Lecture 17 – May 24,Ring Current Dynamics讲座1–5月24日环电流的动力学

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1、ESS 261 Spring 2010Advanced TopicsR.L. McPherronLecture 17 May 24, 2010Ring Current DynamicsOrigin of Concept of “Magnetic Storm”(D. Stern - http:/www-spof.gsfc.nasa.gov/Education/wmagstrm.html) The term magnetic storm, meaning a world-wide magnetic disturbance, was coined by Alexander von Humboldt

2、(1769-1859). A naturalist who gained attention by exploring the jungles of Venezuela, Humboldt devoted much of his life to the promotion of science. He produced five volumes of Kosmos (starting the modern usage of that term), an encyclopedic account covering the broad spectrum of the sciences. It wa

3、s Kosmos which brought to the worlds attention the discovery of the sunspot cycle by Heinrich Schwabe. After journeying through Siberia, Humboldt convinced the Czar to set up a network of magnetic observatories across the Russian lands, and additional stations were established throughout the British

4、 Empire, from Toronto to Tasmania. This network clearly showed that magnetic storms were essentially identical all over the world: a steep decrease of the field over 6-24 hours, followed by a gradual recovery which lasted 1-4 days. The change in the magnetic field was small, in modern units some 50-

5、300 nT (nanotesla) out of a total intensity of 30-60,000 nT, but its world-wide scale suggested that something quite big was happening out in space.Interplanetary Magnetic Field, AE and Dst Indices During StormCoronal mass ejection produce intervals of strong southward Bz at the earthMagnetic reconn

6、ection drives magnetospheric convectionConvection drives currents along field lines and through ionosphereGround magnetometers record effects of ionospheric currents in H and other componentsH traces are used to construct the AE and Dst index-1000100Coupling for Storm with Min at 02:54 UT Oct 11, 19

7、97 Propagated Wind for DoY = 284Sym-HAsy-H-1000-5000500AU/AL (nT)0246PC Index -4-20Ey gsm(mV/m)0510Pdyn (nP) 00.020.040.060.08Ptot (nP) 1997/10/10 17.0 0.0 0.0 1997/10/11 17.0 0.0 0.0 1997/10/12 17.0 0.0 0.0 1997/10/13 17.0 0.0 0.0 1997/10/14 17.0 0.0 0.0 CONTRIBUTIONS TO THE VARIATION IN THE H COMP

8、ONENT00 ( ) ( )( )( )( )( )( )( ) ( ) Secular variation of main field ( ) Solar dynamo in ionosphere SQMPSRCPRCrTSCWSQH tHtHtHtHtHtHtHtHtHtOBSERVED MAGNETIC FIELD ( ) Magnetopause (Chapman-Ferraro) ( ) Symmetric Ring Current ( ) Partial Ring Current ( ) Tail Current ( ) Substorm Current Wedge MPSRCP

9、RCTSCWHtHtHtHtHt0 ( ) ( )( )( ) SQH tH tHtHtDISTURBANCE DAILY VARIATIONLongitudinal Profile of Bj from Magnetospheric CurrentsSymmetric ring should create nearly constant longitudinal profile in H componentLocal time average of H at equator approximates B at center of EarthBut other magnetospheric c

10、urrents create local time dependent deviations from symmetryAssume asymmetric component has zero mean when averaged over local timeDefine the disturbance storm time index Dst as local time average of observed H profile jNjjjstBHND1cos1Local Time0012180612DstB ooooEFFECTS OF MAGNETOPAUSE ON THE Dst I

11、NDEXBalance magnetic pressure against dynamic pressure0510150-10-8-6-4-2246810X (Re)Z (Re)SolarWindNeutralPointk vaBBkavB nTPnPdyn 2202022235()()-6-4-20246-35-30-25-20-15-10-50-Xgsm (Re)Bz (nT)Normal TailInner EdgeTotalEarthA Sheet Current Model of Effect of Tail Current on DstTail Current ModelMagn

12、etic EffectsBzxxxxxxx xxx xxioszRRBBlnRiRo30 nTR12 ReR42 ReNNINOB 1000 nTR7 ReR12 ReSSISOB Magnetic Effects of a Substorm Current WedgeTransverse currents in the magnetosphere are diverted along field lines to the ionosphereViewed from above north pole the projection of the current system has a wedg

13、e shapeMidlatitude stations are primarily affected by field-aligned currents and the equatorial closure (an equivalent eastward current)The local time profile of H component is symmetric with respect to the central meridian of wedgeThe D component is asymmetric with respect to center of wedgeSolar W

14、ind Pressure CorrectionDst is contaminated by the magnetopause currents and incomplete removal of secular variationDynamic pressure brings these currents closer to the Earth and makes them strongerThe correction is usually presented as:Other currents contribute to the Dst index:Partial ring currentI

15、onospheric currentsTail currentField-aligned currentInduced Earth currentsIt is not known how well Dst represents the current produced by particles on closed drift paths around the EarthDstDstb Pcsw*Dessler-Parker-Sckopke DerivationDrift Velocity of an Equatorial Ion in Dipole FieldThe Equatorial Ri

