Published in the Proceedings of the Fourth International Conference on Substorms, Hamanako, Japan, March 9-13, 1998.

THE GOTCHA-KATA-KATA OR "DOMINO" THEORY OF SUBSTORM EXPANSION

W. Calvert
Iowa City, Iowa, 52245, USA

Abstract. Recent studies have shown that substorm expansion can be attributed to a domino effect in which the electrons that cause the aurora are scattered into the loss cone inside local density depletions that are at first caused by an incoming wave, and then by the AKR that is emitted by wave feedback inside these density depletions. This theory will therefore be referred to as the "gotcha-kata-kata" or "domino" theory of substorm expansion, where "gotcha-kata-kata" is the sound that dominoes make in Japan.

1. Introduction

As shown in Figure 1, a filled loss cone at the top of the electron acceleration region that accompanies the aurora during a substorm cannot account for the aurora during substorm expansion, since the electron precipitation that is predicted for this model for the aurora turns out to be nearly an order of magnitude or more greater than the actual electron precipitation during a substorm, as recently discussed by Calvert [1998]. Moreover, as pointed out by Calvert and Hardy [1997], the observations of the auroral electrons that were detected by the Oedipus C rocket that was flown into the auroral zone during a substorm have also shown that the electric potential of the acceleration region does not increase significantly along the magnetic field lines on which the discrete aurora occurs, and that the energy of the electrons that cause discrete arcs also decreases significantly inside these arcs, presumably as a result of scattering into the loss cone inside the electron acceleration region.

Figure 1. Predicted electron precipitation flux and energy flux for a density of 1 electron/cm3 and a filled loss cone at the top of the electron acceleration region, where Wo is the initial electron energy at the top of the acceleration region [see Calvert, 1998].

The aurora during a substorm can therefore be attributed to a partially filled loss cone that is refilled as a result of scattering into the loss cone by the cyclotron maser instability, as previously suggested by Lennartsson [1976] and Calvert [1987]. As pointed out by Calvert [1995], the aurora during a substorm can then be accounted for by the electrons that are scattered into the loss cone inside local density depletions which are at first caused by an incoming wave, and then by the auroral kilometric radiation (AKR) that is emitted by wave feedback inside these density depletions.

This model for the aurora thereby also accounts for substorm expansion, since the AKR that is emitted along the magnetic field lines of one discrete arc should then be capable of triggering another discrete arc along an adjacent field line. This paper will discuss this new theory, and also present new observations that tend to illustrate the validity of this model for substorm expansion. Sections 2 and 3 will then be devoted to a brief summary for the explanation for discrete arcs, Sections 4 and 5 will discuss the new model for substorm expansion, Section 6 will discuss the observations that tend to support this theory, and Section 7 will discuss the implications of this theory to the other explanations for an auroral substorm.

2. Wave Feedback inside Local Density Depletions

As shown in Figure 2, the precipitation that causes the aurora during a substorm can be attributed to the electrons that are scattered into the loss cone by an X-mode wave that is being amplified by the cyclotron maser instability inside the auroral electron acceleration region. According to Wu and Lee [1979], Melrose et al. [1984], and Louarn et al. [1990], the energy for the cyclotron maser instability then comes from the perpendicular energy of the electrons that are scattered into the loss cone or into the trapping region that also occurs inside the acceleration region. For the electrons that are scattered into the loss cone to cause the aurora, this model therefore also accounts for the loss in energy that is found to occur inside discrete arcs by Calvert and Hardy [1997], where the loss in energy then reappears as the AKR that accompanies the aurora during a substorm.

Figure 2. Scattering into the loss cone by the cyclotron maser instability inside the electron acceleration region.

The discrete emission spectrum of AKR that has been reported by Gurnett and Anderson [1981] can then be accounted for as shown in Figure 3, as a result of closed-loop oscillations inside local density depletions that occur along the magnetic field lines on which the aurora occurs.

Figure 3. Wave feedback caused by wave reflections perpendicular to the magnetic field inside a local density depletion.

As shown in Figure 3, this model for AKR also accounts for discrete arcs, where the wave feedback that occurs inside these density depletions also causes the localized wave that is necessary in order to account for the thin structure of these arcs, as pointed out by Calvert [1995]. This wave feedback explanation for discrete arcs is also referred to as "radio lasing," since the wave field that develops inside these density depletions turns out to be identical to the wave field that develops inside an optical laser, as described in detail by Verdeyen [1981].

The density depletions in which the AKR occurs have also been detected by Hilgers [1992] and Hilgers et al. [1992]. See also Louarn et al. [1990]. Other details about this explanation for the discrete spectrum of AKR and the discrete structure of discrete arcs are also discussed by Calvert [1982, 1987, and 1997a].

3. Source of the Density Depletions that Cause Discrete Arcs during Substorm Expansion

As pointed out by Kennel and Petschek [1966], a wave instability that scatters electrons into the loss cone also reduces the density along the field lines on which the aurora occurs. As shown in Figure 4, because of the increased wave gain of the cyclotron maser instability at lower densities, the scattering into the loss cone that occurs along the field lines of a local density depletion also gradually enhances the density depletions in which it occurs.

Figure 4. Enhancement of local density depletions as a result of scattering into the loss cone by the cyclotron maser instability [see Calvert, 1995, Fig. 4].

The density depletions that account for discrete arcs can then be attributed to the gradual enhancement of random density depletions that convect inward from the tail of the magnetosphere, and the diffuse aurora prior to substorm expansion can also be attributed to scattering into the loss cone inside these initially-random density depletions. As a consequence, this model for the aurora therefore also accounts for the aurora that is found to occur before the onset of substorm expansion, as discussed by Calvert [1995].

