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GEOPHYSICAL RESEARCH LETTERS, VOL. 37, L09105, doi:10.1029/2010GL043128, 2010
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Why do equatorial ionospheric bubbles stop rising? J. Krall,1 J. D. Huba,1 S. L. Ossakow,2 and G. Joyce3 Received 3 March 2010; accepted 5 April 2010; published 11 May 2010.
[1] The Naval Research Laboratory (NRL) three‐dimensional simulation code SAMI3/ESF is used to study the long time evolution of equatorial spread F (ESF) bubbles. The ESF bubbles are modeled until they stop rising and become “fossils,” with results analyzed to address previously‐untested hypotheses. Specifically, it has been suggested that bubbles stop rising when either the local electron density inside the bubble is equal to that of the nearby background or the flux‐ tube‐integrated electron density inside the bubble is equal to that of the nearby background. It is shown that equatorial bubbles stop rising when the magnetic flux‐tube‐integrated ion mass density inside the bubble equals that of the surrounding background ionosphere. In the case of a single‐ ion ionosphere this reduces to the condition that the flux‐ tube‐integrated electron densities are in balance, consistent with the hypothesis of Mendillo et al. (2005). Citation: Krall, J., J. D. Huba, S. L. Ossakow, and G. Joyce (2010), Why do equatorial ionospheric bubbles stop rising?, Geophys. Res. Lett., 37, L09105, doi:10.1029/2010GL043128.
1. Introduction [2] Equatorial spread F (ESF) [Haerendel, 1974; Ossakow, 1981; Kelley, 1989; Hysell, 2000] is a post‐sunset phenomenon in which the equatorial F‐region ionosphere becomes unstable: large‐scale (10s km) electron density ‘bubbles’ can develop and rise to high altitudes (≳1000 km). Despite being first observed over 70 years ago [Booker and Wells, 1938] and the subject of intense research for the past 35 years, the underlying physical processes that control the nonlinear evolution of ESF are only now being discovered. For example, we now know that strong upward E × B drifts within an ESF bubble lead to a “super fountain effect” within the bubble [Huba et al., 2008, 2009a] creating density crests [Krall et al., 2010] and unique temperature signatures [Huba et al., 2009b]. [3] Bubbles that cease their upward motion have been referred to as “fossil” bubbles (or “fossil” plumes or “fossil” patches) [Argo and Kelley, 1986; Mendillo et al., 1992; Schunk and Sojka, 1996; Makela, 2006; Sekar et al., 2007]. These fossilized bubbles tend to be observed later in the evening and often last until dawn [Makela, 2004; Pautet et al., 2009]. [4] A long‐standing question has been: Why do equatorial plasma bubbles stop rising? It was initially thought that bubbles would rise until the electron density inside the bubble equaled that of the surrounding background electron 1
Plasma Physics Division, Naval Research Laboratory, Washington, DC, USA. 2 Berkeley Research Associates, Beltsville, Maryland, USA. 3 Icarus Research, Inc., Bethesda, Maryland, USA. Copyright 2010 by the American Geophysical Union. 0094‐8276/10/2010GL043128
density in the equatorial ionosphere (a buoyancy argument) [Ott, 1978; Ossakow and Chaturvedi, 1978]. More recently, Mendillo et al. [2005] argued that upward motion halts when the flux‐tube‐integrated electron densities inside and outside of the bubble are in balance to explain the observation of high altitude bubbles. The origin of the latter hypothesis lies in the fact that geomagnetic field lines are equipotentials for the scale sizes of interest. As a result, the electrodynamics is non‐local leading to growth rates that are dependent on the vertical gradient of the flux‐tube‐integrated electron density [Sultan, 1996] rather than the local electron density. We have previously shown that these integrated growth rates are in reasonable agreement with simulations [Krall et al., 2009a]. [5] In this letter we report the results of the first long time, three dimensional simulations of ESF bubbles that follow their evolution until they stop rising, i.e., become fossilized. We find that ESF bubbles stop rising when the upward E × B drifts at the upper edge of the bubble fall to zero: this corresponds to the condition that the flux‐tube‐integrated ion mass density just inside the bubble is equal to that of the adjacent background. In the case of a single‐ion ionosphere this reduces to the condition that the flux‐tube‐integrated electron densities are in balance, consistent with the hypothesis of Mendillo et al. [2005].
