Table of Contents - Index - Lecture 1 - Lecture 2 - Lecture 3 - Lecture 4
Uji Lectures on the Aurora
THEORY OF THE AURORA
by W. Calvert
Copyright 1997, by W. Calvert, all rights reserved.
This booklet consists of the set of viewgraph transparencies that were used during a series of lectures on the aurora that were given during the summer of 1997 at the Radio Atmospheric Science Center (RASC) at Kyoto University in Uji, Japan. These lectures described a new theory of the aurora which remarkably accounts for all relevant aspects of the aurora during an auroral substorm, including the diffuse aurora prior to substorm expansion, the structure and behavior of the diffuse and discrete aurora during a substorm, the sudden local onset of substorm expansion inside a pre-existing homogeneous diffuse auroral arc, and the poleward expansion of the aurora during a substorm. This theory therefore constitutes a genuine breakthrough for auroral research, since no other theory has ever been able to account for such features of the aurora.
The aurora during a substorm is found to occur on closed magnetic field lines as a result of electrons which have been accelerated downward into the ionosphere by an upward-directed electric field in the high-altitude auroral zone. The altitude region over which these electric fields occur, which turns out to be about 2000 to 15,000 km above the auroral zone, will be referred to as the auroral electron acceleration region. Since particle collisions are negligible at such altitudes above the auroral zone, the trajectory of an electron is determined by its initial velocity, and the magnetic field strength and electric potential as a function of its altitude above the auroral zone. The problem of explaining the aurora then boils down to explaining a source of electrons having velocity vectors inside the so-called loss cone for electron precipitation into the ionosphere, and most theories of the aurora have tacitly assumed that the loss cone for electron precipitation into the ionosphere must be filled at the top of the electron acceleration region.
This theory, which was originally developed by Knight [1973], assumes that the loss cone must be uniformly filled as a result of an isotropic electron velocity distribution which convects inward along an auroral field line from the tail of the Earth's magnetosphere. The predicted electron precipitation flux for a Maxwell-Boltzmann velocity distribution at the top of the acceleration region then turns out to be
where phi is the predicted flux per unit area in the ionosphere, n and Wo are the density and average initial energy of the electrons at the top of the acceleration region, Bi is the magnetic field strength in the ionosphere, Btop is the magnetic field strength at the top of the acceleration region, e is the electron charge, m is the electron mass, and V is the total electric potential between the top and bottom of the acceleration region. Equation (1) then predicts that the resulting electron precipitation flux should increase approximately proportional to the electric potential of the acceleration region, and this forms the basis for the widespread assumption that a latitudinally-localized electric field in the high-altitude auroral zone might cause the structure of the aurora by enlarging the loss cone for electron precipitation into the ionosphere.
According to Knight's theory, which had been developed before it was certain that an auroral substorm occurred on closed field lines, a filled loss cone at the top of the acceleration region could be attributed to an isotropic electron velocity distribution in the central plasma sheet region in the tail of the Earth's magnetosphere. This region of the magnetosphere, on the other hand, corresponds to the polar cap at the high-latitude edge of the auroral zone, and it is therefore also necessary to assume that the electrons which cause the aurora convect inward as a result of the electric field across the tail of the magnetosphere. This process is analyzed in Transparencies 27-35, with the conclusion that the loss cone on the auroral field lines on which a substorm occurs ought to be almost completely empty as a result of electron precipitation into the ionosphere at higher latitudes in the auroral zone.
In order to circumvent this difficulty with Knight's original theory, others have assumed that the loss cone for electron precipitation into the ionosphere ought to be refilled as a result of scattering into the loss cone above the electron acceleration region. This theory, which relies upon Knight's predictions without justifying his assumptions, will be referred to as the "filled-loss-cone theory of the aurora." The main problem with the filled-loss-cone theory is that this amounts to acknowledging the problem without supplying a solution, since nobody has identified the wave mode or wave instability which supplies the loss-cone electrons which this model requires.
