The electric field in the crystal planar channels is studied by the Thomas-Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numerical s...The electric field in the crystal planar channels is studied by the Thomas-Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numerical solution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles of channelling protons in them arc shown. Reasonable agreements with the experimental data are obtained. The results show that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channel electric field with the contribution of all atoms and the atomic ionization being taken into account is practical.展开更多
Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic ...Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.展开更多
基金国家自然科学基金，the Chinese High Performance Computing Center (Beijing)
文摘The electric field in the crystal planar channels is studied by the Thomas-Fermi method. The Thomas-Fermi equation and the corresponding boundary conditions are derived for the crystal planar channels. The numerical solution for the electric field in the channels between (110) planes of the single crystal silicon and the critical angles of channelling protons in them arc shown. Reasonable agreements with the experimental data are obtained. The results show that the Thomas-Fermi method for the crystal works well in this study, and a microscopic research of the channel electric field with the contribution of all atoms and the atomic ionization being taken into account is practical.
基金the National Natural Science Foundation of China(Grant Nos.12172321 and 11472239)the Hebei Provincial Natural Science Foundation of China(Grant No.A2020203007).
文摘Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.
