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~10 nT/year

Equatorial field intensity in recent millenia, as deduced from measurements on archeological samples and recent observatory data. ~10 nT/year.

edan-knight
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~10 nT/year

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  1. Equatorial field intensity in recent millenia, as deduced from measurements on archeological samples and recent observatory data. ~10 nT/year Reversals have been documented as far back as 330 million years. During that time more than 400 reversals have taken place, one roughly every 700,000 years on average. However, the time between reversals is not constant, varying from less than 100,000 years, to tens of millions of years. In recent geological times reversals have been occurring on average once every 200,000 years, but the last reversal occurred 780,000        years ago. At that time the magnetic field underwent a transition from a "reversed" state to its present "normal state". ASEN 5335 Aerospace Environment -- Radiation Belts

  2. Alfred Wegener "The Origin of Continents and Oceans" [Wegener, 1929] Map of magnetic striping of the seafloor near the Reykjanes ridge [Heirtzler, 1968] ASEN 5335 Aerospace Environment -- Radiation Belts A radiation belt is a population of energetic particles fairly-trapped by the magnetic field.

  3. The Radiation Belts ASEN 5335 Aerospace Environment -- Radiation Belts A radiation belt is a population of energetic particles fairly-trapped by the magnetic field.

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  5. Review of Charged Particle Motions • Gyromotion motion: =p2/2mB (1st), T_g~10-3 sec • Bounce Motion: J= p||ds (2nd), T_b~100 sec • Drift motion: =BdA (3th) , T_d~103 sec ASEN 5335 Aerospace Environment -- Radiation Belts

  6. According to Faraday's Law of Magnetic Induction, a time rate of change of magnetic flux will induce an electric field ( and hence a force on the particle ): Therefore, the requirement that no forces act in the direction of motion of the rotating particle demands that ASEN 5335 Aerospace Environment -- Radiation Belts

  7. In other words, that the magnetic flux enclosed by the cyclotron path of the charged particle is constant: Assuming B does not vary spatially within the gyropath, where r = gyroradius = . We previously defined the magnetic moment , implying ASEN 5335 Aerospace Environment -- Radiation Belts

  8. First Adiabatic Invariant Note: same as saying that K.E. does not change if there are no forces parallel to v Or,  = constant . This is called the first adiabatic invariant of particle motion in a magnetic field. We should note that the above has assumed that B is constant within at least one orbital period of the particle. This is only approximately true, and the term "invariant" is also an approximation, but one that reflects the first-order constraints on the particle motion. ASEN 5335 Aerospace Environment -- Radiation Belts

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  10. Since, (i.e, the K.E. of the particle remains constant since the only forces act  to V), then  must increase as B increases, and correspondingly the distribution ofK.E. between and changes: If  increases to 90° before the particle collides vigorouslywiththe neutral atmosphere, the direction of will change sign (at the "mirror point") and the particle will follow the direction of decreasing B. ASEN 5335 Aerospace Environment -- Radiation Belts

  11. For a given particle the position of the mirror point is determined by the pitch angle as the particle crosses the equator (i.e., where the field is weakest) since Therefore, the smaller eq the larger BM , and the lower down in altitude is the altitude of BM. ASEN 5335 Aerospace Environment -- Radiation Belts

  12. Loss Cone and Pitch Angle Distribution Particles will be lost if they encounter the atmosphere before the mirror point. Obviously thiswill happen if eq is too small, because that then requires a relatively large BM (|B| at the mirror point). The equatorial pitch angles that will be lost to the atmosphere at the next bounce define the loss cone, which will be seen as a depletion within the pitch angle distribution. B loss cone ASEN 5335 Aerospace Environment -- Radiation Belts

  13. Magnetic Mirroring in a Dipolar magnetic Field Trajectory of particle inside the loss cone. this particle will encounter the denser parts of the atmosphere (I.e., below 100 km) and precipitate from the radiation belts. Trajectory of particle outside the atmospheric bounce loss cone. This particle will bounce between mirror points ASEN 5335 Aerospace Environment -- Radiation Belts

