Matter In Magnetic Field Research Articles

SRF material research using muon spin rotation and beta-detected nuclear magnetic resonance

Muon spins precess in transverse magnetic fields and emit a positron preferentially in the spin direction at the instant of decay, enabling muon spin rotation (μSR) as a precise probe of local magnetic fields in matter. μSR has been used to characterize superconducting radio-frequency (SRF) materials since 2010. At TRIUMF, a beam of 4.2 MeV μ+ is implanted at a material-dependent depth of approximately 150 μm. A dedicated spectrometer was developed to measure the field of first vortex penetration and pinning strength in SRF materials in parallel magnetic fields of up to 300 mT. A low-energy beam available at PSI implants μ+ at variable depth in the London layer allowing for direct measurements of the London penetration depth from which other material parameters relevant for SRF applications, such as the lower critical field and the superheating field, can be calculated. Beta-detected nuclear magnetic resonance (β-NMR) is a technique similar to low-energy μSR using beams of low-energy β radioactive ions. With a recent upgrade, it is capable of detecting the penetration of parallel magnetic vortices, depth resolved with nanometer resolution at applied fields of up to 200 mT. In this paper, we review the impact and capabilities of these techniques for SRF research.

Strong magnetic field effects on neutron stars within f(T) theory of gravity

We investigate in this paper the structures of neutron stars under a strong magnetic field in the framework of f(T) gravity, where T denotes the scalar torsion. The TOV equations in this theory of gravity have been considered and the numerical resolution of these equations has been performed within the perturbative approach taking into account the equation of state of neutron dense matter in magnetic field. We simplify the problem by considering the very strong magnetic field which considerably affects the dense matter; and for quadratic and cubic corrections to the teleparallel term, one finds that the mass of neutron stars can increase for different values of the perturbation parameter. The deviation from the teleparallel term for different values of magnetic field is found out and this feature is very appreciable in the case of cubic correction. Our results are related to the hadronic particles description with very small hyperon contributions and the mass-radius evolution is consistent with the observational data.

Creation of large scale strong magnetic fields in matter with parity violation

We show that the Standard Model electroweak interaction of ultrarelativistic electrons with nucleons (eN interaction) in a neutron star (NS) permeated by a seed large-scale helical magnetic field provides its growth up to ≳1015 G during a time comparable with the ages of young magnetars ∼104 yr. The magnetic field instability originates from the parity violation in the eN interaction entering the generalized Dirac equation for right and left massless electrons in an external uniform magnetic field. We calculate the averaged electric current given by the solution of the modified Dirac equation containing an extra current for left and right electrons (positrons), which turns out to be directed along the magnetic field. Such current includes both a changing chiral imbalance of electrons and the eN potential given by a constant neutron density in NS. Then we derive the system of the kinetic equations for the chiral imbalance and the magnetic helicity which accounts for the eN interaction. By solving this system, we show that a sizable chiral imbalance arising in a neutron protostar due to the Urca-process eL−+p→N+νeL diminishes very rapidly because of a huge chirality flip rate. Thus the eN term prevails the chiral effect providing a huge growth of the magnetic helicity and the helical magnetic field.

Transport properties of hadronic matter in magnetic field

We study the effect of magnetic field on the transport properties like shear and bulk viscosities of hot and dense hadronic matter within hadron resonance gas model. We estimate the bulk viscosity using low energy theorems for bilocal correlators of the energy–momentum tensor generalized to finite temperature, density and magnetic field. We use Gaussian ansatz for the spectral function at low frequency. We estimate shear viscosity coefficient using molecular kinetic theory. We find that vacuum contribution due to finite magnetic field dominates the bulk viscosity (ζ) for the temperatures up to 0.1 GeV and increases with magnetic field while ratio ζ/s decreases with magnetic field. We also find that shear viscosity coefficient of hadronic matter decreases with magnetic field.

Magnetic neutron stars in f(R) gravity

Neutron stars with strong magnetic fields are considered in the framework of f(R) gravity. In order to describe dense matter in magnetic field, the model with baryon octet interacting through $\sigma$$\rho$$\omega$-fields is used. The hyperonization process results in softening the equation of state (EoS) and in decreasing the maximal mass. We investigate the effect of strong magnetic field in models involving quadratic and cubic corrections in the Ricci scalar $R$ to the Hilbert-Einstein action. For large fields, the Mass-Radius relation differs considerably from that of General Relativity only for stars with masses close to the maximal one. Another interesting feature is the possible existence of more compact stable stars with extremely large magnetic fields ($\sim 6\times 10^{18}$ G instead of $\sim 4\times 10^{18}$ G as in General Relativity) in the central regions of the stars. Due to cubic terms, a significant increasing of the maximal mass is possible.

Magnetization of neutron star matter

The magnetization of neutron star matter in magnetic fields is studied by employing the FSUGold interaction. It is found that the magnetic susceptibilities of the charged particles (proton, electron and muon) can be larger than that of neutron. The effects of the anomalous magnetic moments (AMM) of each component on the magnetic susceptibility are examined in detail. It is found that the proton and electron AMM affect their respective magnetic susceptibility evidently in strong magnetic fields. In addition, they are the protons instead of the electrons that contribute most significantly to the magnetization of the neutron star matter in a relative weak magnetic field, and the induced magnetic field due to the magnetization can be appear to be very large. Finally, the effect of the density-dependent symmetry energy on the magnetization is discussed.

