Space charge flow kirstein download pdf

Analysis of non-laminar space-charge flow. Authors Authors and affiliations E. Erickson A. The growing trend toward the generation of millimeter wavelengths and of megawatts of c. The central problem, that of predicting analytically the curvilinear behavior of electrons when space-charge effects are gross, is subject to attack from two differing viewpoints: 1. This is a preview of subscription content, log in to check access.

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Need an account? Click here to sign up. Download Free PDF. Relativistic space-charge-limited bipolar flow Physical Review E. Robert Rosner. A short summary of this paper. Relativistic space-charge-limited bipolar flow. Litwin and R. Relativistic generalization of the Child-Langmuir law is derived for flows involving two oppositely charged species.

A large enhancement of the space-charge-limited current in the ultrarelativistic limit, in which both species are accelerated to energies exceeding their rest-mass energies, is demonstrated.

To be of practical value, detailed information about the solutions must be obtained. It appears that closed form solutions for the equations of motion are not practical even if they are possible, since one needs the numerical data for the solutions. It is usually more convenient to have a computer solve the differential equations than to evaluate a closed form solution of the differential equations. All of the equations for computations will be written as first order differential equations with respect to time as the independent variable.

This makes each of the necessary differential equations well behaved at the cathode and allows. Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available.