Breakdown of the frozen-in condition in the Earth s magnetotail

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006ja012000, 2007 Breakdown of the frozen-in condition in the Earth s magnetotail A. T. Y. Lui, 1 Y. Zheng, 1 H. Rème, 2 M. W. Dunlop, 3 G. Gustafsson, 4 and C. J. Owen 5 Received 2 August 2006; revised 27 November 2006; accepted 6 December 2006; published 28 April [1] We investigate in detail the breakdown of the frozen-in condition detected by Cluster at the downstream distance of 19 R E in the midnight sector of the magnetotail during a substorm expansion on 22 August It is found that the breakdown occurred (1) in a low-density environment with moderate to large proton plasma flow and significant fluctuations in electric and magnetic fields, (2) in regions with predominantly dissipation but occasionally dynamo effect, and (3) at times simultaneously at two Cluster satellites separated by more than 1000 km in both X- and Z-directions. Evaluation of the terms in the generalized Ohm s law indicates that the anomalous resistivity contribution arising from field fluctuations during this event is the most significant, followed by the Hall, electron viscosity, and inertial contributions in descending order of importance. This result demonstrates for the first time from observations that anomalous resistivity from field fluctuations (implying kinetic instabilities) can play a substantial role in the breakdown of the frozen-in condition in the magnetotail during substorm expansions. Consideration of several observed features in the breakdown regions indicates that the breakdown occurs in a turbulent site resembling observed features found in current disruption and dipolarization sites. Citation: Lui, A. T. Y., Y. Zheng, H. Rème, M. W. Dunlop, G. Gustafsson, and C. J. Owen (2007), Breakdown of the frozen-in condition in the Earth s magnetotail, J. Geophys. Res., 112,, doi: /2006ja Introduction [2] There are four outstanding research topics in basic plasma physics that are interrelated. These are magnetic reconnection, current disruption, turbulence, and particle acceleration. All these topics involve energy transformation from one form to another via the breakdown of the frozen-in condition, which is a condition describing a tight coupling between the magnetic field and charged particles. The frozen-in condition is an intrinsic feature of the ideal magnetohydrodynamic (MHD) fluid concept first introduced by Alfvén [1942]. It implies that the magnetic flux through every surface remains constant [e.g., Lundin et al., 2005; Roth, 2003]. Any violation of this condition is connected with a transfer of energy, a key topic in space plasma research [e.g., Lundin, 1988]. [3] There are previous attempts to examine the breakdown of the frozen-in condition from data analysis of magnetospheric plasma measurements. For instance, on the basis of a fortuitous prolonged Polar observation of a magnetic reconnection separatrix region at the dayside 1 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 2 Centre d Etude Spatiale des Rayonnements, Toulouse, France. 3 Space Science and Technology Department, Rutherford Appleton Laboratory, Didcot, UK. 4 Swedish Institute of Space Physics, Uppsala Division, Uppsala, Sweden. 5 Mullard Space Science Laboratory, University College London, Dorking, UK. Copyright 2007 by the American Geophysical Union /07/2006JA magnetopause, Scudder et al. [2002] have determined the main factor for violation of the frozen-in condition for that event to be the electron pressure gradient from the offdiagonal terms of the electron pressure tensor, also known as electron viscosity. This observational result is consistent with some theoretical work on the force balance near an X- line [e.g., Sonnerup, 1988; Lyons and Pridmore-Brown, 1990] and several numerical simulation results [e.g., Cai et al., 1994; Cai and Lee, 1997]. Lundin et al. [2003, 2005] have described several means by which the breakdown may be detected, one of which is by the existence of plasma differential drift in multispecies (non-maxwellian) plasmas. They have found these features in the magnetospheric boundary layer and in the magnetosheath plasma transients. Mozer et al. [2002, 2003, 2005] have used Cluster electric field measurements to identify the breakdown region and have noted the electron diffusion region to exhibit large turbulent convective flows with enhanced counterstreaming electron fluxes. [4] Besides electron viscosity, anomalous resistivity has also been invoked to account for the required dissipation in collisionless reconnection. However, the nature of this anomalous resistivity remains to be an open unanswered question in magnetic reconnection research [e.g., Lui et al., 2005]. Recently, Drake et al. [2003] have performed threedimensional particle simulations of magnetic reconnection that show the development of turbulence driven by intense electron beams formed near the X-line and separatrices. The electron beams are produced from electric field acceleration along the X-line. The turbulence created by the electron beams, suggested by Drake et al. [2003] to arise from the Buneman instability, collapses into localized three- 1of15

