Potential symmetry and invariant solutions of Fokker-Planck equation in cylindrical coordinates related to magnetic field diffusion in magnetohydrodynamics including the Hall current

Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some simplifications allow to obtain a Fokker-Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flow and the Hall-current. Some interesting side results of this approach are new exact solutions that do not seem to have been reported in the literature.     

Analytic treatment of the relativistic motion of charged particles in electric and magnetic field

Summary Using the Boris mover, or other standard methods, the error pile-up in the computation of the relativistic orbit of charged particles in electric and magnetic fields becomes quickly excessive, if one wants to keep reasonably limited the number of points employed to build the particle orbit. An analytical solution becomes, therefore, desirable and its construction is the subject of the present work.

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Riassunto Unsando il metodo di Boris, oppure altri metodi standard, l'accumulazione degli errori nella determinazione numerica delle orbite relativistiche di particelle cariche in campi elettrici e magnetici diventa intollerabile, se il numero dei punti impiegati per costruire le orbite stesse è mantenuto basso. Una soluzione analitica diviene quindi utile, e questa costituisce l'argomento del presente lavoro.

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Резюме В рамках стндартных методов погрешность при вычислении релятивистской орбиты заряженных частиц в электронном и магнитном полях становится чрезмерно большой, если для построения орбиты часицы используется ограниченное число точек. В связи с этим конструируется аналитическое решение.

     

Enhancement of the guide field during the current sheet formation in the three-dimensional magnetic configuration with an X line

Results are presented from studies of the formation of current sheets during exciting a current aligned with the X line of the 3D magnetic configuration, in the CS-3D device. Enhancement of the guide field (parallel to the X line) was directly observed for the first time, on the basis of magnetic measurements. After the current sheet formation, the guide field inside the sheet exceeds its initial value, as well as the field outside. It is convincingly demonstrated that an enhancement of the guide field is due to its transportation by plasma flows on the early stage of the sheet formation. The in-plane plasma currents, which produce the excess guide field, are comparable to the total current along the X line that initiates the sheet itself.     

Counterion distribution in a spherical charged sparse brush

The counterion distribution within a spherical polyelectrolyte sparse brush was measured by small-angle X-ray scattering using contrast variation with different counterions by means of ion dialysis. The brush was made by self-association of charged diblock copolymers. Thanks to the contrast variation method, we were able to separate the signal due to the monomers and the signal due to the counterions. At a small length scale, it is demonstrated that the system behaves as independent charged rods whose counterion distribution follows the Poisson-Boltzmann model. Received 14 February 2001 and Received in final form 2 May 2001     

Dynamics and correlations in magnetic colloidal systems studied by X-ray photon correlation spectroscopy

We have studied the static and dynamic behaviour of magnetic colloidal systems (ferrofluids) by Small-Angle X-ray Scattering (SAXS) and X-ray Photon Correlation Spectroscopy (XPCS). The main features of the novel XPCS technique will be illustrated by data taken on a model system, colloidal silica spheres. We will then present the results obtained on an optically opaque suspension of magnetic colloids (maghemite) in the wave vector range from 10^-3 to 10^-2?^-1. Translational diffusion in zero field and anisotropic diffusion under external magnetic fields will be discussed. Received 9 August 1999 and Received in final form 26 July 2000     

On the influence of anisotropy on the magnetic small-angle neutron scattering of superparamagnetic particles

This paper presents a calculation of the magnetic small-angle neutron scattering cross-section resulting from a dilute ensemble of superparamagnetic particles exhibiting uniaxial magnetic anisotropy. We focus on the two experimentally relevant scattering geometries in which the incident neutron beam is perpendicular or parallel to an applied magnetic field, and we discuss several orientations of the anisotropy axes with respect to the field. Magnetic anisotropy has no influence on the magnetic small-angle neutron scattering when the particles are mobile, as is the case e.g. in ferrofluids, but, when the particles are embedded in a rigid non-magnetic matrix and the orientations of the anisotropy axes are fixed, significant deviations compared to the case of negligible anisotropy are expected. For the particluar situation in which the anisotropy axes are parallel to the applied field, closed-form expressions suggest that an effective anisotropy energy or anisotropy-energy distribution can be determined from experimental scattering data. Received 8 November 2001     

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application. Received 30 August 2001     

Evaluation of forces in magnetic materials by means of energy and co-energy methods

