We propose that the dipolarization in the near-Earth plasma sheet at the substorm expansion onset during prolonged southward interplanetary magnetic field (IMF) can be triggered internally by the Harang discontinuity developed during substorm growth phase.

Intensification of the Harang discontinuity is caused by the nonuniform Hall and Pedersen conductances in the ionosphere. During prolonged southward IMF, Hall and Pedersen conductances should increase due to enhancemeant of plasma pressure in the near-Earth plasma sheet during the substorm growth phase.

The Harang discontinuity is the zonal distortion of enhanced convection in the midnight sector originated in the ionosphere. The enhanced zonal convection produced by the Harang discontinuity in the ionosphere results in a whiplash to cause rapid azimuthal convection in the near-Earth plasma sheet (~6-10 Re).

The resulting rapid azimuthal convection in the near-Earth plasma sheet leads to a local reduction of plasma pressure to allow the magnetic tension to snap earthward, causing rapid piling up of magnetic flux. This is proposed to be the direct cause of dipolarization in the near-Earth plasma sheet at the substorm expansion onset.

The Harang discontinuity originated in one hemisphere can cause dipolarization in the near-Earth plasma sheet to result in substorm expansion onset in both hemispheres with different intensities.

Figure 1  Harang discontinuity originated in the ionosphere leads to a whiplash of rapid azimuthal convection in the near-Earth plasma sheet

An example of the inter-relationships of IMF Bz, AE and Dst indeces is summarized in Figure 2 (personal communication, Akasofu, 1998). This data set shows that substorms occur during prolonged southward IMF.

On the other hand, enahnced convection in the near-Earth plasma sheet prior to the onset of storm and substorm can contribute to the nonuniform ionospheric Hall and Pedersen conductances to intensify the Harang discontinuity that triggers the substorm expansion onset.

The proposed substorm-storm relationship can be summarized as follows:

• During prolonged southward IMF, substorms can be triggered by the pre-storm enhancement of ionospheric Hall and Pedersen conductances required to intensify the Harang discontinuity during the growth phase of substorms.
  
  
• Only the most intense substorms with AE > ~1000 nT can cause injection of plasma into within ~6-7 Re radial distance to produce storm-time ring current of Dst > ~50 nT.

Growth Phase of Substorms:

(1) Southward Turning of the IMF

• Following southward turning of the IMF, dayside magnetic reconnection leads to enhanced tailward convection of open field lines over the polar cap and enhanced sunward convection of closed field lines in the magnetosphere and the plasma sheet.
  

(2) Thinning of the Near-Earth Plasma Sheet

• Plasma sheet thinning occurs in the near-Earth plasma sheet due to nonuniform sunward convection in the thinning region that removes more closed field lines on the earthward side than is supplied on the tailward side (Kan, 1990). This is consistent with the Vela satellite results that show no increase of the plasma density or plasma pressure in the thinned plasma sheet (Hones et al., 1971) as shown in Figure 3:

Figure 3. After Hones et al. [1971].  Four possibilities if plasma distribution during thinning. Either (b) or (d) appears to be the actual change.

• In this regard, the plasma sheet thinning has more to do with the evacuation of plasma due to non-uniform enhancemeant of sunward convection in the near-Earth plasma sheet than with the compression from the tail lobes.
  
  
• Sunward convection of closed field lines was enhanced on the dayside due to southward turning of the IMF. The enhanced sunward convection propagated toward the near-earth plasma sheet. When the enhanced sunward convection reaches the earthward side of the near-earth plasma sheet, it removed more closed field lines from the region than is supplied from the tailwardside causing the near-earth plasma sheet to thin down. This has been proposed as the thinning process in the near-Earth plasma sheet [Kan, 1990].
  
  This idea of plasma sheet thinning has been simulated recently by Otto and Hall to show that the entropy constraint makes it impossible for the midtail convection to replenish the magnetic flux evacuated by the enhanced sunward convection in the near-Earth plasma sheet during the growth phase.
  

(3) Brightening of the Equatorward-Most Auroral Arc

• Brightening of the equatorward-most arc at T = 0 was chosen as the onset of substorm by Akasofu [1964].
  
  
• The M-I coupling model [Kan and Sun, 1996] showed that enahnced global convection and nonuniform ionospheric Hall and Pedersen conductances can lead to the development of Harang discontinuity and the brightening of discrete auroral forms during the growth phase of substorm. But cannot produce the intensity of the auroral electrojets and the field-aligned currents as observed during the substorm expansion phase.
  
  
• The substorm expansion onset requires an intense localized electric field in the midnight sector. Such an intense localized electric field can only be produced by dipolarization of magnetic field in the near-Earth plasma sheet.

