Non-adiabatic Ion Acceleration in the Earth Magnetotail and Its Various Manifestations in the Plasma Sheet Boundary Layer

Transcription

1 Space Sci Rev (2011) 164: DOI /s Non-adiabatic Ion Acceleration in the Earth Magnetotail and Its Various Manifestations in the Plasma Sheet Boundary Layer E.E. Grigorenko L.M. Zelenyi M.S. Dolgonosov A.V. Artemiev C.J. Owen J.-A. Sauvaud M. Hoshino M. Hirai Received: 27 August 2011 / Accepted: 11 November 2011 / Published online: 3 December 2011 Springer Science+Business Media B.V Abstract Many physical phenomena in space involve energy dissipation which generally leads to charged particle acceleration, often up to very high energies. In the Earth magnetosphere energy accumulation and release occur in the magnetotail, namely in its Current Sheet (CS). The kinetic analysis of non-adiabatic ion trajectories in the CS region with finite but positive normal component of the magnetic field demonstrated that this region is essentially non-uniform in terms of scattering characteristics of ion orbits and contains spatially localized, well-separated sites of enhanced and reduced chaotization. The latter represent sources from which accelerated and energy-collimated ions are ejected into Plasma Sheet E.E. Grigorenko ( ) L.M. Zelenyi M.S. Dolgonosov A.V. Artemiev Space Research Institute of RAS (IKI), Moscow, Russia elenagrigorenko2003@yahoo.com L.M. Zelenyi lzelenyi@iki.rssi.ru M.S. Dolgonosov cactus@iki.rssi.ru A.V. Artemiev Ante0226@yandex.ru C.J. Owen Mullard Space Science Laboratory, University College, London, UK cjo@mssl.ucl.ac.uk J.-A. Sauvaud IRAP/CNRS, Toulouse, France sauvaud@cesr.fr M. Hoshino M. Hirai University of Tokyo, Tokyo, Japan M. Hoshino hoshino@eps.s.u-tokyo.ac.jp M. Hirai hirai@eps.s.u-tokyo.ac.jp

2 134 E.E. Grigorenko et al. Boundary Layer (PSBL) and stream towards the Earth. Numerical simulations performed as part of a Large-Scale Kinetic Model have shown the multiplet ion structure of the PSBL is formed by a set of ion beams (beamlets) localized both in physical and velocity space. This structure of the PSBL is quite different from the one produced by CS acceleration near a magnetic reconnection region in which more energetic ion beams are generated with a broad range of parallel velocities. Multi-point Cluster observations in the magnetotail PSBL not only showed that non-adiabatic ion acceleration occurs on closed magnetic field lines with at least two CS sources operating simultaneously, but also allowed an estimation of their spatial and temporal characteristics. In this paper we discuss and compare the PSBL manifestations of both mechanisms of CS particle acceleration: one based on the peculiar properties of non-adiabatic ion trajectories which operates on closed magnetic field lines and the other representing the well-explored mechanism of particle acceleration during the course of magnetic reconnection. We show that these two mechanisms supplement each other and the first operates mostly during quiescent magnetotail periods. Keywords Earth Magnetotail Plasma acceleration Beamlets Current Sheet Magnetic reconnection 1 Introduction 1.1 Brief Introduction to Ion Non-adiabatic Acceleration in the Magnetotail Current Sheet (CS) Since its discovery in the middle of 1960s (Ness 1965), the magnetotail has been considered as one of the most complicated and intriguing regions of the Earth s magnetosphere. It forms on the nightside of the Earth due to the antisunward stretching of geomagnetic field lines by the solar wind (Fig. 1). The magnetotail is a very dynamic entity in which energy coming into the magnetosphere from the solar wind is accumulated and then released, often in an explosive manner. The most impressive energy dissipation occurs during the course of substorms. However, the state of the magnetotail during geomagnetically quiet periods, which may last up to a few days, is also interesting, important and not well understood. How the magnetotail can sustain an equilibrium state during such long quiet periods and how the solar wind energy is transformed during these time intervals are still key points to be understood in space plasma physics. Even before the dawn of spacecraft measurements of the magnetotail, reconnection of magnetic field lines was considered likely to be the main process responsible not only for the magnetosphere formation, but also for moderating the energy circulation and plasma acceleration (Dungey 1961; Levy et al. 1964). Subsequently, fluxes of accelerated plasma streaming with velocities up to several hundreds km/s have been observed in different regions of the magnetotail: in the Central Plasma Sheet (CPS) (e.g. Angelopoulos et al. 1992), in the Plasma Sheet (PS) (e.g. Baumjohann et al. 1990) and in the Plasma Sheet Boundary Layer (PSBL) (e.g. DeCoster and Frank 1979; Parks et al. 1998). The latter was considered as the main channel of mass and energy transport, connecting the distant part of the magnetotail with near-earth space (Eastman et al. 1984). The origin of effective plasma acceleration in the geomagnetic tail inspired numerous theoretical studies and numerical modeling. It was obvious that powerful acceleration could occur in regions where charged particle motion became unmagnetized and the particles could be directly accelerated by the potential and/or inductive electric fields. The potential quasisteady dawn-dusk electric field is generated by various types of interaction between the solar

3 Non-adiabatic Ion Acceleration in the Earth Magnetotail 135 Fig. 1 Cut of the Earth s magnetotail in (XZ) GSM plane wind and magnetosphere (e.g. the viscous mode suggested by Axford and Hines 1961 and/or magnetic merging suggested by Dungey 1961). Its typical values in the magnetotail are of the order of mv/m (e.g. Kivelson and Russell 1995). Inductive electric fields may appear due to rapid magnetic X-line formation (Zelenyi et al. 1990b) or in course of the current disruption process (Lui 1996; Lutsenko et al. 2008). Hoshino et al. (1998) reported the generation of dawn-dusk electric field with amplitude several mv/m in magnetic reconnection region. Such field can accelerate ions to the observed energies (up to hundreds kev). Magnetic turbulence developing in the vicinity of the magnetic reconnection region could also become a source of inductive electric fields. Its role in ion acceleration was discussed in detail by Milovanov and Zelenyi (2001) and Artemyev et al. (2009). Finally, large electrostatic oscillations arising near the reconnection region could also contribute to the acceleration of non-adiabatic particles (Hoshino et al. 2000). The common paradigm was that ion acceleration regions should be located in the CS near the magnetic null points formed in the course of reconnection of the magnetic field lines (Amano and Tsuda 1978; Martin and Speiser 1988). As a result, high-velocity plasma flows and beams are injected from the reconnection region into the CPS and PSBL (Hoshino et al. 1998). Signatures of magnetic reconnection, with evidence of an X-line topology, were observed by various space missions both in the near-earth PSBL and in the distant tail (e.g. Nishida et al. 1996; Fujimoto et al. 2001; Nagai et al. 2001; Runovetal.2003; Nakamura et al. 2004a; Alexeev et al. 2005). Crossing of the separatrix region between still open lobe magnetic field lines and those already reconnected is clearly observed in electron velocity distribution functions, which change from being anisotropic along the magnetic field direction (i.e. consisting from the counterstreaming cold and hot (up to a few kev) electron beams), to an almost isotropic nature (Fujimoto et al. 2001; Nakamura et al. 2004a). Simultaneously with the appearance of such electrons, energetic field-aligned ion beams with a large energy spread in the field-parallel direction ( V /V > 0.3) andenergiesupto hundreds of kev are detected (Grigorenko et al. 2009). However, the possibility of ion non-adiabatic acceleration in regions where the normal component of the magnetic field, B Z, has a finite constant, or slowly-varying, positive value was also considered in some theoretical works (e.g., Lyons and Speiser 1982; Speiser and Lyons 1984; Büchner and Zelenyi 1988; Zelenyi et al. 1988; Ashour-Abdalla et al. 1993, 2005). In the latter case, it was suggested that the magnetotail has a stretched magnetic

4 136 E.E. Grigorenko et al. configuration with the X-line located in its distant part (at X< 100 R E ). This leads to a wide region of finite positive B Z in the distant CS earthward from the X-line, where ions could be nonadiabatically accelerated. In such cases, ion acceleration takes place in the regions of closed magnetic field lines on which electrons are still magnetized and isotropic. Ion motion in the CS, with its sharply bent magnetic field lines, is very different from the standard guiding center drift motion typical of a magnetized plasma. The particle gyroradii (ρ) could be much larger than the radius of curvature of the magnetic field lines (R C ) such that the particle dynamics becomes non-adiabatic (Frank et al. 1994) in the sense that the magnetic moment μ is no longer an invariant of motion. The parameter of adiabaticity R C æ = (1) ρ introduced by Büchner and Zelenyi (1989) can be significantly smaller than 1.0 for this type of motion. A simple and elegant model of non-adiabatic particle acceleration in a CS with a finite component of the magnetic field B Z, normal to the CS plane, was first put forward by Lyons and Speiser (1982). In the course of the ion interaction with the CS, each particle gains the energy: W = m ( V ce ) 2 Y (2) 2 B Z where m is particle s mass, V 0 is the initial particle velocity and E Y is the magnetotail dawndusk electric field. Usually ce Y B Z V 0 and, according to (2), the energy increase can be 1 2 orders of magnitude larger than the ion initial energy. Later analysis (Büchner and Zelenyi 1989; Chen and Palmadesso 1986; Büchner 1991) have shown that the Lyons Speiser model is oversimplified because particle motion in the magnetotail is principally chaotic. Instead of acceleration and formation of ion beams, a general energization of the ion population should occur. Nevertheless, there are remarkable exceptions from this chaotic scenario related to the existence of so-called CS resonances (Chen and Palmadesso 1986; Büchner and Zelenyi 1989;Chen1992; Ashour-Abdalla et al. 1993; Zelenyi et al. 2009), where chaotic effects at the particle s entry point to the CS and at the point of its exit compensate each other. Figure 2a illustrates the modern vision of interaction of ions with the CS based on the Lyons Speiser acceleration mechanism and the peculiarities of chaotic particle dynamics. In the region where æ < 1.0, cold ions of mantle and/or ionospheric origin experience a non-adiabatic interaction with the CS and are accelerated by the dawn-dusk electric field E. Non-adiabatic ion motion consists of slow gyration in the CS plane (XY ) around the finite B Z > 0 together with fast oscillations in the perpendicular (Y Z) plane. At each separatrix crossing (marked by 1 and 2 in Fig. 2a), a quasi-adiabatic invariant of ion motion, given by I Z = 1 2π żdz (Sonnerup 1971), experiences a jump. Ion motion in the CS becomes essentially chaotic, but at some locations (resonances) ions experience an integer number of oscillations N (total phase gain is Nπ)andjumpsofI Z are compensated. This N number is considered as a sequential index of particular resonance. At such resonant locations the ions escape the CS almost without scattering and their energy gain (2) transforms almost completely to the kinetic energy of their field-aligned motion. Such ions thus form beams in the PSBL. Thus the nature of the CS resonances is related to the properties of the meandering motion of non-adiabatic particles. At a given resonance, as the theory predicts, the parameter of adiabaticity introduced by (1) should be equal to 1/N. The model developed by Ashour- Abdalla et al. (1993) and illustrated in Fig. 2 assumes that the resonant conditions, which are

