Transcript Document
Aerospace Environment ASEN-5335 • • • Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: [email protected] (preferred) phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix Instructor’s office hours: 9:00-11:00 am Wed at ECOT 534; before and after class Tue and Thu. TA’s office hours: 3:15-5:15 pm Wed at ECAE 166 • • Read Chapter 4 and class notes HW3 due 2/27 • ASEN 5335 Aerospace Environment -- Geomagnetism 1 Solar wind speed and IMF 1995-1999 Descending phase Solar Minimum Ascending phase ASEN 5335 Aerospace Environment -- Geomagnetism 2 Geomagnetism Paleomagnetism Dipole Magnetic Field External Current Systems Geomagnetic Coordinates Sq and L B-L Coordinate system Disturbance Variations L-Shells Kp, Ap, Dst ASEN 5335 Aerospace Environment -- Geomagnetism 3 GEOMAGNETISM It is generally believed that the Earth’s magnetic field is generated by movements of a conducting “liquid” core. The self-sustaining “dynamo” converts the mechanical motions of the core materials into electric currents. We are almost certain that these motions are induced and controlled by convection and rotation (Coriolis force). ASEN 5335 Aerospace Environment -- Geomagnetism 4 GEOMAGNETISM According to Ampere’s Law, magnetic fields are produced by electric currents: Earth's magnetic field is generated by movements of a conducting "liquid" core, much in the same fashion as a solenoid. The term "dynamo" or “Geodynamo” is used to refer to this process, whereby mechanical motions of the core materials are converted into electrical currents. ASEN 5335 Aerospace Environment -- Geomagnetism 5 The core motions are induced and controlled by convection and rotation (Coriolis force). However, the relative importance of the various possible driving forces for the convection remains unknown: • heating by decay of radioactive elements • latent heat release as the core solidifies • loss of gravitational energy as metals solidify and migrate inward and lighter materials migrate to outer reaches of liquid core. Venus does not have a significant magnetic field although its core iron content is thought to be similar to that of the Earth. Venus's rotation period of 243 Earth days is just too slow to produce the dynamo effect. Mars may once have had a dynamo field, but now its most prominent magnetic characteristic centers around the magnetic anomalies in Its Southern Hemisphere (see following slides). ASEN 5335 Aerospace Environment -- Geomagnetism 6 ASEN 5335 Aerospace Environment -- Geomagnetism 7 Measurements from 400 km altitude ASEN 5335 Aerospace Environment -- Geomagnetism 8 ASEN 5335 Aerospace Environment -- Geomagnetism 9 • The main dipole field of the earth is thought to arise from a single main two-dimensional circulation. • • Non-dipole regional anomalies (deviations from the main field) are thought to arise from various eddy motions in the outer layer of the liquid core (below the mantle). Anomalies of lesser geographical extent (surface anomalies) are field irregularities caused by deposits of ferromagnetic materials in the crust. [The largest is the Kursk anomaly, 400 km south of Moscow]. ASEN 5335 Aerospace Environment -- Geomagnetism 10 The magnetic field at the surface of the earth is determined mostly by internal currents with some smaller contribution due to external currents flowing in the ionosphere and magnetosphere In the current-free zone B 1 J 0 o Therefore B V Combined with another Maxwell equation: B 0 Yields 2 V 0 Laplace’s Equation ASEN 5335 Aerospace Environment -- Geomagnetism 11 The magnetic scalar potential V can be written as a spherical harmonic expansion in terms of the Schmidt function, a particular normalized form of Legendre Polynomial: n m V a Pn cos n1m0 = 0 for m > n n = 1 --> dipole n = 2 --> quadrapole an1 m m gn cosm hn sin m r n a r A cosm B sin m m n m n external sources = colatitude = east longitude (geographic polar coordinates) r = radial distance a = radius of earth ASEN 5335 Aerospace Environment internal sources -- Geomagnetism 12 Note on ELECTRIC and MAGNETIC DIPOLES An electrostatic dipole consists of closely-spaced positive and negative point charges, and the resulting electrostatic field is related to the electrostatic potential as follows: E 0 E By analogy, if we consider the magnetic field due to a current