The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order ...The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.展开更多
This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are ...This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are the theoretical basis for the flux mapping method. Using the bi-orthogonality of HOH and the strict formula for eigenvalue estimation. the process and formulas for HOH calculation called as the source iteration method with source correction are derived. The analysis can predict any order of harmonics for 2-or 3-dimensional geometries.Preliminary verification of the capability for flux mapping is also given. and other applications of HOH for reactor operation analysis and failure diagnosis are underway.展开更多
Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfor...Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfortheflux usingthe multi group modelis notcomplete .This paperusesthe assumption thatthe set offlux vectors of HOHfor every group is complete. This assumption can be proven only forthose groups into which noscattering neutrons enter.However,itisalso shownto betrueforseveralpracticalreactor models.Analysisshows thatthe number of HOHwith non zero eigenvaluesis equaltothe numberofdifference meshes withfissile material, and thatthe eigenvalues have positive realvalues.This assumptionis valuablefor HOHapplications,butrequires furthertheoreticalstudyto verify whetheritisuniversally applicable.展开更多
The synchrotron radiation spectra of the spherical grating monochromator(SGM)working in the soft X-ray and VUV region are often contaminated by significant amounts of higher order harmonics.They cannot be suppressed c...The synchrotron radiation spectra of the spherical grating monochromator(SGM)working in the soft X-ray and VUV region are often contaminated by significant amounts of higher order harmonics.They cannot be suppressed completely by suitable filters.Higher order contributions in the spectral radiation standard and metrology beamline were researched using transmission grating(made in-house)and IRD AXUV100G(USA)photodiode detector.The exit beam was dispersed with the transmission grating behind the exit slit of the monochromator,and the contributions of the different orders were analyzed.The higher order distributions were quantitatively determined for three gratings with line densities of 1800,600 and 200 l/mm.Experiment results show that in wavelengths between 5 nm and 15 nm the contributions of the higher orders to the detector signal are restricted to less than 7%even without the use of filters.In wavelength regions between 5 nm and 34 nm,the contributions of the higher orders to the detector signal are less than 14%with proper Al,Si_(3)N_(4) and Zr filters,and after being modified by quantum efficiency of the detector,the higher order contributions are restricted to less than 6.5%.The study also shows that higher orders are almost totally suppressed by MgF_(2) filter when the wavelength ranges between 115–140 nm.展开更多
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0206004)the National Natural Science Foundation of China(Grant No.11375160)the National Science Instruments Major Project of China(Grant No.2012YQ130125)
文摘The extreme ultraviolet and soft x-ray sources are widely used in various domains. Suppressing higher order harmonics and improving spectral purity are significant. This paper describes a novel method of higher order harmonics suppression with single order diffraction gratings in extreme ultraviolet and soft x-ray. The principle of harmonic suppression with single order diffraction grating is described, and an extreme ultraviolet and soft x-ray non-harmonics grating monochromator is designed based on the single order diffraction grating. The performance is simulated by an optical design software. The emergent beams of a monochromator with different gratings are measured by a transmission grating spectrometer. The results show that the single order diffraction grating can suppress higher order harmonics effectively, and it is expected to be widely used in synchrotron radiation, diagnostics of laser induced plasma, and astrophysics.
文摘This paper proposes a flux mapping method directly using the higher order harmonics (HOH) of the neutronics equation of the nominal core. The bi-orthogonality and completeness of the HOH set are studied. and they are the theoretical basis for the flux mapping method. Using the bi-orthogonality of HOH and the strict formula for eigenvalue estimation. the process and formulas for HOH calculation called as the source iteration method with source correction are derived. The analysis can predict any order of harmonics for 2-or 3-dimensional geometries.Preliminary verification of the capability for flux mapping is also given. and other applications of HOH for reactor operation analysis and failure diagnosis are underway.
文摘Applications using higher orderharmonics (HOH) require knowledge ofthe completeness ofthe HOHfor the diffusion difference equation.This papershowsthatthe set of HOHforthefission sourceis complete ,butthat the setfortheflux usingthe multi group modelis notcomplete .This paperusesthe assumption thatthe set offlux vectors of HOHfor every group is complete. This assumption can be proven only forthose groups into which noscattering neutrons enter.However,itisalso shownto betrueforseveralpracticalreactor models.Analysisshows thatthe number of HOHwith non zero eigenvaluesis equaltothe numberofdifference meshes withfissile material, and thatthe eigenvalues have positive realvalues.This assumptionis valuablefor HOHapplications,butrequires furthertheoreticalstudyto verify whetheritisuniversally applicable.
基金This work was supported by the National Natural Science Foundation of China(No.10575097 and 60473133)the 100 Talents Programme of the Chinese Academy of Sciences+1 种基金the National Basic Research Program of China(No.2006CB303102)Specialized Research Fund for the Doctoral Program of Higher Education(No.20060358050).
文摘The synchrotron radiation spectra of the spherical grating monochromator(SGM)working in the soft X-ray and VUV region are often contaminated by significant amounts of higher order harmonics.They cannot be suppressed completely by suitable filters.Higher order contributions in the spectral radiation standard and metrology beamline were researched using transmission grating(made in-house)and IRD AXUV100G(USA)photodiode detector.The exit beam was dispersed with the transmission grating behind the exit slit of the monochromator,and the contributions of the different orders were analyzed.The higher order distributions were quantitatively determined for three gratings with line densities of 1800,600 and 200 l/mm.Experiment results show that in wavelengths between 5 nm and 15 nm the contributions of the higher orders to the detector signal are restricted to less than 7%even without the use of filters.In wavelength regions between 5 nm and 34 nm,the contributions of the higher orders to the detector signal are less than 14%with proper Al,Si_(3)N_(4) and Zr filters,and after being modified by quantum efficiency of the detector,the higher order contributions are restricted to less than 6.5%.The study also shows that higher orders are almost totally suppressed by MgF_(2) filter when the wavelength ranges between 115–140 nm.
