Magnetic field buoyancy in accretion disks of young stars

Buoyancy of the fossil magnetic field in the accretion disks of young stars is investigated. It is assumed that the Parker instability leads to the formation of slender flux tubes of toroidal magnetic field in the regions of effective magnetic field generation. Stationary solution of the induction equation is written in the form in which the buoyancy is treated as the additional mechanism of the magnetic flux escape. We calculate the fossil magnetic field intensity in the accretion disks of young T Tauri stars for the cases when radius of the magnetic flux tubes a _mft = 0.1H,0.5H or 1H, where H is the accretion disk height scale. Calculations show that the buoyancy limits toroidal magnetic field growth, so that its strength is comparable with the vertical magnetic field strength for the case a _mft = 0.1H.     

Effect of strongly perturbed magnetosphere on the cosmic-ray cutoff rigidity

Comprehensive determination of the cosmic-ray cutoff rigidity in strongly perturbed periods has been performed for a number of stations located at different latitudes. To calculate the geomagnetic cutoffs by tracing the trajectories of cosmic-ray particles in the magnetic field of the magnetosphere, the model of strongly perturbed magnetosphere was used [1–3]. The diurnal anisotropy of the geomagnetic cutoff rigidity in the minimum of D _st variation in the geomagnetic field has been estimated.     

Comparing the geomagnetic thresholds of cosmic rays for two empirical models of the magnetosphere during the period of an extreme geomagnetic storm in November 2003

The accuracy of determining the geomagnetic cutoff rigidity (the geomagnetic threshold) is closely related to that of describing the magnetic field of the magnetosphere with the model used for calculations. Geomagnetic thresholds are calculated for two empirical models of the magnetosphere, Ts0l and Ts04, constructed on the basis of the same initial experimental data. The Ts01 model describes the average magnetosphere for certain conditions in the solar wind and interplanetary field. The Ts01 model focuses on describing the large-scale evolution of magnetospheric currents during a storm. A comparison of the geomagnetic thresholds for Ts0l and Ts04 with experimental thresholds calculated by the Spectrographic Global Survey from data of the CR global network stations shows that the Ts01 model describes the magnetic field of the magnetosphere more realistically. Our study was conducted for the period of a strong geomagnetic storm in November 2003.     

On Ohm’s law in the thin current sheets of the Earth’s magnetosphere

The analytical and numerical dependences of the total transverse current on an electric field, the normal component of a magnetic field and the ion and electron temperatures are obtained using analytical approximation of numerical results provided by a self-consistent model of the magnetospheric thin sheet. The dependence of current on the parameters ?, T _i , b _n is shown to be nonlinear. The relative contributions of different plasma components into the total current are estimated.     

Self-similar distribution in “giant” magnetic flux creep

The problem of magnetic field penetration into the half-space is considered in parallel geometry in an external magnetic field increasing with time in accordance with the law B(0, t, τ₀ = B _{c 1} (1 + t/τ₀) ^m , m ≥ 0, t ≥ 0 (τ ₀ is the time of magnetic flux redistribution and B _{c 1} is the lower critical field). It is assumed that the flow of vortices is thermally activated in the “giant” creep mode (i.e., for weak pinning creep and high temperatures). A model equation is derived for describing the magnetic flux evolution. Analytic formulas are obtained for the depth and velocity of magnetic field penetration. It is shown that the giant creep regime is stable for 0 ≤ m ≤ 1/2.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Density ducts formed by heating the Earth’s ionosphere with high-power HF radio waves

The parameters of plasma disturbances at altitudes 660 and 840 km, measured by the instruments onboard the French DEMETER satellite and the US DMSP satellites passing through the magnetic flux tube footed at the region of intense modification of the F ₂ ionospheric layer by the high-power HF radio waves of the Sura heating facility, are presented. The formation of artificial enhanced-density plasma ducts in the outer ionosphere is observed experimentally. Conditions facilitating the formation of such ducts are pointed out.     

Study of the extreme location of the penetration boundary of solar energetic particles (protons) into the Earth’s magnetosphere during the magnetic storms in 2001–2005

The results of studying the relationship between the extreme values of the penetration boundary location of solar energetic particles (protons with energies of 1–5 and 50–90 MeV) in the Earth’s magnetosphere and the geomagnetic indices Dst and K _p are reported.     

