Fine structure

Thefinestructureofatomicenergylevels

Usuallyinsomelighterelements,thissplitisfine,andforheavyelementsthissplitislarger.Thespinandorbitintheatominteract,anddifferentspindirectionscauseenergychanges.Inthecaseofsingleelectron,theelectronspinhastwoorientations.Generally,theenergylevelissplitintotwo,andthefinestructureoftheenergylevelisdouble;inthecaseoftwovalenceelectrons,thetotalspinS=0and1,thecorrespondingenergylevelisfineThestructureissingletandtriplet;inthesameway,inthecaseof3valenceelectrons,thefinestructureofenergylevelisdoubletandquartet,andsoon.Theenergylevelsplitdistanceofthefinestructureisproportionaltothesquareoftheatomicnumber,andproportionaltothesquareofthefinestructureconstantathatcharacterizesthefinestructure.TheenergylevelintervalofthefinestructureobeystheLandeintervalrule,andtheratiooftheadjacentenergylevelintervalisproportionaltothelargerJvalueofthetworelatedtotalangularmomentums,thatis,theJvalue.Fromthis,itcanbedeterminedwhethertheatombelongstoLScoupling.Thefinestructureoftheatomicenergylevelmakesthespectrallinesemittedbytheatomictransitionalsohaveafinestructure.Studyingthefinestructureofthespectrallinescanobtaininformationaboutthespin-orbitinteractionswithintheatoms.

Theeffectoffinestructuremixingrateonlaserperformance

ForalkalimetalvaporlasersP_1/2andP_3/2Theparticlenumberdistributionofthepumpingenergylevelcannotbeprocessedbythemethodofthermalequilibriumassumption.Itisnecessarytousethebidirectionalfinestructuremixingratetodescribeitsrelaxationprocess;whenthefinestructuremixingrateisfargreaterthanthespontaneousemissionrateandtheelectronicstatequenchingrateTheeffectonthelaserthresholdcanbeignored;effectiveabsorptionofthepumpinglightnotonlyrequiresthepumpingspectrumwidthtomatchtheatomicabsorptionspectrumwidth,butalsoasufficientfinestructuremixingratetoovercometheabsorptionsaturationeffect;inpractice,itcanbeachievedbyoptimizingthelasermodeThevolumeandtemperatureachievehigherlight-to-lightconversionefficiencyatalowerfinestructuremixingrate.

Effectonthelaserthresholdpumpingintensity

Theeffectofthefinestructuremixingrateofrubidiumvaporlaseronthethresholdintensity,wheretheabscissaisthefinestructuremixingrateΓ_{32tothespontaneousradiationrateA31,theordinateisthethresholdpumpingintensity.Thecalculationparametersareselectedasfollows:l=3cm,theaveragediameterofthelasermodeinthemediumw=0.6mm,T=110℃,ΔνD2=14GHz(filledwith7.98×10⁴Pahelium),Δνpump=30GHz,ηmode=ηdel=Tr=0.95,Rp=1,Roc=0.2,whenthebuffergaspressureissmall,generallynegligibleQ21,Q31.}

Γ₃₂haslittleeffectonthethresholdpumpingintensity.Itcanbeseenthatwhen_Γ32≥A₂₁+Q₂₁,1/(Γ₃₂^.τ₂₁)canbeignoredcomparedto2exp[(-ΔE/(kT)](1.6at110℃),thisWhenI_thhasnothingtodowithΓ₃₂,thisapproximationisusuallytrueinpractice(filling1.33×10⁴PaethaneΓ₃₂=40^.A₃₁).

Effectonlaserefficiencyandparticlenumberdistribution

BecausetheP_1/2andP_3/2stateenergygapsofalkalimetalatomsareextremelynarrow,TheprincipleoffinebalancedeterminesthattheP_3/2energylevelwillaccumulatealargenumberofparticlesandcannotbeemptied(in110℃thermalequilibriumstaten₃/n₂is161.0%ofpotassium,82.0%ofrubidium,24.9%ofcesium).Theformationofaccumulationandreversalofthenumberofparticlesisunfavorable.

