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TUPSA18 |
About One Way of the Solution of the Hill Equation | |
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| The equation of Hill finds application in the different fields of science and technology, including accelerating technique. The known approaches assume the analysis of stability of the decision after definition of eigenvalues of a matrix of transition from initial values of couple of fundamental decisions to their values through the period of the function defining an oscillation frequency of amplitudes of decisions. Fundamental decisions are defined by the numerical solution of differential equations for amplitude and a phase received immediately from the equation of Hill. The different way of analytical submission of fundamental solutions of the equation of Hill and numerical approach to its decision is given in work. In it matrix approach to a task and the simplified algorithm of its decision corresponding to it is used. The received results are compared to results of the solution of the equation of Hill in the traditional way. On some plane the solution of the equation of Hill will be displayed in the form of closed curves with the repeating sites. At the same time curves will be not periodic if a change of a phase is incommensurable with 2Pi. If the solution of the equation of Hill is not limited, it will be displayed in the form of two spirals. Zero of some integral can judge stability of the decision on equality Thus, the specified technique of the solution of the equation of Hill allows along with finding of couple of fundamental decisions to define their stability. | ||
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THPSC55 |
About a Possibility of Acceleration of Ferromagnetic Objects by the Electromagnetic Fields | |
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| As the accelerated objects in work the possibility of use of separate domains of a ferromagnetic is considered. Also perhaps an existence of solid-state communication of domains is possible. Acceleration is carried out at the expense of a gradient of the base magnetic field. The magnetic field of ferromagnetics creates a longitudinal potential well in the base magnetic field. The gradient of the base magnetic field does not exceed a gradient of this potential well and does not allow the accelerated objects to go beyond its limits. Depth of a potential well can be increased at the expense of the electron stream which is in this potential well. He does not leave area of a well too, being reflected from its walls. There is some semblance of the moving adgezator used at coherent acceleration of protons by electronic rings. A certain similarity of repetition of the idea of acceleration of protons electronic rings due to acceleration of electronic rings external fields is possible. It can be as magnetic fields with the corresponding gradient of a longitudinal field, and electric fields also. Some kind of combination of coherent acceleration of neutral domains of a ferromagnetic by the magnetic and electric field turns out. Estimates show that at number of atoms about 10 in 14 degrees their acceleration to 1 MEV apart approximately in 1 meter is possible. The sizes of domains are about 10 in minus fifth degree of meter. Longitudinal magnetic fields are in range of 1 Tesla. | ||
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