The evaluation of the total force of magnetic origin acting upon a body in a stationary magnetic field is often carried out using the so-called magnetic energy (or co-energy) method, which is based on the derivation of the magnetic energy (or co-energy) with respect to a virtual rigid displacement of the considered body. The application of this method is usually justified by resorting to the energy conservation principle, written in terms both of electrical and of mechanical quantities. In this paper we shall re-examine the whole matter in the context of classical thermodynamics, in order to obtain a more comprehensive and general proof of the validity of the energy (or co-energy) approach and to point out its limitations. Two typical configurations will be discussed; in the first one, the field sources are represented by conducting bodies carrying free currents, whereas in the second one a permanent magnet creates the driving field. All magnetic materials are assumed to be non-hysteretic and permanent magnets are represented by means of the well-known linear model in the second quadrant of the (B,H) plane. Received 25 July 2001 and Received in final form 5 November 2001     

Probing the strange quark condensate by di-electrons from φ-meson decays in heavy-ion collisions at SIS energies

QCD sum rules predict that the change of the strange quark condensate 〈ˉss〉 in hadron matter at finite baryon density causes a shift of the peak position of the di-electron spectra from φ-meson decays. Due to the expansion of hadron matter in heavy-ion collisions, the φ peak suffers a smearing governed by the interval of density in the expanding fireball, which appears as an effective broadening of the di-electron spectrum in the φ region. The emerging broadening is sensitive to the in-medium change of 〈ˉss〉. This allows to probe directly in-medium modifications of 〈ˉss〉 via di-electron spectra in heavy-ion collisions at SIS energies with HADES. Received: 22 November 2002 / Accepted: 30 January 2003 / Published online: 29 April 2003     

Multiparticle correlations in resonance-matter formation

The effect of multiparticle correlations on resonance and pion populations, in relativistic nuclear reactions, is calculated in the context of an intranuclear cascade model which includes N-body (N > 2) collisional processes. The resonance-matter population present in the highly-compressed phase of nucleus-nucleus collisions is investigated, in reactions between different intermediate-mass nuclear systems. Received: 29 December 1998 / Revised version: 20 December 1999     

Quantum Brownian motion on potential surfaces coupled via tunneling in an external electric field[-2mm]

The present paper deals with the motion of a Brownian particle on two identical but shifted potential surfaces, coupled via a tunneling matrix element in an external electric field. Dissipation is induced by a heat bath represented by an infinite set of harmonic oscillators with a continuum range of frequencies. We derive a perturbative solution for the quantum coherence term of the particle system after performing a small-polaron-like transformation. This is subsequently necessary for the extraction of an equation that describes the reduced dynamics and the minimal action path of the Brownian particle. Finally we extract expressions for the population relaxation rate and the pure quantum-dephasing rate of the two-level system. Received 4 January 2001 and Received in final form 12 March 2001     

Crystal and magnetic structures of the oxyphosphates MFePO 5 (M = Fe, Co, Ni, Cu). Analysis of the magnetic ground state in terms of superexchange interactions

We have studied in detail the crystal and magnetic structures of the oxyphosphates MFePO₅ (M: divalent transition metal) using neutron powder diffraction as a function of temperature. All of them are isomorphic to the mixed valence compound α-Fe₂PO₅ with space-group Pnma. No disorder exists between the two metallic sites. The M²⁺O₆ octahedra share edges between them and faces with Fe³⁺O₆ octahedra building zigzag chains running parallel to the b-axis that are connected by PO₄ tetrahedra. The topology of this structure gives rise to a complex pattern of super-exchange interactions responsible of the observed antiferromagnetic order. The magnetic structures are all collinear with the spin directed along the b-axis except for M = Co. The experimental magnetic moments of Cu⁺² and Ni²⁺ correspond to the expected ionic value, on the contrary the magnetic moment of Fe³⁺ is reduced, probably due to covalence effects, and that of Co²⁺ is greater than the spin-only value indicating a non negligible orbital contribution. Using numerical calculations we have established a magnetic phase diagram adapted for this type of crystal structure and determined the constraints to be satisfied by the values of the exchange interactions in order to obtain the observed magnetic structure as the ground state. Received 15 December 2000 and Received in final form 25 June 2001     

