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GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L06105, doi:10.1029/2005GL024901, 2006

Multiplet structure of acceleration processes in the distant magnetotail L. M. Zelenyi,1 E. E. Grigorenko,1,2 J.-A. Sauvaud,3 and R. Maggiolo3 Received 8 October 2005; revised 15 December 2005; accepted 6 February 2006; published 21 March 2006.

[1] We have studied ion distributions measured in the Plasma Sheet Boundary Layer (PSBL) of the Earth’s magnetotail by the Cluster spacecraft at X  15Re. Field-aligned ion beams (beamlets) accelerated in the magnetotail to energies of 30keV are typically observed within the interface region between the Plasma Sheet (PS) and the magnetotail lobes. PSBL beamlets are produced by non-adiabatic ion acceleration in the vicinity of X-line which is located, during quiet periods, in the distant parts of the tail. Earlier kinetic models attributed the filamentary and/or bursty nature of these processes to Current Sheet (CS) resonances and predicted the scaling law for the velocity of subsequent structures as VN  N2/3. Cluster-2 provides experimental evidence from the PSBL from of the existence of such resonant structures in ion velocity space and provides the first statistically proven identification of such a scaling law for quiet and moderately disturbed periods. Citation: Zelenyi, L. M., E. E. Grigorenko, J.-A. Sauvaud, and R. Maggiolo (2006), Multiplet structure of acceleration processes in the distant magnetotail, Geophys. Res. Lett., 33, L06105, doi:10.1029/2005GL024901.

1. Introduction [2] Ion acceleration in the CS is apparently a permanent magnetotail phenomenon since, at the lobeward edge of the PSBL, field-aligned ion beams moving typically earthward with high velocities up to 2500km/s are often observed [DeCoster and Frank, 1979; Eastman et al., 1984; Takahashi and Hones, 1988]. New measurement techniques allow the study of the fine structure of these events, which often consist of smaller scale substructures with burst-like manifestations [Parks et al., 1998; Grigorenko et al., 2002; Sauvaud and Kovrazhkin, 2004]. It is generally accepted that these beamlets could be the result of non-adiabatic ion acceleration in broad region near the X-line in the so-called separatrix layer [Buchner and Zelenyi, 1990; Chen et al., 1990; Ashour-Abdalla et al., 1993]. It was predicted that ion acceleration in the CS should exhibit a resonance character and the PSBL ion distribution should have filamentary observation. Numerous attempts to simulate the consequences of such acceleration sources produced important results: Onsager et al. [1991] suggest a field-aligned ion acceleration at an extended central plasma sheet source so that ion distributions in the near-Earth PSBL are controlled by the time-of-flight effects. Ashour-Abdalla et al. [1993], further 1 Space Research Institute of RAS, Space Plasma Physics Division, Moscow, Russia. 2 Also at Skobeltcyn Institute of Nuclear Physics, Moscow State University, Russia. 3 Centre d’Etudie Spatial des Rayonnements, Toulouse, France.

Copyright 2006 by the American Geophysical Union. 0094-8276/06/2005GL024901

cited as [AA], on the contrary, proposed that ion acceleration takes place in spatially localized sites of the CS with different values of the local magnetic field. So that, particles accelerated due to different resonant conditions would have different energies. Since on the average the magnetic field in the CS decreases tailward, ions which are accelerated closest to the X-line and then are streaming along the outermost PSBL field lines have the highest energies. Considering the resonance character of the acceleration, different predictions about the scaling law for the ion structures have been made. Chen et al. [1990] reported the existence of a resonance scaling law, N  H1/4, for ion distributions observed inside the quiet-time CS (where, H parameterizes the particle energy and magnetic field geometry and N represents the integer sequential index for a certain resonance). A model of Burkhart and Chen [1991] assumed the local nature of resonance without taking into account spatial smearing of these structures due to convection. [3] For the resonant structures observed in the PSBL a scaling law VN  N2/3 was proposed by [AA] (here VN is the ion parallel velocity of the N-th structure). The nature of the current sheet resonances is related to the properties of meandering motion of non-adiabatic particles and has been discussed in papers by Chen and Palmadesso [1986], Buchner and Zelenyi [1989], and [AA]. At a given resonance, as the theory predicts, the parameter of adiabaqffiffiffi ticity æ = rR (where R is the radius of the curvature of 0

magnetic field line which is crossing the CS and r0 is a maximum value of particle’s Larmor radius) [Buchner and Zelenyi, 1986] is equal to 1/N, where N = 1, 2, 3,. . . The [AA] model illustrated in Figure 1 assumes that the resonant conditions which are mostly sensitive to the parameter BZ at the location of the certain N-th resonance are adjusted mostly by the variations of this parameter and are achieved almost simultaneously for rather cold ions which are coming to the CS from the plasma mantle. [4] However experimental evidences in favor of these predictions are scarce. One of the reasons is that the most observations are made near the Earth where ion beams produced by different sources might overlap and resonance structures are generally smeared. In this paper we present experimental observations of a double peaked ion distributions measured by the Cluster spacecraft at X = 15 18 Re which are produced by ion beams accelerated by at least two different resonant processes at spatially separated sites. Furthermore, we provide a statistical comparison of our observations with predictions of the [AA] theory.