2 amplitude and rapid fluctuations of electric and magnetic fields. The equation in SI units from first principle (i.e., from Maxwell s and Vlasov equations without introducing arbitrary parameters) can be written as [e.g., Yoon and Lui, 2006] E þ V B ¼ 1 dj e 0 w 2 pe dt þ J B ne rp e ne 1 ½ n hdedniþ h d ð nv eþdbiš; ð1þ Figure 1. The AU (upper) and AL (lower) indices on 22 August 2001 and the relative positions of four Cluster satellites in the XY- and YZ-planes in GSM coordinates. dimensional nonlinear structures with depleted electron densities. These structures seen in these simulations resemble the electron holes observed in the Earth s magnetosphere that are attributed to be products of magnetic reconnection [Cattell et al., 2005]. [5] Lui et al. [1991] have considered the cross-field current instability as the physical process for the turbulence in current disruption phenomenon in the magnetotail [Lui et al., 1988]. This kinetic instability causes the breakdown of the frozen-in condition. The resulting anomalous resistivity at the saturation stage of the instability evolution has been estimated to be very significant based on quasi-linear calculations [Lui et al., 1993; Yoon and Lui, 1993; Lui, 1996], which can provide the necessary collisionless dissipation needed for onset of magnetic reconnection [e.g., Ugai, 1994]. A 2 1/2-dimensional particle simulation has also been conducted to evaluate the full nonlinear consequences of the instability occurring in a thin current sheet with a thickness comparable to the ion inertial length [Lui, 2004]. The simulation result indicates the occurrence of localized regions within the thin current sheet of dissipation as well as dynamo effect, consistent with current disruption features seen in Cluster observations [Lui et al., 2006]. [6] The above brief overview of the existing literature on the possible cause for the violation of the frozen-in condition indicates that there is no general consensus on a unique cause in the breakdown. It is evident that the new capability of Cluster can help to advance our understanding of the physical process responsible for the breakdown at its natural setting in the Earth s magnetotail. Investigations of the frozen-in condition breakdown can be considered to be complementary to Cluster investigations of magnetic reconnection and substorm phenomena in the tail [e.g., Nakamura et al., 2002; Runov et al., 2003; Lui et al., 2006]. [7] To investigate all potential causes for the breakdown of the frozen-in condition, we consider the generalized Ohm s law for a collisionless plasma with inclusion of large where V is the ion bulk flow, e 0 is the permittivity of free space, w pe is the electron plasma frequency, J is the current density, n is the number density, e is the elementary electric charge, P e is the electron pressure tensor, V e is the electron bulk flow, and d in front of a quantity denotes the highfrequency fluctuations of the quantity. The breakdown in the frozen-in condition occurs when the right-hand side (RHS) of equation (1) is nonzero. The four terms on the RHS are often called inertial, Hall, electron viscosity, and anomalous resistivity, respectively. The anomalous resistivity term arises from field fluctuations associated with turbulence and can further be divided into two contributions, namely, from electric field fluctuations and from magnetic field fluctuations. It is a common practice to use the expression hj to represent the anomalous resistivity term, where h is a scalar resistivity. However, from the expression derived from first principle, the anomalous resistivity term is not necessarily parallel to J and a proper representation of the term calls for h to be a tensor [Yoon and Lui, 2006]. [8] In this paper we show the plasma environment during the intervals when Cluster in the magnetotail detected the breakdown of the frozen-in condition during a magnetospheric substorm on 22 August We use the comprehensive Cluster data set to evaluate the various terms of the generalized Ohm s law in two intervals with prominent differences between E and V B (cross-product of ion bulk flow and magnetic field) to determine the relative significance of each term in the frozen-in condition breakdown. We find that during these two intervals of breakdown, anomalous resistivity from field fluctuations is often more significant than all the other terms on the RHS of equation (1). The result implies that high-frequency wave activity can play a substantial