2. The SAMI3/ESF Model [6] In this study we use the Naval Research Laboratory SAMI3/ESF code [Huba et al., 2008], which is based on the SAMI2 (Sami2 is Another Model of the Ionosphere) ionosphere code [Huba et al., 2000]. The 2D potential equation used in this study is based on current conservation (r · J = 0) [Huba et al., 2008] and is similar to that derived by Haerendel et al. [1992]: @ @ @ @ @Fg pp þ p ¼ @p @p @ @ @
ð1Þ
R where Fg = (rEsin3/D)(B0/c)sHcgp ds. Here, dipole coordinates (q, p, ) are used, F is the electrostatic potential, gp is the component of gravity perpendicular to B, sP is the Pedersen conductivity, Hc ¼
X ni ec i
1 2 = 2 B i 1 þ in i
ð2Þ
is the ion component of the P Hall conductivity divided R P by the ion cyclotron frequency, pp = (pD/bs)sP ds, p = R (1/pbsD)sP ds, D = (1 + 3 cos2 )1/2, Wi = eB/mic, n in is the ion‐neutral collision frequency, B is the local geomagnetic field, B0 is the geomagnetic field at the equator, is the latitude, bs = (r3E/r3)D, rE is the radius of the earth, and field‐line integrations with respect to coordinate s are
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Figure 1. Contours of (left to right) the electron density (log10 ne), flux‐tube averaged electron density (log10hnei), flux‐ tube averaged ion mass density (log10hr/mO+i), flux‐tube‐integrated driving gravity term (log10hFgi), and the electrostatic potential, in the equatorial plane at times 00:05 LT and 03:02 LT. Number densities for ne, hnei, and hr/mO+i, are in units of cm−3 and correspond to the color‐bar scale.
along the entire field line, with the base of the field lines being at 85 km. Equation (1) has been simplified by neglecting Hall‐conductance terms relative to Pedersen‐ conductance terms on the LHS of equation (1), neglecting ∂/∂p terms relative to ∂/∂ terms on the RHS, and by setting the zonal and meridional winds to zero. Examples of the potential equation without these simplifications are given by Krall et al. [2009b] and, in the context of the SAMI3 code, by Huba et al. [2010]. [7] The source term that is retained on the RHS of equation (1) is Fg which “drives” the growth of ESF bubbles. Using equation (2), this driving term can be rewritten as Z Fg ¼
rE sin3 gp cB0 X ni mi ds 2 B 1 þ in2 = 2i i
ð3Þ
RP In the limit n 2in W2i , Fg / i ri ds where ri = nimi is the ion mass density. Thus, to lowest order, the driving term is proportional to the flux‐tube‐integrated ion mass density.
