简介:Inordertoimplementlarge-scaleandhigh-betatokamaksimulation,anewalgorithmoftheelectromagneticgyrokineticPIC(particle-in-cell)codewasproposedandinstalledontheGpic-MHDcode[GyrokineticPICcodeformagnetohydrodynamic(MHD)simulation].Inthenewalgorithm,thevorticityequationandthegeneralizedOhm’slawalongthemagneticfieldarederivedfromthebasicequationsofthegyrokineticVlasov,Poisson,andAmperesystemandareusedtodescribethespatio-temporalevolutionofthefieldquantitiesoftheelectrostaticpotentialφandthelongitudinalcomponentofthevectorpotentialAz.Thebasicalgorithmisequivalenttosolvingthereduced-MHD-typeequationswithkineticcorrections,inwhichMHDphysicsrelatedtoAlfvenmodesarewelldescribed.Theestimationofperturbedelectronpressurefromparticledynamicsisdominant,whiletheeffectsofothermomentsarenegligible.Anotheradvantageofthealgorithmisthatthelongitudinalinducedelectricfield,Etz=-■z/■t,isexplicitlyestimatedbythegeneralizedOhm’slawandusedintheequationsofmotion.Furthermore,theparticlevelocitiesalongthemagneticfieldareused(vz-formulation)insteadofgeneralizedmomentums(pz-formulation),hencethereisnoproblemof’cancellation’,whichwouldotherwiseappearwhenAzisestimatedfromtheAmpere’slawinthepz-formulation.ThesuccessfulsimulationofthecollisionlessinternalkinkmodebythenewGpic-MHDwithrealisticvaluesofthelarge-scaleandhigh-betatokamaksrevealedtheusefulnessofthenewalgorithm.
简介:NonlinearMHDKelvin-Helmholtz(K-H)instabilityinapipeistreatedwiththederiva-tiveexpansionmethodinthepresentpaperThelinearstabilityproblemwasdiscussedinthepastbyChandrasekhar(1961)andXuetal.(1981).Nagano(1979)discussedthenonlinearMHDK-Hinstabilitywithinfinitedepth.Heusedthesingularperturbationmethodandextrapolatedtheob-tainedsecondordermodifierofamplitudevs.frequencytoseekthenonlineareffectontheinstabilitygrowthrateγ.However,inourview,suchanextrapolationisinappropriate.Becausewhentheinstabili-tysetsin,thegrowthratesofhigher,ordertermsontherighthandsideofequationswillexceedthecor-respondingsecularproducingterms,sotheexpansionwillstillbecomemeaninglessevenifthesecularproducingtermsareeliminated.Mathematicallyspeaking,it’simpossibletoderiveformula(39)whenγ02isnegativeinNagano’spaper.Moreover,evenasearlyasγ02→O+,theexpansionbe-comesinvalidbecausethe2ndordermodifierγ2(inhisformula(56))tendstoinfinity.Thisweak-nessisremovedinthispaper,andtheresultisextendedtothecaseofapipewithfinitedepth.
简介:Inthisarticle,wemainlystudythelocalequationofenergyforweaksolutionsof3DMHDequations.WedefineadissipationtermD(u,B)thatstemsfromaneventuallackofsmoothnessinthesolution,andthenobtainalocalequationofenergyforweaksolutionsof3DMHDequations.Finally,weconsiderthe2Dcaseattheendofthisarticle.
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简介:WeprovetheexistenceofaweaksolutionforageneralizedquantumMHDequationina2-dimensionalperiodicboxforlargeinitialdata.Theexistenceofaglobalweaksolutionisestablishedthroughathree-levelapproximation,energyestimates,andweakconvergencefortheadiabaticexponentγ>1.
简介:Magnetohydrodynamic(MHD)acceleratorisproposedasanextgenerationpropulsionsystem.Itcanbeusedtoincreasetheperformanceofapropulsionsystem.TheobjectiveofthisstudyistoinvestigatetheperformanceofMHDacceleratorusingnon-equilibriumairplasmaasworkinggas.Inthisstudy,thefundamentalperformanceofMHDacceleratorsuchasflowperformanceandelectricalperformanceisevaluatedatdifferentlevelsofappliedmagneticfieldusing1-Dnumericalsimulation.ThenumericalsimulationisdevelopedbasedonasetofdifferentialequationswithMHDapproximation.TosolvethissetofdifferentialequationstheMacCormackschemeisused.AspecifiedchanneldesignedanddevelopedatNASAMarshallSpaceFlightCentreisusedinthenumericalsimulation.Thecompositionofthesimulatedairplasmaconsistsofsevenspecies,namely,N2,N,O2,O,NO,NO+,ande-.Theperformanceofthenon-equilibriumMHDacceleratorisalsocomparedwiththeequilibriumMHDaccelerator.
简介:Non-lineardevelopmentofdoubletearingmodesinducedbyelectronviscosityisnumericallysimulated.MHDflowlayersaredemonstratedtomergeinthedevelopmentofthemodes.Theshearedflowsareshowntoliejustattheboundariesofthemagneticislands,andtohavesuffcientlevelsrequiredforinternaltransportbarrier(ITB)formation.PossiblecorrelationbetweenthelayerformationandtriggeringofexperimentallyobservedITBs,preferentiallyformedinproximitiesofrationalfluxsurfacesoflowsafetyfactors,isdiscussed.
简介:有电磁的领域的不同安排的一个MHD生成器将带在三个模式工作的生成器。quasi-one-dimensional近似被用于MHD发电机的模型分析操作模式的内部机制。为有一个一致经常的磁场的MHD发电机,特定的批评电场E<潜水艇class=“a-plus-plus”>cr被要求速度超声的入口流动进亚声的出口流动。否则,发电机比E与一个更大的电场在一个稳定的模式工作稳定的超声的流动在出口在被提供的cr,或发电机比E与一个更小的电场在一个窒息的模式工作超声的入口流动在隧道在被窒息的cr。在不同操作模式的详细流动地特征被讨论,表明有电磁的地的操作模式的关系。
简介:Anewmethodforconstructingthesymmetricformforthehyperbolicsystemsisintroduced.ThenanewsymmetricformoftheequationsofMHDtransverseflowisconstructedbyaddinganadditionalequation.Withthisnewform,weobtainthelocalexistenceofsmoothsolutionincludingthecasethattheinitialdensitymaytendtothevacuumstateatinfinity.Furthermore,theuniformlyaprioriestimationfortheclassicalsolutionsisestablishedandtheglobalsmoothsolutionsforakindofinitialdataareobtained.