role in the breakdown of the frozen-in condition in the magnetotail during substorm expansions. Furthermore, we also discuss from these observations the implications on the spatial extent of the breakdown region based on the simultaneous observations of the Cluster satellites. In addition, we consider the cause-effect relationship between field energy and particle energy based on the comparison of E and V B. 2. Observations 2.1. Substorm Activity [9] Figure 1 shows the ground magnetic activity on 22 August 2001 provided by the quick-look AU/AL indices that are constructed from 10 magnetic stations. The time interval of particular interest is UT marked by the highlighted interval in Figure 1. The AL index shows the strengthening of the auroral electrojet characteristic of 2of15

3 Figure 2. Overview of Cluster observations based on RUMBA (C1) measurements during the substorm on 22 August Dashed lines are used to show the parameters given on the right. All vector components are given in Geocentric Solar Ecliptic (GSE) coordinates. substorm expansion within this interval. The development of substorm expansion activity during this time is also verified by the global auroral imaging data from the IMAGE/FUV instrument [Mende et al., 2000], as reported by Lui et al. [2006]. Prominent low-frequency plasma sheet oscillations occurred during this interval and have been examined previously [Volwerk et al., 2003; Fruit et al., 2004; Louarn et al., 2004]. [10] The relative positions of the four Cluster satellites projected on the Geocentric Solar Magnetospheric (GSM) XY- and YZ-planes are shown in the bottom row of Figure 1. The four satellites labeled as C1, C2, C3, and C4 are called RUMBA, SALSA, SAMBA, and TANGO, respectively. The ion plasma measurements were taken by CIS (Cluster Ion Spectrometry) [Rème et al., 2001]. The proton plasma moments produced by the CODIF (Composition and Distribution Function Analyzer) of the CIS instrument are used here in this report. The electron plasma measurements were made by PEACE (Plasma Electron and Current Experiment) [Johnston et al., 1997]. The electric and magnetic field measurements were obtained by EFW (Electric Field and Wave) [Gustafsson et al., 1997] and FGM (Fluxgate Magnetometer) [Balogh et al., 2001], respectively Frozen-In Condition Breakdown During UT [11] During this period, Cluster was near its apogee in the magnetotail and the plasma environment encountered is 3of15

4 Figure 3. RUMBA (C1) observation of the frozen-in condition breakdown during UT. indicated in Figure 2 by measurements from Cluster spacecraft C1 (i.e., RUMBA). Shown from top to bottom are the number density, the proton temperature, the x- and y-components of the proton plasma flow, the y-components of the electric field and V B, thex- and y-components of the magnetic field, and the z-component of the magnetic field. Dashed lines are used to show the parameters given on the right side of these panels. Cluster crossed the neutral sheet from north to south, as indicated by the reversal from positive to negative values of the B x component. This north to south traversal is typical for Cluster satellites near their apogee. [12] For a closer look at the breakdown of the frozen-in condition, i.e., E 6¼ V B, we show in Figure 3 an interval for which the y-components of E and V B are compared together with the x- and z- components of the proton plasma bulk flow and the local magnetic field. The differential flux spectrogram from CIS/CODIF is also shown to indicate the spread in energy of the proton population. The spectrogram indicates that the breakdown of the frozen-in condition occurred in a low-density region where both the sub-kev ions (probably corresponding to ionospheric escaping ions injected into the plasma sheet) and the 1 kev ions (probably corresponding to the trapped plasma sheet component) were absent. As in Figure 2, only the y-component in the GSE coordinate is compared between E and V B, since E y is the most reliable component of the electric field from the EFW instrument. The error bars on the E y trace represent the standard error of the mean from the high-time resolution measurements of 4of15

