N. A. Kurazhkovskaya and B. I. Klain
Geophysical Observatory Borok, Institute of Physics of the Earth, Borok, Yaroslavskaya Region, Russia
Studies of the long-period irregular geomagnetic pulsations of the ipcl type (irregular pulsations, continuous, long) observed in the regions of the polar cap and dayside cusp had already begun in the 1970s [Bol'shakova et al., 1974; Troitskaya et al., 1973]. During subsequent decades, many publications appeared in Russia and abroad whose goal was to study the ipcl morphology and to analyze their possible excitation mechanisms. However, there is still no consensus regarding the nature of these pulsations and physical conditions for their generation.
Bol'shakova and Troitskaya  drew attention to the fact, that during changes of the interplanetary magnetic field (IMF) from southward to northward there may occur singular intense ipcl bursts. Processing multiyear observations of the magnetic field in the Mirny Observatory ( -77o magnetic latitude (MLAT)), we discovered that observed under moderate geomagnetic activity are not singular bursts of the ipcl pulsations but series of bursts which demonstrate morphological features different from the characteristics of the usual ipcl regime and in no way are related to orientation changes of IMF. What is more, not only the bursts within a particular series but also the occurrence of the series themselves have no relation to the above changes. The morphological features of the series of ipcl bursts detected in our studies differ principally by their structure and dynamics from the singular bursts considered by Bol'shakova and Troitskaya .
The goal of this paper is to study the main morphological characteristics of the ipcl burst series and their relationship to geomagnetic disturbance and solar wind parameters and to reveal physical conditions and mechanisms for ipcl burst formation.
We used the Mirny Observatory (F = -77o MLAT) magnetograms with 90 mm h -1 scanning within the 2.1- to 5.5-mHz frequency band and the J. H. King catalog data [King, 1986]. For the period from 1981 to 1986 we selected about 50 ipcl burst series. We chose the events whose H component burst amplitudes exceeded the background by 6-10 times and were, on average, 20-40 nT. Each series lasted for 2-8 hours. Each series involved 3-8 bursts. The average length of an individual burst was 30-35 min. The burst repetition period was 20-25 min. The average burst-filling frequency was 4.1-5.5 mHz. As the data analysis showed, all events under consideration were observed at moderate geomagnetic activity (Kp 2-3, Bx > 0, By < 0, Bz > 0 ) near noon (0800-1600 magnetic local time (MLT)). It follows from the statistical analysis of the dayside cusp dynamics under various levels of geomagnetic activity, orientation, and magnitude of IMF that the statistical mean position of the cusp in the southern hemisphere corresponds to geomagnetic latitudes of 72o-80 o [Candidi et al., 1989; Newell et al., 1989].
It follows from the aforesaid and the geographic location of the Mirny Observatory that around noon under Kp 2-3 this observatory is located under the region of the dayside cusp projection. Presented below are the results of the studies of the principal characteristics of the most representative ipcl bursts in the H component of the magnetic field registered in the region of the polar cusp.
Figure 1 shows a typical example of the ipcl burst series in the H component revealed from the Mirny Observatory (F = -77o) data obtained April 1, 1986, at 0512-1030 UT. As Figure 1 shows, the bursts are quasi-periodic structures arising against the noise background. It is characteristic that no ipcl burst structures are observed neither under magnetic disturbance increase ( Kp > 3 ) nor under conditions of quiet magnetosphere ( Kp < 2 ).
The diurnal ipcl burst distribution with the local geomagnetic time exhibits two maxima at 0900 and 1300 MLT. Earlier and later the probability of the burst occurrence decreases by an order of magnitude. The two maxima in the distribution of the ipcl burst generation probability with local geomagnetic time are, apparently, connected with the Mirny Observatory crossing the dayside polar cusp boundaries and with the processes in the near-boundary segments of the cusp. As Zanetty et al.  reported, the cusp boundaries are characterized by a pronounced inhomogeneity in the particle density and by intense field-aligned currents which cause the wave turbulence in the cusp.