Bound charges and currents

Bound charges and currents are among the conceptually challenging topics in advanced courses on electricity and magnetism. It may be tempting for students to believe that they are merely computational tools for calculating electric and magnetic fields in matter, particularly because they are usually introduced through abstract manipulation of integral identities, with the physical interpretation provided a posteriori. Yet these charges and currents are no less real than free charges and currents and can be measured experimentally. A simpler and more direct approach to introducing this topic, suggested by the ideas in the classic book by Purcell and emphasizing the physical origin of these phenomena, is proposed.

Quark matter conductivity in strong magnetic background

Applying the ideas and methods of condensed matter physics we calculate the quantum conductivity of quark matter in magnetic field. In strong field quantum conductivity is proportional to the square root of the field.

Dressed Polyakov loop and phase diagram of hot quark matter in a magnetic field

We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu-Jona Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently the phase diagram of the model. We find a tiny split of the two aforementioned crossovers as the strength of the magnetic field is increased. Concretely, for the largest value of magnetic field investigated here, $eB=19 m_\pi^2$, the split is of the order of $10\%$. A qualitative comparison with other effective models and recent Lattice results is also performed.

Ginzburg-Landau theory of type II superconductors in magnetic field

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg-Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the ``distance'' to the superconductor-normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example, in high ${T}_{c}$ materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows one to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain ``glassy'' properties. The irreversibility line and static properties of the vortex glass state are studied using the ``replica'' method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg-Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example, rotating Bose-Einstein condensate.

Strange exotic states and compact stars

We discuss the possible appearance of strange exotic multi-quark states in the interiors of neutron stars and signals for the existence of strange quark matter in the cores of compact stars. We show how the in-medium properties of possible pentaquark states are constrained by pulsar mass measurements. The possibility of generating the observed large pulsar kick velocities by asymmetric emission of neutrinos from strange quark matter in magnetic fields is outlined.

Magnetized Accretion inside the Marginally Stable Orbit around a Black Hole

Qualitative arguments are presented in order to demonstrate that the energy density of magnetic fields in matter accreting onto a black hole inside the marginally stable orbit is automatically comparable to the rest-mass energy density of the accretion flow. Several consequences follow: magnetic effects must be dynamically significant but cannot be so strong as to dominate; the outward energy transport in Alfven waves may alter the effective efficiency of energy liberation; and vertical magnetic stresses in this region may contribute to coronal activity.

Non-relativistic fermions interacting through the Chern-Simons field and the Aharonov-Bohm scattering amplitude

Starting from the non-relativistic field theory of spin- fermions interacting through the Abelian Chern-Simons term, we show that the quantized field theory leads, in the two-particle sector, to a two-particle Aharonov-Bohm-like Schrodinger equation with an antisymmetric (fermionic) wavefunction and without a delta function term. Calculating perturbatively the field-theoretic two-particle scattering amplitude up to one-loop order, we show that, in contrast to the scalar theory, the contribution of all the one-loop diagrams is finite and null, and that of the tree level ones coincides with the exact amplitude. Further, the Pauli matter-magnetic field interaction term is shown not to contribute to the amplitude to this order.

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given.

The stability of matter in magnetic fields

The proof of the stability of matter is three decades old, but the question of stability when arbitrarily large magnetic fields are taken into account was settled only recently. Even more recent is the solution to the question of the stability of relativistic matter when the electron motion is governed by the Dirac operator (together with Dirac's prescription of filling the ``negative energy sea"). When magnetic fields are included the question arises whether it is better to fill the negative energy sea of the free Dirac operator or of the Dirac operator with magnetic field. The answer is found to be that the former prescription is unstable while the latter is stable. This paper is a brief, nontechnical summary of recent work with M. Loss, J.P. Solovej and H. Siedentop.

Stability of Matter in Magnetic Fields

In the presence of arbitrarily large magnetic fields, matter composed of electrons and nuclei was known to be unstable if $\ensuremath{\alpha}$ or $Z$ is too large. Here we prove that matter is stable if $\ensuremath{\alpha}<0.06$ and $Z{\ensuremath{\alpha}}^{2}<0.04$.

Properties of the electron gas in a magnetic field and their implications for Thomas-Fermi type theories of matter

We discuss the energy density of the homogeneous three-dimensional electron gas in a magnetic field in the Hartree-Fock approximation and demonstrate that it exhibits a series of first-order phase transitions when new Landau levels begin to be populated. We investigate consequences of this behavior for Thomas-Fermi type theories of matter in magnetic fields, and show that within this approximation it leads to singular features in electron density profiles.

Surface structure of neutron stars with high magnetic fields

The equation of state of cold dense matter in strong magnetic fields is calculated in the Thomas-Fermi and Thomas-Fermi-Dirac approximations. For use in the latter calculation, a new expression is derived for the exchange energy of the uniform electron gas in a strong magnetic field. Detailed calculations of the density profile in the surface region of a neutron star are described for a variety of equations of state, and these show that the surface density profile is strongly affected by the magnetic field, irrespective of whether or not matter in a magnetic field has a condensed state bound with respect to isolated atoms. It is also shown that, as a consequence of the field dependence of the screening potential, magnetic fields can significantly increase nuclear reaction rates. 38 refs.

Anomalous acoustic velocity at high pressure of condensed matter in a superstrong magnetic field

Discreteness of the energy levels of electrons in matter in a magnetic field (Landau levels) appears for a range of values of the magnetic field and the pressure. Within the framework of a modified Thomas-Fermi model, taking into account Landau quantization, the equation of state of matter in a superstrong magnetic field as well as the acoustic velocity as a function of pressure are calculated. The latter is oscillatory.