5 Figure 4. High-time resolution electric field measurement from RUMBA (C1) to show the large variability during the breakdown of the frozen-in condition interval. EFW (25 samples/s). This high-time resolution measurement is shown for a 1-min interval ( UT) in Figure 4 to demonstrate its variability and transient huge magnitude, close to 200 mv/m. [13] For comparison between E y and (V B) y in Figure 3, one should bear in mind that the response time of V B is longer than that of E. Therefore short-duration spikes of E may not match well with that of V B. Furthermore, the offset of these two traces is not always zero because of the angular resolution of the CIS instrument. With these caveats in mind, one may still notice that there were significant deviations based on the trend/lower-envelopes of these traces for the interval UT. The arrows in the panel for E y and (V B) y are times when the difference between these two terms will be discussed further and the terms of equation (1) are tabulated. Bulk plasma flow was also found in the low-density frozen-in breakdown region. This region consists of moderate to high proton bulk flow component V x of km/s, reversals of the small V z component, noticeable reduction of the B x component, and enhancement of the B z component. The reduction of the B x component indicates that RUMBA entered deeper into the central plasma sheet with embedded large plasma flow V x. In addition, significant magnetic fluctuations are evident during the breakdown of the frozenin condition. The accompanying enhancement of the B z component and the presence of high-frequency magnetic fluctuations resemble magnetic turbulence seen in current disruption and dipolarization events [e.g., Lui et al., 1988]. [14] We can examine the corresponding measurements from another Cluster spacecraft C3 (i.e., SAMBA) for the same time interval, shown here in Figure 5. One may note from Figure 1 that SAMBA was tailward and southward of RUMBA by 1400 km in X GSM and 1300 km in Z GSM. The Y GSM coordinates for these two satellites were almost the same. The breakdown of the frozen-in condition is evident in the two intervals (0940: :45 UT and UT) by judging the differences in the trend/lower-envelopes of these two traces. Noticeable high-frequency magnetic fluctuations can be seen spanning these two intervals of the frozen-in condition breakdown, especially when the magnitude of the B x component was small, i.e., SAMBA was close to the neutral sheet. For the first interval, the proton flow component V x was moderate (500 km/s) to high (up to 1200 km/s). There were reversals in the V z component similar to that seen at RUMBA. [15] For the first breakdown interval at SAMBA, there are similar trends in the time evolutions of the B x and the B z components as at RUMBA, i.e., reduction in B x and enhancement in B z. One may note that the enhancement in the B z component occurred earlier at SAMBA than at RUMBA. Since SAMBA was closer to the neutral sheet than RUMBA based on the magnitude of the B x component and the subsequent neutral sheet crossing by SAMBA, this B z enhancement at an earlier time suggests that the current disruption and dipolarization signatures were seen first at location closer to the neutral sheet, consistent with the cause of current disruption originating close to the neutral sheet and subsequently spreading to the higher latitude of the plasma sheet. The possible interpretation of the observed time lag being due to the dipolarization spreading eastward can be eliminated since SAMBA and RUMBA had almost identical Y GSM coordinates. Furthermore, dipolarization spreading earthward can also be eliminated because dipolarization occurred nearly simultaneously at RUMBA and SALSA (C2), which had a separation distance of 1160 km in the X GSM coordinate as shown in Figure 1. The comparison of the B z component for these three satellites is shown in Figure 6. [16] In the second interval of the frozen-in condition breakdown at SAMBA, the measured E y was dawnward when SAMBA crossed the neutral sheet to the southern portion of the tail. Another noticeable feature is a transient bipolar B z signature from southward to northward near 0942:47 UT, which occurred in an earthward plasma flow environment. At nearly the same time but slightly later, a similar deflection in the B z component was detected at RUMBA even though the sign of the B z component did not change by the deflection (see Figure 6). This feature is consistent with an earthward moving magnetic flux rope since it was associated with earthward plasma flow and RUMBA, located earthward of SAMBA, observed the feature later than SAMBA. This flux rope is a low-density one. The interesting aspect is that SAMBA located closer to the neutral sheet detected the magnetic flux rope in a generally southward B z environment while RUMBA located further away from the neutral sheet detected the magnetic flux rope in a northward B z environment. 5of15