DescribethedeviationofthenumberofparticlesbetweentheenergylevelsofP_1/2andP_3/2Thedegreeofthermalequilibrium.Whenγ=1,itisthethermalequilibriumdistribution.Theeffectsofthefinestructuremixingrateonthelaserefficiencyandparticlenumberdistributionarecalculatedseparately,andthepumpingpowerisP_p=100W,whereη_opt-optoptical-opticalconversionefficiency,η_absorbistheabsorptionefficiencyofthepumplightincidentontheendfaceofthemedium,η_opt-absisthelaserefficiencyrelativetotheabsorptionofthepumplight,andhasthefollowingrelationship：η_opt-opt=η_del^.η_absorb^.η_opt-abs,isthedifferenceinthenumberofparticlesbetweenpumpingenergylevels.p>

WithΓ₃₂Increases,Δ_n13alsoincreases,sothattheabsorptionefficiencyofthemediumforpumpinglightη_absorbalsoincreases,whichisrelativetotheabsorptionofpumpingThelaserefficiencyoflightη_opt-abshasnothingtodowithΓ₃₂,andalwaysmaintainsahighefficiencycloseto90%(Γ_{32issmall,thedecreaseofηopt-absiscausedwhenthespontaneousemissioncannotbeignoredcomparedwiththelaseremissionrate).ThisistheembodimentofDPAL’shighquantumefficiency.Fromthis,itcanbeconcludedthattheeffectiveabsorptionofpumplightbyDPALnotonlyrequiresthepumpingspectrumwidthtomatchtheatomicabsorptionspectrumwidth,butalsoasufficientfinestructuremixingratetoeffectivelyreduceP3/2}energylevelrelaxestotheP_1/2energyleveltoavoidabsorptionsaturation.γisalwaysgreaterthan1andkeepsapproaching1withtheincreaseofΓ₃₂,onlywhenΓ₃₂→∞isP_{3Thenumberofparticlesat/2}andP_1/2energylevelsisthethermalequilibriumdistribution,andwhenΓ₃₂issmall,itdeviatesseriouslyfromthethermalequilibriumstate.Therefore,iftheprocessingmethodofthethermalequilibriumassumptioninthequasi-three-levelsolid-statelaserisadopted,alargeerrorwillbecaused.Thisisbecausethenon-radiativerelaxationratebetweensimilarenergylevelsinthesolidmediumismuchhigherthanthespontaneousandstimulatedemissionrates.,Andthenon-radiativerelaxationrateinDPALisontheorderofpumpabsorptionandlaseremissionrate.

Absorptionsaturationeffectanditssolution

WhenΓ₃₂=300^.A₃₁Theinfluenceofpumpingpoweronlaserperformance,andotherparametersarethesameasabove.Withthecontinuousincreaseofpumpingpower,thelimitedfine-structuremixingratecannoteffectivelytransferthenumberofpumpedupper-levelparticles.WhenΔ_n13→0,aseverepumpingsaturationeffectappears,whichleadstotheoverallThelight-to-lightconversionefficiencydropssharply.Itcanbeseenthatasthepumpingpowerincreases,therequiredfine-structuremixingrate,thatis,thebuffergaspressure,willalsocontinuetoincreaseaccordingly.However,inpractice,thepressureofthebuffergasshouldnotbetoohigh.Thiswillcauseseriouselectronicstatequenchingeffects.Ontheotherhand,itwillnotbeconducivetothehigh-powercalibrationandamplificationofDPAL,suchaswhenthepumpingpowerisintheorderof10,000watts.Inordertoobtain70%efficiency,itisnecessarytochargeabout3.039×10⁷Paofethane,whichisunrealisticfortheactuallasersystem.