Now consider the interplanetary conditions for generation of the ipcl burst series. Using the hourly data from the catalog of King , we constructed the distributions of the solar wind velocity V, plasma density n, field modulus B, dynamic solar wind pressure rV2, IMF components Bx, By, and Bz, and latitude q and longitude j of the IMF vector in the solar-ecliptic frame of reference. The histograms obtained showed that as a rule, series of ipcl bursts are generated under V 400-500 km s -1, n 5-10 cm -3, B 6-8 nT, and rV2 (3-4) 10-8 dyn cm -2. Analysis of the Bx, By, and Bz IMF components shows that in more than 60% of the cases the ipcl bursts are observed in the positive direction of the radial component, the negative direction of the azimuthal component, and the northward direction of the vertical component of the IMF (Bx > 0, By < 0, Bz > 0). Estimates of angles characterizing the IMF orientation show that the ipcl burst series are observed predominantly within the latitude range q 0o-30o and the longitude range j 310o-320o, i.e., when the IMF is directed sunward in the ecliptic plane. The combination of empiric distributions of interplanetary medium parameters demonstrates the moderateness of the magnetospheric disturbance, which serves as a background for the ipcl burst series. Since ipcl bursts are observed at the dayside cusp latitude predominantly at Kp 2-3, Bz > 0, By < 0, and Bx > 0, the generation of the ipcl bursts is not, apparently, related to the IMF southward rotation, and thus it is not related to a development of the impulse reconnection at the dayside magnetopause. Parker  and Vainshtein  showed that the necessary conditions for the latter are high magnetic activity, southward direction of the IMF vertical component (Bz < 0), By > 0, and Bx < 0.
As a principal characteristic of the bursts, their duration t was chosen which is determined as follows: An envelope of the burst amplitude was found for each burst series. The duration of each particular burst was evaluated at the 0.7 level of the maximum amplitude of the burst.
Figure 2a demonstrates a histogram of the ipcl burst lengths. We can see that t ranges from 10 to 100 min. A specific feature of this distribution is a long tail at large t. The distribution of the burst lengths has a maximum at low t and decreases algebraically at large t. In other words, the distribution function of t is rather distinctive, which gives us an opportunity to identify the ipcl burst series observed with modes given by the theoretical concepts.
Figure 1 shows that the ipcl burst series are signals in which in a random way alternate weakly disturbed oscillations and periodical bursts. Such behavior of the signal is typical for the transition to chaos through alternating. Transitions from the chaotic regime to the quasi-periodic regime as well as from chaotic regime (1) to chaotic regime (2) may be observed. The transition to chaos through alternating leads to formation, in the phase space, of the system considered to be of a chaotic attractor [Grebogi et al., 1987]. It is known [e.g., Berzhe et al., 1991] that there exist two types of alternating, each having its own peculiarities.
The classification of transitions to chaos through alternating in three burst types (I, II, and III) is based on three types of linear instabilities of periodical trajectories [Berzhe et al., 1991]. Each type of alternating corresponds to quite definite distribution of the burst duration near the alternating threshold. Evidently, the ipcl burst series registered at Mirny may be considered as an intermediate regime of transition from one chaotic regime to another chaotic regime, the transition occurring though alternating. This means that the signal observed is interrupted by alternating bursts (see Figure 1). Under magnetospheric condition changes the number of bursts increases until the regime becomes completely chaotic (we see this under Kp > 3 ). According to the visual picture of the ipcl pulsation burst series and the typical distribution function of the burst duration (see Figures 1 and 2a) the ipcl burst series have a property of transition to chaos through the alternating of type III. Actually, the burst duration distribution (see Figure 2a) may be identified with the duration distribution of usual periodical oscillations near the alternating threshold typical to alternating of type III according to the classification of Berzhe et al. . Comparison of the experimental data with theoretical calculations confirms this assumption. According to Berzhe et al.  the burst number normalized to the total amount of cases N with the duration t t0 should meet the condition
where P(t) is the probability of burst duration observation, e is a governing parameter, and t0 is the shortest burst duration.
The function N is entirely governed by the e value. Figure 2b shows the comparison between the solutions of (1) and experimental data. We obtained the experimental curve (circles) from the histogram in Figure 2a by summing up the likelihoods of ipcl burst length observations. The theoretical curve (solid line) was obtained from (1). The relation (1) fits best the observations at e = 0.014. The standard deviation is s 0.08. Therefore the experimental distribution of the ipcl burst lengths is in a rather good agreement with the distribution inherent to the type III intermittence. It is worth noting that in the case of other alternating types (I, II) the burst duration distribution is ruled by other laws [Berzhe et al., 1991].