6 Figure 5. SAMBA (C3) observation of the frozen-in condition breakdown during UT. [17] There are two more points worth noting from the comparison of observations between SAMBA and RUMBA. There is an overlap in time ( UT) when both satellites showed the breakdown in the frozen-in condition. Since their separation in the X GSM coordinate was 1400 km and in the Z GSM coordinate was 1300 km, these simultaneous observations suggest that the spatial extent of the breakdown in the frozen-in condition can be more than 1000 km in both X- and Z-directions. Another significant feature is that the breakdown region appeared right after the disappearance of the sub-kev (ionospheric) ions and well before the energized ions suddenly appeared. This feature was found in observations from both satellites. Thus the breakdown region does not coincide with the region where ions are substantially energized. The ion diffusion region in magnetic reconnection is expected to energize ions. Therefore this feature suggests that the breakdown region is not the ion diffusion region in magnetic reconnection Frozen-In Condition Breakdown During UT [18] Figure 7 shows another interval of the breakdown in the frozen-in condition seen by RUMBA. The first interval centered around 0954:30 UT is rather brief but highly significant. The second interval is slightly longer at 0954: :50 UT. Both occurrences correspond to low-density like the interval examined in section 2.2. In these intervals, the corresponding proton flow components were moderate to large at km/s. In the first interval the B x component was rather large and so was the 6of15

7 Figure 6. Comparison of the dipolarization feature in the B z component seen by RUMBA (C1), SALSA (C2), and SAMBA (C3). B z component. High-frequency magnetic fluctuations in the B z component were seen. In the second interval, there were significant changes in both the B x and B z components. In particular, the B x component reversed sign rapidly at two very brief intervals from large positive values to small negative values. This behavior suggests that the current sheet was rather thin because of the short time span in sensing between large positive B x and small negative B x. Similarly, the B z component reversed sign also very briefly at several intervals. Again, these features resemble signatures in current disruption and dipolarization sites where current filamentation in turbulence cause rapid and large changes in the B x and B z components [see, e.g., Lui et al., 1988]. Similar to Figure 3, the arrows in the panel for E y and (V B) y are times when the difference between these two terms will be discussed further and the terms of equation (1) are tabulated. [19] The corresponding measurements by SAMBA for this period are shown in Figure 8. It can be seen that there are intermittent intervals where the frozen-in condition did not hold. The plasma behavior at SAMBA is similar to that at RUMBA, with moderate to large proton flow components, large changes in the B x and B z components. These features indicate both RUMBA and SAMBA were embedded in a turbulent region that is characteristic of current disruption and dipolarization. 3. Evaluation of Terms in the Generalized Ohm s Law 3.1. Contributing Parameters to the Frozen-In Condition Breakdown [20] The Cluster mission with its four satellites in a tetrahedron configuration is designed to have the capability of determining gradients in three dimensions as well as differentiating temporal from spatial variations. This new capability and its full suite of instruments enable us to perform evaluation of the terms in the generalized Ohm s law. For example, the current density J can be evaluated with the curlometer technique that has been examined for accuracy extensively [Dunlop et al., 1988; Chanteur, 1998; Chanteur and Harvey, 1998]. The Lorentz force J B can be calculated using the curlometer technique and the averaged magnetic field components. Unfortunately, no PEACE data were available at SAMBA during this interval, precluding the use of the standard procedure in Cluster tetrahedron constellation to estimate the divergence of the electron pressure tensor for the determination of electron viscosity. However, we note that for tail configuration, the variation along the x-axis is slower than that along the As a result, the dominant terms in (r. P e ) y eyy /@y eyz /@z terms and may be estimated based on the differences of the electron pressure tensor elements between RUMBA and SALSA. More eyy /@y (P eyy,2 P eyy,1 )/dy 21 eyz /@z (P eyz,2 P eyz,1 )/dz 21. The spatial differences between RUMBA and SALSA in y- and z-coordinates are denoted here by dy 21 and dz 21, respectively. [21] Figure 9 presents some of the parameters derived from the Cluster tetrahedron for the time interval of UT that are needed to evaluate the terms on the RHS of equation (1). The y-component of the current density was high and showed considerable fluctuations during the activity interval of UT. It was almost exclusively in the duskward direction for the two breakdown intervals. The y-component of the Lorentz force J B was mainly directed duskward also in these two intervals, although a reversal occurred in between. The electron pressure tensor element P eyy was considerably higher than P eyz for both RUMBA and SALSA, which is expected since P eyy is a diagonal tensor element. However, in terms of gradient, dp