5 Non-adiabatic Ion Acceleration in the Earth Magnetotail 137 Fig. 2 (a) Schematic non-adiabatic ion trajectories in the distant CS (shaded area). Non-adiabatic ions experience slow gyration (shown by dashed line) in the CS plane (XY) around the finite B Z > 0andfast oscillations (shown by solid line) in the perpendicular (YZ) plane. Ions cross magnetic separatrix at points 1 and 2 and in each crossing a quasi-adiabatic invariant of ion motion I Z experiences a jump. At some locations (resonances) jumps of I Z are compensated and ions escape the CS almost without scattering. Such ions form beams in the PSBL (shown by black line). At other CS locations, where jumps of I Z are not compensated, ions experience strong scattering and are trapped inside the CS (shown by grey line). (b) Illustration of ion non-adiabatic resonant acceleration in the CS. Due to the presence of the large-scale dawn-dusk electric field mantle particles experience E B drift towards the CS (shown by blue lines). At localized CS resonances (R1, R2, R3) non-adiabatically accelerated ions are ejected from the CS to the PSBL, where they form field-aligned localized ion beams (or beamlets) streaming Earthward with high velocities (are shown by red, purple and green lines). The most energetic ion beam (shown by red) is accelerated at the farthest resonance (R3) particularly sensitive to the CS magnetic field B Z at the location of the N-th resonance, are controlled mostly by the variations of this parameter and are achieved almost simultaneously for mantle ions arriving at the CS with characteristic field-aligned velocity and thermal spreads. The resonant effects can occur only at a finite number of CS locations (R1, R2, R3,...,see Fig.2b) within the parts of the magnetotail with closed magnetic topology (Ashour- Abdalla et al. 1993). At other CS locations, where jumps of I Z are not compensated, ions experience strong scattering and heating. Such ions are trapped inside the CS. Considering the resonance character of the acceleration, different predictions for the scaling law for the emerging ion structures have been made. Chen et al. (1990) reported the existence of a resonance scaling law, N H 1/4, for ion distributions observed inside the quiet-time CS (where, H parameterizes the particle energy and magnetic field geometry). The model of Burkhart and Chen (1991) assumed the local nature of resonance without taking into account spatial smearing of these structures due to convection. For the resonant structures observed in a two-dimensional PSBL model, Ashour-Abdalla et al. (1993) found a scaling law V N N 2/3 (here V N is the ion parallel velocity of the N-th structure). For efficient ion acceleration (to energies 10 kev) the magnetic field in the CS should be small ( 0.3 nt), but not zero. This means that the acceleration sites may be located quite far earthward from the distant X-line. In these field lines electrons are still magnetized and move along bouncing orbits. Thus their velocity distribution functions detected simultaneously with PSBL ion beams should be near-isotropic. This is a principal difference between the standard X-line acceleration concept and the concept of ion acceleration at a set of localized resonant sites distributed along the magnetotail in the region of closed magnetic field lines. The resonances produce spatially-localized ion beams which were called beamlets because of their localization in physical and velocity space (Ashour-Abdalla et al. 1993). Grigorenko et al. (2009) estimated the width of CS resonance using a linear approximation and showed that the width of ion beamlet velocity distribution function V /V should be about 0.1.

6 138 E.E. Grigorenko et al. Fig. 3 (a) A scatterplot of the values of ion beam energy versus the width of their field-aligned velocity distribution functions V /V. The color of each circle shows the absolute value of skewness parameter S (according to the scale to the right of the figure) calculated from 1D cuts of electron velocity distribution function along the magnetic field direction. These distributions are registered at the lobeward edge of PSBL simultaneously with the particular ion beam. (b) A scatterplot of the values of the width of ion beam velocity distribution functions V /V versus the corresponding value of AL index Thus, a magnetic configuration of the tail can influence the conditions of ion acceleration in the CS determining its regime. This may explain the diversity of properties of accelerated ion beams observed in the PSBL at different times. Below we demonstrate the variety of ion beam characteristics measured in the PSBL during different periods of geomagnetic activity. 1.2 Diversity of Accelerated Ion Beams Observed in the PSBL of Magnetotail A common and well-known feature of PSBL ion beams is their propagation along the magnetic field lines, especially at the lobeward edge of PSBL. Normally, in this region fieldaligned ion beams stream in one direction (e.g. towards the Earth if observations are made at X 20 R E ). As a spacecraft crosses the lobe-ps interface, the unidirectional velocity distribution function transforms to a counterstreaming one and finally to a hot and isotropic distribution inside the PS (e.g. Forbes et al. 1981; Williams 1981; Takahashi and Hones 1988; Parks et al. 1998). However at other times, the energies of the ion beams, as well as the width of their fieldaligned velocity distribution functions ( V /V ), observed in PSBL may differ by up to an order of magnitude. Figure 3 summarizes the observable values of these characteristics detected in PSBL at different times. Each ion beam event is displayed by colored circle in which the color corresponds to a measure of the level of anisotropy of electron velocity distribution function which was observed simultaneously with the ion beam at the lobeward edge of PSBL. In particular, we quantify the degree of anisotropy from 1D cuts of the electron velocity distribution functions along the magnetic field direction, using the skewness parameter: S = μ 3 /σ 3 where μ is the third order moment about the mean and σ 3 is the cube of the standard deviation (Kendall and Stuart 1977). Thus the color of each circle represents the absolute value of S calculated for each electron velocity distribution function. The anisotropy or isotropy of electron velocity distribution function then provides information on whether ion acceleration occurred on open or closed magnetic field lines. Two groups or types of accelerated field-aligned ions can be identified in Fig. 3. The first represents beamlets (Ashour-Abdalla et al. 1993) (or Type-I beams according to classification by Grigorenko et al. 2009) which are strictly localized in velocity space ( V /V < 0.2)

7 Non-adiabatic Ion Acceleration in the Earth Magnetotail 139 and, as we will show below, are localized also in a physical space. Ion beams of this type have their energies below 40 kev (see Fig. 3a) and are always observed along with nearisotropic electrons ( S 0.2). The isotropy of electron velocity distribution functions detected at the lobeward edge of PSBL simultaneously with such ion beams indicates that ions were accelerated at CS sources located in the region of closed magnetic field lines. Hence this acceleration process is not necessarily related to magnetic reconnection. From Fig. 3b it is also evident that the majority of Type-I events ( 80%) were registered during quieter periods when AL < 300 nt. The ion beams of second group (classified by Grigorenko et al as Type-II events) represent more energetic (up to 200 kev, see Fig. 3a) ion beams with broader distributions in parallel velocity ( V /V > 0.2). During the intervals such ion beams are observed, the electron velocity distribution functions, registered at the lobeward edge of PSBL, were anisotropic along the magnetic field direction ( S > 0.4). These distributions are comprised of cold electron beams (<1 kev) moving towards an acceleration source and by hot electrons ( 1 kev) streaming away from the source. This feature implies that the spacecraft crossed a magnetic separatrix between still open and already reconnected field lines and that the ion acceleration in the CS occurs near the magnetic reconnection region. It is also evident from Fig. 3b that such ion beams are mainly observed during disturbed geomagnetic periods when AL 300 nt. The differences between these two groups of PSBL ion beams may indicate that two different regimes of ion acceleration occurred in the CS during the quiet and active magnetotail states respectively. Below we consider the possible scenarios for ion beam acceleration in the CS and discuss their accordance with numerous observations in PSBL performed by Interball-1, Geotail and Cluster spacecraft (s/c). 1.3 Spatial-Temporal Characteristics of Ion Beams PSBL ion beams and their complicated spatial-temporal manifestations have been widely discussed during the last decades. By using timing analysis of ISEE-1 and -2 data, Takahashi and Hones (1988) estimated the thickness of the region of solely Earthward streaming ions to be a few tenths of an Earth radius. According to their interpretation, the finite thickness is produced by the velocity filter (VF) effect spreading ions with different velocities in the Z direction during the course of their propagation to the Earth. From IMP-7 and -8 observations in PSBL, DeCoster and Frank (1979) reported the duration of ion beam to be a few tens of minutes. However, later observations provided by one-spacecraft missions led to estimates for ion beam durations 1 2 min (e.g. Baumjohann et al. 1988; Sergeev et al It was suggested that powerful energization processes related to magnetotail reconnection can be spatially localized in the dawn-dusk direction (Klimas et al. 2000; Nagai et al. 2001; Volwerk et al. 2004). The resulting dawn-dusk spatial localization of PSBL beams then seems to be consistent with the reported finite spatial extents ( 1 3 R E )ofburstybulk flows (BBFs) (Sergeev et al. 1996, 2000a; Angelopoulos et al. 1997; Kauristie et al. 2000; Nakamura et al. 2001, 2004b). BBFs are thought to be the result of magnetotail reconnection (e.g. Angelopoulos et al. 1992) and may also be considered as the CPS counterparts of the PSBL beams. In addition, Øieroset et al. (2004) provided experimental evidence that the energization processes could operate over a rather large duration ( 10 hours) but have a finite spread in dawn-dusk direction ( 1 R E ). To estimate the spatial size of a PSBL ion beam in a given direction, it is necessary to know the corresponding component of velocity with which the magnetic flux tube containing the ion beam crosses spacecraft location and the duration of this crossing. Moreover, to

