Abstract
The model of a vacuum diode under the influence of a strong external magnetic field is considered. The uninsulated variant, when a part of electrons emitted from the cathode reaches the anode, is investigated. The model is described by a singular boundary value problem for a system of ordinary differential equations. The sensitivity of the problem solution to the change of input parameters is investigated. A coordinate descent method to restore parameters of the boundary value problem is implemented numerically.
Highlights
The modern statement of the problem of magnetic isolation was formulated by physicists in the late 80s of the last century
The magnetic insulation effect is that under the influence of a strong external magnetic field the electrons emitted from the cathode do not reach the anode and turn back to the cathode
Numerical solution of the considered inverse problem for the “uninsulated diode” demonstrates an interesting boundary effect associated with the uncertainty of the boundary solution
Summary
The modern statement of the problem of magnetic isolation was formulated by physicists in the late 80s of the last century. The magnetic insulation effect is that under the influence of a strong external magnetic field the electrons emitted from the cathode do not reach the anode and turn back to the cathode. In [Abdallah et al, 1998; Sinitsyn, 2001; Semenov et al, 2010] the limit model of magnetic insulation described by the boundary value problem for the system of two nonlinear second order ordinary differential equations is considered. In [Abdallah et al, 1998; Sinitsyn, 2001; Semenov et al, 2010; Kosov et al, 2012] a number of analytical results were obtained and numerical experiments were carried out to solve boundary value problems with different parameters. This method proved to be quite effective for the problem under consideration
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