Although it may come as a surprise to those who have assumed that Knight's theory adequately accounts for the aurora, the predicted electron precipitation flux and energy flux for this model, which are shown in Viewgraph Transparencies 8 and 9 for a reasonable electron density along an auroral field line, turn out to be about an order of magnitude or more greater than the actual precipitation flux and energy flux of the diffuse and discrete aurora during a substorm. For a potential of 3-10 kV, which is typical of the inverted-V electron events that accompany the aurora, Knight's theory predicts an electron precipitation flux of 2-5 x 109 electrons/cm2 sec and an electron energy flux of 15-100 erg/cm2 sec, whereas the measured electron flux and energy flux of the aurora during a substorm turn out to be in the range of 107 to 109 electrons/cm2 sec, and only about 1-2.5 erg/cm2 sec [see Newell et al., 1996].
This means that the loss cone for electron precipitation into the ionosphere must be only partially filled at the top of the electron acceleration region, thereby contradicting the basic assumption of Knight's theory. Since a partially filled loss cone implies electron precipitation into the conjugate auroral zone, the observation of a partially-filled loss cone also implies that the loss cone ought to be completely empty as a result of electron precipitation into the conjugate auroral zone. The only explanation for a partially filled loss cone is therefore an empty loss cone which is partially filled as a result of scattering into the loss cone somewhere along an auroral field line. Although this is consistent with the filled-loss-cone theory, unless there is some reason to assume that the rate of scattering into the loss cone is proportional to the size of the loss cone, Equation (1) no longer applies, and Knight's theory is no longer an adequate explanation for the aurora.
The idea that electric fields cause the structure of the aurora also requires the assumption that the electric potential of the acceleration region ought to increase significantly along the auroral field lines on which the aurora occurs. As shown in Transparency 14, however, the measured latitudinal thickness of these electric potentials is found to be nearly two orders of magnitude larger than the actual thickness of a thin discrete arc [see Newell et al., 1996; Borovsky et al, 1991]. Lin and Hoffman [1982] have also found intense electron precipitation peaks corresponding to broader discrete arcs inside the well-known inverted-V electron events which accompany the aurora.
As a consequence, it therefore appears that the electric potential of the acceleration region accompanies the aurora without causing its structure, thereby also contradicting the assumption that a latitudinally-localized electric field causes the structure of the aurora. New observations by the Oedipus C rocket which was flown in 1995 have also confirmed this conclusion, as shown in Viewgraph Transparency 21. This rocket was flown into the auroral zone during an expansive phase of a multiple-onset substorm, and carried an electron detector which had a spatial resolution of approximately 100 m. As shown in the top and bottom panels of this figure, this rocket detected the electron precipitation flux of three distinct discrete arcs, while at the same time also measuring, in the middle panel of this figure, the electric potential of the electron acceleration region from the electron energy outside the loss cone during this event. Since there was no detectable increase in the energy of the electrons in the middle panel of this figure, these measurements therefore clearly show that the electric potential of the acceleration region did not increase significantly along the auroral field lines of these discrete auroral arcs.
Although other observations have been interpreted differently, these measurements therefore establish that a latitudinally-localized electric field cannot account for the structure of the aurora. Borovsky [1993] has also shown that the predicted thickness of the aurora according to all current theories which are based upon this assumption also cannot account for the structure of the aurora. As a consequence, latitudinally localized scattering into the loss cone by a localized wave instability then becomes the only feasible explanation for the aurora, as previously suggested by the author more than a decade ago [Calvert, 1987].
According to this theory, which has been developed from the observations of the auroral kilometric radiation which is found to accompany the aurora during a substorm, the wave instability which causes the predicted scattering into the loss cone is presumably the cyclotron maser instability of Wu and Lee [1979], whereupon the emitted wave then becomes the auroral kilometric radiation which accompanies the aurora during substorm expansion [see Calvert, 1982, 1987, 1995; Huff, et al., 1988; Kaiser and Alexander, 1977; and Gurnett, 1974]. The properties of the cyclotron maser instability and the auroral kilometric radiation (AKR) which is found to accompany the aurora are therefore discussed in Viewgraph Transparencies 36-48, with the conclusion that this model correctly predicts the power of the aurora during substorm expansion.