eyz /dz was higher than dp eyz /dy. Many reversals on the direction of these gradient force components can be seen in this activity interval Evaluation of the Nonideal MHD Terms [22] The anomalous resistivity term requires the calculation of the correlation terms shown in equation (1). The EFW instrument on Cluster can provide the high-frequency electric fluctuations. The FGM instrument on Cluster can provide the high-frequency magnetic fluctuations. The spacecraft potential measured by EFW can be used to determine the high-frequency fluctuation in the number density, as was done by Cattell et al. [2005] in obtaining the high-frequency fluctuations of the number density in their analysis of electron holes with Cluster measurements. The PEACE instrument on Cluster can provide the electron bulk flow measurements which are interpolated at the 7of15

8 Figure 7. RUMBA (C1) observation of the frozen-in condition breakdown during UT. sampling frequency of the EFW measurements to obtain d(nv e ). The running average used in the extraction of fluctuations is obtained with a time interval of 60 s, taking into account the oscillation period associated with the ballooning instability [e.g., Cheng and Lui, 1998; Chen et al., 2003]. [23] Since no PEACE data were available on SAMBA during this interval, the evaluation of terms in equation (1) can only be made on RUMBA. It is important to recognize also that some of these terms (E y and anomalous resistivity) are based on local quantities, while terms involving gradient calculation are volumetric quantities and represent the best estimate within the Cluster constellation volume. Therefore precise agreement on the sum of values from the RHS terms and that from the LHS terms is not expected. Nevertheless, a gross agreement is anticipated if values of these terms are approximately correct. [24] The values of these terms are shown in Figure 10 for the interval UT. Note that different scales are used in plotting these parameters. During the interval with significant deviations of E y from (V B) y, the Hall term and the anomalous resistivity term arising from electric fluctuations (E-resistivity) had significant values and their overall temporal profiles were quite similar to that of E y. The anomalous resistivity term arising from magnetic fluctuations (B-resistivity) was considerably weaker than these two terms and had sign reversal intermittently. The electron viscosity term was larger than the inertial term but had small values also in comparison with the Hall and anomalous E-resistivity terms generally. It also had negative 8of15

9 Figure 8. SAMBA (C3) observation of the frozen-in condition breakdown during UT. values intermittently, just like the B-resistivity term. The inertial term had the smallest contribution. Overall, in descending order of magnitude, we have E-Resistivity, Hall, electron viscosity/b-resistivity, and inertial. [25] Figure 11 shows the corresponding parameters for the interval UT. The overall features are similar. More specifically, the profiles of E y, Hall, and E-Resistivity terms are quite similar. The order of importance among these different terms is also essentially the same as in the previous interval. 4. Summary and Discussion [26] This study examines in detail the breakdown of the frozen-in condition in the Earth s magnetotail from Cluster observations during a substorm interval. Cluster was at the downstream distance of 19 R E in the midnight sector of the magnetotail. The breakdown occurred in a low-density environment with moderate to high ion bulk flow and significant fluctuations in electric and magnetic fields. The breakdown can sometimes be seen simultaneously by Cluster satellites separated in the X and Z coordinates by more than 1000 km apart, suggesting that the spatial extent of this breakdown region may exceed this dimension in both the X- and the Z-directions Magnitude of the Nonideal MHD Terms [27] Table 1 lists the values of these terms for several time instances in the unit of mv/m. Included in Table 1 are the sum of the terms on both sides of equation (1) for compar- 9of15

10 Figure 9. Some parameters related to the evaluation of terms in the generalized Ohm s law. ison. If we group the two contributions of anomalous resistivity together, then the values in Table 1 indicate terms in descending order of importance in general to be anomalous resistivity, Hall, electron viscosity, and inertial. In addition, the sum of terms on the RHS of equation (1) agrees amazingly well (most of them within a factor of two) with that on the LHS of equation (1), suggesting that the nonideal MHD terms are estimated to be about the right order of magnitude. [28] It is possible that the Hall and electron viscosity terms may be underestimated since the satellite separation distances are in the order of 1000 km. The