This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller i...This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller is proposed based on the strategy of controlling the halo-chaos. It performs multiparticle simulation to control the halo by using the Gauss function control method. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively, and that the radial particle density is uniform at the centre of the beam as long as the control method and appropriate parameter are chosen.展开更多
In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clif...In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.展开更多
An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simp...An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.展开更多
In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.
We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
基金supported by the National Natural Science Foundation of China (Grant No 10247005)the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant No KJ2007B187)the Scientific Research Foundation of China University of Mining and Technology for the Young (Grant No OK060119)
文摘This paper studies the Kapchinsky-Vladimirsky （K-V） beam through a triangle periodic-focusing magnetic field by using the particle-core model. The beam halo-chaos is found, and an idea of Gauss function controller is proposed based on the strategy of controlling the halo-chaos. It performs multiparticle simulation to control the halo by using the Gauss function control method. The numerical results show that the halo-chaos and its regeneration can be eliminated effectively, and that the radial particle density is uniform at the centre of the beam as long as the control method and appropriate parameter are chosen.
基金supported by NNSF for Young Scholars of China(11001206)
文摘In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl（Vn,n） is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl（Vn,n） are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No.10974179)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y1090073)
文摘An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.
基金supported by the Natural Science Foundation of Jiangxi Province(20144BAB2110001)Humanities and Social Science Planning Foundation in College of Jiangxi Province(TJ1401)the National Social Science Foundation of China(12BTJ014)
基金supported by the Natural Science Foundation of China(61673169,11401191,11371125)the Tianyuan Special Funds of the Natural Science Foundation of China(11626101)the Natural Science Foundation of the Department of Education of Zhejiang Province(201635325)
文摘In the article, we present some refinements of three classes of transformation inequalities for zero-balanced hypergeometric functions by use of the updated monotonicity criterion for the quotient of power series.
文摘We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