loop, the mathematical form for the magnetic field looks just like that for the electric field, hence the "magnetic dipole" analogy: B 0 ASEN 5335 Aerospace Environment -- Geomagnetism B V 13 Standard Components and Conventions Relating to the Terrestrial Magnetic Field “magnetic elements” (H, D, Z) (F, I, D) (X, Y, Z) ASEN 5335 Aerospace Environment -- Geomagnetism 14 Surface Magnetic Field Magnitude (g) IGRF 1980.0 .61 G Max .33 G Min .24 G .67 G ASEN 5335 Aerospace Environment -- Geomagnetism 15 Surface Magnetic Field H-Component (g) IGRF 1980.0 .025 G .40 G .33 G .13 G .025 G ASEN 5335 Aerospace Environment -- Geomagnetism 16 Surface Magnetic Field Vertical Component IGRF 1980.0 .61 G 0.0 G 0.0 G 0.0 G .68 G ASEN 5335 Aerospace Environment -- Geomagnetism 17 Surface Magnetic Field Declination IGRF 1980.0 10° 20° 0° ASEN 5335 Aerospace Environment -- Geomagnetism 0° 18 We will now examine a few simple approximations to the earth's magnetic field and the magnetic coordinate systems that result. SIMPLE DIPOLE Approximation Referring back to the expression on p. 12, neglecting external sources, we have Note that the r-dependence of higher n m V a Pn cos n1m0 a r n1 and higher order dipoles goes as r-n g cosm h sin m m n m n For a single magnetic dipole at the earth's center, oriented along the geographic axis, n=1 m=0 and 0 P cos cos 1 ASEN 5335 Aerospace Environment -- Geomagnetism 0 a V ag1 r 2 cos 19 0 a V ag1 r 2 1g = 10-5 G = 10-9 T (Tesla or Wbm-2) cos = colatitude (southward positive) The field components are: X = 1 V r Y = 0 Z = V r 0 a g1 r = 3 = ASEN 5335 Aerospace Environment -- (northward) northward component of magnetic field at equator at r = a, X 0.31 G (eastward) 0 a 2g1 r sin 3 Geomagnetism cos (radially downward) 20 Total field magnitude: 2 2 X Y Z = 0 a g1 r 2 3 2 1/2 1 3cos A "dip angle", I , is also defined: tanI I = Z 2 cot X 2 Y 2 is positive for downward pointing field 1 I tan 2 cot ASEN 5335 Aerospace Environment -- Geomagnetism (simple dipole field) 21 TILTED DIPOLE Approximation As the next best approximation, let n = 1 , m = 1 We find that 1 P cos sin 1 a V a r 2 and 0 1 1 g1 cos g1 cos h1 sin sin where = longitude (positive eastward). ASEN 5335 Aerospace Environment -- Geomagnetism 22 Physically, the two additional terms could be generated by two additional orthogonal dipoles placed at the center of the earth but with their axes in the plane of the equator. Their effect is to incline the total dipole term to the geographic pole by an amount 1/2 2 1 h1 2 1 2 1 g1 tan g10 In other words, the potential function could be produced by a single dipole inclined at an angle to the geographic pole and with an equatorial field strength 1/2 0 2 1 2 1 2 g1 g1 h1 This "tilted dipole" is tipped 11.5° towards 70°W longitude and has an equatorial field strength of .312G. ASEN 5335 Aerospace Environment -- Geomagnetism 23 It is often more convenient to order data, formulate models, etc., in a magnetic coordinate system. We will now re-write the tilted dipole in that coordinate system rather than the geographic coordinate system. sin sin sino cos coso cos o cos sin o sin cos = geographic latitude = geographic longitude o,o = (79N, 70W ) Rotation axis Dipole latitude DIPOLE COORDINATE SYSTEM Dipole Equator (79S, 70E) 79°N, 290°E ASEN 5335 Aerospace Environment Dipole Axis -- Geomagnetism 24 The above formulation representing dipole coordinates (sometimes called geomagnetic coordinates) is now more or less the same as that on p. 20 & 21. We will now write several relations in terms of dipole latitude , (instead of geographic colatitude, ) and dipole longitude . Dipole longitude is reckoned from the American half of the great circle which passes through (both) the geomagnetic and geographic poles; that is, the zero-degree magnetic meridian closely coincides with the 291°E geographic longitude meridian. Therefore, o 3 M g a 1 M sin V r2 in our previous notation = "dipole moment" = 8.05 ± .02 1025 G-cm3 ASEN 5335 Aerospace Environment -- Geomagnetism 25 From the above expression we can derive the following: 1 V M cos H r r3 V 2M sin Z 3 r r Z tanI 2tan H 1/2 M 2 2 2 B H Z 3 13sin r These look very much like the simple dipole approximation in geographic coordinates. ASEN 5335 Aerospace Environment -- Geomagnetism 26 Aerospace Environment