3. Results [8] The 3D SAMI3/ESF model uses a grid with magnetic apex heights from 90 km to 2400 km, and a longitudinal width of 4° (e.g., ’460 km). The grid size is (nz, nf, nl) = (101, 202, 96) where nz is the number grid points along the magnetic field, nf the number in “altitude,” and nl the number in longitude. This grid has a resolution of ∼10 km × 5 km in altitude and longitude in the magnetic equatorial plane. The grid is periodic in longitude. We use a non‐tilted dipole field, so magnetic latitude and geographic latitude are the same, centered at geographic longitude 0°, so universal and local time are the same. The geophysical parameters are F10.7 = 75, F10.7A = 75, Ap = 4 and day‐of‐year 80. As in previous SAMI3/ESF studies, the simulation is initialized using a SAMI2‐simulated ionosphere at a time after the F layer has been raised by the pre‐reversal enhancement [e.g., Huba et al., 2008]. A seed density perturbation is imposed at t = 0 to initiate ESF. We use a Gaussian‐like perturbation
with a peak ion density perturbation of 15% centered at longitude 0° and altitude z = 320 km and vertical and horizontal half‐widths of about 60 km. [9] In Figure 1 we present contours of the electron density (log10 ne), flux‐tube averaged electron density (log10hnei), flux‐tube averaged ion mass density (log10hr/mO+i), flux‐ tube‐integrated driving gravity term (log10 Fg), and the electrostatic potential, in the equatorial plane. Flux‐tube averaged quantities are denoted by angle brackets and are the flux‐tube‐integrated quantities divided by the length of the magnetic field line. The ion mass density is normalized to the O+ mass. The top panels are near midnight at time 00:05 LT (roughly 4 hrs after the start of the simulation) and the bottom panels are three hours later at time 03:02 LT. As is common in ESF simulations, we see that the seeded bubble at longitude 0° has a narrow “stem” in the dense F layer leading up to a wider “head” in the lower density at high altitudes. Near midnight (00:05 LT) the entire bubble is active, with both ne and hnei having values lower than corresponding background values. Additionally, both hr/mO+i and hFgi have values lower than corresponding background values. At this time there is a large electrostatic potential that produces a large, upward drift of the plasma which causes the bubble to rise. [10] At 03:02 LT, the local electron density ne in the bubble (at an altitude ∼ 1200–1600 km) is depleted at the equator; however, the other flux‐tube averaged quantities (hnei, hr/mO+i, and hFgi) have values approaching those of the evolving background ionosphere. A contour line for the value of the parameters at the top of the bubble has been added in the bottom contour plots to highlight the longitudinal variation of the parameters. The driving term in the potential equation (RHS of equation (1)) depends on a derivative in the ‐direction (i.e, longitude). Thus, when the contours of Fg are uniform in the driving term approaches zero and the potential is reduced accordingly. The associated electric field that drives the bubble rise becomes very small and the bubble stops rising. This is apparent in the bottom panel at an altitude ∼ 1500 km: Fg is
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Figure 2. Contour plots of log10(ne) as well as the O+ ion velocity vectors at longitude 0° (i.e., center of the bubble), and times 00:05 LT and 03:02 LT. Velocity vectors indicate the direction and speed away from the dot. almost uniform in longitude and the potential becomes small and more uniform. The contours of hnei and hr/mO+i also become more uniform in longitude; the integrated ion mass density is somewhat more uniform than the integrated electron density which is consistent with the definition of Fg. [11] In Figure 2 we show contour plots of log10(ne) as well as the O+ ion velocity vectors at longitude 0° (i.e., center of the bubble), at times 00:05 LT and 03:02 LT. (Note: The velocity vectors indicate the flow away from the dot). In the top panel (t = 00:05 LT) the bubble has risen to an altitude ∼1400 km at the equator; it is extended in latitude over the entire range shown ±22° albeit at lower altitudes. At this time the bubble is still rising. A ‘super fountain’ [Huba et al., 2009a] is also apparent from the O+ velocity vectors: the maximum upward velocity at the equator is ∼500 m/s while the maximum velocity along the geomagnetic field line is ∼1500 m/s. The development of the bubble along the entire flux tube displaces the high density plasma of the ionization crests (at ∼±15°) with lower density plasma [e.g., see Huba et al., 2008, Figure 2]. This causes a reduction in plasma pressure that leads to the high velocity plasma flows down the magnetic field lines. [12] The bottom panel of Figure 2 shows the