16、ng Current of the IonThe Magnetic Effect of the Equatorial Ring where is the ion energy and is its charge and is the distance from the earths dipole vE rqMEqrMIqvrBIrEMdd 322342100The Magnetic Effect of Ions GyrationThe Total Magnetic Effect at Earths CenterExpress as Fraction of Surface Field where

17、 is the total field energy outside earthBrEMBBBEMBBEUUs203012044223 units MKSin )(105 . 2 )(32)( Note functioninjection current ring thecalled is )( e wher)()()(decay timecurrent ring theis and current ring theinput toenergy of rate theis )( e wher)()()(earth outside field dipolein energy total thei

18、s particlescurrent ring theofenergy total theis )( field surface equatorial average theis current ring theofeffect theis )( re whe3/ )(2/ )(140*0*0*tUJnTtUEBtQtQtDtQdttDtUtEtUdttdEEtEBtDEtEBtDmststmstmstThe Dessler-Parker-Sckopke Relation and the Burton EquationBurton, R. K., R. L. McPherron, and C.

19、 T. Russell (1975), An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80(31), 4204-4214.The Burton EquationBurton, R., R. McPherron, and C. Russell (1975), An Empirical Relationship Between Interplanetary Conditions and Dst, Journal of Geophysical Research, 80(31

20、), 4204-4214. If we assume the energy in the ring current is governed by injection and decay, the dynamic equation is: Which becomes the Burton equation: Q is the injection term, is the decay timedE tdtU tE t( )( )( )dDstdtQ tDstt*( )( )A Nonlinear Equation for the Rate of Change of DstThe Burton et

21、 al. equation for ring current dynamics is derived from the DPS relationAssume that the ring current is driven by a solar wind coupling function depending on IMF BzCorrect the measured Dst for effects of magnetopause and incorrect base linesObtain a first-order differential equation for Dst with two

22、 solar wind drivers that is nonlinear in the unknown parametersThe equation is non-linear in the model parametersctCpbDpdtdbdtdDcpbDDDtCtCtQDtQdtdDdynstdynstdynststststst)(11rearrange and substitute with observedconvert input solar wind is )( where )()(let )(The model parameters include:b dynamic pr

23、essure constant exponential decay time constant of proportion to Esc Dst base line adjustmentParameterProbableValueProbableValueProbableValueUnitsBurtonOptimumfor BsOptimumfor Bnb1 (1/)7.710.7316.95hoursb2 (b)15.96.988.87nT/nPab3 (c)207.195.8nTb4 ()5.43.23NA(nT/h)/(mV/m)PEF15.737.829.1%Parameters in

24、 the Burton EquationAssume the parameters in the Burton equation are constantsUse the Burton et al. values and calculate the prediction efficiencyUse non-linear inversion to obtain self consistent values for southward IMFRepeat for northward IMFThe Burton parameters are far from optimum values!The s

25、elf consistent decay time is different for IMF north or south, and are longer than BurtonThe self consistent pressure constant is only half as large as BurtonThe self consistent injection constant is lower than Burton because the decay time is longer VBsPPdtdDstdtdDstdyndyn4321211bbbbbbThe OBrien-Mc

26、Pherron Equation The b parameter represents the influence of magnetopause currents on Dst The parameter modulates the reconnection driven convection electric field The V0 parameter scales the total convection electric field)()(*VBsDstVBsQdtdDstPPbDstDst*cccEVBsEVBsEVBsQ0VBsVVqe0 cEQPbDdtPdbdtdDydyns

27、tdynst11The OBrien & McPherron EquationAssume that all parameters depend on VBzBin the data into narrow bins of VBzThe injection term is a constant for each bin so combine with baseline termUse data to determine optimum b, , Q(Ey)-c/ in each binPlot the dependence of parameters on VBzThe Hourly Dst

28、Index Predictor (1)1()stststb tc tDtDbpptA VB 2 10exp /36.902.87exp 4.475 4.590.53 0.53() 0 0.53sssssVBbnTmV mhrsVBcnTnTVBVBhrA VBmVVBsVBsm Ring Current Response to Dynamic Pressure Use model for hourly changes in Dst index at constant VBs for equinox and solstice Fit an exponential function to the

29、pressure parameter as function of in interval -10VBs 3 mV/m The model is poorly determined and could be taken as an exponential decrease with a decay parameter Eo = 9.27 mV/m and bo = 7.84 nT*(nP)1/2 The pressure parameter decreases in strength with stronger VBsmV/m -10VBz3 formV/m nPnT/ .28 , 11.6

30、, 7.7,7.5,ebVBs.39 97.87.8bbRing Current Decay TimeUse model for hourly changes in Dst index at constant VBs for equinox and solsticeFit a complex exponential function to the decay parameter as function of VBzin interval -10VBs 0)/( , )/( ,)/(nT/hr) 223123mmVmmVmmVeVBzVBzQVBz0.752.556.58bbbbbbbInjec