Calculationsshowthatbyincreasingthevolumeofthelasermodeandadjustingthetemperaturetoincreasetheparticlenumberdensity,theeffectiveabsorptionofthepumpinglightcanbeachievedundertheconditionofasmallerfinestructuremixingrate,andahigherlight-to-lightconversioncanbeobtained.Efficiency,whenΓ₃₂=300^.A₃₁Theinfluenceoftemperatureandmediumlengthonlaserefficiency.Forcomparison,thepumpingpowerisselectedasP_p=1000W,whenl=3cm,T=110At℃,η_opt-opt<10%,thecalculationresultsshowthatthelaserefficiencyhasbeensignificantlyimprovedwiththeincreaseoftemperatureandmediumlength.

Preliminarystudyonthefinestructureoftheseasurfaceheightalongtheorbitanditsapplicationtechnology

Introducedtwohigh-precisionstructuresoftheseasurfaceheightalongtheorbitinthefrequencydomainandthemulti-scaledomain,andthenAnewmethodforcalculatingtheaverageseasurfaceheightandsealevelanomalyusingthehigh-precisionstructureoftheseasurfacealongtheorbitisproposed.Finally,thespectrumandmulti-scaledecompositionoftheaverageseasurfaceheightandthesealevelanomalyalongtheorbitarefurtherdiscussed,aswellastheirtime-dependentdecomposition.Changecharacteristics.

Calculationtechnologyofaverageseasurfaceheightandsealevelanomaly

Fromthedefinitionofthehigh-precisionstructureoftheseasurfaceheightmeasurementalongtheorbit,theseasurfaceheightcanberegardedasacertainlinearElementsinspace.Ifthelinearspaceisbasedonthetrigonometricfunctionsystem,thesealevelheightalongtheorbitcanbeexpressedasalinearcombinationoftrigonometricfunctionbasestoobtaintheFouriertransformofthesealevelalongtheorbit,thatis,thefrequencydomainfinestructure.Ifthelinearspaceisbasedonamulti-scalewaveletbase,thesealevelalongtheorbitcanbeexpressedasalinearcombinationofmulti-scalewaveletbases,andthesealevelalongtheorbitcanbedecomposedatmultiplescalestoobtainamulti-scalefinestructure.

Averagesealevelcalculationtechnology

Usually,whencalculatingtheaveragesealevel,thesealevelmeasuredindifferentweeksisregardedasastatisticalsamplingoftheaveragesealevel.Similarly,thefinestructureoftheseasurfacealongtheorbitindifferentweekscanalsoberegardedasastatisticalsamplingofthehighfinestructureoftheaverageseasurfacealongtheorbitinthefrequencydomainandmulti-scaledomain.Fromthelinearspaceadditivity,thefinestructureoftheaverageseasurfaceheightalongtheorbitisequaltotheweightedaverageofthehighfinestructureoftheseasurfacealongtheorbitindifferentcircumferences.Knowingthefinestructureoftheaveragesealevelalongthetrack,theaveragesealevelalongthetrackcanbereconstructed,andthenthegridaveragesealevelcanbecalculated.Themainstepstocalculatetheaverageseaheightusingthehigh-precisionstructureoftheseasurfacealongtheorbit:

1.Calculatethefinestructureofthesealevelheightalongtheorbitindifferentcircumferences;

2,ifthefinestructureisIfitisdescribedinamulti-scaleformat,thenperformsingularityanalysistodetectandsuppressitssingularity;

3.Use(eliminateorsuppressthesingularity)theheightoftheseaalongtheorbitofdifferentcircumferencesCalculatethehigh-precisionstructureoftheaverageseasurfacealongtheorbitwithfinestructure;

4.Reconstructtheaverageseasurfaceheightalongtheorbitfromthehigh-definitionstructureoftheaverageseasurfacealongtheorbit;

5.Theaverageseasurfaceheightalongtherailisadjustedattheintersectionpoint,andtheaverageseasurfaceheightalongtherailaftertheadjustmentiscalculated;

6.Thegridaveragesealevelheightiscalculatedfromtheaverageseasurfaceheightalongtherailaftertheadjustment.

