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This paper represents a continuation of our previous work, where the Bolzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically the unrestricted face model, based on the $\mathfrak{su}(3)_k$ affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum $R$ matrix of the $U_q(\mathfrak{sl} (3))$ quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of $R$ matrix elements., Comment: one figure

Using particle data from the ELFIN satellites, we present a statistical study of 284 proton isotropy boundary events on the nightside magnetosphere, characterizing their occurrence and distribution in local time, latitude (L-shell), energy, and precipitating energy flux, as a function of geomagnetic activity. For a given charged particle species and energy, its isotropy boundary (IB) is the magnetic latitude poleward of which persistently isotropic pitch-angle distributions ($J_{prec}/J_{perp}\sim 1$) are first observed to occur. This isotropization is interpreted as resulting from magnetic field-line curvature (FLC) scattering in the equatorial magnetosphere. We find that proton IBs are observed under all observed activity levels, spanning 16 to 05 MLT with $\sim$100% occurrence between 19 and 03 MLT, trending toward 60% at dawn/dusk. These results are also compared with electron IB properties observed using ELFIN, where we find similar trends across local time and activity, with the onset in $\geq$50 keV proton IB occurring on average 2 L-shells lower, and providing between 3 and 10 times as much precipitating power. Proton IBs typically span $64^\circ$-$66^\circ$ in magnetic latitude (5-6 in L-shell), corresponding to the outer edge of the ring current, tending toward lower IGRF latitudes as geomagnetic activity increases. The IBs were found to commonly occur 0.3-2.1 Re beyond the plasmapause. Proton IBs typically span $<$50 keV to $\sim$1 MeV in energy, maximizing near 22 MLT, and decreasing to a typical upper limit of 300-400 keV toward dawn and dusk, with peak observed isotropic energy increasing by $\sim$500 keV during active intervals. These results suggest that FLC in the vicinity of IBs can provide a substantial depletion mechanism for energetic protons, with the total nightside precipitating power from FLC-scattering found to be on the order of 100 MW, at times $\geq$10 GW.

Earth's magnetotail, a night-side region characterized by stretched magnetic field lines and strong plasma currents, is the primary site for the release of magnetic field energy and its transformation into plasma heating and kinetic energy plus charged particle acceleration during magnetic reconnection. In this study, we demonstrate that the efficiency of this acceleration can be sufficiently high to produce populations of relativistic and ultra-relativistic electrons, with energies up to several MeV, which exceeds all previous theoretical and simulation estimates. Using data from the low altitude ELFIN and CIRBE CubeSats, we show multiple events of relativistic electron bursts within the magnetotail, far poleward of the outer radiation belt. These bursts are characterized by power-law energy spectra and can be detected during even moderate substorms.

Shadow formalism is a technique in two-dimensional CFT allowing straightforward computation of conformal blocks in the limit of infinitely large central charge. We generalize the construction of shadow operator for superconformal field theories. We demonstrate that shadow formalism yields known expressions for the large-c limit of the four-point superconformal block on a plane and of the one-point superconformal block on a torus. We also explicitly find the two-point global torus superconformal block in the necklace channel and check it against the Casimir differential equation.

The magnetotail current sheet's spatial configuration and stability control the onset of magnetic reconnection - the driving process for magnetospheric substorms. The near-Earth current sheet has been thoroughly investigated by numerous missions, whereas the midtail current sheet has not been adequately explored. This is especially the case for the long-term variation of its configuration in response to the solar wind. We present a statistical analysis of 1261 magnetotail current sheet crossings by the Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission orbiting the moon (X~-60 RE), collected during the entirety of Solar Cycle 24. We demonstrate that the magnetotail current sheet typically remains extremely thin, with a characteristic thickness comparable to the thermal ion gyroradius, even at such large distances from Earth's dipole. We also find that a substantial fraction (~one quarter) of the observed current sheets have a partially force-free magnetic field configuration, with a negligible contribution of the thermal pressure and a significant contribution of the magnetic field shear component to the pressure balance. Further, we quantify the impact of the changing solar wind driving conditions on the properties of the midtail around the lunar orbit. During active solar wind driving conditions, we observe an increase in the occurrence rate of thin current sheets, whereas quiet solar wind driving conditions seem to favor the formation of partially force-free current sheets.

