The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle a...The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model. Electrodynamics becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson’s approach. The gyrocenter law of motion is the Schrödinger equation.展开更多
From the linear Vlasov equation, the theoretical investigation on relativistic backward wave oscillator is performed. The relationship between the microwave power and the guiding magnetic field, which accords with the...From the linear Vlasov equation, the theoretical investigation on relativistic backward wave oscillator is performed. The relationship between the microwave power and the guiding magnetic field, which accords with the results of the particle simulation and experiments, is deduced.展开更多
The relativistic interaction of charged particle beams with a circularly polarized electromagnetic wave propagating along a uniform guiding magnetic field in the tunneling of a dielectric medium is analyzed. The accel...The relativistic interaction of charged particle beams with a circularly polarized electromagnetic wave propagating along a uniform guiding magnetic field in the tunneling of a dielectric medium is analyzed. The acceleration mechanism and a self-consistent nonlinear theory are presented for the interaction of relativistic charged particle beams with electromagnetic waves. Numerical results show that the beam particle can be efficiently accelerated in the interaction process.展开更多
In divertor tokamak plasma, the energetic ion losses of edge plasma are considered to be responsible for the negative radial electric field. In the present paper, a guiding center approximation orbit equation is found...In divertor tokamak plasma, the energetic ion losses of edge plasma are considered to be responsible for the negative radial electric field. In the present paper, a guiding center approximation orbit equation is found by assuming the conservation of three integrals of motion, i.e. the total ion energy E, the magnetic moment # and toroidal angular momentum Pc, and it is used to calculate expediently the ion orbit loss region. The direct ion orbit losses in the initial velocity space near the plasma edge of EAST with SN （single null） divertor configuration are analyzed systematically. The ion loss regions are obtained by solving the guiding center approximation orbit equation of critical ions with the effect of the radial electric field taken into account. Under the influence of plasma current Ip, the type of ions, the toroidal field Bt and the changes of the loss regions are analyzed and calculated accordingly.展开更多
Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed b...Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed by scalar product of vectors which does not depend on a choice of system of co-ordinates. Taking into account the necessary corrections in record of a phase of plane waves, it is shown that the decision of the homogeneous wave equation in the form of “belated” potentials is simultaneously and the decision of the equations of movement of a liquid, and “outstripped” potentials does not satisfy them. The analysis of coefficients of reflection and passage of running waves in non-uniform space is carried out. It is shown that on boundary of spaces with different sound speeds, a turning point of a sound wave is the point of full internal reflection. The way of calculation of coefficients of reflection and passage is offered by consideration of all three waves on boundary of spaces as vectors with the set directions and amplitude of a falling wave. Calculation of coefficients of reflection and passage of a sound wave in a wave-guide of canonical type along the chosen trajectory by two methods—under traditional formulas and a vector method is carried out. Results of calculation practically coincide.展开更多
Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),...Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.展开更多
基金This work has been carried out within the framework of the Nonlinear Energetic Particle Dy-namics(NLED)European Enabling Research Project,WP 15-ER-01/ENEA-03,within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053.
文摘The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In gyro-kinetic theory, some interesting novelties appear in a natural way, such as the exactness of the conservation of a magnetic moment, or the fact that the gyro-phase is treated as the non observable fifth dimension of the Kaluza-Klein model. Electrodynamics becomes non local, without the inconsistency of self-energy. Finally, the gyrocenter transformation is considered in the presence of stochastic e.m. fluctuations for explaining quantum behaviors via Nelson’s approach. The gyrocenter law of motion is the Schrödinger equation.
基金State's High-Technology Research and Development Project(863)
文摘From the linear Vlasov equation, the theoretical investigation on relativistic backward wave oscillator is performed. The relationship between the microwave power and the guiding magnetic field, which accords with the results of the particle simulation and experiments, is deduced.
基金supported by National Natural Science Foundation of China(Nos.51275029,51102007 and 11275007)
文摘The relativistic interaction of charged particle beams with a circularly polarized electromagnetic wave propagating along a uniform guiding magnetic field in the tunneling of a dielectric medium is analyzed. The acceleration mechanism and a self-consistent nonlinear theory are presented for the interaction of relativistic charged particle beams with electromagnetic waves. Numerical results show that the beam particle can be efficiently accelerated in the interaction process.
基金supported by National Natural Science Foundation of China(No.10075048)
文摘In divertor tokamak plasma, the energetic ion losses of edge plasma are considered to be responsible for the negative radial electric field. In the present paper, a guiding center approximation orbit equation is found by assuming the conservation of three integrals of motion, i.e. the total ion energy E, the magnetic moment # and toroidal angular momentum Pc, and it is used to calculate expediently the ion orbit loss region. The direct ion orbit losses in the initial velocity space near the plasma edge of EAST with SN （single null） divertor configuration are analyzed systematically. The ion loss regions are obtained by solving the guiding center approximation orbit equation of critical ions with the effect of the radial electric field taken into account. Under the influence of plasma current Ip, the type of ions, the toroidal field Bt and the changes of the loss regions are analyzed and calculated accordingly.
文摘Work is devoted to the analysis of errors meeting in literature in treatment of a spatial part of a phase of running sound waves. In some cases, it is not taken into consideration that this part of a phase is formed by scalar product of vectors which does not depend on a choice of system of co-ordinates. Taking into account the necessary corrections in record of a phase of plane waves, it is shown that the decision of the homogeneous wave equation in the form of “belated” potentials is simultaneously and the decision of the equations of movement of a liquid, and “outstripped” potentials does not satisfy them. The analysis of coefficients of reflection and passage of running waves in non-uniform space is carried out. It is shown that on boundary of spaces with different sound speeds, a turning point of a sound wave is the point of full internal reflection. The way of calculation of coefficients of reflection and passage is offered by consideration of all three waves on boundary of spaces as vectors with the set directions and amplitude of a falling wave. Calculation of coefficients of reflection and passage of a sound wave in a wave-guide of canonical type along the chosen trajectory by two methods—under traditional formulas and a vector method is carried out. Results of calculation practically coincide.
基金Project supported by the National Natural Science Foundation of China(Nos.11502108 and 1611530686)the State Key Laboratory of Mechanics and Control of Mechanical Structures at Nanjing University of Aeronautics and Astronautics(NUAA)(No.MCMS-E-0520K02)and the Key Laboratory of Impact and Safety Engineering,Ministry of Education,Ningbo University(No.CJ201904)。
文摘Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.