Compression of whistler waves in a plasma with a nonstationary magnetic field

We present the results of our experiments in which the propagation of whistler waves in a plasma with a nonstationary magnetic-field perturbation (B=B₀+δB(t), δB/B₀ ≤ 5%) was investigated. The parametric and dispersive phenomena in a variable magnetic field were studied on the unique Krot plasma bench (the plasma column was 4 m in length and 1.5 m in diameter). A periodic field perturbation is shown to lead to an amplitude-frequency modulation of the whistler wave and to fragmentation of the signal into separate frequency-modulated wavepackets followed by their compression. The formation and compression of pulses is attributable to strong whistler group-velocity dispersion near the electron cyclotron frequency (ω ≤ ω_H). The results can be used to interpret the spectral shapes of the signals received from the Earth’s magnetosphere and ionosphere in the electron and ion whistler frequency ranges.     

Magnetic catalysis of stability of quark matter in the Nambu-Jona-Lasinio model

The effect of an external magnetic field H on the stability of quark matter is studied on the basis of the Nambu-Jona-Lasinio model. It is shown that, at H = 0, droplets of quark matter are stable only in the case where the coupling constant G is greater than some value G_bag. If H ≠ 0, stable multiquark formations may exist even for G ≤ G_bag (magnetic catalysis of stability). For G > G_bag, a magnetic field facilitates the formation of stable quark matter.     

Local approximation oscillatory differential method for the analysis of physical processes at the interface between vortex and Meissner regions in superconductors

A “differential” method for local diagnostics of superconductors has been developed. Regular steps with identical heights through certain intervals of an external field have been revealed on the magnetic-field dependences of the trapped magnetic flux density B _tr(H ₀) and the effective demagnetizing factor n _eff (H ₀) of bulk and film YBCO samples. It has been shown that the sample in high magnetic fields “decays” stepwise into subcrystallites and nanocrystallites whose size is much smaller than the depth of penetration of the magnetic field λ.     

Resistive sensor of weak magnetic fields on the basis of a thick HTSC film

The following parameters have been obtained for a thick (thickness t ～50 μm) film of high-temperature superconducting ceramics of the Bi-2223 system have been implemented: magnetosensitivity S _u ～ 29 V T^?1 and resolutions δB ～ 3 nT and δ? ～ 4?₀ in magnetic field and magnetic flux, respectively. It is shown that the film magnetosensitivity can be significantly increased due to the size effect. The expected characteristics, estimated with allowance for the size effect, are S _u ≥ 1000 V T^?1, δB ～ 0.01 nT, δ? ～ 0.01 ?₀, and the range of dynamic measurement ≥150 dB.     

Global synchronization of oscillations in the level of whistlers near Jupiter as a consequence of the spatial detection of the <Emphasis Type="Italic">Q</Emphasis> factor of a magnetosphere resonator

The formation of the space-time structure of the intensity distribution for whistlers, as well as the content of the energetic electrons in the radiation belts of Jupiter, has been considered. Parametric nonlinear processes in a plasma magnetospheric maser have been analyzed. It has been shown that, owing to the azimuthal inhomogeneity of a magnetic trap in combination with the fast rotation of the planet, a component that is characterized by the periodic modulation and is independent of the azimuth coordinate is formed in the Q factor of the magnetospheric resonator. This modulation is manifested as an external force that ensures the synchronization of oscillations in the level of whistlers in individual magnetic field tubes under the global-resonance conditions.     

Magnetic flux annihilation waves in inhomogeneous high-temperature superconductors

The process of magnetic field penetration into polycrystalline high-T _c superconductors of the YBa₂Cu₃O_7?x and Bi₂Sr₂Ca₂Cu₃O_10?x systems has been studied using traditional magnetooptical methods and scanning Hall probe microscopy. It is established that remagnetization of a sample is accompanied by the formation and propagation of a stationary magnetic flux annihilation (MFA) wave. Spatial inhomogeneity of the superconductors studied is manifested by a curvature of the MFA wave front.     

Maximal supercurrent of a Josephson junction in a field of magnetic particles

The maximal supercurrent I_m of a short Josephson junction formed by an edge contact of two superconducting films is calculated for the case where the junction is placed in a periodic field produced by a chain of magnetic nanoparticles. The commensurability effects occurring when the magnetic flux of a homogeneous external field H₀ through an elementary cell is equal to an integral number of magnetic flux quanta Φ₀ are considered. The effects give rise to additional maxima in the I_m(H₀) dependence.     