According to this theory, the predicted scattering into the loss cone occurs inside the electron acceleration region as a result of the increased electron energy which then becomes available to power the cyclotron maser instability. This theory moreover should not be interpreted as assuming that AKR causes the aurora, since the AKR and the aurora are both byproducts of the same process which scatters electrons into the loss cone, and the wave power of the AKR is extracted from the electrons which are scattered into the loss cone to cause the aurora. The altitude range over which AKR originates is also found to coincide with the electron acceleration region, thereby also confirming the assumption that the predicted scattering into the loss cone occurs inside the electron acceleration region.
Additional evidence for this process also turns out to be available from the electron observations of Oedipus C. As shown in Transparency 21, and also discussed in Viewgraph Transparency 49, the electron energy in the middle panel of this figure shows that the electric potential of the acceleration region during this event was approximately constant and about 3 kV, whereas the electron energy of the electrons in the top panel of this figure shows that the energy of the electrons which contributed to the observed increases in the electron precipitation flux were found to vary from about 3 kV to significantly less than 3 kV. Since the electrons which caused these increases in flux presumably originated with the same electric potential at the top of the electron acceleration region, these measurements therefore suggest that the electrons which cause the discrete aurora must lose part of their energy inside the electron acceleration region. This observation therefore also rules out a local source of loss-cone electrons at the top of the acceleration region, since this does not explain why the mirroring electrons in the middle panel of this figure did not also suffer the same loss in energy on their way through the acceleration region. The mechanism that causes the discrete aurora must therefore operate independently of the electric potential of the acceleration region, and also extract energy from the electrons which end up inside the loss cone at the bottom of the acceleration region. Although it remains to be shown whether the proposed theory can account for the observed decrease in electron energy which was detected by Oedipus C, this model for the aurora is also the only current theory which is consistent with a loss in electron energy inside the electron acceleration region, since all other theories assume that the electrons which cause the aurora originate inside the loss cone at the top of the acceleration region.
It thus appears that the filled-loss-cone theory cannot account for any relevant feature of the aurora during a substorm, much less for substorm onset, substorm expansion, or the poleward expansion of the aurora during substorm expansion. As a consequence, this new theory, which is summarized below, also becomes the only theory which can account for the actual properties of the aurora during a substorm.
Lecture 1 discusses the deficiencies of the previous filled-loss-cone theory, Lecture 2 explains why inward convection followed by scattering into the loss cone can account for the loss-cone electrons which cause the aurora, Lecture 3 accounts for the structure and behavior of the diffuse and discrete aurora during a substorm, and Lecture 4 explains substorm expansion and the predicted triggering of the aurora by a satellite radio transmitter. The basic elements of this theory, which are discussed in greater detail in the published version [Calvert, 1995], can then be summarized as follows.
According to this theory, the electron precipitation flux which causes the aurora during a substorm results from scattering into the loss cone by the cyclotron maser instability. The diffuse aurora prior to substorm expansion can then be attributed to enhanced scattering inside local density depletions as a result of the increased wave gain of the cyclotron maser instability at lower densities. This model thereby accounts for the initial irregular structure of the diffuse aurora as a result of random density variations which convect inward from the tail of the magnetosphere. Moreover, since the resulting electron precipitation into the ionosphere also decreases the electron density along an auroral field line, the resulting diffuse electron precipitation should also enhance the density depletions in which it occurs, thereby causing deeper density depletions which gradually spread out in longitude because of energy-dependent particle drifts.
This model therefore accounts for the spontaneous formation of homogeneous diffuse arcs prior to substorm expansion, along with the formation of arc-shaped density depletions which gradually sharpen and deepen as a consequence of the enhanced electron precipitation which is caused by the increased wave gain of the cyclotron maser instability at lower densities. The onset of substorm expansion can then be attributed to the sudden onset of closed-loop oscillations inside these local density depletions, thereby accounting for the sudden local transformation of a pre-existing homogeneous diffuse arc into the first discrete arc of substorm expansion. This model for the onset of substorm expansion thus also explains the sudden onset of auroral kilometric radiation exactly coincident with the onset of substorm expansion, since the emission of AKR is also attributed to the same local oscillations that cause discrete auroral arcs. The wave feedback mechanism, which is referred to as "radio lasing," thereby accounts for both the discrete aurora and the auroral kilometric radiation which accompanies the aurora during a substorm.
