AN ANALYTICAL SOLUTION OF THE COSMIC RAYS TRANSPORT EQUATION IN THE PRESENCE OF THE GEOMAGNETIC FIELD

2002 ◽  
Vol 17 (12n13) ◽  
pp. 1645-1653
Author(s):  
MARINA GIBILISCO

In this work, I study the propagation of cosmic rays inside the magnetic field of the Earth, at distances d ≤ 500 Km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role inside the cosmic rays transport equation; finally, I present an analytical method to solve such an equation through a factorization technique.

2001 ◽  
Vol 16 (13) ◽  
pp. 2293-2310
Author(s):  
MARINA GIBILISCO

In this work, I study the propagation of cosmic rays inside the magnetic field of the earth, at distances d≤500 km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role in the cosmic rays transport equation; then, I present an analytical method to solve such an equation through a factorization technique. In this way, it is possible to reduce the initial second-order, partial derivatives differential equation into a more simple, Riccati-like equation, which, finally, can be solved by using standard Runge–Kutta–Merson routines. The results here obtained may have some interest in view of the future AMS (Alpha Magnetic Spectrometer) data, which will be collected at an altitude of about 400 km above the earth surface. Moreover, the study of the propagation of particles having different charges and masses may also help in testing the presence of antimatter and antinuclei in cosmic rays; some theoretical implications of this possibility will also be discussed in the light of the perspectives opened by the AMS Experiment.


Author(s):  
William Lowrie

The Earth is surrounded by a magnetic field, which originates inside its molten core, and which for centuries has helped travellers to navigate safely across uncharted regions. The magnetic field protects life on the Earth by acting as a shield against harmful radiation from space, especially from the Sun. ‘The Earth’s magnetic field’ explains that the magnetic field at the Earth’s surface is dominantly that of an inclined dipole. The Sun’s deforming effect on the magnetic field outside the Earth is described, as are the magnetic fields of other planets. The magnetism of rocks forms the basis of palaeomagnetism, which explains how plate tectonics displaced the continents and produced oceanic magnetic anomalies whenever the geomagnetic field reversed polarity.


A theory of the aurora polaris is proposed which attempts to explain many features of the complicated morphology of auroral displays. One basis of the theory is the presence, during magnetic disturbance, of additional or enhanced magnetic fields due to electric currents within a distance of several earth radii from the earth’s centre. One such field (denoted by DCF) is due to electric currents flowing near the inner surface of the solar stream that then envelopes the earth. A hollow is carved in the stream by the geomagnetic field. The other field (denoted by DR) is that of an electric ring current, additional or enhanced, that flows westward round the earth. This is carried by the particles of the Van Allen belts. A third field (denoted by DP) is that of the disturbance currents that flow in the ionosphere, under the impulsion of electromotive forces generated mainly in polar regions. We consider it likely that during magnetic storms and auroral displays, neutral lines appear in the magnetic field near the earth. These will lie mainly on the dark side of the earth, in or near the equatorial plane, on the nearer side of the ring current. At times these lines may extend over more than 180° of longitude, so that a part of them may lie on the sunward side of the earth. These neutral lines are of two types, which we call O and X they appear together, in pairs. During disturbed conditions there may be more than one pair. Lines of force cross at points on X neutral lines, but they do not pass through O neutral lines. As Dungey has shown, charged particles will tend to be concentrated near X points (of which the X neutral lines are the locus). Charges drawn toward the neutral line will be discharged into the earth’s atmosphere along the lines of magnetic force. We suggest that the location, nature and motions of the auroral forms are determined by the position, form and motion of the X neutral lines, lying in or near the plane of the geomagnetic equator. It seems necessary to suppose, in addition, that an electric field arises sporadically along the X lines. When this is absent, the aurora appears as a quiet arc. The onset of the suggested electric field concentrates the charges more narrowly near the X line and near the lines of force that extend from it to the auroral zone. This produces extremely thin-rayed auroral arcs. The above concentration of electrons near an X neutral line produces a large flux of electrons, while the proton flux is diminished. A dynamical instability due to this flux difference (the space charge density is supposed to be very small) produces a slight separation of protons and electrons along and near the lines of force through the X line. Hence in the auroral ionosphere there is an associated electric field. This is usually directed towards the equator. It drives electric current, usually westward, along the auroral zones, and produces the strong magnetic disturbances (DP) there observed. Birkeland called these polar elementary storms. The rapid auroral changes are ascribed to instabilities of the magnetic field in the region near the X line or lines, to the rear of the earth, where the resultant magnetic field is weak. The ray structure in the auroral arc is ascribed to an instability of the thin sheet of electron flow. Cosmic rockets have shown that the magnetic field, up to and beyond ten earth radii, departs from the values corresponding to the internally produced main geomagnetic field. As yet these explorations do not seem to have disclosed the existence of reversals of the field in or near the magnetic equatorial plane. But on the basis of our auroral hypothesis, we predict with considerable confidence that such reversals will be found to occur, on the dark side of the earth, during great auroral displays. The theory here proposed is discussed in connexion with recent I. G. Y. and I. G. C. auroral, magnetic and other data.