4. Explanation for the Onset of Substorm Expansion

As pointed out by Akasofu [1964], more than thirty years ago, the aurora during a substorm usually begins as diffuse aurora that suddenly develops into discrete arcs at the onset of substorm expansion. This behavior can then be accounted for by the sudden onset of radio lasing inside local density depletions that are caused by the electron precipitation that causes the diffuse aurora prior to substorm expansion.

According to this theory, substorm onset can then be attributed to the incoming cosmic and solar radio noise that scatters electrons into the loss cone prior to substorm expansion. The time that it takes for this to occur, which can be calculated from the diffuse electron precipitation prior to substorm expansion and the density depletions that are required for radio lasing, turns out to be a half hour or more, depending upon the amplitude of the incoming radio noise that occurs prior to substorm expansion. As discussed by Calvert [1995], this model for the onset of substorm expansion therefore also accounts for the otherwise unexplained triggering of AKR by an incoming wave, as previously reported by Calvert [1981, 1985].

Figure 5. Latitudinal expansion of the aurora as a result of the AKR that is emitted by wave feedback inside previous density depletions along an adjacent field line.

5. Explanation for Substorm Expansion

As discussed by Akasofu [1964], substorm expansion then occurs because of the sudden brightening of additional discrete arcs along an adjacent field line. Although these arcs tend to move equatorward, presumably as a result of the cross-tail electric field in the near-Earth plasma sheet, the progressive latitudinal expansion of these new arcs also accounts for the well-known latitudinal expansion of the aurora during a substorm. The latitudinal expansion of the aurora during a substorm can then be explained as shown in Figure 5, in which the AKR that is emitted by one local density depletion also causes other density depletions along an adjacent field line. As shown in Figure 6, substorm expansion can therefore be attributed to a domino effect in which the AKR that causes discrete arcs also causes the latitudinal expansion of these arcs to higher and/or lower latitudes in the auroral zone during a substorm.

Figure 6. The gotcha-kata-kata or "domino theory of substorm expansion.

6. Observations of Diffuse Electron Precipitation during Substorm Expansion

This explanation for substorm expansion also predicts diffuse electron precipitation along an adjacent field line, as shown in Figure 7, in which the upper panel shows the electron energy spectrum of precipitating electrons that were detected by the Oedipus C rocket, and the lower panel shows the corresponding energy spectrum for mirroring electrons that are reflected back upward by the Earth's magnetic field. As discussed by Calvert and Hardy [1997], the electron precipitation of discrete arcs in the upper panel of this figure shows the loss in energy that is found to occur inside these arcs, whereas the lower panel also shows the corresponding lack of increase in the electric potential of the electron acceleration region. The diffuse electron precipitation that occurs outside these arcs in the upper panel is therefore found to occur at a latitudinal distance of approximately 7 to 18 km on the high-latitude side of these arcs, and the precipitation flux for this enhancement is also found to be in the range of 10⁷ to 10⁸ electrons /cm² sec, corresponding to the electron precipitation flux of the diffuse aurora prior to substorm expansion.

Figure 7. Oedipus C observations of electron precipitation outside discrete arcs during substorm expansion.

7. Discussion

As discussed at this meeting, an auroral substorm is usually attributed to the sudden dipolarization of the Earth's magnetic field, presumably as a result of a disruption of the cross-tail current by the current that causes the aurora during a substorm. This new theory, on the other hand, which accounts for all relevant aspects of the aurora during a substorm, can also account for the sudden onset and latitudinal expansion of the discrete aurora during substorm expansion.

Although the direction of substorm expansion is not specifically predicted by this model, it is interesting to note that this model can account for the latitudinal expansion to higher latitudes during a substorm, simply because the aurora begins at a relatively low latitude in the auroral zone, presumably because of the shorter electron bounce period and the shorter time that it takes to cause local density depletions at lower latitudes in the auroral zone.

Figure 1 proves that a filled loss cone cannot account for the aurora, whereas the new results of Calvert and Hardy [1997] have also shown that the discrete aurora during a substorm can be attributed to scattering into the loss cone inside the electron acceleration region. These studies therefore also tend to confirm that scattering into the loss cone by the cyclotron maser instability is the source of the electrons that cause the aurora during a substorm, as previously discussed by Calvert [1997b].

8. Conclusions

It has been found that the aurora during a substorm can be attributed to scattering into the loss cone inside local density depletions that are at first caused by an incoming wave, and then by the AKR that is generated by wave feedback inside these local density depletions. As a consequence, substorm expansion can then be attributed to a domino effect in which the AKR that is emitted along the magnetic field lines of one discrete arc also causes other discrete arcs along an adjacent field line. Since this result was first discussed in a series of lectures on the aurora that were published at Kyoto University during the summer of 1997, this theory will therefore be referred to as the "gotcha-kata- kata," or "domino" theory of substorm expansion, where "gotcha-kata-kata" is the sound that dominoes make in Japan [see Calvert, 1997a].

Acknowledgments. This work was supported in part by NASA contract NAS5-96020. The cute little man who is triggering the aurora in Figure 6 was provided courtesy of Corel Corporation, Ottawa, Ontario, Canada, and the sound of the aurora that is shown in this figure was suggested by Mrs. Mitsuko Abe of the Radio Atmospheric Science Center (RASC), at Kyoto University in Uji, Japan. Other useful discussions with Y. Omura, K. Hashimoto, and H. Matsumoto of RASC are also gratefully acknowledged.

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Correspondence: W. Calvert, 219 Friendship Street, Iowa City, Iowa, 52245, USA; email: calvert@fyiowa.infi.net.