  14. Second Adiabatic Invariant (Longitudinal Invariant) The second adiabatic invariant says that the integral of parallel momentum over one complete bounce between mirror points is constant (this once again results from no external forces): where ds means integration along B and B = BM at M1, M2. Since and m,v are constant, then second adiabatic invariant ASEN 5335 Aerospace Environment -- Radiation Belts

  15. The second adiabatic invariant (I2 = const) assumes that B does not change appreciably during 1 bounce period (about 1 second). I2 is a property of the field configuration and also of the mirror point (or equivalently, the equatorial pitch angle) since I2 = const defines the surface, or shell, on which the particle remains as it drifts around the earth. This is called the longitudinal invariant surface or L-shell. Recall our previous discussion of the L-shell and its connection with invariant latitude. ASEN 5335 Aerospace Environment -- Radiation Belts

  16. The Earth’s magnetic field is compressed on the dayside and drawn out on the night-side, so that the field configuration is zonally asymmetric solar wind How does this affect particles as they drift around the Earth ? Since the dominant adiabatic invariant governing particle motion is different for low and high pitch angle particles, we consider these separately. ASEN 5335 Aerospace Environment -- Radiation Belts

  17. Review of Adiabatic Invariants 1 & 2 First adiabatic Invariant: [K.E. (& magnetic moment) of particle remains constant] Second adiabatic Invariant: (integral of parallel momentum over one complete bounce between mirror points is constant) ASEN 5335 Aerospace Environment -- Radiation Belts

  18. High Pitch Angle Particles High pitch angle particles have mirror points not far from the equator. They are mostly affected by the magnitude of the B-field. High pitch angle particles originating on the night-side, when drifting to the dayside, keep moving radially outward to stay at a constant B-value, since the dayside field is compressed with respect to the night-side field. By the time these particles reach the noon meridian, they reach the boundary of the magnetopause and are lost. High pitch angle particles originating on the dayside similarly descend on the night-side, but since they have such large pitch angles, they are not lost. The above introduces a drift loss cone at high pitch angles at nighttime. ASEN 5335 Aerospace Environment -- Radiation Belts

  19. Low Pitch Angle Particles Low pitch angle particles travel long distances along a field line; the second adiabatic invariant is important for these particles. They try to stay on field lines whose lengths are about the same for a given BM . At a given equatorial distance from Earth, day-side field lines are longer than night-side field lines. A low pitch angle particle on the (mainly outer) day-side field lines, when drifting over to the night-side, will seek higher and higher field lines. These particles can find themselves on open field lines on the night-side or be lost by other processes. The above introduces a drift loss cone at small pitch angles at daytime. ASEN 5335 Aerospace Environment -- Radiation Belts

  20. Pseudo-Trapping Regions; Shell-Splitting These particles, with high pitch angles, descend on the night-side, but since they have such large pitch angles, they are not lost, and return. These particles, with high pitch angles beyond ~7 RE are lost on the day-side Thus, there are some regions from which trapped particles are unable to make a complete circuit of the earth, being lost en route in the magnetotail or beyond the magnetopause. These are called the pseudo- trapping regions. This phenomenon is referred to as shell-splitting. These particles, with small pitch angles, and mirroring at low altitudes, are lost on the night-side These particles return to the night-side ASEN 5335 Aerospace Environment -- Radiation Belts

  21. Third Adiabatic Invariant The third adiabatic invariant, or flux invariant, states that the magnetic flux enclosed by the charged particle longitudinal drift must be a constant: (This is analogous to the application of Faraday’s law on p. 4, except in this case is due to longitudinal drift of particle) In other words, as B varies (with longitude), the particle will stay on a surface such that the total number of field lines enclosed remains constant. However, since most temporal fluctuations in B occur over time scales short compared to the longitudinal drift period (~ 30-60 minutes), the assumptions underlying this invariant law are usually not obeyed. ASEN 5335 Aerospace Environment -- Radiation Belts

