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The influence of sampling parameters on the adequacy of three-dimensional numerical models of magnetrons


A. S. Ershov, V. B. Baiburin, A. A. Terentyev

A mathematical model of the magnetron is offered. That model takes into account the split-anode structure, the presence of end-shields, the radius change of the cathode in height. Its adequacy was checked. It is known that the adequacy of numerical models, convergence and stability of the obtained with their help results, time accounts, etc. are essentially determined by the digitization parameters. The major ones include: "initial" number of large particles, the magnitude of solution error of the Poisson’s equation, the number of grid points in radial, azimuthal and axial directions in the interaction space. Our calculations, according to which magnitude of mentioned digitization parameters ranged, allowed us to determine their optimal values. Calculations showed that the number of initial large particles did not affect the final results of the simulation. The calculations also showed that the number of initial large particles in the steady state was approximately equal to 10000. The optimal value of the admissible solution error of the Poisson's equation is equal to =5∙10-4. Investigation of the dependence of simulation results on the number of nodes in the radial, axial and azimuthal directions showed the following: the optimum grid dimension in the radial direction was 15-20 knots, in the azimuth direction – 80, and in the axial direction – 20. The results of the present work with the digitization parameters found provide adequacy of three-dimensional numerical model of the magnetron-type devices.

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