External Uniform Magnetic Field Research Articles

Reply to the Comment by Yubo Wang et al.

Abstract In the Reply, we suppose that although the higher order correction terms of the combined field with a tightly focused Gaussian laser pulse and an external uniform magnetic field have certain influence on the dynamics and radiation spectrum of the electron, it does not affect the issues and concerns studied in our paper [EPL, 139 (2022) 14001]. Therefore, it is feasible for us to adopt the lowest order approximation for the tightly focused Gaussian laser pulse and it does not affect the main ideas and conclusions of our paper.

On the rheology and magnetization of dilute magnetic emulsions under small amplitude oscillatory shear

A dilute magnetic emulsion under the combined action of a uniform external magnetic field and a small amplitude oscillatory shear is studied using numerical simulations. We consider a three-dimensional domain with a single ferrofluid droplet suspended in a non-magnetizable Newtonian fluid. We present results of droplet shape and orientation, viscoelastic functions and bulk emulsion magnetization as functions of the shear oscillation frequency, magnetic field intensity and orientation. We also investigate how the magnetic field induces mechanical anisotropy by producing internal torques in oscillatory conditions. We found that, when the magnetic field is parallel to the shear plane, the droplet shape is mostly independent of the shear oscillation frequency. Regarding the viscometric functions, we show how the external magnetic field modifies the storage and loss moduli, especially for a field aligned to the main velocity gradient. The bulk emulsion magnetization is studied in the same fashion as the viscoelastic functions of the oscillatory shear. We show that the in-phase component of the magnetization with respect to the shear rate reaches a saturation magnetization, at the high frequencies limit, dependent on the magnetic field intensity and orientation. On the other hand, we found a non-zero out-of-phase response, which indicates a finite emulsion magnetization relaxation time. Our results indicate that the magnetization relaxation is closely related to the mechanical relaxation for dilute magnetic emulsions under oscillatory shear.

Dynamically tunable lamellar surface structures from magnetoactive elastomers driven by a uniform magnetic field.

Stimuli responsive materials are key ingredients for any application that requires dynamically tunable or on-demand responses. In this work we report experimental and theoretical investigation of magnetic-field driven modifications of soft-magnetic elastomers whose surface was processed by laser ablation into lamellar microstructures that can be manipulated by a uniform magnetic field. We present a minimal hybrid model that elucidates the associated deflection process of the lamellae and explains the lamellar structure frustration in terms of dipolar magnetic forces arising from the neighbouring lamellae. We experimentally determine the magnitude of the deflection as a function of magnetic flux density and explore the dynamic response of lamellae to fast changes in a magnetic field. A relationship between the deflection of lamellae and modifications of the optical reflectance of the lamellar structures is resolved.

A spin 1 particle in a cylindric basis: the projective operator method

In this paper, the system of equations describing a spin 1 particle is studied in cylindric coordinates with the use of tetrad formalism and the matrix 10-dimension formalism of Duffin – Kemmer – Petieau. After separating the variables, we apply the method proposed by Fedorov – Gronskiy and based on the use of projective operators to resolve the system of 10 equations in the r variable. In the presence of an external uniform magnetic field, we construct in an explicit form three independent classes of wave functions with corresponding energy spectra. Separately the massless field with spin 1 is studied; there are found four linearly independent solutions, two of which are gauge ones, and other two do not contain gauge degrees of freedom. Meanwhile, the method of Fedorov – Gronskiy is also used.

Частица Штюкельберга во внешнем магнитном поле. Метод проективных операторов

We study the St¨uckelberg equation for a relativistic particle
 with two spin states S = 1 and S = 0 in the presence of
 an external uniform magnetic field. The particle is described
 by an 11-component wave function consisting of a scalar, a
 vector, and an antisymmetric tensor. On the solutions of the
 equation, the operators of energy, the third projection of the
 total angular momentum, and the third projection of the linear
 momentum along the direction of the magnetic field are
 diagonalized. After separation of variables, a system for 11
 radial functions is obtained. Its solution is based on the use of
 the Fedorov-Gronsky method, in which all 11 radial functions
 are expressed in terms of three main functions. Exact solutions
 with cylindrical symmetry are constructed. Three series
 of energy levels are found.