2. Observations [5] We have selected 32 PSBL crossings by Cluster spacecraft for quiet conditions (AE < 100nT during three

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Figure 1. The sketch of resonant acceleration in the localized CS domains of ions, streaming from the mantles (solid blue lines) equatorward. An asymmetry of mantle sources is assumed (northern source dominates). At the odd resonances ions are ejected at the same hemisphere and at the even ones ions are ejected in the opposite one. Beams formed by the ions of northern mantle origin are indicated by the red lines and beams consisting of ions from southern mantle are shown by the green dotted lines. Multiplet distribution measured within DZ interval at Cluster position consisting of two separated ion beams (with V|| = V3; V5) is formed due to 2 reasons: 1) counteraction of ‘‘place of birth’’ and velocity filter effect and 2) lack of ions with intermediate energy from the resonance ‘‘4’’ because of the mantle source asymmetry. hours before and after the crossing) and for moderate disturbed periods (AE < 300nT). In each case spacecraft encounter with the PSBL is characterized by the detection of high-velocity (jVparallelj  2000 km/s) ion beams and by the simultaneous detection of ions with lower velocities (600 km/s  jVparallelj  1500 km/s). Both ion populations are field-aligned, moving earthward and have well-defined demarcation in energy. In the events studied below these populations are clearly separated in velocity space (with a gap of at least one energy channel). We will call such kind of velocity distributions ‘‘multiplet’’ distributions. Figures 2 and 3 display an example of such a phenomenon. At 08:00 UT on September 1, 2003 Cluster was in the southern lobe (at [18;0;4]RE) and at 08:09 UT it entered PSBL and observed field-aligned ion beams which were streaming earthward and were clearly separated in energy. These two energetic ion populations, one with an energy of about 5 keV and the other with an energy close to the instrument threshold (30keV) are observed during 2.5 min onboard three Cluster satellites: Cl-1,-3 (data from HIA instrument which measures all ion components without mass resolution) and Cl – 4 (H+ data from CODIF instrument, are not shown) (Figure 2). 2D cuts of the 3D velocity distribution functions in the plane containing the magnetic field and the

Figure 3. Cluster observation of ‘‘double-peaked’’ ion distributions in the PSBL on 01.09.03. Each pair of columns represents from left to right: (Vper, Vpar) ion velocity distribution functions accumulated for 12s (by HIA devices) and their 1D cut along the magnetic field. Two left columns represent the data obtained by Cl-3 and the right ones are from Cl-1. convection velocity show two enhancements of phase density corresponding to two ion populations streaming mostly along the magnetic field. Note that the three spins (i.e. 12s) are generally needed to obtain a 3D distribution function. Cuts of the distributions along the magnetic field also show two clearly separated peaks corresponding to field-aligned ions moving with parallel velocities of 2400 km/s and 1000 km/s (Figure 3). pffiffiffiffiVertical lines indicate statistical errors calculated as N , (N is total count number). We may assume that this feature exists in the ion distribution for at least 3min so it seems to have spatial than temporal character.

3. Discussion [6] Our discussion is based on two assumptions: 1) ions, forming quiet-time beamlets, are accelerated at spatially localized sites (‘‘resonance’’ sites) in the distant CS and 2) ions, which are accelerated at different localized sites (different resonances), have different energies. The latter assumption corresponds to the so-called ‘‘place of birth’’ effect [AA]: the BZ component in the CS is not constant and, on average, it decreases tailward, so it is a function of the distance from the Earth, BZ = BZ(X). Since ions, accelerated by non-adiabatic mechanism in the CS, reach   the energy W 

Figure 2. E-T spectrograms obtained from Cluster (by HIA spectrometers) on 01.09.2003. From top to bottom: spectrograms of earthward and tailward ions observed by Cl-3; the same for Cl-1.