Interaction-Round the Face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e., the models the Boltzmann weights of which satisfy the quantum Yang-Baxter equation, are of particular interest. In this paper, we investigate trigonometric Boltzmann weights of integrable IRF models. By using an ansatz proposed by one of the authors in some previous works, the Boltzmann weights of the restricted IRF models based on the affine Lie algebras $\mathfrak{su}(2)_k$ and $\mathfrak{su}(3)_k$ are computed for fundamental and adjoint representations for some fixed levels $k$. New solutions for the Boltzmann weights are obtained. We also study the vertex-IRF correspondence in the context of an unrestricted IRF model based on $\mathfrak {su}(3)_k$ (for general $k$) and discuss how it can be used to find Boltzmann weights in terms of the quantum $\hat{R}$ matrix when the adjoint representation defines the admissibility conditions.

Utilizing observations from the ELFIN satellites, we present a statistical study of $\sim$2000 events in 2019-2020 characterizing the occurrence in magnetic local time (MLT) and latitude of $\geq$50 keV electron isotropy boundaries (IBs) at Earth, and the dependence of associated precipitation on geomagnetic activity. The isotropy boundary for an electron of a given energy is the magnetic latitude poleward of which persistent isotropized pitch-angle distributions ($J_{prec}/J_{perp}\sim 1$) are first observed to occur, interpreted as resulting from magnetic field-line curvature scattering (FLCS) in the equatorial magnetosphere. We find that energetic electron IBs can be well-recognized on the nightside from dusk until dawn, under all geomagnetic activity conditions, with a peak occurrence rate of almost 90% near $\sim$22 hours in MLT, remaining above 80% from 21 to 01 MLT. The IBs span a wide range of IGRF magnetic latitudes from $60^\circ$-$74^\circ$, with a maximum occurrence between $66^\circ$-$71^\circ$ (L of 6-8), shifting to lower latitudes and pre-midnight local times with activity. The precipitating energy flux of $\geq$50 keV electrons averaged over the IB-associated latitudes varies over four orders of magnitude, up to $\sim$1 erg/cm$^2$-s, and often includes electron energies exceeding 1 MeV. The local time distribution of IB-associated energies and precipitating fluxes also exhibit peak values near midnight for low activity, shifting toward pre-midnight for elevated activity. The percentage of the total energy deposited over the high-latitude regions ($55^\circ$ to $80^\circ$; or IGRF $L\gtrsim 3$) attributed to IBs is 10-20%, on average, or about 10 MW of total atmospheric power input, but at times can be up to $\sim$100% of the total $\geq$50 keV electron energy deposition over the entire sub-auroral and auroral zone region, exceeding 1 GW in atmospheric power input.

Force-free current sheets are local plasma structures with field-aligned electric currents and approximately uniform plasma pressures. Such structures, widely found throughout the heliosphere, are sites for plasma instabilities and magnetic reconnection, the growth rate of which is controlled by the structure's current sheet configuration. Despite the fact that many kinetic equilibrium models have been developed for one-dimensional (1D) force-free current sheets, their two-dimensional (2D) counterparts, which have a magnetic field component normal to the current sheets, have not received sufficient attention to date. Here, using particle-in-cell simulations, we search for such 2D force-free current sheets through relaxation from an initial, magnetohydrodynamic equilibrium. Kinetic equilibria are established toward the end of our simulations, thus demonstrating the existence of kinetic force-free current sheets. Although the system currents in the late equilibrium state remain field aligned as in the initial configuration, the velocity distribution functions of both ions and electrons systematically evolve from their initial drifting Maxwellians to their final time-stationary Vlasov state. The existence of 2D force-free current sheets at kinetic equilibrium necessitates future work in discovering additional integrals of motion of the system, constructing the kinetic distribution functions, and eventually investigating their stability properties., Comment: Published in ApJ, 20 pages with 14 figures