On the other hand, according to Grebogi et al. , in the vicinity of the critical transitions, the following relation must be true for the intermittence modes:
where p is any parameter which characterizes the system, pc is the critical value of the parameter under which the system transits from one regime to another, and g is the critical power index. Herein p - pc e, where e is the governing parameter from (1). In our case the role of parameter p may be played by the frequency of the filling of bursts ( f ). Analyzing the relation between the burst duration and the frequency of the filling of bursts, we found a relation between t and f similar to (2). Figure 3 shows the average ipcl burst length versus the average burst-filling frequency. Each circle in Figure 3 corresponds to an individual ipcl burst series. The analysis was performed for ipcl burst series having the average burst filling frequency of 2.1-4.2 mHz. When f > 4.2 mHz, the shape of the t (f) dependence changes. Figure 3 shows that in this frequency band, t decreases inversely to f. The function (2) fits the dependence t (f) adequately. The solid line shows the theoretical dependence of t on f. The value of the critical power index g was evaluated by the least squares method and was found equal to about 0.5. This means that the mean burst duration diverges as e-0.5 (f - fc)-0.5 when approaching the alternating threshold.
According to theoretical concepts the critical power index for the type III intermittent processes is expected to be g 0.66. We can see that g found from experimental data for the ipcl burst series agrees with the theoretical critical exponent [Berzhe et al., 1991].
Thus the qualitative behavior of the functions N = N(t > t0) and t = t (f) leads to the conclusion that ipcl pulsation burst series are an alternating process. Such processes have universal properties, are detected in numerous experiments, and in nature are related to the transition to turbulence. Since the ipcl burst series, registered at the cusp latitudes, demonstrate characteristic properties typical for a transition to chaos through alternating, probably ground observations of such series are a manifestation of the turbulence development dynamics in the cusp.
We studied further the relation between the average duration of the ipcl pulsation bursts and the parameters of the solar wind and interplanetary magnetic field such as n, V, rV2, B, Bx, By, and Bz components. The burst duration t was found to depend on the IMF modulus (Figure 4). The dependence of t on B is based on the ipcl burst series for which there were data on IMF in the King  catalog. Each point in Figure 4 corresponds to a particular burst series. The IMF modulus was averaged for several hours of burst series observations. Within each ipcl burst series the IMF modulus changed only slightly, so the standard deviation did not exceed 10% of the mean values of B.
Figure 4 shows that when B increases, the burst length decreases by ~3 times. When B reaches a certain critical value ( B = 7 nT), the character of t (B) dependence changes. When the field modulus increases further, t also increases, and at B > 9 nT, the ipcl bursts are not observed.
Thus the t dependence on B obtained experimentally leads to an assumption that the destruction of the burst structure begins at B> 7 nT and only a ipcl homogeneous background exists under further increase of the IMF modulus. In other words, when B reaches its critical value, there occurs a destruction of the attractor of the ipcl pulsation vibrational process (a crisis according to the terminology of Grebogi et al. ). It should be noted that we detected no dependence of the burst mean duration on other parameters of the solar wind and IMF.
There are at least two approaches to the problem of excitation of long-period irregular pulsations of the ipcl type. For example, based on the analysis of the homogeneous regime of the ipcl irregular pulsation generation (the regime appears under a change of the IMF vertical component from the northward to southward), Bol'shakova and Troitskaya  suggested that the pulse reconnection is a cause of ipcl. A different approach was considered by Friis-Christensen et al.  and McHenry et al. . Using the observations of ipcl pulsations at the Greenland chain of observatories, they showed that ipcl excitation is accompanied by traveling vortices of convection in the ionosphere. It should be noted that occurrence of both the pulse reconnection and the ionospheric vortices is related to formation of the field-aligned current tubes, their behavior depending significantly on the character of the solar wind flowing around the magnetosphere.
As the analysis of the ipcl burst series characteristics and of the interplanetary medium conditions for generation of the ipcl bursts shows that the generation of the ipcl quasi-periodic bursts at the dayside cusp latitude does not agree with the impulse reconnection model. We obtained a number of experimental facts demonstrating that the ipcl burst series are the intermittent processes. Moreover, under Bz > 0, By < 0 ipcl pulsations burst series are observed in the cusp region of the southern hemisphere magnetosphere. It is widely known that under these conditions there exists an intense system of field-aligned currents in the polar cusp. Thus the fact that the ipcl generation is related to the large-scale field-aligned currents is a common feature for all the ipcl regimes observed.