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E BZ ð X Þ

2

, (E is dawn-dusk electric field),

their energy is also a function of X. This effect coupled to the energy dispersion, resulting from the E B velocity filter, is responsible for the peculiarities of PSBL beams. [7] One of the prominent features predicted by the theory of resonant particle acceleration is the structuring of the ion distributions in velocity space. The scaling law for resonant structures predicted by this theory is: VN = C N2/3, here VN is velocity of N-th ion beam produced by the N resonance (N represents integers) and C is a normalization constant, C  700 km/s, scaled as a velocity of a lower energy

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Figure 4. Statistical verification of the scaling low for resonance structures predicted by the [AA]: VN = C N2/3. The values of V1/V2 (empty and black circles) are plotted versus h the i value of low-velocity beams, V1. The levels of

N N þ2

2=3

are shown by grey lines. Solid line represents

the function F(V1) inferred from the scaling law mentioned above. The numbers of double-peaked distributions corresponding to the each resonance are indicated by the black solid lines in the right of the Figure. beamlet. To check this scaling law we have analyzed velocity distribution functions, measured for 32 PSBL crossings by Cluster (at X = 15  18RE), in which, at least two field-aligned ion beams streaming earthward with parallel V1 and V2 velocities, (V1 < V2), could be reliably discerned. It must be stressed that the ‘‘place of birth’’ effect and velocity filter effect have an opposite influences on the beamlet location in Z [Zelenyi et al., 1990]. Normally ion beams accelerated at different CS sites are registered near the Earth at different Z locations (in Figure 1 these beams are shown as being accelerated at the sources 1 and 5). Therefore, as the spacecraft crosses the PSBL it observes typical beamlet distribution function with one maximum corresponding to the highest ion velocity at the outer boundary of PSBL and as the spacecraft moves deeper into the PSBL the maximum of the ion distribution shifts towards lower velocities [Takahashi and Hones, 1988]. But if the distance DX between different CS resonant sites is large enough the action of the global velocity filter could ‘‘combine’’ these earthward beams at Cluster location during one 3D ion distribution measurement cycle, providing observed ‘‘double-peaked’’ distributions (ion beams from the sources 3 and 5 shown in Figure 1). For instance, to estimate the spatial widths of the resonant sites for ion beams observed on 01.09.2003 and the distance between the resonances, we traced the ions back tailward until the crossing with the Neutral Sheet in Tsyganenko-96 model, (taking into account the influence of convection). We obtain that separation between resonances (6 Re) is at least twice as large as their individual width and their coalescence should not occur. [8] In the early model of CS particle acceleration [AA] a symmetry of northern and southern mantle sources has been assumed. In general case, however, one could think about many effects producing an asymmetry (i.e., dipole tilt which might produce strong seasonal effect, the peculiarities of dayside reconnection which are producing asymmetry of plasma flows around magnetopause), so here we will make more general assumption that the sources are significantly asymmetric. This produces important quantitative effect.

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Particles accelerated at odd resonances are returning to the same hemisphere where was their source, while particles from even resonances are going to the opposite hemisphere after acceleration so at given observation point one could simultaneously register particles either only from odd or only from even resonances. Indirectly such asymmetry effect is helping us to resolve multiplet energetic distributions reported in this paper. Chances to resolve well isolated energy peaks V1 and V2 are significantly higher when they are having larger separation in velocity space V1/V2  [N/N + 2]2/3 instead of [N/N + 1]2/3 for adjoining resonances. This asymmetry effect is illustrated in Figure 1 (notice that particles from resonance ‘‘4’’ are almost absent at observation site). [9] In order to compare our experimental observations with the resonance scaling law predicted by the theory we calculate the ratio V1/V2, (where V1 is the ion parallel velocity corresponding to lower- V maximum of the distribution function and V2 is the parallel velocity corresponding to the higher-V and compare h maximum) i these values with the ratio

N N þ2

2=3

, where N represents

integer numbers of resonances from 1 to 10. In Figure 4 we display the values of V1/V2 (by empty and black circles h ifor horizontal stratification) versus V1. The levels of

N N þ2

2=3

are shown by grey lines, near the first and last levels we indicated the corresponding values of N. The vertical dotted lines show the errors of V1/V2 values caused by the finite width of each energy channel. At the right of Figure 4 the black bars indicate the number of cases of ‘‘double-peaked’’ distributions in which the value of V1/V2 equals (up to error margins) to the value of the corresponding level. Total ‘‘effective’’ number of cases >32 due to multiple PSBL h i2=3 boundary encounters. on the [10] The dependencies of V1/V2 and NNþ2 velocity of the low-speed beamlet (V1) for each of the analyzed cases both are in a reasonably good agreement. [11] But as N increases the interval between the neighboring resonance lines shrinks and becomes less than the measurement error of the V1/V2 ratio. For N  4 the comparison becomes already questionable. It is worth to mention that for higher velocities (i.e. for higher N values) beamlets begin to smear and higher order beamlets become undistinguishable not only due to uncertainties of their experimental registration but due to intrinsic overlapping of adjacent higher-order resonances. [12] Higher order beamlets should have higher energies and to verify this dependence one can derive analytical expression for the dimensionless ratio of relative beamlet energies in a given multiplet from the energy of a lower partner. From the scaling law given above one can get: V1 V1/V2 = F(V1) = 2=3 < 1, where as we C ½ðV 1=C Þ3=2 þ2:0 discussed above C  700 km/s is a constant from [AA] theory, corresponding to the velocity of low-energy N = 1 beamlet). This dependence is shown in the Figure 4 by black solid line. There is a good agreement between the experimental data and the theory prediction at least for N  5 (the main part of experimental measurements corresponds to a lower N numbers). From this we may conclude that the observation of ‘‘double-peaked’’ ion distribution in the

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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 = C N2/3.