(4) Plasma Pressure Enhancement Within ~6-7 Re in the Near-Earth Plasma Sheet

• The plasma pressure is proposed to increase around L = 7 during the initial phase of a geomagnetic storm. It extends earthward during the main phase of a storm as the ring current intensifies as shown in Figure 4.

Figure 4. After Frank [1967]. Proton (200 eV < E < 50 keV) energy densities as functions of L at the geomagnetic equator during two moderate geomagnetic storms on June 25 and July 9, 1967. The energy density profile for June 23 is the typical quiet-time signature

(5) Intensification of the Harang discontinuity in the ionosphere during the substorm growth phase

• The Hall and Pedersen conductances are enhanced due to enhanced diffuse auroral precipitations associated with pre-storm and pre-substorm enhancement of plasma pressure in the near-Earth plasma sheet.
  
  
• Intensification of the Harang discontinuity in the ionosphere depends on the nonuniformity of and the ratio of Hall to Pedersen conductances. The poleward boundary of the enhanced diffuse auroral conductance in the midnight sector appears to be the favorable location to intensify the Harang discontinuity during the substorm growth phase.

Substorm Expansion Phase:

(6) Substorm Expansion Onset Caused Directly by Dipolarization in the Near-Earth Plasma Sheet

• The direct cause of substorm expansion onset is the dipolarization in the near-Earth plasma sheet (~6-10 Re) [Kan, 1998; Vasyliunas, 1998]. The rate of dipolarization leading to the substorm expansion onset was quantified by Kan [1998].
  
  
• The direct cause of dipolarization in the near-Earth plasma sheet is proposed to be the whiplash of rapid azimuthal convection driven by the zonal flow produced by the Harang discontinuity in the ionosphere.
  
  Whiplash speed can be supersonic. A well known example of whip speed is that of a bullwhip. The hand moves left-right rapidly at subsonic speed, but the tip of the whip can reach supersonic speed to generate cracking sound of shock waves. The right-left motion transmitted along the whip is at the rope speed which depends on the tension on the rope. The MHD speed is equivalent to the rope speed. The whiplash speed is equivalent to the supersonic speed to generate shock waves. The whiplash speed can be much greater than the MHD speed.
  
  
• Explosive thinning [Ohtani et al., 1992] can be considered as an integral part of the dipolarization process. The local pressure reduction created by the whiplash leads to the explosive thinning followed immediately by dipolarization in the near-Earth plasma sheet.
  
  
• The rapid azimuthal convection in the near-Earth plasma sheet reduces the plasma pressure to allow the magnetic tension to snap earthward to result in pileup of field lines, known as dipolarization in the near-Earth plasma sheet.
  
  
• The intense dipolarization electric field launches Alfven waves from the near-Earth plasma sheet toward the ionosphere to develop the substorm current wedge, the substorm electrojects and the expansion of bright auroras during the substorm expansion phase.  
  
  
• The Harang discontinuity is proposed to trigger the dipolarization process in the near-Earth plasma sheet to initiate the substorm expansion onset. However, complicated nonlinear plasma dynamics must come into play to complete the dipolarization process. This was discussed by Kan [1998] and updated as shown in Figure 5.
  

• The rate of dipolarization is the rate of flux pileup in near-Earth plasma sheet. The dipolarization rate has been estimated to be greater than ~3 (mV/m)/Re at the substorm expansion onset [Kan, 1998]:

• The flow speed ~30 Re radial distance in the plasma sheet is observed to be ~1000 km/s. If Bz ~ 1 nT, the electric field Ey ~1 mV/m. This information will be included in the electric field profile shown in Figure 6.
  
  
• A snapshot of dipolarizing electric field profile in the near-Earth plasma sheet leading to the substorm expansion onset:

Figure 6.   Snapshots of the evolving electric field profile during dipolarization in the near-Earth plasma sheet leading to the substorm onset. The dipolarizing region is labeled D; the thinning region is labeled T.

• The time between the initiation of dipolarization triggered by the braking of enhanced sunward convection (profile in red) to the substorm expansion onset at t = To (profile in blue) is of the order of 20 seconds as estimated from observational data [Ohtani et al., 1992].
  
  

• Sunward convection should be enhanced earthward of the plasma sheet thinning region during the grwoth phase [Kan, 1990].
  
  
• Sunward convection in the near-Earth plasma sheet should be reduced leading to dipolarization prior to the substorm expansion onset.  Thus, the equatorward convection in the midnight sector can be expected to be reduced just before the substorm expansion onset.
  
  
• Ionospheric conductance in the diffuse auroral region should be enhanced during prolonged southward IMF prior to the substorm expansion onset.
  
