In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over ...In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).展开更多
An orbit code is a special constant dimension subspace code,which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space.This paper presents some methods of c...An orbit code is a special constant dimension subspace code,which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space.This paper presents some methods of constructing new orbit codes from known orbit codes.Firstly,we introduce the sum operation,intersection operation and union operation of subspace codes,and then we give some methods to obtain new orbit codes from known orbit codes by fully applying the sub-orbits of permutation groups and the direct product operation of the groups.Finally,as a special application,partial spread codes are researched and a condition of orbit codes with constant distance is given.展开更多
Fusion born α particle confinement is one of the most important issues in burning plasmas,such as ITER and CFETR.However,it is extremely complex due to the nonequilibrium characteristics,and multiple temporal and spa...Fusion born α particle confinement is one of the most important issues in burning plasmas,such as ITER and CFETR.However,it is extremely complex due to the nonequilibrium characteristics,and multiple temporal and spatial scales coupling with background plasma.A numerical code using particle orbit tracing method(PTC)has been developed to study energetic particle confinement in tokamak plasmas.Both full orbit and drift orbit solvers are implemented to analyze the Larmor radius effects on α particle confinement.The elastic collisions between alpha particles and thermal plasma are calculated by a Monte Carlo method.A triangle mesh in poloidal section is generated for electromagnetic fields expression.Benchmark between PTC and ORBIT has been accomplished for verification.For CFETR burning plasmas,PTC code is used for α particle source and slowing down process calculation in 2D equilibrium.In future work,3D field like toroidal field ripples,Alfven and magnetohydrodynamics instabilities perturbation inducing α particle transport will be analyzed.展开更多
Purpose Tune shift and spread due to the space charge effects and collective instabilities in intense proton synchrotrons,such as the CSNS/RCS,a rapid cycling synchrotron at China Spallation Neutron Source,are the mai...Purpose Tune shift and spread due to the space charge effects and collective instabilities in intense proton synchrotrons,such as the CSNS/RCS,a rapid cycling synchrotron at China Spallation Neutron Source,are the main causes of beam loss.Tune shift/spread is large when the beam kinetic energy is low and will cause particles to cross dangerous resonances,while they will gradually decay with the increase of kinetic energy.Methods An efficient way,which was verified in operational accelerators,is to tune the working point during different acceleration periods:injection,acceleration and extraction.With the newly added function of time-dependent lattice in the ORBIT code,one can simulate the physical performance with different tune patterns to find the best way to reduce beam loss.Results The method to tune the working point by time-dependent lattice to weaken the crossing of dangerous resonances has been exploited,and implemented in the ORBIT code.It is the first of such try to apply the method in CSNS/RCS.Conclusions The results presented in this paper show that the time-dependent lattice method does help reduce beam loss in the injection and early acceleration.展开更多
基金Supported by Research Funds of Hubei Province(D20144401,Q20174503)。
文摘In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).
基金This paper is supported by the Fundamental Research Funds of the Central Universities of China Civil Aviation University of Key Projects of Natural Science(No.3122019192).
文摘An orbit code is a special constant dimension subspace code,which is an orbit of a subgroup of a general linear group acting on the set of all subspaces in the given ambient space.This paper presents some methods of constructing new orbit codes from known orbit codes.Firstly,we introduce the sum operation,intersection operation and union operation of subspace codes,and then we give some methods to obtain new orbit codes from known orbit codes by fully applying the sub-orbits of permutation groups and the direct product operation of the groups.Finally,as a special application,partial spread codes are researched and a condition of orbit codes with constant distance is given.
基金Supported by the National Natural Science Foundation of China (Grant Nos.11975068 and 11925501)the National Key Research and Development Program of China (Grant No.2017YFE0300501)。
文摘Fusion born α particle confinement is one of the most important issues in burning plasmas,such as ITER and CFETR.However,it is extremely complex due to the nonequilibrium characteristics,and multiple temporal and spatial scales coupling with background plasma.A numerical code using particle orbit tracing method(PTC)has been developed to study energetic particle confinement in tokamak plasmas.Both full orbit and drift orbit solvers are implemented to analyze the Larmor radius effects on α particle confinement.The elastic collisions between alpha particles and thermal plasma are calculated by a Monte Carlo method.A triangle mesh in poloidal section is generated for electromagnetic fields expression.Benchmark between PTC and ORBIT has been accomplished for verification.For CFETR burning plasmas,PTC code is used for α particle source and slowing down process calculation in 2D equilibrium.In future work,3D field like toroidal field ripples,Alfven and magnetohydrodynamics instabilities perturbation inducing α particle transport will be analyzed.
基金the National Natural Science Foundation of China(Projects:11575214)the National Key Research and Development Program of China(Project:2016YFA0401600)and the CSNS Project.
文摘Purpose Tune shift and spread due to the space charge effects and collective instabilities in intense proton synchrotrons,such as the CSNS/RCS,a rapid cycling synchrotron at China Spallation Neutron Source,are the main causes of beam loss.Tune shift/spread is large when the beam kinetic energy is low and will cause particles to cross dangerous resonances,while they will gradually decay with the increase of kinetic energy.Methods An efficient way,which was verified in operational accelerators,is to tune the working point during different acceleration periods:injection,acceleration and extraction.With the newly added function of time-dependent lattice in the ORBIT code,one can simulate the physical performance with different tune patterns to find the best way to reduce beam loss.Results The method to tune the working point by time-dependent lattice to weaken the crossing of dangerous resonances has been exploited,and implemented in the ORBIT code.It is the first of such try to apply the method in CSNS/RCS.Conclusions The results presented in this paper show that the time-dependent lattice method does help reduce beam loss in the injection and early acceleration.
