Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser（FEL）,optimization of the undulator lattice becomes important.In this paper,the tra...Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser（FEL）,optimization of the undulator lattice becomes important.In this paper,the transfer matrix of the planar undulator is obtained from differential equations of the electron motion.Based on this,the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology（HUST-FEL） is optimized and the expressions of the average beta function are derived.The accuracy of the optimization result was confirmed well by the numerical method.The application range of this analytical method is given as well.At last,the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.展开更多
This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the ...This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.展开更多
文摘Since the beta function of the electron beam within the undulator has a great influence on the power gain of the free electron laser（FEL）,optimization of the undulator lattice becomes important.In this paper,the transfer matrix of the planar undulator is obtained from differential equations of the electron motion.Based on this,the lattice function of the planar undulator in a terahertz FEL oscillator proposed by Huazhong University of Science and Technology（HUST-FEL） is optimized and the expressions of the average beta function are derived.The accuracy of the optimization result was confirmed well by the numerical method.The application range of this analytical method is given as well.At last,the emittance growth in the horizontal direction due to the attenuation of the magnetic field is discussed.
基金the National Natural Science Foundation of China(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005)Taishan University Youth Teacher Science Foundation(Grant No.QN-01-201901).
文摘This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.