We review comprehensive observations of electromagnetic ion cyclotron (EMIC) wave-driven energetic electron precipitation using data from the energetic electron detector on the Electron Losses and Fields InvestigatioN (ELFIN) mission, two polar-orbiting low-altitude spinning CubeSats, measuring 50-5000 keV electrons with good pitch-angle and energy resolution. EMIC wave-driven precipitation exhibits a distinct signature in energy-spectrograms of the precipitating-to-trapped flux ratio: peaks at 0.5 MeV which are abrupt (bursty) with significant substructure (occasionally down to sub-second timescale). Multiple ELFIN passes over the same MLT sector allow us to study the spatial and temporal evolution of the EMIC wave - electron interaction region. Using two years of ELFIN data, we assemble a statistical database of 50 events of strong EMIC wave-driven precipitation. Most reside at L=5-7 at dusk, while a smaller subset exists at L=8-12 at post-midnight. The energies of the peak-precipitation ratio and of the half-peak precipitation ratio (our proxy for the minimum resonance energy) exhibit an L-shell dependence in good agreement with theoretical estimates based on prior statistical observations of EMIC wave power spectra. The precipitation ratio's spectral shape for the most intense events has an exponential falloff away from the peak (i.e., on either side of 1.45 MeV). It too agrees well with quasi-linear diffusion theory based on prior statistics of wave spectra. Sub-MeV electron precipitation observed concurrently with strong EMIC wave-driven 1MeV precipitation has a spectral shape that is consistent with efficient pitch-angle scattering down to 200-300 keV by much less intense higher frequency EMIC waves. These results confirm the critical role of EMIC waves in driving relativistic electron losses. Nonlinear effects may abound and require further investigation.

Electron ring velocity space distributions have previously been seen in numerical simulations of magnetic reconnection exhausts and have been suggested to be caused by the magnetization of the electron outflow jet by the compressed reconnected magnetic fields [Shuster et al., ${\it Geophys.~Res.~Lett.}, {\bf 41}$, 5389 (2014)]. We present a theory of the dependence of the major and minor radii of the ring distributions solely in terms of upstream (lobe) plasma conditions, thereby allowing a prediction of the associated temperature and temperature anisotropy of the rings in terms of upstream parameters. We test the validity of the prediction using 2.5-dimensional particle-in-cell (PIC) simulations with varying upstream plasma density and temperature, finding excellent agreement between the predicted and simulated values. We confirm the Shuster et al. suggestion for the cause of the ring distributions, and also find that the ring distributions are located in a region marked by a plateau, or shoulder, in the reconnected magnetic field profile. The predictions of the temperature are consistent with observed electron temperatures in dipolarization fronts, and may provide an explanation for the generation of plasma with temperatures in the 10s of MK in super-hot solar flares. A possible extension of the model to dayside reconnection is discussed. Since ring distributions are known to excite whistler waves, the present results should be useful for quantifying the generation of whistler waves in reconnection exhausts., Comment: Accepted for publication in Journal of Geophysical Research: Space Physics

Magnetic field line reconnection is a universal plasma process responsible for the magnetic field topology change and magnetic field energy dissipation into charged particle heating and acceleration. In many systems, the conditions leading to the magnetic reconnection are determined by the pre-reconnection configuration of a thin layer with intense currents -- otherwise known as the thin current sheet. In this study we investigate two such systems: Earth's magnetotail and helmet streamers in the solar corona. The pre-reconnection current sheet evolution has been intensely studied in the magnetotail, where in-situ spacecraft observations are available; but helmet streamer current sheets studies are fewer, due to lack of in-situ observations -- they are mostly investigated with numerical simulations and information that can be surmised from remote sensing instrumentation. Both systems exhibit qualitatively the same behavior, despite their largely different Mach numbers, much higher at the solar corona than at the magnetotail. Comparison of spacecraft data (from the magnetotail) with numerical simulations (for helmet streamers) shows that the pre-reconnection current sheet thinning, for both cases, is primarily controlled by plasma pressure gradients. Scaling laws of the current density, magnetic field, and pressure gradients are the same for both systems. We discuss how magnetotail observations and kinetic simulations can be utilized to improve our understanding and modeling of the helmet streamer current sheets.