8 140 E.E. Grigorenko et al. be confident that the spacecraft is still crossing the beam under study, it is necessary to monitor the characteristics of ion velocity distribution function. When a spacecraft approaches its apogee in the magnetotail, the velocity of the spacecraft is generally negligible in comparison to the velocity of magnetic flux tubes convecting past the spacecraft as a result of the global flapping of magnetotail or other large-scale perturbations. Grigorenko et al. (2007) suggested that the spatial scale of ion beam, Z, in the direction perpendicular to the main magnetic field and to the surface of the PSBL (which corresponds approximately to the south-north direction) could be estimated as: Z = T2 T 1 V Z dt, where T 1 and T 2 are the times of the crossings of the high-latitude and low-latitude boundaries of the ion beam respectively, which are each determined from the analysis of ion velocity distribution functions. The value of V Z is defined as the value of the corresponding component of perpendicular velocity of low-energy ions registered within the lobe-ps interface. Low-energy plasma, traveling tailward, consists mostly of ions of ionospheric origin: H +,He +,O + (Lennartson and Shelley 1986; Sauvaud et al. 2001; Sekietal.2003). Normally this ion population is very cold and is not fully measured by a charged spacecraft. However, in the vicinity of plasma boundaries, for example, near the PSBL boundary, low-energy ions may quite often obtain large velocities perpendicular to the main magnetic field, which are caused by magnetic disturbances propagating in the PSBL (Sauvaud et al. 2004a; Zelenyi et al. 2004; Grigorenko et al. 2010a). As a result their energies are increased to the point that these plasma populations become detectable. An estimation of the temporal scales associated with the ion beams is another difficult task, especially for single-point observations. As a result of the flapping motions of the PS, it is usually impossible to distinguish spatial and temporal effects. Indeed, some authors have concluded PSBL ion beams are long-lived spatial structures (e.g. Ashour-Abdalla et al. 1995) and explained the short duration of their observations by fast magnetotail flapping. Conversely other authors have attributed the short observation of PSBL beams to their impulsive generation in the CS with the characteristic timescales 1 2 min (e.g. Baumjohann et al. 1988; Sergeev et al. 1992). Multipoint observations from the Cluster mission have allowed a more accurate determination of the real duration of ion beams. Grigorenko et al. (2007) estimated the minimum durations of PSBL ion beams by using multiple successive crossings of the PSBL by the different Cluster s/c and simultaneously monitoring the value of parallel velocity of the beam at the lobeward edge of PSBL. Figure 4 illustrates the application of this method to analysis of the spatial-temporal characteristics of a quasi-steady ion beam (duration 17 min) observed in the PSBL by three of the Cluster s/c on 10 October, The spatial scale of this beam was estimated to be 0.5 R E. Figure 5 summarizes the spatial-temporal characteristics of ion beams estimated by applying this method to 138 PSBL crossings made by the Cluster s/c during different levels of geomagnetic activity. These intervals also satisfied the following necessary criteria: (1) the Cluster s/c crossed the full extent of the PSBL, i.e. from its lobeward edge to the PS or vice versa; (2) the density of the cold ion population, n C, was large enough for a reliable convection velocity determination (n C > 0.01 cm 3 ); (3) the magnetic field depression due to diamagnetic effect of the PSBL plasma was clear and observed by all four Cluster s/c, allowing a derivation of the normal to the PSBL surface (Z direction) through an analysis of the relative timings of the occurrence of this boundary at each spacecraft; (4) multiple

9 Non-adiabatic Ion Acceleration in the Earth Magnetotail 141 Fig. 4 Adapted from Grigorenko et al. (2007). Long-living ion beam observed on 10 October From top to bottom: 2D ion velocity distribution functions in the (V,V ) plane, as measured by Cluster-1 at the lobeward edge of PSBL at the times indicated by the red arrows; energy-time spectrograms of ions measured by Cluster-1, -3 and of oxygen ions obtained by Cluster-4; density of low energy ions (W 2keV) and Z -component of their velocity measured by Cluster-1, -3; B X component of the magnetic field obtained by four Cluster s/c; the values of ion beam field-aligned velocity V obtained from the velocity distribution functions measured for each 12-s interval during the whole period of interest (black circles represent Cluster-1 data and green circles represent Cluster-3 data). In the bottom panel Z -locations of PSBL boundary calculated according to Cluster-1, -3 data are shown by black and green circles respectively. Z -positions of Cluster-1, -3 s/c are shown by the solid black and green lines respectively. PSBL intervals are shaded by the pink color. Data from CIS (Réme et al. 2001) and FGM (Balogh et al. 2001) experiments on Cluster were used

10 142 E.E. Grigorenko et al. Fig. 5 Spatial-temporal characteristics of ion beams estimated for 138 PSBL crossings by Cluster s/c. No selection according to the values of AL index was made. The spatial scale of each beam, Z,aswellas its duration, T, were estimated using the methods described by Grigorenko et al. (2007). Each beam is presented by the colored circle and the color corresponds to ion field-aligned velocity, V, given by the scale shown to the right of the figure PSBL crossings by the Cluster s/c took place with a period 3 min. The last criterion is especially important for the estimation of ion beam duration. Each circle in Fig. 5 represents an ion beam observed during a particular PSBL crossing, and the color of the circle indicates the parallel velocity of the ion beam as measured at the lobeward edge of PSBL, as represented in the scale shown to the right of the figure. The observed durations of the ion beams ranged from 1to23minandtheirspatialscales, Z, from R E. Thus, PSBL ion beams apparently occur in spatially localized plasma structures: in this data set there are no cases with Z 1R E. Conversely, the durations of the ion beams cover a wide range of values. The majority of short events (<5 min) have relative high parallel velocities (>2000 km/s), while long-lasting events, as a rule, have V < 2000 km/s. This means that the short events could be accelerated by impulsive mechanism, while the acceleration of the long-lasting events had rather quasi-steady character. Below we will show that these groups of events correspond to two types of ion beams introduced in previous subsection. 1.4 Possible Auroral Manifestations of PSBL Ion Beams Ion beams observed in the magnetotail PSBL may precipitate into the ionosphere near the poleward boundary of the polar cap. Numerous observations performed in this region show a wealth of dispersed ion structures in which ions having different energies were observed at different latitudes or at different times (e.g. Galperin and Feldstein 1989). These structures are roughly split into two classes: Velocity Dispersed Ion Structures (VDISs) (e.g. Zelenyi et al. 1990a; Bosqued et al. 1993) and Time Dispersed Ion Structures (TDISs) (e.g. Sauvaud et al. 1999; Sergeev et al. 2000b). Ion energy dispersion in such structures is basically formed as a result of three main effects: (1) the pure time-of-flight (TOF) effect, which spreads ions of different energies along the magnetic field line; (2) the VF effect due to magnetotail E B convection, which produces an equatorward drift of accelerated ions while they propagate from their source to the Earth (Andrews et al. 1981; Williams 1981); and (3) the place of birth (PB) effect related to the ion acceleration mechanism whose efficiency might depend on the local conditions in the CS, such that the energy gained by the ions during their interaction with the CS may vary with location (Ashour-Abdalla et al. 1993).

11 Non-adiabatic Ion Acceleration in the Earth Magnetotail 143 Fig. 6 From Sauvaud and Kovrazhkin (2004b). (a) VDIS event on 18 January From top to bottom: the variations of the AE and AO magnetic indices (the number of stations used to produce the indices is given on the right side of the upper panel); the electron energy-time spectrogram between 0.5 and 22 kev; O + and proton energy-time spectrograms between 0.7 and 14 kev obtained by Interball-Auroral s/c. (b) TDISevent on 19 June Same presentation as VDIS event except O + energy-time spectrogram (between 0.7 and 14 kev) which is shown below the electron spectrogram The VF effect produces a spatial structuring (layering) of ions according to their energy value, with the highest-energy ions appearing closest to the lobeward edge of PSBL and lower energy ions showing deeper in the PSBL (e.g. Takahashi and Hones 1988; Onsager et al. 1991). Such spatial dispersion is commonly associated with VDIS. The most wellknown examples of VDIS, (Zelenyi et al. 1990a) are those located near the poleward oval boundary (which maps to the outer boundary of the PS). Such structures exhibit increases in the low-energy cutoff of observed ions with increasing latitude and have 1 2 width in invariant latitude. The ion energies in VDIS do not exceed 20 kev. The average energy of electrons accompanying VDIS is kev, i.e. less than the energy of PS electrons. The duration of VDIS may reach tens of minutes (see Fig. 6a) so that they should be formed by some quasi-steady acceleration mechanism. They are most clearly visible during quiet and substorm recovery phase conditions and have their sources located in the distant magnetotail (Elphinstone et al. 1995; Sauvaud and Kovrazhkin 2004b). The transient acceleration and pure TOF effect (in which more energetic particles are seen earliest in time) were initially considered as the possible origin of TDIS structures. The dominance of temporal effect for TDIS formation was also confirmed by the one-toone correspondence of multiple-dispersed beams with concurrent auroral activations in the conjugate ionosphere (Sergeev et al. 2000b). According to the summary by Sauvaud and Kovrazhkin (2004b), TDIS are common in the poleward part of the oval (especially during substorms), have durations of 1 3 min and apparent recurrence period of 3 min(see Fig. 6b), consistent with the temporal scales of BBFs (Angelopoulos et al. 1992, 1994). Studies of both phenomena occurring simultaneously were made by Sergeev et al. (2000a)

12 144 E.E. Grigorenko et al. and Kazama and Mukai (2005). If one neglects the contribution of spatial effects, the TOF analysis gives injection distances for ions forming TDIS of the order of 8 40 R E downtail (Sauvaud and Kovrazhkin 2004b). Thus, if the energy-dispersed ion structures observed near the poleward boundary of the polar cap are composed of ions accelerated in the magnetotail CS, the different modes of this acceleration should be responsible for VDIS and TDIS formation. Below we will discuss the possible relationship between VDIS, TDIS and two types of ion beams observed in magnetotail PSBL. 2 Non-reconnection-Associated Ion Acceleration in the Earth Magnetotail. Quiet PSBL: Type-I Ion Beams In this section we present observations of accelerated ion beams in PSBL of magnetotail during quiet or moderately disturbed geomagnetic periods ( AL < 300 nt). As one could see from Fig. 3b approximately 80% of ion beams observed in PSBL during such periods belong to the Type-I events. An example of Type-I ion beam observed by the Geotail s/c is shown in Fig. 7. During the interval of interest Geotail was located in the southern hemisphere of the magnetotail, at [ 48, 0.5, 6.6] R E in the GSM coordinate system. It was a very quiet geomagnetic period: AL < 50 nt. Energy-collimated ( V /V 0.1) ions, moving Earthward with almost constant field-aligned velocity 900 km/s, were detected in the PSBL for a period of 5.5 min. Electrons with almost isotropic velocity distribution functions were detected together with the ion beam. Tailward moving ions (which had been reflected near the Earth) were observed only deep inside the PSBL, so the field-aligned ions detected at the highlatitude edge of the PSBL were accelerated at a source located tailward from the Geotail s/c. The electron temperature exhibits a very gradual increase towards the PS and it was well below 1 kev in PSBL. These features indicate that non-adiabatic, quasi-steady ion acceleration occurred in the CS Earthward of any distant X-line, i.e. in a region containing closed magnetic field lines (with finite B Z > 0). Thus, the particular features of this type of events are: (1) a strong collimation in velocity space ( V /V < 0.2); (2) ion energies which are below the characteristic value of the potential drop across the magnetotail (<40 kev); (3) an isotropy ( S 0.2) in the electron velocity distribution functions at the lobeward edge of the PSBL detected simultaneously with the ion beams (Grigorenko et al. 2009). We will consider below the spatial-temporal and energy characteristics of these beams on the basis of a comprehensive analysis of 342 events observed in the magnetotail PSBL by the Cluster and Geotail s/c and discuss the possible scenario of their acceleration in the CS. 2.1 Spatial and Temporal Characteristics of Type-I Ion Beams To define statistically the typical Z size of ion beams propagating in the PSBL during quiet or moderately disturbed geomagnetic periods ( AL < 300 nt), 65 intervals of PSBL crossings by Cluster s/c (at X = 15 to 19 R E ) were analyzed by using the methods described in the previous section. In all the intervals studied Type-I beams of accelerated ions were observed. The results of this analysis are presented in Fig. 8. Each circle represents a Type-I ion beam observed during a particular PSBL crossing. The color of the circle corresponds to the