ASEN-5335 • • • Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: [email protected] (preferred) phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix Instructor’s office hours: 9:00-11:00 am Wed at ECOT 534; before and after class Tue and Thu. TA’s office hours: 3:15-5:15 pm Wed at ECAE 166 • • • Read Chapter 4 and class notes HW3 due 2/27 Quiz-4 on March 4, Tue, close book. • ASEN 5335 Aerospace Environment -- Geomagnetism 27 A field line is defined by d r r d Z H d H 1 r dr Z 2 tan , so rdH B d and we may integrate to get dr, Z 2 r r cos o This is the equation for a field line. If = 0 (dipole equator), r = ro ; ro is thus the radial distance to the equatorial field line over the equator, and its greatest distance from earth. ASEN 5335 Aerospace Environment -- Geomagnetism ro 28 The point (magnetic or dipole latitude) where the line of force meets the surface is given by a 2 cos ro 1/2 a cos ro Note also that the declination, D, which is the angle between H and geographic north, is tanD = Y/X X = H cosD Y = H sinD ASEN 5335 Aerospace Environment -- Geomagnetism 29 The B-L Coordinate System "L-shells" Let us take our previous equation for a dipolar field line 2 r r cos o and re-cast it so the radius of the earth (a) is the unit of distance. Then R = r/a and 2 R R cos o where R and Ro are now measured in earth radii. The latitude where the field line intersects the earth's surface (R = 1) is given by 1/2 cos R o ASEN 5335 Aerospace Environment -- Geomagnetism 30 Now we will discuss an analagous L-parameter (or L-shell) nomenclature for non-dipole field lines, often used for radiation belt and magnetospheric studies. We will understand its origin better when we study radiation belts; basically, the L-shell is the surface traced out by the guiding center of a trapped particle as it drifts in longitude about the earth while oscillating between mirror points. For a dipole field the L-value is the distance, in earth radii, of a particular field line from the center of the earth (L = Ro on the previous page), and the L-shell is the "shell" traced out by rotating the corresponding field line around the earth. Curves of constant B and constant L are shown in the figure on the next page. Note that on this scale, the L-values correspond very nearly to dipole field lines. ASEN 5335 Aerospace Environment -- Geomagnetism 31 The B-L Coordinate System: Curves of Constant B and L The curves shown here are the intersection of a magnetic meridian plane with surfaces of constant B and constant L (The difference between the actual field and a dipole field cannot be seen in a figure of this scale. ASEN 5335 Aerospace Environment -- Geomagnetism 32 By analogy with our previous formula for calculating the dipole latitude of intersection of a field line with the earth's surface, we can determine an invariant latitude in terms of Lvalue: 1/2 cos L where = invariant latitude Here L is the actual L-value (i.e., not that associated with a dipole field). Where does this L map to at high altitude, such as at the equatorial plane depend on the geomagnetic activity. As an approximation, this L usefully serves to identify field lines even though they may not be strictly dipolar. ASEN 5335 Aerospace Environment -- Geomagnetism 33 Paleomagnetism Natural remnant magnetism (NRM) of some rocks (and archeological samples) is a measure of the geomagnetic field at the time of their production. Most reliable -- thermo-remnant magnetization -- locked into sample by cooling after formation at high temperature (i.e., kilns, hearths, lava). Over the past 500 million years, the field has undergone reversals, the last one occurring about 1 million years ago. See following figures for some measurements of long-term change in the earth's magnetic field. ASEN 5335 Aerospace Environment -- Geomagnetism 34 Equatorial field intensity in recent millenia, as deduced from measurements on archeological samples and recent observatory data. ~10 nT/year ASEN 5335 Aerospace Environment -- Geomagnetism 35 Change in equatorial field strength over the past 150 years ASEN 5335 Aerospace Environment -- Geomagnetism 36 External Current Systems Sept-aurora ASEN 5335 Aerospace Environment -- Geomagnetism 37 External Current Systems and Ionosphere ASEN 5335 Aerospace Environment -- Geomagnetism 38 