Microphase separation in weakly charged hydrophobic polyelectrolytes

Aqueous solutions of a well-defined poly(N-isopropylacrylamide-co-sodium 2-acrylamido-methylpropanesulfonate) (NIPAM/NaAMPS in a 95/5 molar ratio) have been investigated by means of small-angle neutron scattering (SANS) and rheological experiments as a function of temperature ( 25^° C T 60^° C) and polymer concentration ( 0.5wt% C 12wt%). The solutions remain optically transparent and isotropic over the whole temperature range, in contrast with the homopolyNIPAM which precipitates above its lower critical solution temperature (LCST = 32^° C). Upon addition of salt, the systems undergo a micro-macrophase separation. At temperatures above 45^° C, the SANS spectra exhibit a sharp peak at a scattering wave vector, q _max, which increases slightly with temperature. At high temperature ( T∼ 60^° C), the scattered intensity follows a power law I(q) ∼q ^-4 in the asymptotic regime, characteristic of two-density media with sharp interfaces, and q _max is found to vary with polymer concentration as q _max∼C ^0.22. Estimates of the typical sizes give values between 40 ? and 200 ?. These results provide a strong evidence of a thermally induced microphase separation, which is corroborated by the very sharp increases of the viscosity (over 2 decades) and of the stress relaxation time of the solutions, occurring in the temperature range where the scattering peak is observed. The results are discussed and compared with the theoretical models proposed for weakly charged polyelectrolytes in a poor solvent. Received 1 October 2001     

Magnetization and neutron scattering studies of the pressure effect on the magnetic transition in Er Y Co

Neutron powder diffraction was employed to study the pressure effect on the magnetic transition in the pseudobinary Laves-phase compound Er_0.57Y_0.43Co₂ and to determine the magnetic moments of the Er- and Co-subsystems. Our studies reveal that the onset of long-range magnetic order for both the localized 4 f (Er) and itinerant 3 d (Co) electron moments appears at about the same temperature at ambient pressure. The pressure effect on T_c is found to be negative and equal for both sublattices, namely T _c / p ∼ - 0.4 K/kbar. The values of the magnetic moments of the Er and the Co ions are found = 5.40±0.15μ _B /atom, = 0.50±0.07μ _B /atom and 5.35±0.15μ _B /atom, 0.37±0.09μ _B /atom, for p = 0 and 6 kbar, respectively. Our experimental results give evidence for short-range magnetic order formation at temperatures already above T_c and for a coexistence short- and long-range order below T_c down to 4 K. Received 20 December 2001 / Received in final form 12 June 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: andrew.podlesnyak@psi.ch     

Neutron diffraction study of the magnetic ordering in the series R 2 BaNiO 5 (R = Rare Earth)

A neutron diffraction study, as a function of temperature, of the title compounds is presented. The whole family (space group Immm, a ≈ 3.8?, b ≈ 5.8?, c ≈ 11.3?) is structurally characterised by the presence of flattened NiO₆ octahedra that form chains along the a-axis, giving rise to a strong Ni-O-Ni antiferromagnetic interaction. Whereas for Y-compound only strong 1D correlations exist above 1.5 K, presenting the Haldane gap characteristic of 1D AF chain with integer spin, 3D AF ordering is established simultaneously for both R and Ni sublattices at temperatures depending on the rare earth size and magnetic moment. The magnetic structures of R₂BaNiO₅ ( R = Nd, Tb, Dy, Ho, Er and Tm) have been determined and refined as a function of temperature. The whole family orders with a magnetic structure characterised by the temperature-independent propagation vector = (1/2, 0, 1/2). At 1.5 K the directions of the magnetic moments differ because of the different anisotropy of the rare earth ions. Except for Tm and Yb (which does not order above 1.5 K), the magnetic moment of the R³⁺ cations are close to the free-ion value. The magnetic moment of Ni²⁺ is around 1.4 , the strong reduction with respect to the free-ion value is probably due to a combination of low-dimensional quantum effects and covalency. The thermal evolution of the magnetic structures from T _N down to 1.5 K is studied in detail. A smooth re-orientation, governed by the magnetic anisotropy of R³⁺, seems to occur below and very close to T _N in some of these compounds: the Ni moment rotates from nearly parallel to the a-axis toward the c-axis following the R moments. We demonstrate that for setting up the 3D magnetic ordering the R-R exchange interactions cannot be neglected. Received 19 July 2001     

Electronic correlation effects on the properties of an half-filled octahedron cluster in a magnetic field