13 Non-adiabatic Ion Acceleration in the Earth Magnetotail 145 Fig. 7 Type-I event observed in the PSBL by Geotail s/c on 22 December The interval of the PSBL crossing is indicated by the light-yellow color. From top to bottom: ion velocity distribution functions in the (V,V ) plane and their 1D cuts along the magnetic field direction; electron velocity distribution functions in the (V,V ) plane and their 1D cuts along the magnetic field direction; energy-time spectrograms of the Earthward and tailward moving ions and the omni directional electrons. Three components of the magnetic field in the GSM coordinate system are shown below the spectrograms. In the bottom panel the electron temperature is presented. Data from the Low-Energy Particle experiment (LEP) (Mukai et al. 1994) and the magnetic field (Kokubun et al. 1994) experiments were used ion beam field-aligned velocity according to the scale shown to the right of the figure. It is evident that the spatial size Z of all beams does not exceed 0.6R E.Accordingtothemultipoint Cluster measurements the minimum observed duration of such beams exceeds 5 min and in some events reaches 23 min. Thus during quiet or moderately disturbed geomagnetic periods a quasi-steady rather than impulsive mechanism of ion acceleration appears to operate in the magnetotail CS. While the observations of ion beam localization in the Z direction can be accomplished even using one-point measurements, a reliable determination of their localization in the direction perpendicular to the main magnetic field but tangential to the PSBL surface, (i.e. nominally in the dawn-dusk, Y, direction) is possible only from multipoint observations.

14 146 E.E. Grigorenko et al. Fig. 8 A scatterplot of spatial and temporal characteristics of Type-I ion beams observed in the PSBL during quiet or moderately disturbed geomagnetic periods. The format of the figure is the same as that of Fig. 5 For the best result the satellites should be located at similar Z coordinates but be separated in Y -direction during the crossing. An example of Cluster observation of an ion beam localized in Y direction is shown in Fig. 9. On between 12:02 12:12 UT, the Cluster s/c were located in the southern lobe at [ 17, 4.3, 6.4] R E (GSE) and due to the magnetotail flapping they crossed the PSBL and encountered the PS region. The timing analysis of ion, electron and magnetic field measurements performed by Grigorenko et al. (2007) has shown that while all four Cluster s/c encountered the PS, only three of them (Cluster-1, -3, and -4) observed the PSBL ion beam. The analysis of the ion beam and velocity distribution functions observed in the first and second PSBL crossings by Cluster-1 and -4 demonstrated that this observation pattern could be formed only as a result of ion beam localization in Y direction ( Y 0.7 R E ) and not due to its temporal termination (the observed duration of the ion beam was 5.5 min). Such observations could be explained by the combination of two effects: magnetotail flapping in Z direction and the large-scale fluctuations of PSBL magnetic flux tubes in the (X Y ) plane propagating towards the Earth with the local Alfvén velocity (here X axis is directed along the undisturbed lobe magnetic field and Y is tangential to the PSBL surface and completes the orthogonal system). Using methodology similar to that used to determine the Z -scale, the Y -scale of ion beam can be estimated as: Y = T2 T 1 V Y (t)dt Here, V Y is the Y -component of the transverse velocity of PSBL magnetic flux tubes. Depending on the direction of crossing of the lobe-ps interface by Cluster s/c, T 1 and T 2 are either the times of the switch of the ion velocity distribution function from field-aligned to a more isotropic one (or vice versa), or the times the spacecraft enter/exit from the lobe (where accelerated ion beams are absent) to the PSBL. Figure 10 illustrates these possibilities. The V Y component may appear, for example, due to the propagation of the MHD Alfvén waves (see e.g. Keiling et al. 2009). These waves may be excited by different types of plasma instabilities (Angelopoulos et al. 1989; Takada et al. 2005, 2006), including Kelvin-Helmholtz instability arising in PSBL due to propagation of accelerated field-aligned plasma flows with velocities larger than twice the Alfvén velocity (Burinskaya 2008; Grigorenko et al. 2010a). According to the results of the analysis performed by Grigorenko et al. (2007), the PSBL ion beams can be strictly localized in Y direction during quiet and moderately-disturbed

15 Non-adiabatic Ion Acceleration in the Earth Magnetotail 147 Fig. 9 Adapted from Grigorenko et al. (2007). Cluster observations of ion beam localized in the (X Y ) plane on 16 September 2002 between 12:03 12:10 UT. Left part of the figure, from top to bottom: ionenergy-time spectrograms obtained by Cluster-3, -4 and -1; X-component of the magnetic field measured by the four Cluster s/c. The bottom panel illustrates the spatial structure of the magnetic flux tube containing the ion beam in (X Y ) plane, which roughly corresponds to the plane of the PSBL surface. The large-scale fluctuations which cause the kink-like perturbation of the flux tubes propagate Earthward along the direction of the undisturbed magnetic field (X ) with the local Alfvén velocity V. Right part of the figure: Cluster s/c locations in the (Y Z) GSE plane. During the interval of interest the Cluster s/c were located in the southern hemisphere at X = 17 R E periods: Y 0.7 R E. Thus, during these periods, the PSBL ion beams are localized not only in velocity space but also in physical space, i.e. they propagate in magnetic flux tubes of a finite cross-section. Consequently, the sources of ion resonant acceleration located in the CS in the region of closed magnetic field lines can be localized not only in the radial direction, as it was suggested in the earlier models (e.g. Ashour-Abdalla et al. 1993)but also in the dawn-dusk direction. Since the condition of ion resonant acceleration in the CS is sensitive to the local value of the normal magnetic field B Z (e.g. Büchner and Zelenyi 1989; Chen 1992; Ashour-Abdalla et al. 1993) then such localization of acceleration sources could be due to the variation of B Z component along the dawn-dusk direction, Y. For example, theincreaseofcsb Z towards the magnetotail flanks was reported by Petrukovich et al. (2005). According to model results by Ashour-Abdalla et al. (1993) the sites of ion resonant acceleration and sites of enhanced scattering (where the resonant condition is not fulfilled) may alternate in the CS along the radial direction due to the B Z (X) dependence (see Fig. 2b). If one takes into account the possibility of B Z (Y ) dependence then the similar pattern could be observed also in the dawn-dusk direction, so that the regions of resonant acceleration

16 148 E.E. Grigorenko et al. Fig. 10 Illustration of a possible 3D structure of the lobe-ps interface. The X axis is directed along the undisturbed lobe magnetic field; Z is directed along the normal to the PS surface and Y axis completes the orthogonal system. The field-aligned ion beam propagates in the magnetic flux tube of the finite cross-section (shown in pink). These field lines are connected with the spatially localized source of ion resonant acceleration which is located in the region of closed magnetic field lines near the CS midplane. The neighboring magnetic field lines are not connected with the acceleration source but remain closed and filled by more isotropic PS-like plasma (shown by the light-brown). The combination of the motion of magnetic flux tubes in the Z direction (due to flapping or PS expansions) and the motions along the Y direction (due to large-scale fluctuations) results in the Cluster s/c observing either field-aligned ion beam or PS-like distribution at the lobe-ps interface could be represented as isolated spots. Quantitative estimates of spatial characteristics of these spots are the subject of our future work. Ion beam localization in the dawn-dusk direction may explain why sometimes fieldaligned ion beams are not observed at the PS-lobe interface, i.e. a spacecraft moving from the lobe towards the PS may just observe the hot and isotropic (PS-like) ion distribution without any accelerated beams. Indeed the absence of PSBL ion beams during the substorm recovery phase was reported earlier by Angelopoulos et al. (1993). They suggested that during such periods ion acceleration does not occur in the CS. However this conclusion contradicts the earlier measurements, obtained by DeCoster and Frank (1979), who reported that the occurrence frequency of PSBL ion beams actually increases during the recovery phase. Keeping in mind the possibility of ion beam localization in the dawn-dusk direction we tried to resolve this problem by using multipoint Cluster observations in PSBL collected for the period from 2001 to 2006, during which time the typical distance between the satellites changed from 0.1 to 1R E. Figure 11 shows the dependence of the probability of observing an accelerated ion beam by at least one Cluster s/c on the dawn-dusk distance between the satellites. It is evident that during the periods when Cluster separation was small (<0.5 R E ) the probability of observing PSBL ion beams was about 40%. This is comparable to the observation probability obtained from one-point measurements (see Grigorenko et al. 2009). When the Cluster separation increases and becomes more than 0.5 R E (a distance comparable to the typical width-scale of an ion beam) the probability of observing an ion beam by at least one Cluster s/c increases to 90%. This indicates that the absence of ion beam observations does not necessarily mean the absence of the acceleration process in the magnetotail. A spacecraft may not cross the magnetic flux tube in which an ion beam is propagating due to its finite cross-section. Instead it crosses neighboring flux tubes which are not connected with the acceleration source and so are either filled by the isotropic plasma resembling the plasma sheet population (in the case of closed flux tube) or are void of hot plasma (i.e. belong to the lobe region), if the magnetic flux tube appears to be open.