External Current Systems Currents flowing in the ionosphere and magnetosphere also induce magnetic field variations on the ground. These field variations generally fall into the categories of "quiet" and "disturbed". We will discuss the quiet field variations first. The solar quiet daily variation (Sq) results principally from currents flowing in the electrically-conducting E-layer of the ionosphere. Sq consists of 2 parts: Sqo due to the dynamo action of tidal winds; and Sqp due to current exhange between the high-latitude ionosphere and the magnetosphere along field lines (see following figure). ASEN 5335 Aerospace Environment -- Geomagnetism 39 p Sq o Sq dawn dusk ASEN 5335 Aerospace Environment -- Geomagnetism 40 Solar Quiet Current systems Sqo Sq Sqo Sqp 10,000 A between current density contours ASEN 5335 Aerospace Environment -- Geomagnetism 41 Geographic Distribution of Magnetic Observatories ASEN 5335 Aerospace Environment -- Geomagnetism 42 A Magnetogram ASEN 5335 Aerospace Environment -- Geomagnetism 43 Local time Sq ground magnetic perturbations g northward ASEN 5335 Aerospace Environment -- Geomagnetism eastward vertical 44 Note: • According to Ampere's law, a current will induce a magnetic field, and conversely a time-changing magnetic field will induce a current to flow in a conductor. • Currents flowing in the ionosphere induce a magnetic field variation in the ground .... this is the "external" source we referred to before. • But, some of this changing magnetic flux links the conducting earth, causing currents to flow there. • These, in turn, induce a changing magnetic field on the ground which is also measured by ground magnetometers. These induced earth currents contribute about 25-30% of the total measured Sq field. • The above mutual feedback is very much like "mutual inductance" ASEN 5335 Aerospace Environment -- Geomagnetism 45 An interesting phenomenon, the equatorial electrojet, which is stronger than the sum of the two Sq, occurs at the magnetic equator: E look ing dow n eastward electric field induced by dynamo action N E B “Hall conductivity” m agne tic e quator “Pedersen conductivity” ASEN 5335 Aerospace Environment J E Ez 1 2 Jz 2 E 1Ez -- Geomagnetism 46 Pedersen and Hall conductivity Pederson conductivity creates electric currents that are perpendicular to the magnetic field and parallel to the electric field, Hall currents are perpendicular both to the electric and magnetic fields ASEN 5335 Aerospace Environment -- Geomagnetism 47 J E Ez 1 2 is an intense eastward current (the equatorial electrojet) driven by the vertical polarization field. (2) E z compensating vertical Jz 2 E 1Ez (1) Charge separation due to (downward Hall current, upward e-) 2 E 2Ez (3) field to maintain J z = 0. (no vertical currents due to insulating boundaries) look ing e as tw ard - - - - - B (The above scenario only occurs within a re gion of few degrees of the conductivity equator, otherwise the polarization charges 100 k m can leak away.) 150 k m + + + + + + 2 22 E J 1 E 3 E Note: E Z 1 1 ASEN 5335 Aerospace Environment -- Geomagnetism = Cowling conductivity 48 L-variation Another quiet current system, the lunar daily variation, L, similarly exists because of lunar tidal winds in the ionospheric E-region. These are gravitational tides, as opposed to solar-driven (thermally-driven) atmospheric tidal oscillations. The L variation is about 10-15% of the Sq variation. M fg fc fg r-2 ASEN 5335 Aerospace Environment -- Geomagnetism 49 Ionospheric currents inferred from the observed L variation. Current between adjacent contours is 1,000A, and each dot indicates a vortex center with the total current in thousands of Amperes. ASEN 5335 Aerospace Environment -- Geomagnetism 50 DISTURBANCE VARIATIONS In addition to Sq and L variations, the geomagnetic field often undergoes irregular or disturbance variations connected with solar disturbances. Severe magnetic disturbances are called magnetic storms. Storms often begin with a sudden storm commencement (SSC), after which a repeatable pattern of behavior ensues. However, many storms start gradually (no SSC), and sometimes an impulsive change (sudden impulse or SI) occurs, and no storm ensues. disturbed value of a magnetic element (X, Y, H, etc.): disturbed field X storm-time variation, the average of