Частица Штюкельберга во внешнем магнитном поле. Нерелятивистское приближение. Точные решения

The St¨uckelberg equation for a particle with two spin states, S = 1 and S = 0, is studied in the presence of an external uniform magnetic field. In relativistic case, the particle is described by an 11-component wave function. On the solutions of the equation, the operators of energy, the third projection of the total angular momentum, and the third projection of the linear momentum along the direction of the magnetic field are diagonalized. After separation of variables, we derive a system for 11 functions depending on one variable. We perform the nonrelativistic approximation in this system. For this we apply the known method of deriving nonrelativistic equations from relativistic ones, which is based on projective operators related to the matrix Γ0 of the relativistic equation. The nonrelativistic wave function turns out to be 4-dimensional. We derive the system for 4 functions. It is solved in terms of confluent hypergeometric functions. There arise three series of energy levels with corresponding solutions. This result agrees with that obtained for the relativistic St¨uckelberg equation.

Litz wire loss performance and optimization for cryogenic windings

AbstractLitz wires operating in a cryogenic environment can potentially improve both the efficiency and power density of electrical machines and passive components. However, due to the low resistivity and high magnetic fields, eddy‐current losses may become significant in cryogenically cooled windings, especially in airgap winding arrangements or in the case of significant slot leakage fields, unless the litz wire parameters are carefully chosen. A framework for litz wire loss performance optimization and experimental characterisation at cryogenic temperatures is provided. An optimum operating temperature for minimum loss is derived based on analytical expressions, which highlights the role of litz wire parameters, current density and external field. The proximity loss model, used to calculate the optimum operating temperature, is validated experimentally. Two test rigs with different magnetic cores were designed and built. Copper and aluminium litz wires with a strand diameter down to 0.1 mm were tested in a liquid nitrogen bath with a uniform harmonic external magnetic field up to 0.5 T peak and a frequency up to 1 kHz. Measurements show good agreement with the theoretical results and confirm that the proposed model can be confidently used during the preliminary design of cryogenic windings.

Electrodeposited magnetic nanoporous membrane for high-yield and high-throughput immunocapture of extracellular vesicles and lipoproteins.

Superparamagnetic nanobeads offer several advantages over microbeads for immunocapture of nanocarriers (extracellular vesicles, lipoproteins, and viruses) in a bioassay: high-yield capture, reduction in incubation time, and higher capture capacity. However, nanobeads are difficult to "pull-down" because their superparamagnetic feature requires high nanoscale magnetic field gradients. Here, an electrodeposited track-etched membrane is shown to produce a unique superparamagnetic nano-edge ring with multiple edges around nanopores. With a uniform external magnetic field, the induced monopole and dipole of this nano edge junction combine to produce a 10× higher nanobead trapping force. A dense nanobead suspension can be filtered through the magnetic nanoporous membrane (MNM) at high throughput with a 99% bead capture rate. The yield of specific nanocarriers in heterogeneous media by nanobeads/MNM exceeds 80%. Reproducibility, low loss, and concentration-independent capture rates are also demonstrated. This MNM material hence expands the application of nanobead immunocapture to physiological samples.

Neutral pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model: Mixing effects

Mixing effects on the mass spectrum of light neutral pseudoscalar and vector mesons in the presence of an external uniform magnetic field $\vec B$ are studied in the framework of a two-flavor NJL-like model. The model includes isoscalar and isovector couplings both in the scalar-pseudoscalar and vector sectors, and also incorporates flavor mixing through a 't Hooft-like term. Numerical results for the $B$ dependence of meson masses are compared with present lattice QCD results. In particular, it is shown that the mixing between pseudoscalar and vector meson states leads to a significant reduction of the mass of the lightest state. The role of chiral symmetry and the effect of the alignment of quark magnetic moments in the presence of the magnetic field are discussed.