  22. Violations of the Invariant Constraints The adiabatic invariants are said to be violated when electric or magnetic field variations take place near or above the adiabatic motion frequency in question, i.e., 1/Tgyro, 1/Tbounce, 1/Tdrift For instance, violation of the third invariant permits transport of the particles across field lines. If these violations occur frequently enough, in a statistical sense the net result can be thought of as radial diffusion. Similarly, the paths of radiation belt particles are affected by collisions with neutral atoms and by E-M interactions of plasma waves. On time scales short compared to Tgyro and Tbounce, these interactions manifest themselves statistically in what is called pitch angle diffusion. (leading to diffusion into the loss cone.) ASEN 5335 Aerospace Environment -- Radiation Belts

  23. Radial diffusion transports radiation belt particles across the di-polar-like magnetic field lines in the radial direction. Pitch angle diffusion alters the particle pitch angle (or equivalently, the mirror point location). In both cases the earth's atmosphere is a sink; for radial diffusion by transport to very low L-shells, and for pitch angle diffusion by lowering the mirror points into the atmosphere. A conceptual representation of pitch angle and radial diffusion in Earth’s radiation belts. Diffusion occurs in either direction, but in most cases there is a net diffusion flux towards the atmosphere, because that is where the net sink is. ASEN 5335 Aerospace Environment -- Radiation Belts

  24. Obviously trapping is not perfect, and there exist mechanisms for introducing particles into the radiation belts, as well as loss mechanisms. Before discussing these mechanisms, let us get a rough idea of the distributions of particles and their energies. • The Explorer I spacecraft • carried a geiger counter • to measure cosmic rays. • However, there were times • when the counter became • saturated, and Van Allen • and his group correctly • concluded that this was • the result of energetic • particles. On the basis • of these measurements, • the 'radiation belts' were • Defined, at that time consisting of an inner zone and an outer zone. ASEN 5335 Aerospace Environment -- Radiation Belts

  25. A Schematic View of the Locations of Radiation Belts • Blue: inner belt, >100MeV protons, rather stable • Purple: outer belt, 100s keV and MeV electrons and ions, not stable at all • Slot region in between • Yellow: ACRs, stable • White line: Earth’s magnetic field, approx. by a dipole field ASEN 5335 Aerospace Environment -- Radiation Belts

  26. Asymmetrical magnetic field and SAAdrift loss cone • The Earth’s magnetic field azimuthally asymmetrical with internal and external factors. • The internal magnetic field is sometimes approximated as an off-centered and titled dipole. • The magnetic field strength is much weaker at the south Atlantic area, called the South Atlantic Anomaly (SSA). It is a large sink of radiation belt particles. It results in the drift loss cone in the particle pitch angle distribution. ASEN 5335 Aerospace Environment -- Radiation Belts

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  29. SAMPEX measured Anomalous Cosmic Ray Particles (Oxygen Nuclei, >200 keV/nucl) ASEN 5335 Aerospace Environment -- Radiation Belts

  30. 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&5 and class notes • HW4 due 3/13 • Quiz-4 today, close book. ASEN 5335 Aerospace Environment -- Radiation Belts

  31. Sources and Sinks of Radiation Belt Particles The following processes are involved: • Injection of charged particles into the trapping region • Radial diffusion or radial transport within the region • Local acceleration of particles to high energy • Loss processes removing particles from the trapping region (loss through magnetopause and loss by precipitating into atmosphere). Inner Zone < 2.5 RE Production: Galactic cosmic-ray proton impinge on neutral atoms neutron decay (half life time ~ 10 min)  proton and electron. Loss Mechanisms: Coulomb collisions  loss cone scattering Charge exchange  Energetic neutron escapes (H+energetic + H  Henergetic + H+) These processes explains well the inner proton belt. ASEN 5335 Aerospace Environment -- Radiation Belts