Size Dependences of the Magnetic Properties of Superconducting Lead–Porous Glass Nanostructures

Superconducting structures Pb–PG formed by filling a porous glass matrix with the lead from melt under pressure have been investigated. Samples with characteristic pore structure diameters of d ≈ 7, 3, and 2 nm have been studied. It has been found that the critical temperature of the superconducting transition in the samples under study is similar to the corresponding value T_c ≈ 7.2 K for bulk lead. At the same time, it has been observed that the critical magnetic field of the nanocomposites, which attains H_c(T = 0 K) ≈ 165 kOe for Pb–PG (3 nm), exceeds several times the value H_c(0) = 803 Oe for bulk lead. The low-temperature magnetic- field dependences of magnetic moment M(H) contain quasi-periodic flux jumps, which vanish with a decrease in the lead nanostructure diameter. A qualitative model of the observed effects is considered.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

Effect of the magnetic anisotropy energy distribution of MnSb clusters on spontaneous magnetization reversal of GaMnSb thin films

Temperature m(T) and time m(t) dependences of the magnetic moment of GaMnSb thin films with MnSb clusters have been measured. The m(t) dependences are straightened in semilogarithmic coordinates m(lnt). The temperature dependences of magnetic viscosity S(T) corresponding to the slope of straight lines m(lnt) have been studied. It have been demonstrated that the behavior of dependences S(T) is governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters. It have been found that the behavior of dependences m(T) measured after the films were cooled in zero magnetic field and in magnetic field H = 10 kOe is also governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters.     

Nonperturbative phenomena in QCD at finite temperature in a magnetic field

The norperturbative QCD vacuum at finite temperature in a external magnetic field is studied. Equations that relate nonperturbative QCD condensates at finite temperature to the thermodynamic pressure at T ≠ 0 and H ≠ 0 are obtained, and low-energy theorems are derived. The free energy of the QCD vacuum in the hadronic phase at H ≠ 0 is calculated, and expressions for the quark and gluon condensates are obtained. Various limiting cases for the behavior of the condensates at low and high temperatures and in weak and strong magnetic fields are investigated. A new interesting phenomenon that consists in the freezing of the quark condensate by a magnetic field is found. The character of spontaneous chiral-symmetry breaking in finite-temperature QCD in a magnetic field is studied. For this purpose, the Gell-Mann-Oakes-Renner formula relating the pion mass M _π and the axial-vector coupling constant F _π to the quark condensate is derived at T ≠ 0 and H ≠ 0. It is shown that this formula preserves its form at finite temperature after taking into account a magnetic field—that is, no additional terms independent of T and H appear. Thus, the scheme of soft chiral-symmetry breaking remains unchanged. The quark-hadron phase transition in QCD in a magnetic field is studied. It is shown that the phase-transition temperature becomes lower than that in the case of zero magnetic field.     

Magnetic geodynamics

Several decades since the work E. P. Velikhov, Zh. Éksp. Teor. Fiz. 36, 1398 (1959) [Sov. Phys. JETP 9, 995 (1959)] [1] concerning magnetorotational instability was published, great astrophysical interest has been manifested in the mechanism of generating a magnetic field in a rotating well-conducting medium in view of difficulties in the development of the theory of anomalous matter transfer in accretion discs both upon the formation of stars and planets from gaseous conglomerations and upon the formation of a galactic core with a black hole at the center { S. A. Balbus and J. F. Hawley, Astrophys. J. 376, 214 (1991) [2] and G. Ruediger and R. Hollerbach, The Magnetic Universe (Wiley-VCH, Weinheim, 2004) [3]}. Attempts to experimentally observe the magnetorotational instability were successful only for spherical geometry in experiments initially devoted to the verification of geomagnetic dynamo theory {D. R. Sisan et al., Phys. Rev. Lett. 93, 114502 (2004) [4]}. In experiments with liquid sodium in the complete absence of temperature gradients and, therefore, convection, which is very important for the conventional theory of the geomagnetic dynamo, the generation of the magnetic field was obtained due to the development of the magnetorotational instability, which is usually ignored when developing the theory of the origin of the Earth’s magnetic field. The results obtained in this work enable one to develop a theory of geomagnetic dynamo that is primarily based on the magnetorotational instability, which provides a new insight into not only the origin of the Earth’s magnetic field but its evolution in time.