The magnetotail current sheet configuration determines magnetic reconnection properties that control the substorm onset, one of the most energetic phenomena in the Earth's magnetosphere. The quiet-time current sheet is often approximated as a two-dimensional (2D) magnetic field configuration balanced by isotropic plasma pressure gradients. However, reconnection onset is preceded by the current sheet thinning and the formation of a nearly one-dimensional (1D) magnetic field configuration. In this study, using particle-in-cell simulations, we investigate the force balance of such thin current sheets when they are driven by plasma inflow. We demonstrate that the magnetic field configuration transitions from 2D to 1D thanks to the formation of plasma pressure nongyrotropy and reveal its origin in the nongyrotropic terms of the ion distributions. We show that substorm onset may be controlled by the instability and dynamics of such nongyrotropic current sheets, having properties much different from the most commonly investigated 2D isotropic configuration., Comment: 16 pages, 4 figures

Many in-situ spacecraft observations have demonstrated that magnetic reconnection in the Earth's magnetotail is largely controlled by the pre-reconnection current sheet configuration. One of the most important thin current sheet characteristics is the preponderance of electron currents driven by strong polarized electric fields, which are commonly observed in the Earth's magnetotail well before the reconnection. We use particle-in-cell simulations to investigate magnetic reconnection in the 2D magnetotail current sheet with a finite magnetic field component normal to the current sheet and with the current sheet polarization. Under the same external driving conditions, reconnection in a polarized current sheet is shown to occur at a lower rate than in a nonpolarized current sheet. The reconnection rate in a polarized current sheet decreases linearly as the electron current's contribution to the cross-tail current increases. In simulations with lower background temperature the reconnection electric field is higher. We demonstrate that after reconnection in such a polarized current sheet, the outflow energy flux is mostly in the form of ion enthalpy flux, followed by electron enthalpy flux, Poynting flux, ion kinetic energy flux and electron kinetic energy flux. These findings are consistent with spacecraft observations. Because current sheet polarization is not uniform along the magnetotail, our results suggest that it may slow down reconnection in the most polarized near-Earth magnetotail and thereby move the location of reconnection onset downtail., Comment: 37 pages, 11 figures

Magnetic field-line reconnection is a universal plasma process responsible for the conversion of magnetic field energy to the plasma heating and charged particle acceleration. Solar flares and Earth's magnetospheric substorms are two most investigated dynamical systems where magnetic reconnection is believed to be responsible for global magnetic field reconfiguration and energization of plasma populations. Such a reconfiguration includes formation of a long-living current systems connecting the primary energy release region and cold dense conductive plasma of photosphere/ionosphere. In both flares and substorms the evolution of this current system correlates with formation and dynamics of energetic particle fluxes. Our study is focused on this similarity between flares and substorms. Using a wide range of datasets available for flare and substorm investigations, we compare qualitatively dynamics of currents and energetic particle fluxes for one flare and one substorm. We showed that there is a clear correlation between energetic particle bursts (associated with energy release due to magnetic reconnection) and magnetic field reconfiguration/formation of current system. We then discuss how datasets of in-situ measurements in the magnetospheric substorm can help in interpretation of datasets gathered for the solar flare.

The terrestrial magnetopause is the boundary that shields the Earth's magnetosphere on one side from the shocked solar wind and its embedded interplanetary magnetic field on the other side. In this paper, we show observations from two of the Time History of Events and Macroscales Interactions during Substorms (THEMIS) satellites, comparing dayside magnetopause crossings with flank crossings near the terminator. Macroscopic properties such as current sheet thickness, motion, and current density are examined for a large number of magnetopause crossings. The results show that the flank magnetopause is typically thicker than the dayside magnetopause and has a lower current density. Consistent with earlier results from Cluster observations, we also find a persistent dawn-dusk asymmetry with a thicker and more dynamic magnetopause at dawn than at dusk.