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  33. There are 3 types of cosmic rays of interest here: Galactic Cosmic Rays Anomalous Cosmic Rays Solar Energetic Particles ASEN 5335 Aerospace Environment -- Radiation Belts

  34. Cosmic Rays • Cosmic rays are high energy charged particles, originating in outer space, that travel at nearly the speed of light and strike the Earth from all directions. Most cosmic rays are the nuclei of atoms, ranging from the lightest to the heaviest elements in the periodic tables, but dominated by protons (89% hydrogen, 10% helium, and about 1% heavier elements). Cosmic rays also include high energy electrons, positrons, and other subatomic particles. • The term “cosmic rays” usually refers to galactic cosmic rays, which originate in source outside the solar system, distributed throughout and possibly beyond our Milky Way galaxy. • Studying the energetic particle population is very important for two reasons: • These particles represent considerable hazard for both humans and radiation-sensitive systems in space, because they can penetrate through large amount of shielding materials. • They carry information about the large-scale properties of the heliosphere and the galaxy. Discovery and Early Research: Cosmic rays were discovered in 1912 by Victor Hess, when he found that an electroscope discharged more rapidly as he ascended in a balloon. He attributed this to a source of radiation entering the atmosphere from above, and in 1936 was awarded the Nobel prize for his discovery. For some time it was believed that the radiation was electromagnetic in nature (hence the name cosmic “ray”). However, during the 1930’s it was found that cosmic rays must be electrically charged because they are affected by the Earth’s magnetic field (How was this known?). ASEN 5335 Aerospace Environment -- Radiation Belts

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  36. Cosmic Ray Energies and Acceleration • The energy of cosmic rays is usually measured in units of MeV and GeV. Most galactic cosmic rays have energies between 100 MeV (corresponding to a velocity of protons of 43% of the speed of light) and 10 GeV ( 99.6% of the speed of light). The highest energy cosmic rays measured to date have had more than 1020 eV, equivalent to the kinetic energy of a baseball traveling at about 100 mph! • It is believed that most galactic cosmic rays derive their energy from supernova explosions, which occur approximately once every 50 years in our Galaxy. To maintain the observed intensity of cosmic rays over millions of years requires that a few percent (even >10%) of the more than 1051 ergs released in a typical supernova explosion be converted to cosmic rays. • The energy contributed to the Galaxy by cosmic rays (~1eV/cm3 ) is about that contained in galactic magnetic fields, and in the thermal energy of the gas that pervades the space between the stars, ASEN 5335 Aerospace Environment -- Radiation Belts

  37. Cosmic Rays in the Galaxy • Because cosmic rays are electrically charged they are deflected by magnetic fields, and their directions have been randomized, making it impossible to tell where they originated. However, cosmic rays in other regions of the Galaxy can be traced by the electromagnetic radiation they produce. Supernova remnants such as the Crab Nebula are known to be a source of cosmic rays from the radio synchrotron radiation emitted by cosmic ray electrons spiraling in the magnetic fields of the remnant. Show above is an image of the Crab Nebula in the X-ray band. In the center lies the powerful Crab pulsar, a spinning neutron star with mass comparable to our Sun but with the diameter of only a small town. The pulsar expels particles and radiation in a beam that sweeps pass the Earth 30 times/sec. The supernova that created the Crab Nebula was seen by ancient Chinese astronomers and possibly even the Anasazi Indians in 1054, perhaps glowing for a week as bright as the full moon. • Observations of high energy (10 MeV – 1000 MeV ) gamma rays resulting from cosmic ray collisions with interstellar gas show that most cosmic rays are confined to the disk of the Galaxy, presumably by its magnetic field. Observations show that, on average, cosmic rays spend about 10 million years in the Galaxy before escaping into inter-galactic space. ASEN 5335 Aerospace Environment -- Radiation Belts