Naturally, a question arises whether it is possible to construct directly a model with a finite number of degrees of freedom which can simulate adequately the qualitative aspects of the described turbulence structuring derived from the ipcl pulsation observations. According to Volkov and Zubarev , a generation of large-scale vortex-like structures, which are described by the model analogous to the Lorentz model, is possible in the current-containing plasma-like medium. The processes in which a transfer to chaos through alternating are related to such models [Berzhe et al., 1991]. Taking into account the results of this paper and those of Volkov and Zubarev , one is able to understand at a qualitative level the mechanism of ipcl burst generation. Most likely, the ipcl temporal structures are associated with the polar cusp vortex current structures whose randomization causes the observed effects.
The main results of this paper are as follows:
1. Using the observations at the Mirny Station, ipcl pulsation burst series, which have some specific properties not typical for the usual ipcl regime, are detected and studied.
2. It is demonstrated that the ipcl burst series are not related to the IMF reversal and are observed at moderate geomagnetic activity within the 0008-1600 MLT interval which corresponds to the passage over Mirny of the dayside cusp projection.
3. We found that the burst length distribution agrees well with the theoretical distribution for the systems in which the transition to chaos goes on by way of the type III intermittence.
4. We revealed the existence of a critical value of the IMF intensity modulus at which the burst structures are destroyed.
5. We assumed that the ipcl burst series observed at the dayside polar cusp latitude are induced by stochastic processes of large-scale current vortex structures.
Berzhe, P., I. Pomo, and K. Vidal', Order in Chaos (in Russian), 367 pp., Mir, Moscow, 1991.
Bol'shakova, O. V., and V. A. Troitskaya, Impulse reconnection as a possible source of ipcl pulsations, Geomagn. Aeron. (in Russian), 22 (5), 877, 1982.
Bol'shakova, O. V., I. N. Men'shutina, and M. I. Pudovkin, Relationship of the high-latitude dayside geomagnetic field pulsations with periods of 5-10 min to the solar wind parameters, Antarktika (in Russian), 13, 5, 1974.
Candidi, M., et al., Evidence of influence of the interplanetary magnetic field azimuthal component on polar cusp configuration, J. Geophys. Res., 94 (A10), 13,585, 1989.
Friis-Christensen, E., et al., Irregular magnetic pulsations in the polar cleft caused by travelling ionospheric convection vortices, Adv. Space Res., 8 (9-10), 9311, 1988.
Grebogi, C., et al., Critical exponents for crisis-induced intermittency, Phys. Rev. A, 36 (11), 36, 1987.
King, J. H., Interplanetary Medium Data Book, Suppl. 3, 1977-1985, World Data Cent. A for Rockets and Satellites, Greenbelt, Md., 1986.
McHenry, M. A., C. R. Clauer, and E. Friis-Christensen, Relationship of solar wind parameters to continuous, dayside high-latitude traveling ionospheric convection vortices, J. Geophys. Res., 95 (A9), 15,007, 1990.
Newell, P. T., et al., Some low-altitude cusp dependencies on the interplanetary field, J. Geophys. Res., 94 (A7), 8921, 1989.
Parker, E. N., Cosmic Magnetic Fields, Clarendon, Oxford, England, 1979.
Sandholt, P. E., et al., Large- and small-scale dynamics of the polar cusp, J. Geophys. Res., 90 (5), 4407, 1985.
Troitskaya, V. A., O. V. Bol'shakova, and V. B. Hessler, Irregular geomagnetic pulsations in the polar cap, Rep. Assem. IAGA, Int. Assoc. of Geomagn. and Aeron., Rockville, Md., 1973.
Vainshtein, C. I., Magnetic Hydrodynamics of Space Plasma and Current Layers (in Russian), 192 pp., Nauka, Moscow, 1985.
Volkov, N. B., and N. M. Zubarev, A model for initial phase of a laminar-turbulent transition within the current-bearing plasma-type medium, Zh. Eksp. Teor. Fiz. (in Russian), 107 (6), 1868, 1995.
Zanetty, L. J., et al., Magnetic-field-aligned electron distribution in the dayside cusp, J. Geophys. Res., 86, 8957, 1981.