electron density and velocity vectors at time 03:02 LT. At this time the bubble has reached an altitude ∼ 1500 km and has stopped rising. Moreover, the electron density is significantly reduced in the altitude range 1000–1500 km; this is associated with the plasma “falling” to lower altitudes along the geomagnetic field because of the plasma flows shown in the top panel (at the earlier time). A high density plasma is reestablished for latitudes ≳±10° and plasma flows are substantially reduced. This also leads to the increase of the flux‐tube averaged quantities, in particular the flux‐tube averaged ion mass density (log10hr/mO+i), shown in Figure 1. Thus, a fossilized bubble has formed: a high‐ altitude region of reduced electron density that is not rising. [13] Figure 3 provides further information on the temporal evolution of the ESF bubble. Shown are contour plots of the E × B velocity and electron density as a function of local time (hrs) and altitude (km) at longitude 0°. Although the
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vertical E × B velocity associated with the instability starts at ∼21:30 LT, it does not become large (i.e., 500 m/s) until ∼22:15 LT; at this time it has an impact on the plasma density leading to the development of the upwelling plasma bubble as seen in the bottom panel. The large upward velocity at the top of the bubble slows significantly at time 23:30 LT (altitude ∼ 1200 km). At time ∼ 00:30 LT the upward velocity becomes very small (i.e., ∼10 m/s) and the height of the bubble approaches an asymptotic value of about 1600 km. Also at this time the electron density in the altitude range 1200–1600 km becomes very small because of the ‘drainage’ of the plasma to lower altitudes. [14] A key result is that, as observed, the bubble persists for hours after it has stopped rising (t > 0100 LT). In comparing these results to observations [e.g., Tsunoda, 1981] we acknowledge that the idealizations of a single‐ bubble perturbation and zero wind lead to a maximum bubble height of 1600 km which is unusual for such low values of the F10.7 and F10.7A indices. Additional simulations, not shown, indicate that the maximum bubble height is reduced for nonzero winds or in cases where multiple bubbles are seeded. For small perturbations we also find that simulated growth tends to occur at later times than actual ESF growth for the same conditions. This suggests that ESF growth begins even as the F layer is being raised by the electric field of the pre‐reversal enhancement, a global‐scale effect that is necessarily absent in SAMI3/ESF. To properly address this, simulations of ESF must be carried out in the context of a global ionosphere code that includes self‐
Figure 3. Contour plots of the E × B velocity and electron density as a function of local time (hrs) and altitude (km) at longitude 0°.
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consistent solutions of the potential on the global and local scales. Such simulations are currently under development.
4. Discussion [15] We have presented the first three‐dimensional study of the long‐time evolution of ESF bubbles to answer the question, why do ESF bubbles stop rising? We find that ESF bubbles cease rising when the upward E × B drifts at the upper edge of the bubble fall to zero; this corresponds to the condition that the flux‐tube‐integrated ion mass density just inside the upper edge of the bubble is equal to that of the adjacent background. In the case of a single‐ion ionosphere this reduces to the condition that the flux‐tube‐integrated electron densities are in balance, consistent with the hypothesis of Mendillo et al. [2005]. This result can be understood by examining the drivingR term P for the instability in the potential equation (1): Fg / i ri where ri = nimi is the ion mass density in the limit n 2in W2i . Thus, to lowest order, the driving term is proportional to the flux‐tube‐ integrated ion mass density. [16] Figure 3 shows that the bubble continues to evolve after 0100 UT, when upward motion has largely ceased. The importance of flux‐tube‐integrated quantities is illustrated by the fact that the local “buoyancy” of the bubble at its apex continues to increase after the bubble stops; this additional local buoyancy has no effect on the motion of the bubble. In other simulations performed with differing initial or ambient conditions (not shown in this Letter) we find that upward motion ceases when hri at the upward edge of the ESF plume is approximately equal to that of the adjacent background. This condition is represented in all cases as is the tendency of ESF plumes to continue to evolve to form various “fossil” configurations after upward motion has halted. [17] Acknowledgments. This work was supported by the Office of Naval Research and NASA.