The present study focuses on electronic correlation effects on magnetic energy, the spin-spin correlation function of an octahedron cluster in the (3↑, 3 ↓) electronic configuration threaded by a magnetic field. Some other spin configurations are also discussed and various field directions are considered. An accurate diagonalisation technique has been used to solve the Hubbard Hamiltonian. A result is analysed on a linear energy stabilisation at low magnetic flux. Moreover, two types of antiferromagnetic transition versus the flux occurring for a correlation term larger than a critical one have been observed, i.e. the likelihood of a charge excitation before the antiferromagnetic transition. Finally, a comparison between the results obtained from the exact diagonalisation and the Gutzwiller method has been carried out, leading to a suggested modification of the Gutzwiller approach in order to improve it. Received 23 June 1999 and Received in final form 28 July 2000     

Interpretation of the magnetoresistance in doped magnetic tunnel junctions

We present a quantum mechanical model of the magnetoresistance in ferromagnetic tunnel junctions artificially doped by the introduction of layers of impurities in the middle of the barrier. The electron transport across the barrier is described by a combination of direct tunneling, tunneling assisted by spin-conserving scattering and tunneling assisted by spin-flip scattering. With this model, we interpret recent experimental results concerning the dependence of the TMR amplitude on the amount of impurities in the barrier and on temperature. Received 1st February 2001 and Received in final form 14 June 2001     

Nanoparticle chain-like formation in electrical double-layered magnetic fluids evidenced by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was performed on a series of Electric Double-Layered Magnetic Fluids (EDL-MF) composed of ferrite type-- CoFe₂O₄, MnFe₂O₄, ZnFe₂O₄, NiFe₂O₄ and CuFe₂O₄--nanoparticles of different crystalline sizes ( D _XR ranging from 40 to 139?, as determined by X-ray diffraction). The information concerning the scattering objects was obtained through the analysis of the distance distribution function p(r) and of the size distribution function D(R), both retrieved from SAXS data. The results show that EDL-MF, in the absence of an applied magnetic field, are composed of small magnetic particle aggregates in solution. These agglomerates are elongated in one direction (chain-like) with the longest dimension varying from 240 to 330?. The cross-section size is of the order of D _XR. The data also demonstrate that the maximum dimension of these aggregates is independent of the ferrite type. On the other hand, the number of aggregated magnetic particles is nanoparticle-size-dependent. Accordingly, larger ferrite-type nanoparticles as those with D _XR = 139? form aggregates composed of 2-3 magnetic particles, whereas smaller ones with D _XR 40? form agglomerates of about 6 magnetic particles in solution. As the nanoparticle size is reduced, it might increase the particle surface defects. Such occurrence would affect the particle surface charge density, which could reduce the electrostatic screening, favoring the agglomeration phenomenon. Received 28 February 2000 and Received in final form 28 August 2000     

Structure of colloidal complexes obtained from neutral/poly- electrolyte copolymers and oppositely charged surfactants

We report on the phase behavior and scattering properties of colloidal complexes made from block copolymers and surfactants. The copolymer is poly(sodium acrylate)-b-poly(acrylamide), hereafter abbreviated as PANa-PAM, with molecular weight 5000 g/mol for the first block and 30000 g/mol for the second. In aqueous solutions and neutral pH, poly(sodium acrylate) is a weak polyelectrolyte, whereas poly(acrylamide) is neutral and in good-solvent conditions. The surfactant is dodecyltrimethylammonium bromide (DTAB) and is of opposite charge with respect to the polyelectrolyte block. Combining dynamical light scattering and small-angle neutron scattering, we show that in aqueous solutions PANa-PAM diblocks and DTAB associate into colloidal complexes. For surfactant-to-polymer charge ratios Z lower than a threshold (Z(C) approximately 0.3), the complexes are single surfactant micelles decorated by few copolymers. Above the threshold, the colloidal complexes reveal an original core-shell microstructure. We have found that the core of typical radius 100-200 A is constituted from densely packed surfactant micelles connected by the polyelectrolyte blocks. The outer part of the colloidal complex is a corona and is made from the neutral poly(acrylamide) chains. Typical hydrodynamic sizes for the whole aggregate are around 1000 A. The aggregation numbers expressed in terms of numbers of micelles and copolymers per complex are determined and found to be comprised between 100-400, depending on the charge ratio Z and on the total concentration. We have also shown that the sizes of the complexes depend on the exact procedure of the sample preparation. We propose that the driving mechanism for the complex formation is similar to that involved in the phase separation of homopolyelectrolyte/surfactant systems. With copolymers, the presence of the neutral blocks prevents the macroscopic phase separation from occurring.