17 Non-adiabatic Ion Acceleration in the Earth Magnetotail 149 Fig. 11 The probability of observing a PSBL ion beam by at least one Cluster s/c as a function of the Cluster separation in the dawn-dusk direction, Y This suggestion is in agreement with the model of ion resonant acceleration in the magnetotail (Büchner and Zelenyi 1989; Ashour-Abdalla et al. 1993). According to this model, the ions interact with the CS almost without scattering only in the special spatially localized CS regions (resonances). If non-adiabatic ions interact with the CS outside these resonances they gain the energy (which could be estimated from (2)), but also experience strong scattering and are subsequently trapped inside the PS, where they contribute to its hot and isotropic plasma population. Moreover CS resonances may shift to new locations in the course of their operation due to nonlinear effects (Zelenyi et al. 2006b) and so magnetic flux tubes initially populated by accelerated field-aligned ions may be disconnected from the resonant sources. The ion population in such tubes will gradually isotropize due to mirroring between northern and southern hemispheres. Therefore the ion velocity distribution functions at the lobeward surface of the PSBL could be non-uniform in the dawn-dusk direction, i.e. it may consist of intermittent magnetic flux tubes containing alternately field-aligned ion beams and isotropic PS-like ion population. 2.2 Location of Type-I Acceleration Sources in Magnetotail and Particle Energy Gain It has been suggested that the PSBL ion beams are accelerated in the distant magnetotail at X 100 R E (e.g. Lyons and Speiser 1982; Speiser and Lyons 1984; Eastman et al. 1984; Onsager et al. 1991; Ashour-Abdalla et al. 1993, 2005). In order to estimate statistically the location of ion acceleration sources Grigorenko et al. (2009) used Geotail measurements in the PSBL collected in the period when the spacecraft scanned the magnetotail within the radial distance range of 20 to 220 R E. These authors considered the direction of the ion beam moving along the lobeward edge of PSBL, which indicates on the position of acceleration source relative to the spacecraft. Figure 12 shows the occurrence frequency of Earthward and tailward moving Type-I ion beams versus the distance from the Earth. The plot indicates that even when the Geotail s/c was located at X 110 R E, the majority of ion beams observed at the lobeward edge of the PSBL had Earthward motion, i.e. their acceleration sources were located somewhere tailward of the s/c. Since all beams of this type were observed simultaneously with isotropic electrons distribution functions, the ion acceleration occurred somewhere Earthward from the distant X-line, in a region of closed magnetic field lines. This finding agrees with the earlier statistical study of the ratio between the Earthward-moving northward magnetic flux and the tailward moving southward magnetic flux performed on basis of Geotail observations which was used to determine that the average location of the distant X-line is at about 140 R E (Nishida et al. 1996). Another point concerns the ion beam energy gain which is related to the mechanism of their acceleration in the CS. In the previous section it was shown that during quiet or moderately disturbed geomagnetic periods the duration of the ion beams be tens of minutes. i.e.

18 150 E.E. Grigorenko et al. Fig. 12 Adapted from Grigorenko et al. (2009). The dependence of Earthward (shown in light-grey) and tailward (shown in dark-grey) ion beam of Type-I occurrence frequency registered at the lobeward edge of PSBL on the Geotail X-location. In the upper part of each plot the number of PSBL crossings in which Earthward or tailward ion beams were observed is indicated for each 30 R E X-bin Fig. 13 Adapted from Grigorenko et al. (2009). Distributions of energies of Type-I ion beams versus Y location of Geotail. An aberrated X Y Z coordinate system was used. This coordinate system was obtained by rotating the (XY ) plane of the GSM system at the aberration angle α = arctg(v Y /V X ).HereV Y and V X are the respective components of solar wind velocity in the GSM coordinate system measured by IMP-8 (or by the ACE s/c when applicable) accounting for the time delay required for solar wind propagation from the spacecraft location to the distant tail. The limit of ion energy gain (shown by the dashed lines) was calculated assuming quasi-steady ion acceleration by the uniform potential dawn-dusk electric field (for E = 0.1, 0.3, and 1.0 mv/m) during propagation of non-adiabatic ions across the tail their acceleration is more a quasi-steady process than bursty one. In these cases ion beams may be accelerated by a quasi-steady dawn-dusk electric field. If this is true then the ion energy gain should not exceed the value of the potential drop across the magnetotail, which is typically 50 kv during such periods (Cauffman and Gurnett 1971; Mozer 1974; Wolf 1975). To check this suggestion, Grigorenko et al. (2009) studied the distribution of energy of Type-I ion beams in the dawn-dusk direction. The results, shown in Fig. 13, demonstrate that the energies of Type-I ion beams are below the typical values of potential drop across the tail. Moreover, the cross-tail energy distribution is more or less in agreement with that expected from the quasi-steady acceleration model: higher energy ion beams are observed in the midnight sector and in the dusk flank with almost no ion beams (except a few low-energy events) observed on the far dawn flank. Electrons observed in PSBL simultaneously with Type-I ion beams have, as a rule, temperatures below 1 kev (see Fig. 14). As in the case shown in Fig. 7, the electron temperature measured in the PSBL during intervals of Type-I ion beam propagation increases very gradually with distance towards the Neutral Sheet (NS). This behavior may be explained by the electron acceleration scenario proposed by Lyons (1984): the interaction of electrons with the CS in the distant magnetotail provides only a very small energy gain (comparing to ions) but electrons gradually acquire significant energy during their subsequent adiabatic (the first and second magnetic moments const)

19 Non-adiabatic Ion Acceleration in the Earth Magnetotail 151 Fig. 14 Adapted from Grigorenko et al. (2009). The observation probability of Type-I ion beams versus the temperature of accompanying electrons Earthward convection into the region of stronger magnetic field. Since the electron energy increases with their approach to the Earth and more energetic electrons are observed at more inward magnetic shells, one should not expect to observe high-energy electrons in the PSBL for this type of acceleration. 2.3 Signatures of Multi-source Acceleration at Closed Magnetic Field Lines According to the model proposed by Ashour-Abdalla et al. (1993) particles which have been accelerated at CS sites with different resonant conditions acquire different energies. This PB effect combined with the VF effect results in a spatial energy dispersion in the PSBL. Due to the presence of the dawn-dusk electric field, charged particles, propagating towards the Earth, are displaced equatorward in proportion to their time-of-flight from the source to the observation point. At some (X, Z) location in the PSBL, the energy difference between the ions accelerated at different resonances may be compensated for by the difference between the lengths of their pathways along the magnetic field lines in the PSBL. As a result, two ion beams with different energies can overlap (Zelenyi et al. 2006a, 2009) and be observed simultaneously (see Fig. 15). This phenomenon of ion beam overlapping was simulated using a large-scale kinetic (LSK) model by Ashour-Abdalla et al. (1993) and Zeleny et al. (2007). This demonstrated that the PSBL ion distribution may indeed have a multiplet structure consisting of several small-scale accelerated ion beams. In the model of CS particle acceleration proposed by Ashour-Abdalla et al. (1993), a symmetry of northern and southern mantle sources was assumed. More generally, however, many effects produce an asymmetry (for example, the dipole tilt introduces strong seasonal effects, or the peculiarities of dayside reconnection which produces an asymmetry in plasma flows around magnetopause (e.g. Cowley and Owen 1989). The dependence of dayside reconnection on IMF B Y produces the gradient of mantle density across the tail which has opposite signs in northern and southern lobe (Gosling et al. 1985). This also contributes to the asymmetry of mantle sources. Zelenyi et al. (2006a) made a more general assumption that the mantle sources could also be significantly asymmetric. This produces an important quantitative effect. Particles accelerated at the odd resonances return to the same hemisphere as their mantle source location, while particles from the even resonances exit into to the opposite hemisphere after CS acceleration. Thus at a given observation point one could simultaneously observe particles either only from the odd or only from the even resonances. Indirectly such asymmetry effects may help to resolve multiplet energetic particle distributions. It is much easier to resolve well-isolated energy peaks V N and V N+2 since they have larger separation in velocity space: V N /V N+2 [N/(N +2)] 2/3 instead of [N/(N +1)] 2/3 for neighboring resonances. This asymmetry effect is illustrated in Fig. 16. Note particularly that particles from the resonance N = 2 are absent at observation site in this representation.

20 152 E.E. Grigorenko et al. Fig. 15 Schematic of ion beamlet overlapping. Low-energy ions (their trajectories calculated in a model magnetic field (Zwingmann 1983) areshownbyblue lines) come from the plasma mantle and non-adiabatically interact with the distant CS. At resonant sites Resonant 1 and Resonant 2 ions are accelerated along magnetic field lines almost without scattering and form two ion beamlets in PSBL (shown by red and light violet). Due to the different resonance locations in the CS, and thus to the different local values of the magnetic field, the ion beams have different energies (PB effect). In course of their propagation towards the Earth beamlets also experience E B drift, which causes beamlet displacements towards the CS according their time of flight (VF effect). Due to the combination of PB and VF effects ion beamlets may overlap at some PSBL location (at the meeting point) The progress in measurement techniques achieved during last decade has allowed the study of these fine structures. Cluster observations of ion beam overlapping in magnetotail PSBL were reported by Zelenyi et al. (2006a). An example of such an event is presented in Fig. 17. During a period of 2.5 min, the Cluster-1, -3 and -4 spacecraft simultaneously observed two field-aligned, energy-collimated ion beams moving Earthward with energies 5 kev and 30 kev. They formed two pronounced narrow peaks in the velocity space. The electron velocity distribution functions measured during this interval were almost isotropic, both at the time of the ion beam observation and even in region located on the lobe side of the ion beams. Asin the example shownin Fig.7, the electron temperature increases very gradually towards the PS. All these features indicate that the observed ion beams belong to the Type-I class and that their acceleration sources in the CS were located on closed magnetic field lines. Tracing of these beams back downtail in Tsyganenko-96 magnetic field model (also taking into account a drift velocity V = (E B)/B 2 50 km/s) provides an estimate of the radial distance between the two resonances X R1 X R2 6R E which is approximately twice the width of each of these resonances (Zelenyi et al. 2006a). Such observations provide the first experimental confirmation of the theoretical prediction that at least two resonant sources of non-adiabatic ion acceleration may simultaneously operate in the CS in the region of closed magnetic field lines. Zelenyi et al. (2006a) have also performed a statistical analysis of ion velocity distribution functions observed by the Cluster spacecraft in the magnetotail PSBL (in ) and found nearly one hundred cases of double-peaked distributions formed by pairs of

