Unstable electron flow in a diode

Lomax, R.J.

doi:10.1049/pi-c.1961.0018

Cited by 9 publications

(11 citation statements)

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“…In accordance with earlier studies, we find that the C-overlap branch is unstable to linear perturbations, and we follow these into non-linear regime [3,17,18].…”

Section: Equilibrium Solutionssupporting

confidence: 92%

Stability and energetics of Bursian diodes

Rosin

Sun

2013

Phys. Rev. E

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We present an analysis of the stability, energy, and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of equilibrium solutions for the same boundary conditions, one solution is found to be stable and the other unstable to linear perturbations. Following the linearly unstable solutions into the nonlinear regime, we find they relax to the stable equilibrium. A description of this process in terms of kinetic, potential and boundary-flux energies is given, and the relation to a Hamiltonian formulation is commented on. A nonlocal torque integral theorem relating the prescribed boundary data to the average current in the domain is also provided. The results will be useful for numerical verification purposes, and understanding Bursian diodes in general.

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“…In accordance with earlier studies, we find that the C-overlap branch is unstable to linear perturbations, and we follow these into non-linear regime [3,17,18].…”

Section: Equilibrium Solutionssupporting

confidence: 92%

Stability and energetics of Bursian diodes

Rosin

Sun

2013

Phys. Rev. E

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“…In this work, we extend previous analysis [1][2][3][4] of the linear stability of the space charge limited flow to the case when the current is determined by a current-field relation at the emitter. We consider a planar diode with flat parallel electrodes, which allows a one dimensional treatment.…”

Section: Introductionmentioning

confidence: 73%

Linear stability of electron flow produced by field emission

Rokhlenko¹,

Lebowitz²

2013

Journal of Applied Physics

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A linear stability analysis of the planar one dimensional space charge limited flow is performed when the current is determined by a current-field relation, e.g., the Fowler-Nordheim or any other emission model. The initial velocity is assumed the same for all emitted electrons. The flow is shown to be stable with decaying oscillations depending on the nature of the emission law, including in some situations non-oscillating slowly decaying modes. When the emission variations are due only to changes of the initial flow velocity, the time of decay can be much longer than the electron transit time for a given flow setup. V

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“…This allows to find uniquely the electric field E(τ, t) as well as ϕ(τ, t) and current density j(τ, t) at the point x, t. (This somewhat sloppy use of the same notation in the new units will not lead to confusion). A straightforward analysis in these variables [3] shows that if T is the time needed for an electron, emitted at τ , to cross the diode then this electron is located at…”

Section: Main Equations and Setup Of 1d Flow Modelmentioning

confidence: 99%

“…While the main features of the steady flow in a diode have been known for a century [1], [2] an important step in studying time dependent states was made by Lomax [3] in 1960, who applied the Lagrange formulation of flow dynamics. This approach has been developed in many works, in particular in [4]- [8], where the authors found conditions for flow stability and modes of oscillations.…”

Section: Introductionmentioning

confidence: 99%

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Time evolution of electron flow in a model diode: Non-perturbative analysis

Rokhlenko

Lebowitz

2013

Journal of Applied Physics

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Using a combination of Eulerian and Lagrangian variables we obtain some exact results and good approximation schemes for the time evolution of the electron flow from a no-current state to a final stationary current state in a planar one-dimensional diode. The electrons can be injected externally or generated by the cathode via field emission governed by a current-field law. The case of equipotential electrodes and fixed injection is studied along with a positive anode potential. When the current is fixed externally the approach to the stationary state goes without oscillations if the initial electron velocity is high enough and the anode can absorb the injected flow. Otherwise the accumulated space charge creates a potential barrier which reflects the flow and leads to its oscillations, but our method of analysis is invalid in such conditions. In the field emission case the flow goes to its stationary state through a train of decaying oscillations whose period is of the order of the electron transit time, in agreement with earlier studies based on perturbation techniques. Our approximate method does not permit very high cathode emissivity, though the method works when the stationary current density is only about 10% smaller than the ChildLangmuir limit.

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Unstable electron flow in a diode

Cited by 9 publications

References 0 publications

Stability and energetics of Bursian diodes

Stability and energetics of Bursian diodes

Linear stability of electron flow produced by field emission

Time evolution of electron flow in a model diode: Non-perturbative analysis

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