Einstein-Rosen waves with two polarizations are cylindrically symmetric solutions to vacuum Einstein equations. Einstein equations in this case reduce to an integrable system. In 1971, Geroch has shown that this system admits an infinite-dimensional group of symmetry transformations known as the Geroch group. The phase space of this system can be parametrized by a matrix-valued function of spectral parameter, called monodromy matrix. The latter admits the Riemann-Hilbert factorization into a pair of transition matrices, i.e. matrix-valued functions of spectral parameter such that one of them is holomorphic in the upper half-plane, and the other is holomorphic in the lower half-plane. The classical Geroch group preserves the determinants of transition and monodromy matrices by construction. The algebraic quantization of the quadratic Poisson algebra generated by transition matrices of Einstein-Rosen system was proposed by Korotkin and Samtleben in 1997. Paternain, Perasa and Reisenberger have recently suggested a quantization of the Geroch group, which can be considered as a symmetry of the quantum algebra of observables. They have shown that commutation relations involving quantum monodromy matrices are preserved by the action of the quantum Geroch group. In present paper we introduce the notion of the determinant of the quantum monodromy matrix. We derive a factorization formula expressing the quantum determinant of the monodromy matrix as a product of the quantum determinants of the transition matrices. The action of the quantum Geroch group is extended from the subalgebra generated by the monodromy matrix onto the full algebra of observables. This extension is used to prove that the quantum determinant of the quantum monodromy matrix is invariant under the action of quantum Geroch group.

The Electron Loss and Fields Investigation with a Spatio-Temporal Ambiguity-Resolving option (ELFIN-STAR, or simply: ELFIN) mission comprises two identical 3-Unit (3U) CubeSats on a polar (~93deg inclination), nearly circular, low-Earth (~450 km altitude) orbit. Launched on September 15, 2018, ELFIN is expected to have a >2.5 year lifetime. Its primary science objective is to resolve the mechanism of storm-time relativistic electron precipitation, for which electromagnetic ion cyclotron (EMIC) waves are a prime candidate. From its ionospheric vantage point, ELFIN uses its unique pitch-angle-resolving capability to determine whether measured relativistic electron pitch-angle and energy spectra within the loss cone bear the characteristic signatures of scattering by EMIC waves or whether such scattering may be due to other processes. Pairing identical ELFIN satellites with slowly-variable along-track separation allows disambiguation of spatial and temporal evolution of the precipitation over minutes-to-tens-of-minutes timescales, faster than the orbit period of a single low-altitude satellite (~90min). Each satellite carries an energetic particle detector for electrons (EPDE) that measures 50keV to 5MeV electrons with deltaE/E<40% and a fluxgate magnetometer (FGM) on a ~72cm boom that measures magnetic field waves (e.g., EMIC waves) in the range from DC to 5Hz Nyquist (nominally) with <0.3nT/sqrt(Hz) noise at 1Hz. The spinning satellites (T_spin~3s) are equipped with magnetorquers that permit spin-up/down and reorientation maneuvers. The spin axis is placed normal to the orbit plane, allowing full pitch-angle resolution twice per spin. An energetic particle detector for ions (EPDI) measures 250keV-5MeV ions, addressing secondary science. Funded initially by CalSpace and the University Nanosat Program, ELFIN was selected for flight with joint support from NSF and NASA between 2014 and 2018., Comment: Submitted to Space Science Reviews April 2020. 51 pages, 7 tables, 21 figures

Weighted constellations give graphical representations of weighted branched coverings of the Riemann sphere. They were introduced to provide a combinatorial interpretation of the $2$D Toda $\tau$-functions of hypergeometric type serving as generating functions for weighted Hurwitz numbers in the case of polynomial weight generating functions. The product over all vertex and edge weights of a given weighted constellation, summed over all configurations, reproduces the $\tau$-function. In the present work, this is generalized to constellations in which the weighting parameters are determined by a rational weight generating function. The associated $\tau$-function may be expressed as a sum over the weights of doubly labelled weighted constellations, with two types of weighting parameters associated to each equivalence class of branched coverings. The double labelling of branch points, referred to as "colour" and "flavour" indices, is required by the fact that, in the Taylor expansion of the weight generating function, a particular colour from amongst the denominator parameters may appear multiply, and the flavour labels indicate this multiplicity., Comment: 37 pages. Added remark 2.7. Corrected eqs. (4.10) and (4.17). Corrected several notational inconsistencies and added missing reference citations

The KP $\tau$-function of hypergeometric type serving as generating function for quantum weighted Hurwitz numbers is used to compute the Baker function and the corresponding adapted basis elements, expressed as absolutely convergent Laurent seriesin the spectral parameter. These are equivalently expressed as Mellin-Barnes integrals, analogously to Meijer $G$-functions, but with an infinite product of $\Gamma$-functions as integral kernel. A matrix model representation is derived for the $\tau$-function evaluated at trace invariants of an externally coupled matrix., Comment: 19 pages. arXiv admin note: text overlap with arXiv:1904.03770

