简介:Beamhalo-chaosinhigh-currentacceleratorshasbecomeakeyconcernedissuebecauseitcancauseexcessiveradioactivityfromtheacceleratorsthereforesignificantlylimitstheirapplicationsinindustry,medicine,andnationaldefense.Somegeneralengineeringmethodsforchaoscontrolhavebeendevelopedinrecentyears,buttheygenerallyareunsuccessfulforbeamhalo-chaossuppressionduetomanytechnicalconstraints.Beamhalo-chaosisessentiallyaspatiotemporalchaoticmotionwithinahighpowerprotonaccelerator.Inthispaper,someefficientnonlinearcontrolmethods,includingwaveletfunctionfeedbackcontrolasaspecialnonlinearcontrolmethod,areproposedforcontrollingbeamhalo-chaosunderfivekindsoftheinitialprotonbeamdistributions(i.e.,Kapchinsky-Vladimirsky,fullGauss,3-sigmaGauss,water-bag,andparaboladistributions)respectively.Particles-in-cellsimulationsshowthataftercontrolofbeamhalo-chaos,thebeamhalostrengthfactorisreducedtozero,andotherstatisticalphysicalquantitiesofbeamhalo-chaosaredoublyreduced.Themethodswedevelopedisveryeffectiveforsuppressionofprotonbeamhalo-chaosinaperiodicfocusingchannelofaccelerator.Somepotentialapplicationofthebeamhalo-chaoscontrolinexperimentsisfinallypointedout.
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简介:给出了对称的完全二部有向图K*m,n存在P2k-因子分解的充分必要条件为m=n≡0(modk(2k-1)).