2020 ◽  
Vol 10 ◽  
pp. 55
Author(s):  
Barbara Perri ◽  
Allan Sacha Brun ◽  
Antoine Strugarek ◽  
Victor Réville

Cosmic rays are remarkable tracers of solar events when they are associated with solar flares, but also galactic events such as supernova remnants when they come from outside our solar system. Solar Energetic Particles (SEPs) are correlated with the 11-year solar cycle while Galactic Cosmic Rays (GCRs) are anti-correlated due to their interaction with the heliospheric magnetic field and the solar wind. Our aim is to quantify separately the impact of the amplitude and the geometry of the magnetic field, both evolving during the solar cycle, on the propagation of cosmic rays of various energies in the inner heliosphere (within Earth orbit). We focus especially on the diffusion caused by the magnetic field along and across the field lines. To do so, we use the results of 3D magnetohydrodynamics (MHD) wind simulations running from the lower corona up to 1 AU. This gives us the structure of the wind and the corresponding magnetic field. The wind is modeled using a polytropic approximation, and fits and power laws are used to account for the turbulence. Using these results, we compute the parallel and perpendicular diffusion coefficients of the Parker cosmic ray transport equation, yielding 3D maps of the diffusion of cosmic rays in the inner heliosphere. By varying the amplitude of the magnetic field, we change the amplitude of the diffusion by the same factor, and the radial gradients by changing the spread of the current sheet. By varying the geometry of the magnetic field, we change the latitudinal gradients of diffusion by changing the position of the current sheets. By varying the energy, we show that the distribution of values for SEPs is more peaked than GCRs. For realistic solar configurations, we show that diffusion is highly non-axisymmetric due to the configuration of the current sheets, and that the distribution varies a lot with the distance to the Sun with a drift of the peak value. This study shows that numerical simulations, combined with theory, can help quantify better the influence of the various magnetic field parameters on the propagation of cosmic rays. This study is a first step towards the resolution of the complete Parker transport equation to generate synthetic cosmic rays rates from numerical simulations.


Author(s):  
Roswitha Wiltschko ◽  
Wolfgang Wiltschko

AbstractThe magnetic field of the Earth provides animals with various kinds of information. Its use as a compass was discovered in the mid-1960s in birds, when it was first met with considerable skepticism, because it initially proved difficult to obtain evidence for magnetic sensitivity by conditioning experiments. Meanwhile, a magnetic compass was found to be widespread. It has now been demonstrated in members of all vertebrate classes, in mollusks and several arthropod species, in crustaceans as well as in insects. The use of the geomagnetic field as a ‘map’ for determining position, although already considered in the nineteenth century, was demonstrated by magnetically simulating displacements only after 2000, namely when animals, tested in the magnetic field of a distant site, responded as if they were physically displaced to that site and compensated for the displacement. Another use of the magnetic field is that as a ‘sign post’ or trigger: specific magnetic conditions elicit spontaneous responses that are helpful when animals reach the regions where these magnetic characteristics occur. Altogether, the geomagnetic field is a widely used valuable source of navigational information for mobile animals.


Author(s):  
A. Cook

Edmond Halley was interested in magnetism from his schooldays to the end of his life, and of all his notable contributions to natural knowledge, his survey of the magnetic field over the Atlantic Ocean surely stands out both for its achievement at the time and for its lasting value. His identification of the westerly drift and his speculations about its origin, his description of aurorae and his connection of them with the geomagnetic field, all demonstrate his physical insight, the grounds for which have only quite recently become apparent. How profound were Halley's studies of geomagnetism has become much more evident in the 57 years that have passed since Sidney Chapman's Halley lecture on the same topic; the advances in geophysics that have taken place in the intervening years are my justification for returning to the subject.


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