Wave turbulence in inertial electron magnetohydrodynamics

A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol {B_0} = B_0 \hat {\boldsymbol {e}}_\|$ . This regime is relevant for scales smaller than the electron inertial length $d_e$ . We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ( $\perp$ ) to $\boldsymbol {B_0}$ . The exact stationary solutions (Kolmogorov–Zakharov spectra) are obtained for which we prove the locality. We also found the Kolmogorov constant $C_K \simeq 8.474$ . In the simplest case, the study reveals an energy spectrum in $k_\perp ^{-5/2} k_\|^{-1/2}$ (with k the wavenumber) and a momentum spectrum enslaved to the energy dynamics in $k_\perp ^{-3/2} k_\|^{-1/2}$ . These solutions correspond to a magnetic energy spectrum ${\sim }k_\perp ^{-9/2}$ , which is steeper than the EMHD prediction made for scales larger than $d_e$ . We conclude with a discussion on the application of the theory to space plasmas.

Coupled effect of spatio-temporal variation of Laguerre–Gaussian laser pulse on electron acceleration in magneto-plasma

In this work, the acceleration of electrons via incidence of a Laguerre–Gaussian laser pulse in a plasma medium with relativistic non-linearity in the presence of a uniform external magnetic field along the direction of propagation has been presented. The moment theory approach has been used to obtain the two non-linear second-order differential equations, which have been further solved numerically to determine the variation in the radial and temporal width of the laser pulse in the plasma medium. The propagation of the laser pulse in the plasma medium excites the electron plasma wave, which acts as a wakefield for electron acceleration. The effect of radial and temporal variation on electron acceleration has also been investigated. Furthermore, the spatio-temporal variation and energy gain have been studied for different Laguerre modes of lasers, their intensities, and plasma densities.

Threshold of Convection in a Spherical Cavity Filled with a Magnetic Fluid in the Uniform External Magnetic Field

Threshold of Convection in a Spherical Cavity Filled with a Magnetic Fluid in the Uniform External Magnetic Field

Radiation Power of a Short High-Current Vacuum Arc at High Current Densities

The radiation of a vacuum arc was measured in the spectral region <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200~\text {nm} \le \lambda \le 1100$ </tex-math></inline-formula> nm. The arc was initiated in the center of the cathode by breaking the current in the auxiliary circuit and was fed by the rectangular current pulse with a duration of 10 ms. The interelectrode gap was fixed at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h = 4$ </tex-math></inline-formula> mm, and the butt <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2r =30$ </tex-math></inline-formula> -mm CuCr30 electrodes were used. The arc was stabilized by an external uniform axial magnetic field (AMF). The radiation was coming out of the vacuum chamber through quartz ultraviolet (KU)-1 quartz window. The radiation detector was a silicon photodiode with a diameter of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d =1.2$ </tex-math></inline-formula> mm. It was located on an axis intersecting the axis of symmetry of the discharge in the center of the interelectrode gap. The distance from the diode to the axis of symmetry was <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L =1340$ </tex-math></inline-formula> mm. After amplification, the signal from the diode was recorded on an oscilloscope. The measurements were made in a range of currents from 10 to 25 kA in order to cover the modes with the anodic activity. It was found that under the conditions of these experiments, the anode activity begins to manifest itself at the end of the pulse, starting with currents exceeding 15 kA. As the current increases, the activity begins closer to the beginning of the pulse. Considering the type of the spectral sensitivity of the diode, two series of measurements were made—measurements without a filter and through a yellow filter ZhS-10 that cuts off radiation with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda \le400$ </tex-math></inline-formula> nm. The results obtained made it possible to analyze the dependence of the radiation power on the arc current. The results showed that at high current densities in the developed vacuum arc with anodic activity, a significant part of the power is transferred by radiation. At the end of a pulse with a current of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 25$ </tex-math></inline-formula> kA, the radiation power is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{\mathrm {uv}}~\approx ~150$ </tex-math></inline-formula> kW, while in the discharge, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{a} ~\approx ~800$ </tex-math></inline-formula> kW is released. That is, at high current densities at the end of the pulse, the radiation power reaches almost 20% of the power released in the arc at this time. Estimates of lateral losses due to radiation are made.