Hall term can be underestimated through the curlometer procedure if intense current filaments with dimensions much less than 1000 km exist in the breakdown region. The electron viscosity term is expected to be important only near the electron diffusion region with dimension of 10 s km in the z-direction. Therefore the spatial separation for the Cluster constellation during these events may lead to a gross underestimate of the electron viscosity term. However, even when these two terms were underestimated, it does not diminish the fact that the combined anomalous resistivity term had significant values comparable to the sum of terms on the LHS of equation (1). In several time instances (e.g., 0942:16, 0942:40, 0942:56, 0943:36 UT), the sum of the RHS terms agrees so well with the sum of the LHS terms that no large unknown contribution is required. Therefore it is reasonable to state that the nonideal MHD terms are evaluated rather accurately at these times and that this evaluation shows the 10 of 15

11 Figure 10. Evaluation of terms in the generalized Ohm s law during UT at RUMBA (C1). anomalous resistivity playing a significant role in breaking the frozen-in condition Spatial Extent of the Breakdown Region [29] We may rearrange terms in equation (1) as E þ V e B ¼ 1 dj e 0 w 2 pe dt rp e ne 1 ½ n hdedniþ h d ð nv eþdbiš ð2þ by moving the Hall term to the LHS. In this form, one may examine whether the motion of electrons in the breakdown region remain tied to the motion of magnetic field lines, i.e., whether it is an electron diffusion region. If the sum of terms on the RHS of equation (2) is significant in comparison with the value on the LHS of equation (2), then the breakdown region is an electron diffusion region. [30] As we have noted earlier, the breakdown involves significant contribution from the anomalous resistivity term. Therefore the observed breakdown region is an electron diffusion region. The electron diffusion region in magnetic reconnection is expected to have a small spatial extent in the order of several kilometers [Mozer et al., 2005]. In addition, no large ion flow is expected in the electron diffusion region. Therefore the observed large spatial extension of the electron diffusion region (exceeding 1000 km in both the X- and the Z-directions) and the strong ion flow are incompatible with the expectations from magnetic reconnection. On the other hand, current disruption can occur within a spatial extent comparable to an ion inertial length in the order of 1000 km. Kinetic instabilities in the current disruption region can lead to electron diffusion and the Lorentz force due to current disruption can accelerate ions to large velocities. These are features of current disruption that are distinct from features 11 of 15

12 Figure 11. Evaluation of terms in the generalized Ohm s law during UT at RUMBA (C1). of magnetic reconnection. Therefore the observed breakdown in the frozen-in condition is quite consistent with the current disruption phenomenon. The overall features of the breakdown region are illustrated in Figure Energy Transformation [31] Lundin et al. [2005] pointed out an important aspect in the study of the frozen-in condition breakdown. They showed that if one considers the integral Z Z df rðvbþ ds; where is the magnetic flux through a surface, a negative d/dt based on the Faraday-Henry law implies induction and plasma forcing by, for example, electric currents inducing magnetic fields from the Ampere s law. Conversely, a positive d/dt implies magnetic field changes producing currents that lead to plasma acceleration. In the ð3þ differential form with the application of Faraday s law, the above consideration can be equated to a comparison of E and V B. We may also see the energy transformation by performing the dot product on both sides of equation (1) ( J ðe þ V BÞ ¼ J E 0 1 dj ¼ J e 0 w 2 pe dt rp e ne ) 1 ½ n hdedniþ h d ð nv eþdbiš : ð4þ The new variable E 0 denotes the electric field in the rest frame of the plasma. Notice the absence of the Hall term on the RHS of equation (4) because its dot product with J is zero, i.e., the Hall term is not a dissipative term. By noting that J y was persistently positive in the breakdown region (Figure 9), we find that if E y > (V B) y, then J y E y 0 >0, i.e., dissipation in the rest frame of the plasma. This implies that the electric and magnetic field energies are being 12 of 15