21 Non-adiabatic Ion Acceleration in the Earth Magnetotail 153 Fig. 16 Illustration of the asymmetry effect in ion resonant acceleration in the magnetotail CS. Ions coming to the CS from the northern mantle (assumed here to be a strong source, shown by solid blue lines) are accelerated at the odd resonances (R1 and R3) and are ejected into the PSBL of the same (northern) hemisphere, where they are observed by the Cluster s/c. Ions coming to the CS from the southern hemisphere (assumed here to be a weak source, shown by the dashed blue lines) and being accelerated at the even resonance (R2) are ejected in the PSBL of the opposite (i.e. northern) hemisphere. Since the initial flux of ions from the southern mantle is weaker than the one from the northern mantle Cluster s/c observes lack of ions from R2 source (shown by dotted purple line). As a result, the Cluster s/c observes in the northern PSBL a double-peak velocity distribution function formed by ion beams moving with V 1 and V 3 field-aligned velocities (from R1 and R3 resonant sources). Simultaneously an observer in the southern PSBL could register (a relatively weak) one-peak velocity distribution function formed by the ion beam accelerated at R2 resonance Type-I ion beams. The energies of the two beams forming double-peaked distributions differed by factors of In order to compare the experimental observations with the resonance scaling law predicted by the theory, these authors calculated the ratio V 1 /V 2 (where V 1 is the ion parallel velocity corresponding to lower peak in the double-peaked distribution function and V 2 is the parallel velocity corresponding to the higher peak) and compared these values with the ratio [N/(N + 2)] 2/3,whereN represents integer numbers of resonances from 1 to 10. The result of this analysis is shown in Fig. 18. Here the measured values of V 1 /V 2 are displayed by black circles and are shown versus V 1. The levels of [N/(N + 2)] 2/3 are presented by grey lines, and near the first and last levels plotted the corresponding values of N are indicated. The vertical dotted lines show the errors of V 1 /V 2 values associated with the finite width of each instrument energy channel. At the right part of the figure the black bars indicate the number of cases of double-peaked distributions in which the value of V 1 /V 2 equals (up to error margins) to the value of the corresponding level. The agreement between V 1 /V 2 and [N/(N + 2)] 2/3 for each of the analyzed cases is reasonably good. Howeveras N increases the interval between the neighboring resonance lines shrinks and becomes less than the measurement error of the V 1 /V 2 ratio. For N 4 the comparison is already questionable. It is worth noting that for higher velocities (i.e. for higher N values) the ion beams begin to smear. Thus the beams associated with higher order resonances become almost undistinguishable due to both the uncertainties of their experimental registration and the intrinsic overlapping of adjacent higher-order resonances (Zelenyi et al. 2009).However, there is a rather good agreement between the experimental data and the theory prediction at least for N<4 (the main part of experimental measurements corresponds to a lower N

22 154 E.E. Grigorenko et al. Fig. 17 Ion beamlet overlapping observed by Cluster on 01 September 2003 between 08:09 08:11:30 UT. Cluster was located in the southern hemisphere at [ 18.8; 2; 3.4] R E (GSM). Two ion beamlets moving Earthward with V km/s and V km/s are clearly observed in the ion velocity distribution functions whose 2D (in V,V plane) and 1D (along the magnetic field) cuts (count per spectrum units were used) are shown in the upper part of the figure. Vertical lines in the 1D cuts indicate the statistical error calculated as N 1/2 (where N is total count). Ion velocity distributions were measured at the moments marked by red arrows above ion energy-time spectrograms. Energy-time spectrograms of ions measured by Cluster-3, -1 and of H +,O + and electrons measured by Cluster-4, are presented from top to bottom below ion velocity distribution functions. Electron 2D pitch-angle distributions and 1D cuts of their distributions plotted for electrons with 0, 90 and 180 pitch-angles are shown below the spectrograms (energy flux units, de (1/cm 2 -s-str-ev) were used). Electron distributions were accumulated by PEACE spectrometer (e.g. Owen et al. 2001) over the intervals indicated above each pitch-angle distributions. The center time of each interval is shown by red arrow below the electron spectrogram

23 Non-adiabatic Ion Acceleration in the Earth Magnetotail 155 Fig. 18 Adapted from Zelenyi et al. (2006a). Statistical verification of the scaling low for resonance structures predicted by Ashour-Abdalla et al. (1993): V 1 /V 2 =[N/(N + 2)] 2/3. The values of the measured V 1 /V 2 ratio (black circles representing the observed double-peaked velocity distribution functions) are plotted versus the velocity, V 1, of the corresponding lower beam peak. Dotted vertical lines crossing each circle show an error of V 1 /V 2 measurements due to the finite width of the instrument energy channels. The calculated values of [N/(N + 2)] 2/3 are shown by horizontal grey lines, wheren are integer resonance numbers (from 1 to 10). The black solid lines shown in the right part of the figure indicate the number of measurements of double-peaked distributions corresponding to the each particular N-th resonant level numbers). Zelenyi et al. (2009) thus concluded that, for quiet and moderately-disturbed geomagnetic periods, the near-earth PSBL may be explained in the framework of the theory of resonant particle acceleration in the distant CS which leads to a scaling law V N 2/ Field-Aligned Currents in Quiet PSBL: Ion Beams or Flows? It is widely believed that field-aligned currents (FACs) are a key component of the coupling between the magnetosphere and the ionosphere (e.g. Kivelson and Russell 1995). Early FACs studies, based on observations of magnetic field variations (Aubry et al. 1972; Fairfield 1973; Sugiura 1975; Elphic et al. 1985; Ohtanietal.1988; Uenoetal.2002), as well as on the analysis of 3D electron velocity distribution functions (Frank et al. 1981) in the midtail region, were aimed at revealing their role in establishing the large-scale Region 1 and Region 2 current systems appearing in low-altitude spacecraft observations (Iijima and Potemra 1978). It was also reported that during quiet geomagnetic periods the Region 1 and Region 2 currents become weaker (Rich and Gussenhoven 1987) or even disappear. FACs continue to be present, but appear as small-scale structures scattered over the auroral oval and entire polar cap (Hoffman et al. 1988). FAC are conventionally observed as a magnetic field perturbation normal to the main component, which corresponds to the disturbance of the B Y component in the canonical tail configuration assuming that the FAC occurs in a planar sheet. Under this assumption, the current density of a sheet current is determined as B Y /(μ 0 Z), where Z is the thickness of sheet. A weak point of this method is an uncertainty in the Z calculation, since single spacecraft observations failed to distinguish reliably spatial and temporal effects. Multipoint measurements provided by the Cluster s/c have enabled the first determination of the spatial and temporal scales, as well as the current density in FAC. This method is based on the

24 156 E.E. Grigorenko et al. so-called curlometer technique a difference estimate of B by treating the current as constant over the tetrahedral volume formed by the four Cluster s/c (Chanteur 1998). In reality the current varies to some degree over the tetrahedron and the knowledge of this could come from the estimate of B under the same assumptions. Because of the solenoidality of the magnetic field ( B = 0) any non-zero value of B could appear only due to the presence of nonlinear gradients. So that in many cases B/ B can be used to evaluate the quality of the current density estimates (Paschmann and Daly 1998). Grigorenko et al. (2010b) estimated the current densities of FACs by using Cluster observations during intervals of Type-I and Type-II ion beam propagation in the magnetotail PSBL. It was found that Type-I ion beams are not accompanied by any significant FAC. An example of Type-I ion beam and the associated FAC observed in magnetotail PSBL on by Cluster s/c is presented in Fig. 19. This was a very quiet geomagnetic period ( AL < 50 nt during almost the entire day). The value of FAC density in the PSBL does not exceed 2 na/m 2. In such cases the contribution of field-aligned ions to FAC J ion = env ion (here e is elementary charge, n and V ion correspond to ion density and parallel velocity) is significantly larger than the total FAC density calculated as J curl = ( B) by the curlometer technique. Indeed the analysis of FAC densities measured in 129 PSBL crossings by Cluster s/c, in which Type-I ion beams were observed, demonstrated that in the majority of cases the total FAC density was significantly smaller than the density of net ion FAC, J ion (see Fig. 20). This means that the ion FAC is almost completely compensated by the electron FAC, i.e. accelerated field-aligned ions are moving together with the bulk of the electron distribution. In such cases the average field-aligned velocity of PSBL electrons is much smaller than their thermal velocity. This should be taken into account especially for analysis of the mechanism of plasma instabilities in the PSBL. For example, large-scale fluctuations of the PSBL magnetic flux tubes with wave lengths of the order of several R E, which are often observed during Type-I ion beam propagation, may be caused by the Kelvin-Helmholtz instability excited by the jump of field-aligned plasma flow velocity in the PS-lobe interface when the value of this jump exceeds twice the local Alfven velocity (Belova et al. 1987; Burinskaya2008; Grigorenko et al. 2010a). 2.5 Possible Auroral Manifestations of Type-I PSBL Ion Beams Unfortunately to date no conjugate case studies of PSBL ion beams observed in the magnetotail and dispersed ion structures observed in high-latitude auroral region have been made. Nevertheless, an important link between Type-I ion beams and VDIS structures can be established. They have similar time scales, ion and electron characteristic energies, and are mainly observed during the similar geomagnetic conditions. The sources of Type-I ion beams as well as VDIS are located in the distant tail. Thus all VDIS features currently identified perfectly match the properties of Type-I ion beams observed in PSBL of magnetotail. Sauvaud and Kovrazhkin (2004b) and Keiling et al. (2004) reported the observation of small-scale substructures within VDIS, which were identified as beamlets. These authors have shown that while the average pattern of the VDIS and its embedded beamlets conforms well with the earlier LSK simulations (Ashour-Abdalla et al. 1993), the dispersion of each local substructure differs, sometimes significantly, from the average dispersion of the VDIS itself. Specifically, on the outbound pass of the event considered by Sauvaud and Kovrazhkin (2004b) the sign of the dispersion reverses (see Fig. 21). Both groups of authors concluded that ion TOF effects need to be taken into account to explain the mismatch of

25 Non-adiabatic Ion Acceleration in the Earth Magnetotail 157 Fig. 19 Adopted from Grigorenko et al. (2010b). Cluster observation of Type-I ion beam on 21 September 2001 between 18:22 18:32 UT. Cluster was located at [ 16, 2.6, 6.4] R E (GSE). From top to bottom:2dion velocity distribution functions in the (V,V ) plane (counts per spectrum C units were used) and electron pitch angle distributions (energy flux units, def (1/cm 2 -s-str-ev) were used); ion (a) and electron (b) energy-time spectrograms measured by Cluster-3 and -4 correspondingly; (c) ion field-aligned velocity corresponding to the maximum of the velocity distribution functions measured by three Cluster s/c; (d) (f) three GSE components of the magnetic field measured by four Cluster s/c; (g) density of FAC J and of two perpendicular components of current, calculated from ( B); (h) ion(j ion ) and electron (J ele) contributions to FAC. Electron contribution was calculated as J ele = ( B) J ion ;(i) ratio of ( B)/( B)