This theory then goes on to account for substorm expansion as a result of the triggering of adjacent discrete arcs by the emitted auroral kilometric radiation. This explanation for an auroral substorm, which I have referred to as the "domino theory of substorm expansion" is discussed in Viewgraph Transparencies 82-86. According to this model for an auroral substorm, a substorm results from the onset of radio lasing at low latitudes in the auroral zone, rather than any external effects which dictate the electric potential of the electron acceleration region, and this model for the aurora also leads to the unexpected conclusion that an auroral substorm results from the electron precipitation which caused the aurora, rather than the other way around.
This theory also produces a number of testable predictions which can be used to confirm the validity of this theory. The first is simply that this theory adequately accounts for the structure and behavior of the diffuse and discrete aurora during a substorm, including the thin structure of discrete arcs and the sudden onset of substorm expansion inside a pre-existing homogeneous diffuse auroral arc. This theory also predicts diffuse electron precipitation adjacent to discrete arcs, a decrease in the electron energy inside these arcs, and the lack of any significant increase in the electric potential of the electron acceleration region along the auroral field lines on which the aurora occurs, all of which have already been confirmed by the Oedipus-C in Viewgraph Transparencies 21, 49, and 84.
Although these lectures have presented the first complete explanation for the aurora which has fascinated mankind for centuries, they have also covered a great deal more than simply another competing explanation for the aurora, since I have also explained substorm onset, substorm expansion, and the triggering of auroral kilometric radiation, in addition to disproving the previous filled-loss-cone theory. It is also no wonder that this theory has been successful where others have failed, since it was based upon deduction from the observations, as shown in Viewgraph Transparencies 97 and 98, beginning with the unexpected triggering of AKR and ending up with the new observations of Oedipus C.
It's like picking up pebbles in a pond, and the key to making a new discovery in this field is to correctly interpret a contradiction which everyone else has ignored. Behind each new discovery, on the other hand, lurks another new contradiction waiting to be unleashed on the auroral research community by a new secret society which I have decided to call the "Wakaru Club", where "wakaru" means to understand and is pronounced "wah-car-roo" in Japanese. If you would like to become an aurora-tora (tiger) in the Wakaru Club, simply sign the certificate, click your heels three times, and say "Hai, yoku wakarimashita!" (Yes, I understand.).
Borovsky, J. E., Auroral arc thicknesses as predicted by various theories, J. Geophys. Res., 98, 6101-6138, 1993.
Borovsky, J. E., D. M. Suszcynsky, M. I. Buchwald, and H. V. DeHaven, Measuring the thickness of auroral curtains, Arctic, 44, 231, 1991.
Calvert, W., A feedback model for the source of auroral kilometric radiation, J. Geophys. Res., 87, 8199-8214, 1982.
Calvert, W., Auroral precipitation caused by auroral kilometric radiation, J. Geophys. Res., 92, 8792-8794, 1987.
Calvert, W., An explanation for auroral structure and the triggering of auroral kilometric radiation, J. Geophys. Res., 100, 14,887-14,894, 1995.
Gurnett, D. A., The Earth as a radio source: Terrestrial kilometric radiation, J. Geophys. Res., 79, 4227-4238, 1974.
Huff, R. L., W. Calvert, J. D. Craven, L. A. Frank, and D. A. Gurnett, Mapping of auroral kilometric radiation sources to the aurora, J. Geophys. Res., 93, 11,445-11,454, 1988.
Kaiser, M. L., and J. K. Alexander, Relationship between auroral substorms and the occurrence of terrestrial kilometric radiation, J. Geophys. Res., 82, 5283-5286, 1977.
Kennel, C. F., and H. E. Petschek, Limit on stably trapped particle fluxes, J. Geophys. Res., 71, 1-28, 1966.
Knight, S., Parallel electric fields, Planet. Space Sci., 21, 741-750, 1973.
Lin, C. S., and R. A. Hoffman, Narrow bursts of intense electron precipitation fluxes within inverted-V events, Geophys. Res. Lett., 9, 211-214, 1982.
Newell, P. T., K. M. Lyons, and C-I. Meng, A large survey of electron acceleration events, J. Geophys. Res., 101, 2599, 1996.
Wu, C. S., and L. C. Lee, A theory of the terrestrial kilometric radiation, Astrophys. J., 230, 621- 626, 1979.
Other references are also listed in the relevant viewgraph transparencies.