]155, 1621, a cold electron beam propagates without collisions between an emitter located at z = 0 and a collector located at z = d , the two electrodes being externally. shorted.…”

Section: A the Pierce Diodementioning

confidence: 99%

The Physics of Bounded Plasma Systems (BPS's): Simulation and Interpretation

Kühn

1994

Contrib. Plasma Phys.

View full text Add to dashboard Cite

show abstract

“…It has another overstable range for 20.9ϽDϽ22.9 and becomes oscillatory damped for DϾ22. 9. The nondimensional growth rates are roughly half of those of the precedent case.…”

Section: Solutions Of the Linear Dispersion Relationmentioning

confidence: 57%

“…IV we have shown the modifications that the so-called marginal states of planar systems undergo in cylindrical systems. 8,9 In the amplitude vs D diagrams of cylindrical diodes, an exchange of stability of nonlinear steady states, occurs at D 2 , D 4 ,..., etc. For x i Ͻ1, and with increasing D, we pass from unstable to stable nonlinear states.…”

Section: Discussionmentioning

confidence: 99%

Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

et al. 1997

View full text Add to dashboard Cite

A special class of Pierce diodes, that consists of a pair of grounded coaxial cylindrical electrodes, with electrons streaming radially between them, is studied. The full set of roots of the dispersion relation of the Pierce instability is obtained by solving the dispersion relation numerically. The nonlinear behaviour of the system is then investigated using particle simulation. It is shown that the behaviour of cylindrical systems depends on two nondimensional parameters. Linear and nonlinear properties are different for convergent and divergent configurations. Several remarkable differences between cylindrical and planar Pierce diodes are reported.

show abstract

“…Moreover, the transition from instability to stability just below each odd multiple of p is described by a Hopf bifurcation. 10…”

Section: Pierce Diodementioning

confidence: 99%

Edge state and crisis in the Pierce diode

Muñoz¹,

Barroso

Chian

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We study the chaotic dynamics of the Pierce diode, a simple spatially extended system for collisionless bounded plasmas, focusing on the concept of edge of chaos, the boundary that separates transient from asymptotic dynamics. We fully characterize an interior crisis at the end of a periodic window, thereby showing direct evidence of the collision between a chaotic attractor, a chaotic saddle, and the edge of chaos, formed by a period-3 unstable periodic orbit and its stable manifold. The edge of chaos persists after the interior crisis, when the global attractor of the system increases its size in the phase space.

show abstract

The Pierce diode with an external circuit. I. Oscillations about nonuniform equilibria

Cited by 31 publications

References 6 publications

The Physics of Bounded Plasma Systems (BPS's): Simulation and Interpretation

The Physics of Bounded Plasma Systems (BPS's): Simulation and Interpretation

Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

Edge state and crisis in the Pierce diode

Contact Info

Product

Resources

About