Multicurrent correlators associated to KP $\tau$-functions of hypergeometric type are used as generating functions for weighted Hurwitz numbers. These are expressed as formal Taylor series and used to compute generic, simple, rational and quantum weighted single Hurwitz numbers., Comment: 23 pages

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1+1 dimensions. The model describes weakly interacting instantons and anti-instantons in the $O(3)$ non-linear sigma model. In our previous work [arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations., Comment: 49 pages, 8 figures

Field-aligned currents in the Earth's magnetotail are traditionally associated with transient plasma flows and strong plasma pressure gradients in the near-Earth side. In this paper we demonstrate a new field-aligned current system present at the lunar orbit tail. Using magnetotail current sheet observations by two ARTEMIS probes at $\sim60 R_E$, we analyze statistically the current sheet structure and current density distribution closest to the neutral sheet. For about half of our 130 current sheet crossings, the equatorial magnetic field component across-the tail (along the main, cross-tail current) contributes significantly to the vertical pressure balance. This magnetic field component peaks at the equator, near the cross-tail current maximum. For those cases, a significant part of the tail current, having an intensity in the range 1-10nA/m$^2$, flows along the magnetic field lines (it is both field-aligned and cross-tail). We suggest that this current system develops in order to compensate the thermal pressure by particles that on its own is insufficient to fend off the lobe magnetic pressure., Comment: 7 pages, 3 figures, preparing to submit to GRL

Dawn-dusk asymmetries are ubiquitous features of the coupled solar-wind-magnetosphere-ionosphere system. During the last decades, increasing availability of satellite and ground-based measurements has made it possible to study these phenomena in more detail. Numerous publications have documented the existence of persistent asymmetries in processes, properties and topology of plasma structures in various regions of geospace. In this paper, we present a review of our present knowledge of some of the most pronounced dawn-dusk asymmetries. We focus on four key aspects: (1) the role of external influences such as the solar wind and its interaction with the Earth's magnetosphere; (2) properties of the magnetosphere itself; (3) the role of the ionosphere and (4) feedback and coupling between regions. We have also identified potential inconsistencies and gaps in our understanding of dawn-dusk asymmetries in the Earth's magnetosphere and ionosphere.

Bukhvostov and Lipatov have shown that weakly interacting instantons and anti-instantons in the $O(3)$ non-linear sigma model in two dimensions are described by an exactly soluble model containing two coupled Dirac fermions. We propose an exact formula for the vacuum energy of the model for twisted boundary conditions, expressing it through a special solution of the classical sinh-Gordon equation. The formula perfectly matches predictions of the standard renormalized perturbation theory at weak couplings as well as the conformal perturbation theory at short distances. Our results also agree with the Bethe ansatz solution of the model. A complete proof the proposed expression for the vacuum energy based on a combination of the Bethe ansatz techniques and the classical inverse scattering transform method is presented in the second part of this work [40]., Comment: 28 pages, 10 figures

The representative measurements of the second harmonic in ac magnetization complemented by neutron depolarization have been performed for single-crystal La0.85Sr0.15CoO3 in the temperature range 97 K < T < 230 K, where occurrence of a small fraction (~ 0.001) of nanoscale ferromagnetic clusters (FMC) has been found. Magnetic, geometrical and dynamical parameters of the FMC system have been evaluated in the temperature range T < 140 K, where superparamagnetic regime installs, by means of the formalism involving the Fokker-Planck equation (FPE). With lowering the temperature, the amount of clusters fraction, the cluster size and magnetic moment along with its diffusion relaxation time strongly increase, each in its own temperature interval. Below 130 K, FMC contribute essentially to the total linear magnetic susceptibility. The damping factor of the order 0.1 proves the importance of precession in thermal relaxation of the cluster magnetic moment. The FMC are a precursor of long-range ferromagnetic correlations seen below 100 K with neutron-scattering techniques. The employed technique supplemented with FPE-based data-treatment formalism is a novel method for studying superparamagnetic systems., Comment: 18 pages, 6 figures, 1 table, typos added