X around a circle of constant latitude ASEN 5335 Aerospace Environment = Xobs - Xq = Dst(t) + DS(t) -- Geomagnetism t=t’ longitude Disturbance local time inequality (“snapshot” of the X variation with longitude at a particular latitude) t = storm time, time lapsed from SSC 51 Typical Magnetic Storm SSC followed by an "initial" or "positive" phase lasting a few hours. During this phase the geomagnetic field is compressed on the dayside by the solar wind, causing a magnetopause current to flow that is reflected in Dst(H) > 0. During the main phase Dst(H) < 0 and the field remains depressed for a day or two. The Dst(H) < 0 is due to a "westward ring current" around the earth, reaching its maximum value about 24 hours after SSC. During recovery phase after ~24 hours, Dst slowly returns to ~0 (time scale ~ 24 hours). ASEN 5335 Aerospace Environment -- Geomagnetism 52 (Temerin and Li , JGR, 2002) Prediction efficiency=91% Linear correlation coeff.=0.95 ASEN 5335 Aerospace Environment -- Geomagnetism 53 Real Time Forecast of The Dst Index http://lasp.colorado.edu/~lix ASEN 5335 Aerospace Environment -- Geomagnetism 54 Various indices of activity have been defined to describe the degree of magnetic variability. For any station, the range (highest and lowest deviation from regular daily variation) of X, Y, Z, H, etc. is measured (after Sq and L are removed); the greatest of these is called the "amplitude" for a given station during a 3-hour period. The average of these values for 12 selected observatories is the ap index. The Kp index is the quasi-logarithmic equivalent of the ap index. The conversion is as follows: The daily Ap index, for a given day, is defined as ASEN 5335 Aerospace Environment -- Geomagnetism 8 Ap ap n1 55 Ap and Solar Cycle Variation Long-term records of annual sunspot numbers (yellow) show clearly the ~11 year solar activity cycle The planetary magnetic activity index Ap (red) shows the occurrence of days with Ap ≥ 40 ASEN 5335 Aerospace Environment -- Geomagnetism 56 Auroral Electrojet Index (AE) AE is the "envelope" of deviations (of H from its quiet value) from a selection of high-latitude stations -- it is the difference between the curves AU and AL ("upper" and "lower") drawn through the max and min excursions of the deviations. ASEN 5335 Aerospace Environment -- Geomagnetism 57 Density Variation from Orbital Drag of a High-Latitude Low-Perigee (~150 km) Satellite vs. AE and Kp ASEN 5335 Aerospace Environment -- Geomagnetism 58 ASEN 5335 Aerospace Environment -- Geomagnetism 59 ASEN 5335 Aerospace Environment -- Geomagnetism 60 ASEN 5335 Aerospace Environment -- Geomagnetism 61 Transformer Heating Saturation of the transformer core produces extra eddy currents in the transformer core and structural supports which heat the transformer. The large thermal mass of a high voltage power transformer means that this heating produces a negligible change in the overall transformer temperature. However,localized hot spots can occur and cause damage to the transformer windings ASEN 5335 Aerospace Environment -- Geomagnetism 62 ASEN 5335 Aerospace Environment -- Geomagnetism 63 ASEN 5335 Aerospace Environment -- Geomagnetism 64 ASEN 5335 Aerospace Environment -- Geomagnetism 65 How Geomagnetic Variations Affect Pipelines Time-varying magnetic fields induce time-varying electric currents in conductors. Variations of the Earth's magnetic field induce electric currents in long conducting pipelines and surrounding soil. These time varying currents, named "telluric currents" in the pipeline industry, create voltage swings in the pipeline-cathodic protection rectifier system and make it difficult to maintain pipe-to-soil potential in the safe region. During magnetic storms, these variations can be large enough to keep a pipeline in the unprotected region for some time, which can reduce the lifetime of the pipeline. See example for the 6-7 April 2000 geomagnetic storm on the following page. ASEN 5335 Aerospace Environment -- Geomagnetism 66 geomagnetic field variations at Ottawa magnetic observatory pipe-to-soil potential difference on a pipeline in Canada During the magnetic storm the pipe-to-soil potential difference went outside the 5335 Aerospace Environment 67 safeASEN region. That can increase--theGeomagnetism possibility of corrosion.