Reconstructedfromthefrequencydomainfinestructureoftheremainingaveragesealevelalongthe53rdarcoftheTOPEX/Poseidonsatellite.Itcanbeseenfromthecomparisonthattheresultsoftheaverageseasurfaceheightalongtheorbitreconstructedfromthefrequencydomainfinestructureandthemulti-scalefinestructureareslightlydifferent.Theaccuracyofthedetailedstructureisrelativelyhigh.

Sealevelanomalycalculationtechnology

Themainstepsforcalculatingsealevelanomaliesusingthefinestructureofsealevelheightmeasurementalongthetrack:

1.DifferentcalculationsElevatethefinestructureoftheseasurfacealongtheorbit;

2.Ifthefinestructureisdescribedinamulti-scaleform,performsingularityanalysistodetectandeliminateorsuppressitssingularity;

2.p>

3.Calculatethefinestructureoftheaveragesealevelalongthetrackfromthefinestructureofthesealevelheightmeasuredindifferentweeks(eliminateorsuppressthesingularity);calculatethefinestructureoftheaveragesealevelalongthetrackfromthefinestructureoftheaverageseaheightalongthetrackAndcarryouttheintersectionadjustment;recalculatethefinestructureoftheaverageseasurfaceheightalongtheorbitfromtheadjustedaverageseasurfaceheight;Calculatethefinestructureofthesealevelanomalyalongtherailbyusingthehigh-precisionstructureoftheheightmeasurementsurfacealongtheorbitandtheaveragesealevelaftertheadjustment;

5.ReconstructionofthefinestructurefromthesealevelanomalyalongtherailThesealevelanomalyalongtherail;

6.Calculatethegridsealevelanomalyfromthesealevelanomalyalongtherail.Thesealevelanomalyalongtheorbitofthe53rdarcoftheTOPEX/Poseidonsatellitefrom120to232weeksisgivenagraphevery5weeks(thetimesequenceisfromtoptobottom,fromlefttoright).Theunitofabscissais(°)andtheunitofordinateism.

Becauseofthehighaccuracyofthehigh-precisionstructureoftheaverageseasurfacealongtheorbit,thesealevelanomalyalongtheorbitalwaysswingsaroundzero,whichintuitivelyreflectsthecharacteristicsofthesealevelchangeovertime.Itcanbeseenthat,comparedwiththesealevelanomaliesreconstructedfromthefrequencydomainfinestructure,thedetailedfeaturesofthesealevelanomaliesreconstructedfromthemulti-scalefinestructurearemoreprominent.

First,calculatethefinestructureoftheseaheightalongtheorbitondifferentcircumferences,soastofullytakeintoaccountthedetailedstructureoftheseaheightalongtheorbit,andavoidprocessingallhigh-frequencyinformationasnoise.Thencalculatethefinestructureoftheaverageseasurfaceheightalongtheorbitbymeasuringthehigh-precisionstructureoftheseasurfaceheightalongtheorbitofdifferentcircumferences.Thisstepisessentiallytocalculatethefinestructureoftheaverageseasurfaceheightalongtheorbitinthefrequencydomainormulti-scaledomain.Theprocessofreconstructingtheaverageseasurfaceheightalongtheorbitfromthehigh-precisionstructureoftheaverageseasurfacealongtheorbitisessentiallytorecovertheaverageseasurfaceheightalongtheorbitfromthefrequencydomainormulti-scaledomain.Thesealevelanomalyalongtheorbitisreconstructedfromthefinestructureoftheweeklysealevelanomaly,insteadofdirectlysubtractingtheaveragesealevelfromthesealevelalongtheorbitasintheconventionalmethod,soastofullyconsiderthespatialandtemporalchangesofsealevel.Differencesincharacteristics.