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Huba, J. D., G. Joyce, and J. Krall (2008), Three‐dimensional equatorial spread F modeling, Geophys. Res. Lett., 35, L10102, doi:10.1029/ 2008GL033509. Huba, J. D., J. Krall, and G. Joyce (2009a), Atomic and molecular ion dynamics during equatorial spread F, Geophys. Res. Lett., 36, L10106, doi:10.1029/2009GL037675. Huba, J. D., G. Joyce, J. Krall, and J. Fedder (2009b), Ion and electron temperature evolution during equatorial spread F, Geophys. Res. Lett., 36, L15102, doi:10.1029/2009GL038872. Huba, J. D., G. Joyce, J. Krall, C. L. Siefring, and P. A. Bernhardt (2010), Self‐consistent modeling of equatorial dawn density depletions with SAMI3, Geophys. Res. Lett., 37, L03104, doi:10.1029/2009GL041492. Hysell, D. L. (2000), An overview and synthesis of plasma irregularities in equatorial spread F, J. Atmos. Sol. Terr. Phys., 62, 1037. Kelley, M. C. (1989), The Earth’s Ionosphere, Academic, San Diego, Calif. Krall, J., J. D. Huba, G. Joyce, and S. T. Zalesak (2009a), Three‐dimensional simulation of equatorial spread F with meridional wind effects, Ann. Geophys., 27, 1821. Krall, J., J. D. Huba, and C. R. Martinis (2009b), Three‐dimensional modeling of equatorial spread F airglow enhancements, Geophys. Res. Lett., 36, L10103, doi:10.1029/2009GL038441. Krall, J., J. D. Huba, G. Joyce, and T. Yokoyama (2010), Density enhancements associated with equatorial spread F, Ann. Geophys., 28, 327. Makela, J. (2004), Analysis of the seasonal variations of equatorial plasma bubble occurrence observed from Haleakala, Hawaii, Ann. Geophys., 22, 3109. Makela, J. (2006), A review of imaging low‐latitude ionospheric irregularity processes, J. Atmos. Sol. Terr. Phys., 68, 1441. Mendillo, M., J. Baumgardner, X. Pi, P. Sultan, and R. Tsunoda (1992), Onset conditions for equatorial spread F, J. Geophys. Res., 97, 13,865. Mendillo, M., E. Zesta, S. Shodham, P. J. Sultan, R. Doe, Y. Sahai, and J. Baumgardner (2005), Observations and modeling of the coupled latitude‐altitude patterns of equatorial plasma depletions, J. Geophys. Res., 110, A09303, doi:10.1029/2005JA011157. Ossakow, S. L. (1981), Spread F theories: A review, J. Atmos. Terr. Phys., 43, 437. Ossakow, S. L., and P.K. Chaturvedi (1978), Morphological studies of rising equatorial spread F bubbles, J. Geophys. Res., 83, 2085. Ott, E. (1978), Theory of Rayleigh‐Taylor bubbles in the equatorial ionosphere, J. Geophys. Res., 83, 2066. Pautet, P.‐D., M. J. Taylor, N. P. Chapagain, H. Takahashi, A. F. Medeiros, F. T. Sao Sabbas, and D. C. Fritts (2009), Simultaneous observations of equatorial F‐region plasma depletions over Brazil during spread‐F experiment (SpreadFEx), Ann. Geophys., 27, 2371. Schunk, R. W., and J. J. Sojka (1996), Ionosphere‐thermosphere space weather issues, J. Atmos. Terr. Phys., 58, 1527. Sekar, R., D. Chakrabarty, S. Sarkhel, A. K. Patra, C. V. Devasia, and M. C. Kelley (2007), Identification of active fossil bubbles based on coordinated VHF radar and airglow measurements, Ann. Geophys., 25, 2099. Sultan, P. J. (1996), Linear theory and modeling of the Rayleigh‐Taylor instability leading to the occurrence of equatorial spread F, J. Geophys. Res., 101, 875. Tsunoda, R. T. (1981), Time evolution and dynamics of equatorial backscatter plumes 1: Growth phase, J. Geophys. Res., 86, 139. J. D. Huba and J. Krall, Naval Research Laboratory, Code 6790, Washington, DC 20375‐5000, USA. (
[email protected]) G. Joyce, Icarus Research, Inc., PO Box 30780, Bethesda, MD 20824‐ 0780, USA. S. L. Ossakow, Berkeley Research Associates, 6551 Mid Cities Ave., Beltsville, MD 20705‐1434, USA.
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