13 Figure 12. A schematic diagram to illustrate the electron diffusion region with spatial dimensions >1000 km in both the X- and Z-directions. The irregularities of the magnetic field lines in the electron diffusion region illustrate the high fluctuation nature of the magnetic field. The different symbol sizes of current density J y and electric field E y illustrate the different magnitude of these quantities, which have mostly positive values but occasionally negative values as well. The electron diffusion region is thus mostly dissipative but occasionally has dynamo effect in localized regions. converted to particle energy (motor). Conversely, when E y < (V B) y, particle energy is being converted to electric and magnetic field energies (dynamo). Therefore a comparison between E and V B would permit determination on the cause-effect relationship on the energy exchange between field and particle in the breakdown region. [32] Comparison between E y and (V B) y indicates that both situations can occur during the breakdown in the frozen-in condition. For instance, E y < (V B) y occurred during UT at SAMBA in Figure 5, one brief instance at 0954:52 UT at RUMBA in Figure 7, and several instances at SAMBA in Figure 8. From Figure 11, one may identify the E-resistivity and the Hall terms contribute to the condition E y < (V B) y. The negative value of resistivity from electric field fluctuations indicates that the anomalous resistivity term can occasionally become the dynamo, not always dissipative in nature. However, the more common situation for the breakdown is E y > (V B) y, i.e., electric and magnetic field energies are being converted to particle energy with particle acceleration and dissipation. The existence of both dissipation and dynamo effect in a turbulent region is consistent with the observation and simulation results of current disruption reported by Lui et al. [2006] Turbulence Versus X-Line [33] The overall plasma behavior in the breakdown region fits well with a medium with turbulence. In section 4.2 it is noted that the observed spatial extent of the breakdown region is incompatible with the electron diffusion region envisioned in the magnetic reconnection process. There are Table 1. Terms in the Generalized Ohm s Law During the Frozen-In Condition Breakdown Time E y (V B) y Hall Inertial e Viscosity E-Resistivity B-Resistivity LHS RHS 0942: : : : : : : of 15

14 some more difficulties in relating the breakdown region to a magnetic reconnection site. During the interval of breakdown, an earthward moving flux rope and intermittent large southward magnetic field were detected during earthward plasma flow. It is difficult to fit the large variability of the magnetic field observed (especially the coincidence of southward magnetic field and earthward ion bulk flow) during the breakdown to a well-defined magnetic field configuration expected from a magnetic reconnection site (e.g., Lin and Swift [1996], Ma and Bhattacharjee [2001], and articles on GEM reconnection challenge in the same issue of JGR). For magnetic reconnection, only northward magnetic field is expected to accompany earthward plasma flow. In other words, it is evident that the plasma flow is not ordered by the magnetic field geometry envisioned in the magnetic reconnection process. Furthermore, on the basis of the plasma environment observed by SAMBA during UT, dawnward directed electric field was seen by SAMBA, whereas for magnetic reconnection in the magnetotail, only duskward directed electric field is anticipated. In addition, the plasma environment during a reversal of plasma flow in this same interval of activity was examined in detail by Lui et al. [2006]. During the plasma flow reversal interval, it is found that (1) there was no clear quadrupole Hall current system signature organized by the flow reversal time, (2) the x-component of the Lorentz force did not change sign while the other two did, (3) the timing sequence of flow reversal from the Cluster configuration did not match tailward motion of a single plasma flow source, (4) the electric field was occasionally dawnward, producing a dynamo effect, and (5) the electric field was occasionally larger at the high-latitude plasma sheet than near the neutral sheet. It is unlikely that the introduction of multiple remote X-lines could alter the intrinsic local characteristics of an X- line to the point that these observed features would be matched. Therefore these departures from the magnetic reconnection picture suggest that the breakdown region is more appropriately interpreted as a turbulent region expected from current disruption and dipolarization than the ion and/or electron diffusion region in a simple picture of a magnetic reconnection site. However, turbulence may provide dissipation in a collisionless plasma to initiate turbulent magnetic reconnection. In this case, it is unclear whether turbulence or magnetic reconnection is the main driver of the plasma dynamics. [34] Acknowledgments. This work was supported by the NASA grant NNG04G128G and NSF grant ATM to the Johns Hopkins University Applied Physics Laboratory. [35] Zuyin Pu thanks Rickard Lundin and another reviewer for their assistance in evaluating this paper. 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