4. Summary [13] The simultaneous observations in the near-Earth PSBL of ion multiplets consisting of at least two fieldaligned ion beams with distinct parallel velocities (with difference up to two times) provide an evidence of the simultaneous operation of different acceleration sources in the magnetotail CS. The ‘‘double-peaked’’ feature of ion distributions is in good agreement with the scaling law VN  N2/3 predicted by the theory of resonant particle acceleration. In this paper we present a qualitative explanation of the possible scenario which produces such kind of distributions. Although our model considers the observed beamlets as spatial filamentary-like structures, we understand the finiteness of their lifetime and will estimate corresponding temporal effects more precisely in subsequent publications. [14] Acknowledgments. The authors thank Cluster CIS and FGM teams for providing the data, E. Penou, E. Budnik and A. Fedorov for valuable data software (DD System and CL) and for advice. We thank INTAS grant 03-51-3738, INTAS YS Fellowship 03-55-1880; RFBR grants 04-02-17371, 03-02-16967; grant HIII-1739.2003.2 and Russian Science Support Foundation.

References Ashour-Abdalla, M., J. P. Berchem, J. Buchner, and L. M. Zelenyi (1993), Shaping of the magnetotail from the mantle: Global and local structuring, J. Geophys. Res., 98, 5651. Buchner, J., and L. M. Zelenyi (1986), Deterministic chaos in the dynamics of charged particles near a magnetic field reversal, Phys. Lett. A, 118, 395.

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Buchner, J., and L. M. Zelenyi (1989), Regular and chaotic charged particle motion in magnetotail-like field reversals: 1. Basic theory of trapped motion, J. Geophys. Res., 94, 11,821. Buchner, J., and L. M. Zelenyi (1990), The separatrix tentacle effect on the ion acceleration in the PSBL, Geophys. Res. Lett., 17, 127. Burkhart, G. R., and J. Chen (1991), Differential memory in the Earth’s magnetotail, J. Geophys. Res., 96, 14,033. Chen, J., and P. J. Palmadesso (1986), Chaos and nonlinear dynamics of single-particle orbits in a magnetotail-like magnetic field, J. Geophys. Res., 91, 1499. Chen, J., G. R. Burkhardt, and C. Y. Huang (1990), Observational signatures of NL magnetotail particle dynamics, Geophys. Res. Lett., 17, 2237. DeCoster, R. J., and L. A. Frank (1979), Observations pertaining to the dynamics of the plasma sheet, J. Geophys. Res., 84, 5099. Eastman, T. E., L. A. Frank, W. K. Peterson, and W. Lennartsson (1984), The plasma sheet boundary layer, J. Geophys. Res., 89, 1553. Grigorenko, E. E., A. O. Fedorov, and L. M. Zelenyi (2002), Statistical study of transient plasma structures in magnetotail lobes and plasma sheet boundary layer: Interball-1 observations, Ann. Geophys., 20, 329. Onsager, T. G., M. F. Thomson, R. C. Elphig, and J. T. Gosling (1991), Models of electron and ion distributions in the plasma sheet boundary layer, J. Geophys. Res., 96, 2099. Parks, G., et al. (1998), New observations of ion beams in the plasma sheet boundary layer, Geophys. Res. Lett., 25, 3285. Sauvaud, J.-A., and R. A. Kovrazhkin (2004), Two types of energydispersed ion structures at the plasma sheet boundary, J. Geophys. Res., 109, A12213, doi:10.1029/2003JA010333. Takahashi, K., and E. W. Hones (1988), ISEE 1 and 2 observations of ion distributions at the plasma sheet-tail lobe boundary, J. Geophys. Res., 93, 8558. Zelenyi, L. M., R. A. Kovrazhkin, and J. M. Bosqued (1990), Velocitydispersed ion beams in the nightside auroral zone: AUREOL-3 observations, J. Geophys. Res., 95, 12,119. 

E. E. Grigorenko and L. M. Zelenyi, Space Research Institute of RAS, Space Plasma Physics Division, Profsoyuznaya 84/32, Moscow 117997, Russia. ([email protected]; [email protected]) R. Maggiolo and J.-A. Sauvaud, Centre d’Etudie Spatial des Rayonnements, BP 4346, 9 avenue du colonel Roche, F-31028 Toulouse, France. ([email protected]; [email protected])

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