  
• The rate of dipolarization at substorm expansion onset has been quantified to be greater than ~3 (mV/m)/Re [Kan, 1998]. This is based on the dipolarization theory that the sunward convection is enhanced on the earthward side of the thinning region and the dipolarization is caused by braking of the enhanced sunward convection when the ring current is enahced to a certain level during prolonged southward IMF.

Akasofu, S.-I., and S. Chapman, J. Geophys. Res., 66, 1321, 1961.

Frank, L. A., On the extraterristrial ring current during geomagnetic storms, J. Geophys. Res., 72, 3753, 1967.

Hones, E. W., Jr.,Asbridge J. R., and Bame, S. J., J. Geophys. Res., 76, 4402, 1971.

Kan, J. R., Geophys. Res. Lett., 17, 2309, 1990.

Kan, J. R., and W. Sun, J. G. R., 101, 27,271, 1996.

Kan, J. R., J. Geophys. Res., 103, 11,787, 1998.

Ohtani, S., K. Takahashi, L. J. Zametti, T. A. Potemra, and R. W. McEntire, J. Geophys. Res., 97, 19,311, 1992.

Vasyliunas, V. M., Theoretical considerations on where a substorm begins, Proceedings of ICS-4, Terra Scientific Publishing Co./Kluwer Academic Publishers, 1998.

Question (Vytenis Vasyliunas):

A question about your web poster: "As the plasma sheet thins down, the normal component of the magnetic field decreases and the sunward convection of closed field lines speeds up."

Why do you say "the sunward convection of closed field lines speeds up"? I am aware of no particular observational evidence for this, and it certainly is not expected theoretically, quite the contrary: there has to be a reason why the sunward convection is non-uniform, and I think the most likely explanation is that sunward convection, enhanced elsewhere, is impeded by the thin plasma sheet.

To me that is THE question about substorm expansion onset: what is it that does produce the enhanced sunward flow that then piles up to make dipolarization?

Answer (Joe Kan):

I agree with your comment and revised the text in the third bullet under (2):

Sunward convection of closed field lines was enhanced on the dayside due to southward turning of the IMF. The enhanced sunward convection propagated toward the near-earth plasma sheet. When the enhanced sunward convection reaches the earthward side of the near-earth plasma sheet, it removed more closed field lines from the region than is supplied from the tailwardside causing the near-earth plasma sheet to thin down. This has been proposed as the thinning process in the near-Earth plasma sheet (Kan, 1990).

My line of reasoning suggests that the line-tying effect caused by enhanced diffuse auroral conductance in the ionosphere should contribute to the braking of the sunward convection during prolonged southward IMF, leading to dipolarization in the near-Earth plasma sheet at the substorm expansion onset.

Do you know of any observational evidence that lends support to this prediction?

Answer (Gang Lu):

The best conductance data source that we have is the Polar UVI images, from which auroral condutances are derived. But we do not distinguish between diffuse an discrete auroral conductances in AMIE.

I am not sure what are the exact features of line-tying effect in the ionoshere. But we do see systemetic changes in conductances (as shown by the UVI emissions), convection and field-aligned currents. But since the AMIE time resolution is limited by the input data resolution (for UVI-derived conductances, they are usually in 3-min time resolution and ground magnetometers are in 1-min resolution), it may be difficult for us to distinguish what such changes occur before or after the dipolarization based on AMIE patterns. I can bring one event study to the workshop to you there.

Question (Joe Kan):

Do Superdarn electric field data (or other large-scale electric field data measured in the ionosphere) support the prediction that the convection in the midnight sector is enhanced prior to substorm expansion onset, reduced just before onset and much enhanced after the substorm expansion onset?

Answer (Bill Bristow):

After a southward turning of the IMF, convection is enhanced throughout the high-latitude regions. Enhanced convection leads to the formation of the Harang discontinuity. After some period of time, there is an additional
enhancement of velocity that is observed on the night side apparently poleward of the Harang discontinuity. The enhancements have been observed starting about 5 to 20 minutes prior to substorm expansion onsets. Very
close to the time of expansion onset, the velocity magnitude decreases substantially and the Harang discontinuity disappears. After expansion, the convection seems to be strongly influenced by localized regions of auroral
brightness. Velocities are lower in regions of brightness. It often appears that the plasma tends to flow around bright regions. This leads to localized vortices as would be expected for localized field-aligned currents.

Slides 25-30, and 44, of the presentation (Bristow's Web poster) best illustrate these observations. Perhaps the next time you are in the GI, you could stop by and look over my notebooks of plots. If there are some plots that you want, I would be happy to get them for you.