26 158 E.E. Grigorenko et al. Fig. 20 Scatterplot of the total FAC densities (J curl ) calculated as ( B) versus the densities of the net ion FAC J ion observed in 129 PSBL crossings by the Cluster s/c during intervals of Type-I ion beam propagation Fig. 21 From Sauvaud and Kovrazhkin (2004b). Detail of the energy-time spectrogram of protons between 16:00:42 and 16:05:00 UT on 3 November 1996 obtained by Interball-Auroral Probe average and local dispersions found in their measurements. Independently, they suggested that the beamlets within the VDIS were produced by a set of non-correlated impulsive injections from different locations in the tail which somehow combined to form the enveloping global VDIS structure. Generally speaking, the interpretation based on such perfect coincidence seems to be rather improbable and thus the consideration of other mechanisms is very desirable. Later, Ashour-Abdalla et al. (2005) used LSK calculations carried out in the fields obtained from a global magnetohydrodynamic (MHD) simulation of this event and showed that during the inbound pass, the stochastic sea a region of weak magnetic field just Earthward of the near-earth X-line was the source of the smaller scale beamlets observed by the Cluster s/c. However, no regular pattern of small-scale structures embedded in a large-scale envelope emerges from these simulations. An alternative approach to that of Sauvaud and Kovrazhkin (2004b) and Keiling et al. (2009) is needed to determine the cause of local beamlet dispersions in the Cluster VDIS observations. The earlier LSK simulations by Ashour-Abdalla et al. (1993) were carried out without feedback between the particles and magnetic field. Peroomian et al. (2000) and

27 Non-adiabatic Ion Acceleration in the Earth Magnetotail 159 Peroomian and Zelenyi (2001) incorporated self-consistently the current carried by nonadiabatic ions into the 2D Birn-Zwingmann equilibrium magnetic field model (Birn et al. 1975; Zwingmann 1983) and found that the tail evolved into a quasi-periodic state characterized by the motion of the X-line in the magnetotail. These studies did not investigate the formation of beamlets due to statistical limitations, but found multiple VDIS-like injections as a result of the quasi-periodic nature of their system. Zelenyi et al.(2006b) made the first step towards the self-consistent description of the generation of ion beams in the magnetotail by taking into account the weighted contribution of the cross-tail currents carried by the beam ions to the magnetotail current system. The computation of the current perturbation was performed considering the whole ion population, but phase filtration during the interaction of particles with the CS resonantly selects the group of particles moving mostly in the field-aligned direction (beams) which also carrying the major fraction of the cross-tail current while moving in the vicinity of the tail midplane. These authors calculated modifications of the original magnetic configuration and then investigated the fine structure of ion beams in this non-linearly modified geometry. As the perturbed profile of CS magnetic field B Z (X) contains intervals where B z / x > 0, it may be expected that the ion beams generated at these parts of the sources would have an inverse local dispersion: ions accelerated at larger X obtain smaller energies than ions accelerated at smaller X (according to (2)). Such dispersion is opposite to the one produced at those parts of the source regions where B z / x < 0. The stronger the ion current at the sources, the stronger the perturbation of B Z (X) and the steeper the slope of the local energy dispersion in each of the small-scale beams. Unfortunately the number of cases with such pronounced non-linear effects manifested in alternating normal/inverse dispersive structures is very small. The reason for such uniqueness is probably related to the VF effect, which modifies the ion energy dispersion in the course of ion beam propagation to the Earth. Thus ions with lower energies are displaced towards lower latitudes and any initially inverse energy dispersion is gradually transformed to the normal one. This process is illustrated in Fig. 22, where three occurrences of the same beamlet in the northern hemisphere, obtained at different virtual X-detectors (located at 70 R E ;40R E, and 10 R E from the Earth), are plotted. The figure clearly illustrates that the original inverse dispersion of the beam is completely modified by the VF effect causing a counter-clockwise rotation in the northern hemisphere as the ion beam approaches the Earth (correspondingly, a clockwise rotation of beams in the southern hemisphere). This propagation effect can mask the formation of inversely dispersed beams, which were accelerated far downstream, even if the nonlinear modifications of the B z (X) profile are strong enough to reverse the local dispersion of beams at their generation sites. Thus, the longer the ion beam pathway from the source to the Earth the stronger is influence of VF effect. However, if an acceleration source(s) is located rather close to the Earth, the slope in energy inherent to a particular ion beam may significantly differ from the global dispersion slope in the PSBL. Thus events similar to the one shown in Fig. 21, although rare, could be observed in high-latitude auroral region. 2.6 Summary: Ion Acceleration in Magnetotail CS During Quiet Periods The analysis of 1642 intervals of PSBL crossings by the Cluster and Geotail s/c (at X = 20 to 220 R E ) has shown that during quiet or moderately-disturbed geomagnetic periods ( AL < 300 nt, covering 886 PSBL crossings) the majority of field-aligned ion beams ( 80% of events) are classified as Type-I beams, i.e. they are characterized by: (1) energy-collimated velocity distribution functions: V /V 0.15;

28 160 E.E. Grigorenko et al. Fig. 22 Simulation of transformation of the initial inverse ion beam energy dispersion, generated at the distant acceleration source due to non-linear effects, to the normal one observed in the near-earth PSBL of the northern hemisphere. This transformation is due to the operation of VF effect as the ion beam propagates towards the Earth. Ion beam energy dispersion in the PSBL was measured by virtual detectors placed at different radial distances: near the source at X =70 R E, in the mid-tail at X =40 R E and near the Earth, at X =10 R E (2) an isotropy of the electron velocity distribution functions simultaneously observed at the lobeward edge of PSBL; (3) an average observed duration 10 min. The observed width of ion beam velocity distribution functions is comparable with that estimated by Grigorenko et al. (2009) on the basis of a resonant mechanism of ion acceleration in the CS at spatially-localized source(s). The Earthward directions of the ion beams moving along the lobeward edge of the PSBL even at X 110 R E confirm that their source(s) are located in the distant tail (at X 110 R E ). The isotropy of electron velocity distributions observed at the high-latitude edge of PSBL together with all registered Type-I ion beams clearly indicates that the ion acceleration occurs in the region of closed magnetic field lines, which could be located rather far from the distant X-line. It is also worth noting that, in the majority of these cases, the temperature of the electrons accompanying Type-I ion beams is less than 1 kev. This increases very gradually as a spacecraft moves toward the NS. Such behavior may be explained by the fact that the acceleration of Type-I ion beams mostly occurs during the periods of stretched magnetotail configuration with X-line located in the distant part of the tail CS. Ions are non-adiabatically accelerated by the potential electric field E Y at closed magnetic field lines where electrons are still adiabatic. Electrons do not experience efficient acceleration in the distant CS unless

29 Non-adiabatic Ion Acceleration in the Earth Magnetotail 161 Fig. 23 Possible scenario for ion non-adiabatic acceleration in the magnetotail CS during quiet or moderately-disturbed geomagnetic periods. Quasi-steady resonant acceleration occurs at spatially-localized sources (resonances) located far from the distant X-line in regions with finite B Z > 0. Each resonance produces an energy-collimated ion beam with energy W (shown by the colored line) which increases with the distance from the Earth (red color represents the most energetic ion beam). Since ion acceleration occurs on closed magnetic field lines, ion beams observed in PSBL are embedded in the layer of isotropic electrons (shown by the light-yellow color) non-stationary mechanisms become involved. In spite of this, they could gain energy relatively slowly due to the combination of betatron and Fermi mechanisms while convecting towards the Earth towards a region with stronger magnetic field (Lyons 1984; Zelenyi et al. 1990c). The average observed duration of these beams is 10 min and in some events it reaches up to 23 min. This indicates the quasi-steady character of the Type-I acceleration process. Ion energies in such beams are below the typical value of the potential drop across the tail. Moreover their energy distribution in the dawn-dusk direction demonstrates that the energy of ion beams generally increases towards the midnight sector and dusk flank. This implies that the quasi-steady dawn-dusk electric field is responsible for Type-I ion beam acceleration. Therefore the scenario of Type-I ion beam acceleration illustrated in Fig. 23 may be appropriate: ions are accelerated at localized sources (resonances) scattered over a very wide region located rather far from the distant X-line where magnetic field lines are closed (finite B Z > 0). The acceleration process lasts, at least, several minutes and has a quasi-steady rather than a transient character. The similarity of Type-I ion beam characteristics to ones predicted by the theory of ion resonant acceleration in the CS, suggests that these beams represent the beamlets predicted in the paper by Ashour-Abdalla et al. (1993). This acceleration scenario is realized in the quiet magnetotail configuration which is consistent with the fact that statistically Type-I ion beams are observed during quiet or moderately-disturbed geomagnetic periods. Finally in this discussion of Type-I ion beams, we should note that the term beam or beamlet is not quite appropriate for these structures. The analysis of FAC densities performed on the basis of Cluster measurements of ( B) has shown that during intervals of Type-I ion propagation these values are a few times smaller than the densities of the net ion FAC observed simultaneously. This implies that during such intervals the accelerated field-

30 162 E.E. Grigorenko et al. aligned ions move together with electrons (the electron bulk velocity is thus much smaller than their thermal velocity and is close to the value of the ion bulk velocity). Therefore, strictly speaking, these ions are part of high-velocity field-aligned plasma flows rather than beams. 3 Reconnection-Associated Particle Acceleration in the Earth CS. Active PSBL: Type-II Ion Beams In this section we consider plasma structures observed in PSBL during geomagnetically disturbed periods ( AL > 300 nt). As mentioned in Sect. 1, during these periods 90% of the field-aligned ion beams registered in the PSBL belong to Type-II. In particular, these beams are characterized by the significant width of their velocity distribution functions, V /V 0.3 and are accompanied by electrons which have anisotropic velocity distributions along the magnetic field lines. The appearance of the latter feature indicates that a spacecraft has crossed the magnetic separatrix separating still open magnetic field lines from those which have already undergone reconnection. Below we discuss the spatial-temporal characteristics of Type-II ion beams and the peculiarities of their CS acceleration which may influence the observed features of the ion velocity distribution functions. 3.1 PSBL Manifestations of Ion Acceleration Near the Magnetic Reconnection Region An example of a Type-II ion beam observed by the Geotail s/c is presented in Fig. 24. In contrast to the Type-I events, during this PSBL crossing an energetic field-aligned ion beam (W 30 kev) with a wide distribution in parallel velocities was observed. Inside the PSBL the value of ratio V /V was about 0.7 and it reached 0.9 when integrated over the entire PSBL region from its lobeward edge to the boundary with the PS. Field-aligned ions streamed tailward even at the lobeward edge of the PSBL. Thus their acceleration source was located in the near-earth magnetotail, somewhere Earthward of the Geotail s/c, which was located at X 46R E. During this interval electrons with at least three types of non-maxwellian velocity distributions were identified. These types of distributions have been classified by Hoshino et al. (2001) as: (1) a truncated-cone (in which phase space density in the lower-energy range is almost flat). Electrons with such distributions were observed at 19:18:43 UT, when Geotail was in the PS. (2) A football distribution with T >T. This was observed at 19:19:07 UT, when Geotail was in the PS but close to the PSBL. (3) Shifted-football distributions with counter-streaming cold and hot electron components. Such distributions were measured after 19:19:31 UT, when Geotail was in the PSBL and crossing its lobeward edge. Thus the electron distributions detected during this PSBL crossing were essentially anisotropic: the skewness parameter ranges from 0.4 to 0.6. Electron temperature in PSBL increased up to 1.9 kev and exceeded the value measured previously in the PS. We would like to emphasize the significant width of ion velocity distribution function in parallel velocities observed during this event, in comparison with the Type-I events considered in the previous section. For energy collimated ion beams (Type-I events), a spacecraft crossing of the entire PSBL region was accompanied by only slight variations of ion parallel velocities. Moreover, the width of the ion velocity distribution function, V, remained small even when it was integrated over the entire PSBL region. Conversely, for the Type-II events the energetic field-aligned ions encountered at the lobeward edge of the PSBL do not disappear even deep inside the PSBL. In these ion beams, the high-energy field-aligned ions

