It is indicated in the article that the study of the electron bunching process in the drift space of a transit klystron is an urgent task that allows one to establish general laws applicable to more complex models. In this connection, the behavior of the pre-modulated electron beam in the drift space of the transit klystron has been investigated. A numerical model has been implemented that takes into account the effect of space charge fields and the interaction of charged particles with elements of an electrodynamic system. A series of numerical experiments with different values of the current and initial velocities of electrons, as well as their comparison with theoretical data, have been carried out. As a result of numerical experiments, data were obtained that characterize the dynamics of the electron flux in the drift space of the transit klystron at different values of the initial velocity (0.5 s, 0.9 s) and cathode current (10 mA, 1A, 10A).
Keywords: flyby klystron, mathematical model, numerical simulation, large particle method, particle-particle method, drift space, convection current distribution, electron flow, multithreaded calculations, system of differential equations
This paper considers the vectorization and parallelization of the "particle-particle" method used to take into account interactions between objects in the mathematical modeling of physical processes, using the example of taking into account the space charge when calculating the dynamics of charged particles. Comparison and estimation of time costs are carried out (as a test problem, the expansion of a multicomponent ion beam during one nanosecond with a step of Δt = 10-12 s was considered), taking into account the acceleration due to vectorization and parallelization between processor cores. It is concluded that the results of the work clearly demonstrate that the vectorization of computations can significantly speed up the computation time, and the explicit replacement of scalar operations with vector ones makes it possible to obtain additional speed-up in comparison with the use of automatic optimization of the program code. Key words: parallel computations, "particle-particle" method, vectorization of computations, numerical modeling, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model.
Keywords: parallel computations, particle-particle method, vectorization of computations, numerical simulation, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model
The article considers the dynamics of an ion beam in a laser mass – EMAL-2 spectrometer.a numerical model based on the "large - particle" method is Implemented, taking into account the influence of spatial charge fields and the interaction of charged particles with the field of an electrodynamic system. The software package that implements the mathematical model of ion beam motion consists of two parts. The first part is a program written in C++, in which initial conditions are set, the Coulomb interaction between large particles is calculated using the "particle-particle" method, the system of differential equations (1) is integrated using the fourth-order Runge-Kutta method, and the results are recorded and processed. The second part is a script for the FreeFem++ package, which implements the solution of partial differential equations using the finite element method. A series of numerical experiments and their comparison with the data obtained experimentally are carried out.
Keywords: large particle method, laser mass spectrometer, particle-particle method, electrodynamic system, Runge-Kutta method, laser plasma, magnetic analyzer, ion beam, focusing system, triangulation
The article deals with the dynamics of an ion beam in a tandem laser mass-reflectron. The software package that implements the mathematical model of the ion beam motion is based on the "large - particle" method.it takes into account the influence of the spatial charge field and the interaction of ions with the field of the electrodynamic system. The potential distribution in the device nodes is obtained by numerical solution of the Laplace equation using the mathematical package Freefem++, which implements the solution of partial differential equations by the finite element method. The absence of inhomogeneity of the electric field inside the reflectors is shown. A series of numerical experiments has been carried out, which has shown the convenience of using the finite element method for numerical solution of problems of electrostatics and ion optics, as well as the effectiveness of using numerical modeling to develop and optimize the parameters of mass spectrometers.
Keywords: large particle method, laser mass spectrometer, particle-particle method, electrodynamic system, Runge-Kutta method, laser plasma, ion beam, focusing system, triangulation, gas-forming impurities, time-of-flight mass spectrometer
The article discusses several equivalent circuits constructed by sequentially connecting circuits for the membrane and protoplasm. The solution was made using the Cardano formula for cubic equations. The roots in the expression for the determination of resonant frequencies determined the resonant frequencies for the given parameters for the membrane and intercellular fluid; to obtain numerical values, values were used within several permissible limits. In the course of the calculations, it was confirmed that most resonant frequencies are in the millimeter and submillimeter ranges. It is also shown that the cell vibration frequencies occupy the decimeter, centimeter, millimeter and submillimeter wavelengths. Obviously, it is the impact on biological systems of electromagnetic radiation in the indicated wavelength ranges that will be most effective and can lead to a maximum biological response (effect).
Keywords: equivalent equivalent circuit, biological structure, membrane, oscillatory circuit, Cardano formula, protoplasm, resonant frequencies, electrical processes, equivalent equivalent circuit, electromagnetic radiation