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Aerospace Environment ASEN-5335

Aerospace Environment ASEN-5335. Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) Contact info: e-mail: lix@lasp.colorado.edu (preferred) phone: 2-3514, or 5-0523, fax: 2-6444, website: http://lasp.colorado.edu/~lix

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Aerospace Environment ASEN-5335

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  1. AerospaceEnvironmentASEN-5335 • Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) • Contact info: e-mail: lix@lasp.colorado.edu (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

  2. Solar wind speed and IMF 1995-1999 Descending phase Solar Minimum Ascending phase ASEN 5335 Aerospace Environment -- Geomagnetism

  3. Geomagnetism Paleomagnetism External Current Systems Sq and L Disturbance Variations Kp, Ap, Dst Dipole Magnetic Field Geomagnetic Coordinates B-L Coordinate system L-Shells ASEN 5335 Aerospace Environment -- Geomagnetism

  4. 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

  5. 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

  6. 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

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  8. Measurements from 400 km altitude ASEN 5335 Aerospace Environment -- Geomagnetism

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  10. • 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

  11. 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 Therefore Combined with another Maxwell equation: Yields Laplace’s Equation ASEN 5335 Aerospace Environment -- Geomagnetism

  12. 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: internal sources external sources r = radial distance = colatitude = east longitude a = radius of earth (geographic polar coordinates) = 0 for m > n n = 1 --> dipole n = 2 --> quadrapole ASEN 5335 Aerospace Environment -- Geomagnetism

  13. 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: 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: ASEN 5335 Aerospace Environment -- Geomagnetism

  14. 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

  15. Surface Magnetic Field Magnitude (g) IGRF 1980.0 .61 G Max .33 G Min .24 G .67 G ASEN 5335 Aerospace Environment -- Geomagnetism

  16. Surface Magnetic Field H-Component (g) IGRF 1980.0 .025 G .40 G .33 G .13 G .025 G ASEN 5335 Aerospace Environment -- Geomagnetism

  17. 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

  18. Surface Magnetic Field Declination IGRF 1980.0 0° 20° 10° 0° ASEN 5335 Aerospace Environment -- Geomagnetism

  19. 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 For a single magnetic dipole at the earth's center, oriented along the geographic axis, n = 1 m = 0 and Note that the r-dependence of higher and higher order dipoles goes as r-n ASEN 5335 Aerospace Environment -- Geomagnetism

  20. 1g = 10-5 G = 10-9 T (Tesla or Wbm-2)  = colatitude (southward positive) The field components are: X = = (northward) Y = 0 (eastward) Z = = (radially downward) northward component of magnetic field at equator at r = a, X  0.31 G ASEN 5335 Aerospace Environment -- Geomagnetism

  21. Total field magnitude: = A "dip angle", I , is also defined: = I is positive for downward pointing field (simple dipole field) ASEN 5335 Aerospace Environment -- Geomagnetism

  22. TILTED DIPOLE Approximation As the next best approximation, let n = 1 , m = 1 We find that and where  = longitude (positive eastward). ASEN 5335 Aerospace Environment -- Geomagnetism

  23. 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 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 This "tilted dipole" is tipped 11.5° towards 70°W longitude and has an equatorial field strength of .312G. ASEN 5335 Aerospace Environment -- Geomagnetism

  24. 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. • = geographic • latitude • = geographic • longitude • = 79°N, 290°E ASEN 5335 Aerospace Environment -- Geomagnetism

  25. 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, in our previous notation = "dipole moment" = 8.05 ± .02  1025 G-cm3 ASEN 5335 Aerospace Environment -- Geomagnetism

  26. From the above expression we can derive the following: These look very much like the simple dipole approximation in geographic coordinates. ASEN 5335 Aerospace Environment -- Geomagnetism

  27. AerospaceEnvironmentASEN-5335 • Instructor: Prof. Xinlin Li (pronounce: Shinlyn Lee) • Contact info: e-mail: lix@lasp.colorado.edu (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

  28. A field line is defined by , so and we may integrate to get 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. rdH B d dr, Z  ro ASEN 5335 Aerospace Environment -- Geomagnetism

  29. The point (magnetic or dipole latitude) where the line of force meets the surface is given by 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

  30. The B-L Coordinate System "L-shells" Let us take our previous equation for a dipolar field line and re-cast it so the radius of the earth (a) is the unit of distance. Then R = r/a and 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 ASEN 5335 Aerospace Environment -- Geomagnetism

  31. 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

  32. 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

  33. 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 L-value: 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

  34. 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

  35. 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

  36. Change in equatorial field strength over the past 150 years ASEN 5335 Aerospace Environment -- Geomagnetism

  37. External Current Systems Sept-aurora ASEN 5335 Aerospace Environment -- Geomagnetism

  38. External Current Systems and Ionosphere ASEN 5335 Aerospace Environment -- Geomagnetism

  39. 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: due to the dynamo action of tidal winds; and due to current exhange between the high-latitude ionosphere and the magnetosphere along field lines (see following figure). ASEN 5335 Aerospace Environment -- Geomagnetism

  40. dawn dusk ASEN 5335 Aerospace Environment -- Geomagnetism

  41. Solar Quiet Current systems 10,000 A between current density contours ASEN 5335 Aerospace Environment -- Geomagnetism

  42. Geographic Distribution of Magnetic Observatories ASEN 5335 Aerospace Environment -- Geomagnetism

  43. A Magnetogram ASEN 5335 Aerospace Environment -- Geomagnetism

  44. Local time Sq ground magnetic perturbations  northward eastward vertical ASEN 5335 Aerospace Environment -- Geomagnetism

  45. 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

  46. An interesting phenomenon, the equatorial electrojet, which is stronger than the sum of the two Sq,occurs at the magnetic equator: eastward electric field induced by dynamo action “Hall conductivity” “Pedersen conductivity” ASEN 5335 Aerospace Environment -- Geomagnetism

  47. 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

  48. (3) is an intense eastward current (the equatorial electrojet) driven by the vertical polarization field. Charge separation due to (downward Hall current, upward e-) compensating vertical field to maintain = 0. (no vertical currents due to insulating boundaries) (The above scenario only occurs within a few degrees of the equator, otherwise the polarization charges can leak away.) = Cowling conductivity Note: ASEN 5335 Aerospace Environment -- Geomagnetism

  49. 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 a r-2 ASEN 5335 Aerospace Environment -- Geomagnetism

  50. 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

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