31 Non-adiabatic Ion Acceleration in the Earth Magnetotail 163 Fig. 24 Adopted from Grigorenko et al. (2009). An example of a Type-II ion beam observed in the PSBL on 12 December 1994 by the Geotail s/c, located at [ 46.7, 1, 6.1] R E (GSM). The format of the figure is the same as Fig. 7. The interval of PSBL crossing containing the ion beam observation is shaded in light-yellow are observed simultaneously with those of lower energy. The resulting local velocity distributions become wide, especially when integrating over the entire PSBL region. Obviously some complicated, unsteady and powerful mechanism of acceleration operates during these events. The possible scenario of the formation of this type of ion velocity distributions is discussed in Sect Spatial and Temporal Characteristics of Type-II Ion Beams To estimate the typical spatial and temporal scales of Type-II ion beams, the methods, described in Sect. 1, were applied to the analysis of 74 PSBL crossings by the Cluster s/c

32 164 E.E. Grigorenko et al. Fig. 25 A scatterplot of spatial and temporal characteristics of Type-II ion beams observed in the PSBL during disturbed geomagnetic periods. The format of the figure is the same as that of Fig. 8 in which Type-II ion beams have been registered. All these intervals occurred during geomagnetically disturbed periods ( AL 300 nt). The results of this analysis are shown in Fig. 25, which has the same format as Fig. 8. In contrast to the Type-I ion beams, the spatial scales Z of Type-II ion beams vary over a wider range: from 0.2 R E to 0.9R E. The observed durations of these beams ranged from 1 min to 5 min. Only one event has a duration as large as 8 min. The average duration of Type-II ion beams is 2 min.this conforms to the time scale of impulsive ejections into the PS during reconnection events estimated by Sergeev et al. (2000b, 2007). 3.3 Location of Acceleration Sources in Magnetotail and Energy Gain of Type-II Ion Beams To statistical estimate the location of the Type-II ion beam sources, 274 intervals of PSBL crossings by the Geotail s/c within the radial distance range of 20 to 220 R E were analyzed (Grigorenko et al. 2009). In each of these crossings, Type-II ion beams were observed. Figure 26 shows the occurrence frequency of the Earthward/tailward direction of ion beams streaming along the lobeward edge of PSBL as a function of the radial position, X, of the Geotail s/c. It is seen that the majority of ion beams observed at X 50 R E stream tailward, i.e. they have sources located in the CS somewhere at X> 50 R E.Even when Geotail was located within the interval 50 to 20 R E, Type-II ion beams move tailward in almost 40% of events, i.e. their acceleration sources are located in the near-earth magnetotail (Grigorenko et al. 2009). Figure 27 presents the energy distribution of Type-II ion beams across the magnetotail. Since statistically the observed duration of Type-II ion beams is significantly shorter than that of Type-I ion beams, it is natural to suggest that the mechanism for Type-II ion beam acceleration may have a more impulsive rather than a quasi-steady character. Actually, the cross-tail distribution of Type-II ion beams is practically impossible to explain in terms of the model of quasi-steady acceleration by the constant (even large) cross-tail electric field. A significant fraction of energetic ion beams are observed in the dawn flank and their appearance could be explained by the quasi-steady acceleration only under the unrealistic assumption of very high values of the potential dawn-dusk electric field ( 1.0 mv/m). Therefore, the electrostatic dawn-dusk electric field accounts for neither the energy, nor the dawn-dusk distribution of Type- II ion beams. Hoshino et al. (1998) reported the existence

33 Non-adiabatic Ion Acceleration in the Earth Magnetotail 165 Fig. 26 Adapted from Grigorenko et al. (2009). The dependence of Earthward (shown in light-grey) and tailward (shown in dark-grey) ion beam of Type-II occurrence frequency registered at the lobeward edge of PSBL on the Geotail X-location. The format of the figure is the same as that of Fig. 12 Fig. 27 Adapted from Grigorenko et al. (2009). Distributions of energies of Type-II ion beams versus Y location of Geotail. The format of the figure is the same as that of Fig. 13. For the analysis of energetic events (>40 kev) EPIC data were used (Williams et al. 1994) Fig. 28 Adapted from Grigorenko et al. (2009). The observation probability of Type-II ion beams versus the temperature of accompanying electrons of non-potential dawn-dusk electric fields up to several mv/m in the active reconnection region during perturbed periods (when the majority of Type II ion beams have been observed). Experimental observations also show that these non-potential electric fields (in contrast to the potential ones) are spatially localized (Ieda et al. 1998). Concluding the discussion of the scatterplot shown in Fig. 27 we argue that the class of Type-II events includes both ion beams which could be moderately accelerated up to 100 kev near a quasi-stationary X-line (in the course of a quasi-steady magnetic reconnection, which lasts at least during several minutes) and ion beams accelerated near more dynamic X-lines (in the course of a transient, unsteady reconnection) where the contribution of strong inductive electric fields may explain the observations of highly-accelerated (W >100 kev) ion beams. The electrons observed in PSBL simultaneously with Type-II ion beams have temperatures larger than 1 kev (see Fig. 28), which is comparable with the temperature of PS electrons. In some events of this type, the electron temperature in the PSBL reaches val-

34 166 E.E. Grigorenko et al. ues up to a few kev and even exceeds the electron temperatures observed previously in the PS, as in the event presented in Fig. 24. This indicates that significant electron heating and acceleration also takes place near the ion acceleration source. 3.4 FAC Associated with Type-II Ion Beams Spacecraft observations have demonstrated that a strong shear magnetic field may exist in the PS-lobe interface indicating the presence of FAC (e.g. Ueno et al. 2002; Nakamura et al. 2004a). Geotail observations have shown a systematic FAC pattern in the inflow/outflow region close to the reconnection region as consequence of the Hall current closure in the course of magnetotail reconnection process (Nagai et al. 2001, 2003). The same signatures of FAC have been observed during dipolarization at the outer edge of the PS boundary away from the reconnection site, suggesting that current closure takes place on a more global scale which contributes to magnetosphere-ionosphere coupling (Fujimoto et al. 2001; Uenoetal. 2002). In order to identify the origin of these transient features, it is essential to determine their spatial and temporal scales. Nakamura et al. (2004a) reported Cluster and Geotail observations of a strong flow shear event near the PS boundary during a substorm interval. By using multipoint measurements they obtained typical timescales for these events of 1 5 min. They showed that FACs consist of upward and downward current layers, with the latter located at the outermost edge of the plasma sheet and concentrated in a region with a thickness of 1600 km. Nakamura et al. (2005) have also identified a consistent temporal/spatial scale for the FAC system in the conjugate ionosphere. Grigorenko et al. (2010b) analyzed FACs associated with Type-II PSBL ion beams (see Fig. 29) and reported a FAC pattern similar to the one observed by Nakamura et al. (2004a). They estimated the thickness of the Earthward (downward) current layer 1600 km and of tailward (upward) current layer 1 R E. The currents were well-observed during at least 6.5 min (from 07:27 to 07:33:40 UT). Moreover, weak signatures of the Earthward (downward) current, registered before 07:26 UT and after 07:34 UT, may indicate that this FAC system existed even longer: during 11 min. Thus, the duration of this FAC system was longer than in the event studied by Nakamura et al. (2004a): 1 5 min. This indicates that in the event studied by Grigorenko et al. (2010b) the FAC current system could be formed in the course of a quasi-steady magnetic reconnection. In order to check statistically the presence of a FAC system in the PSBL during intervals of Type-II ion beam propagation, 165 PSBL crossings by the Cluster s/c were analyzed. In each crossing ion beam, moving along the lobeward edge of PSBL, was directed earthward, so that, its acceleration source was located tailward from the Cluster s/c. All these intervals corresponded to the disturbed geomagnetic periods ( AL 300 nt). In each case current density was estimated for time intervals when all four s/c were located inside PSBL and the ratio B/ B was less than 0.2, which confirms the reliability of these data. Figure 30 presents the distribution of FAC density and direction measured near the lobeward edge of PSBL and deeper within PSBL. The lobeward PSBL boundary is represented by the horizontal dotted line. FAC densities measured in each crossing near the lobeward edge of PSBL are shown in Fig. 30 by the vertical lines drawn upward from the horizontal dotted line. Correspondingly, FAC densities measured deeper within PSBL are presented by the vertical lines drawn downward from the horizontal dotted line. Since the analyzed PSBL crossings took place in both hemispheres, the densities of Earthward and tailward FACs can have either positive or negative values in dependence on B X direction. Therefore, to make this distribution more visual we used in Fig. 30 only absolute values of FAC densities and show the direction of particular FAC by the color: the black color corresponds

35 Non-adiabatic Ion Acceleration in the Earth Magnetotail 167 Fig. 29 Adapted from Grigorenko et al. (2010b). An earthward moving Type-II ion beam and the associated system of FAC observed in the PSBL on 14 September 2002 by the Cluster s/c. Cluster s/c was in the southern hemisphere, so that parallel velocity of the ion beam as well as the earthward FAC has negative values. From top to bottom: 2D ion velocity distribution functions in the (V,V ) plane (counts per spectrum C units were used) and electron pitch angle distributions (energy flux units, def (1/cm 2 -s-str-ev) were used); proton (a) and electron (b) energy-time spectrograms measured by Cluster-4 correspondingly; (c), (d) ion energy-time spectrograms obtained by Cluster-1 and -3 correspondingly; (e), (f) B X and B Y components of the magnetic field (X axis is parallel to the non-disturbed lobe magnetic field and directed sunward, so that B X is negative in the southern lobe; Z is directed along the normal to the PS boundary obtained from the timing analysis of diamagnetic depressions of the magnetic field and Y completes the orthogonal system); (g) density of FAC J and of two perpendicular components of current, calculated as ( B); (h) ratio of ( B)/( B); (i) ion(j ion ) and electron (J ele ) contributions to FAC. The electron contribution was calculated as J ele = ( B) J ion ;(j) Z -component of electric field calculated as (V B) Z (velocities of low-energy oxygen ions were used)