31、tion Function and Coupling Constant The injection rate is determined from a model parameter Fit the rate with a function having zero value and slope at VBz=0 Determine slope of data and of fit to dataImproved Estimates of Dst Model ParametersMake Taylor series about bin center for parameter QFind av

32、erage value of this over bin of width and assign to center of massUse the probability distribution N of samples in the bin to determine center of mass of x in the binRepeat for five bins of different width and obtain an over determined set of equations for Q(x0) and Q(x0) as function of distance fro

33、m algebraic centerFit a line to these five paired valuesThe intercept of this line is the value of the parameter Q(x0) VBz0AlgebraiccenterCenterofmass 00000000000000001But centerrbin is and Let xxdxxNxQxQxQxdxNxdxNxxxQxdxNxQxQxdxNxxxQxdxNxQxQxxxQxQxQxVBxbinbinbinbinbinbinzComparison of Models for al

34、l Subsets cEQPbDdtPdbdtdDydynstdynst11Conclusions from Empirical ModelThe Dst pressure constant is not the value used by most numerical modelsThe Dst pressure constant decreases to zero as VBz becomes more negativeThe decay time is shorter for large negative VBzThe injection rate is not a linear fun

35、ction of VBz using better estimates of Q at more negative valuesThe coupling parameter increases continuously towards negative VBzb 8 nT/(pdyn)1/2b goes to 0 near -10 mV/m3 tau 16 hrThe injection rate Q goes to zero nonlinearly as VBz 0There is no detectable seasonal difference in couplingThere is n

36、o detectable difference in coupling as function of Alfven Mach number or plasma betaSmall & Big Storms050100150-120-100-80-60-40-20020Dst Comparison for storm 1980-285Dst (nT)0501001500123456Ec = 0.49 mV/m VBs mV/mEpoch HoursDst Model (1hr step) Model (multi-step)VBs 020406080100120140160180-250-200

37、-150-100-50050Dst Comparison for storm 1982-061Dst (nT)020406080100120140160180051015VBs mV/mEpoch HoursDst Model (1hr step) Model (multi-step)VBs Ec = 0.49 mV/m Dst Parameters for High and Low Alfven Mach #Low Mach # solar wind has a weak B field so VBz does not reach large negative valuesThere are

38、 many high Mach # values at strong negative VBzThe parameters are not well determined for low Mach #In the overlapping range there is no significant difference!Dst Parameters for High and Low BetaHigh beta solar wind has a weak B field so VBz does not reach large negative valuesThere are many low be

39、ta values at strong negative VBzThe parameters are not well determined for high betaIn the overlapping range there is no significant difference!Simulated Dst IndexEbihara, Y., and M. Ejiri (2000), Simulation study on fundamental properties of the storm-time ring current, J. Geophys. Res., 105(A7), 1

40、5843-15859. A storm in 1997 was simulated using polar cap potential and plasma sheet density as drivers The thick line in bottom panel using actual density slightly overestimates Dst A simulation with a constant smaller density seriously underestimates Dst Both convection field and plasma sheet dens

41、ity are important driversThe Ring Current Coupling ConstantThe coupling constant is defined as the slope of the injection functionCalculate this numerically from injection function by a running linear fit to seven points (blue)Compare this to the derivative of a fit to the injection function with co

42、nstraints listed aboveCoupling decreases to zero at VBz = +0.75 mV/mFor large negative VBz it approaches 6.6 (nT/hr)/(mV/m)2311bbbVBzeVBzddQDependence of Coupling on Dipole Tilt Separate data into two seasons: equinox and solstice Create the injection function for each season Fit function to injecti

43、on rate and calculate coupling constant from its derivative There is a substantial reduction in coupling when the dipole is far from orthogonal to the Sun vector50607080901001101201302.533.544.555.5Tilt Angle (deg)VBs Coupling Constant (nT/hr)/(mV/m)coup = -4.893*Sin2(VBs COUPLING VERSUS DIPOLE TILT

44、 ANGLE= 4.274 Neural Network Determination of Burton Parameters Create a neural network that is trained to represent the Dst index at time t as a function of Dst(t-1), VBs(t), pdyn(t), pdyn(t-1), sin & cos of WDDOY and WHUT Use the NN to estimate the various parameters in Burton equation as function

45、s of the tilt angle Fit the Svalgaard function S() to each of the parameters in the OBrien-McPherron equation Parameters characterizing ring current dynamics depend on the dipole tilt angleDst Prediction - Driver TermsDst Prediction - ConstantsEmpirical Prediction of Dst IndexDay in Year 2000Dst Ind

46、ex (nT)(Temerin, M., and L. Xinlin (2002), A new model for the prediction of Dst on the basis of the solar wind, J. Geophys. Res., 107(A12), 1472, doi:1410.1029/2001JA007532) msoffset ter termb IMFdirect termpressure321zdstdstdstDst 21352. 22221sin termpressurepvpnbp decay termmdriver ter)()(tdstxdttdstx 11zsin478. 0 termb IMFdirect zb2543212sinsmsoffset tertstssyrtsThe End!