摘要
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.
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.