  38. 101 100 10-1 The figure to the right Illustrates differential energy spectra for GCR outside the magnetosphere at maximum and minimum solar activity. 10-2 10-3 10-4 GCR typically consists of 108-109 eV particles, but some GCR particles can have energies as high as 1020 eV. SSMIN 10-5 SSMAX 10-6 10-7 101 102 103 104 105 106 ASEN 5335 Aerospace Environment -- Radiation Belts kinetic energy (MeV/nucleon)

  39. Cosmic Rays in the Solar System • Just as cosmic rays are deflected by the magnetic field in interstellar space, they are also affected by the IMF embedded in the solar wind, and therefore have difficulty reaching the inner solar system. Spacecraft venturing out towards the boundary of the solar system have found that the intensity of galactic cosmic rays increases with distance from the Sun. As solar activity varies over the 11 year solar cycle the intensity of cosmic rays at Earth also varies, so does the inner radiation belt particles, in anti-correlation with the sunspot number. Ionosphere expansion also plays a key role ….. SAMPEX measured protons (19-27.4 MeV) and the sunspot numbers • The Sun is also a sporadic source of cosmic ray nuclei and electrons that are accelerated by shock waves traveling through the corona, and by magnetic energy released in solar flares. The solar particle events are more frequent during the active phase of the solar cycle. The maximum energy reached in solar particle events is typically 10 to 100 MeV, occasionally reaching 1 GeV (roughly once a year) to 10 GeV (roughly once a decade). Solar energetic particles can be used to measure the elemental and isotopic composition of the Sun, thereby complementing spectroscopic studies of solar materials. ASEN 5335 Aerospace Environment -- Radiation Belts

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  44. Effects of Starfish lasted until the early 1970’s Telstar was Launched 1 day after Starfish, and was the first satellite failure due to radiation exposure. Telstar received a total radiation dose 100 times that expected. ASEN 5335 Aerospace Environment -- Radiation Belts

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  46. Anomalous Cosmic Rays (ACRs) • Since the beginning of the space age, it was known that two main sources of energetic particles that pervade the interplanetary space: (a) Galactic Cosmic Rays (GCR), originated from supernova explosions, which occur approximately once every 50 years in our galaxy. (b) Solar Energetic Particles (SEP) , from solar flares or CME. So the Anomalous Cosmic Rays (ACRs) belong to neither of them by definition. • In 1973, the anomalous excesses of several elements in low-energy cosmic rays led to the discovery of this so called ACRs. For Examples: O/C > 30, He/H>1 • Fisk et al. [1974] proposed the origin of the ACRs. ASEN 5335 Aerospace Environment -- Radiation Belts

  47. Origins of ACRs ASEN 5335 Aerospace Environment -- Radiation Belts

  48. A Schematic View of the Locations of Radiation Belts • Blue: inner belt, >10MeV protons, rather stable • Purple: outer belt, 100s keV and MeV electrons and ions, not stable at all • Slot region in between • Yellow: ACRs, stable • White line: Earth’s magnetic field, approx. by a dipole field ASEN 5335 Aerospace Environment -- Radiation Belts

  49. Origin of Anomalous Cosmic Rays ASEN 5335 Aerospace Environment -- Radiation Belts

  50. Trapping ACRs • ACRs singly charged, picked up by solar wind, heading to the termination shock, where some of them can be further energized and some of them come back. • Gyroradius inversely proportional to the number of the charge. A singly charged ion can be further stripped of its electrons when it happens to skim the Earth’s atmosphere, the gyroradius is reduced many times and the ion can become trapped. • This scenario was predicted far in advance [Blake et al., 1978]. • First evidence from Russian COSMOS satellites. • SAMPEX pin pointed the location of the narrow belt of ARCs. ASEN 5335 Aerospace Environment -- Radiation Belts

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