Quantum Brownian motion of a charged oscillator in a magnetic field coupled to a heat bath through momentum variables

We study the Quantum Brownian motion of a charged particle moving in a harmonic potential in the presence of an uniform external magnetic field and linearly coupled to an Ohmic bath through momentum variables. We analyse the growth of the mean square displacement of the particle in the classical high temperature domain and in the quantum low temperature domain dominated by zero point fluctuations. We also analyse the Position Response Function and the long time tails of various correlation functions. We notice some distinctive features, different from the usual case of a charged quantum Brownian particle in a magnetic field and linearly coupled to an Ohmic bath via position variables.

Magnetic field and strain effects in Janus-like Weyl semimetals MoTeSe with four Weyl points

We suggest a new Janus-like Weyl semimetal (WSM) candidate MoTeSe with only four Weyl points (WPs) by alloying route from prototype Td-phase WSM MoTe2 with twelve WPs. The topological properties and topological responses under external uniform magnetic field B and strain of MoTeSe have been investigated by Wannier-function-based tight-binding Hamiltonian and first-principles method. Our calculations show WSM state is robust in a large B with the magnitude of order 10 meV and the separation distance of WPs can be effectively modulated by changing the direction and strength of B. The four WPs move away from the kz = 0 plane and the energy of WP changes parabolically with the increase of c-axial B. By contrast, the energy of WP varies linearly and approaches to the Fermi level with the increasing a-/b-axial B. We further consider the influence of in-plane B on the topological response of MoTeSe and reveal a more complex and diverse behavior. In addition, four-WP MoTeSe displays good robustness within the moderate strain and can be transit into other multi-node WSM or non-WSM under larger strain. Our findings provide an excellent few-node WSM platform for understanding the behavior of Weyl fermion under external magnetic or strain field and a potential candidate for applications of WSM in topological electronic devices.

Enhanced radiation of nonlinear Thomson backscattering by a tightly focused Gaussian laser pulse and an external magnetic field

The electron dynamics and the Thomson backscattering of an electron moving in a combined field of a tightly focused Gaussian laser pulse and an external uniform magnetic field are investigated in detail. It is found that by considering the tightly focused Gaussian laser pulse, the electron can be pushed out from the laser pulse by the ponderomotive force, resulting in the symmetry breaking of the electron dynamics from the Gaussian envelope, which can dramatically enhance the radiation intensity. It is also found that by introducing an external magnetic field, the emergence of the cyclotron motion of the electron under the external magnetic field also breaks the symmetry of the electron dynamics and enhances the radiation. Especially in the resonance case, i.e., the cyclotron frequency of the electron is close to the laser frequency, the emission spectrum is further enhanced due to the great extension of the interaction time and the symmetry breaking by the beat wave between the helix motion and the cyclotron motion of the electron in the combined field, and a platform with high radiation intensity containing the THz band has also appeared.

Generalized Helicity Operator for a Spin 2 Particle in the Presence of an External Uniform Magnetic Field

The eigenvalue problem for generalized helicity operator for a spin 2 particle in the presence of a uniform magnetic field is solved. After separating variables in the basis of cylindrical tetrad the system of 10 first order differential equations is derived, it is split into two independent subsystems of four and six equations. First, the free particle is studied. The system of four equations is solved straightforwardly in terms of the confluent hypergeometric functions, there are found corresponding eigenvalues and eigenfunctions. Subsystem of six equations leads to one ordinary 4-th order differential equation. Corresponding operator is factorized into the product of two commuting 2-nd order operators, so the problem reduces to solving two differential equations of the 2-nd order. Their solutions are constructed in terms of the Bessel functions. The problem is extended to a presence of an external uniform magnetic field, the method is much the same, the explicit solutions are constructed in terms of the confluent hypergeometric functions. The helicity eigenvalues are described in an implicit form, as solutions of the polynomial equations of 3-rd and 5-th orders.

Thermal properties of quantum rings in monolayer and bilayer graphene

In this work, we use two different statistical mechanics formalisms like, Shannon and Tsallis formalisms (extensive and non-extensive), to study the thermodynamic properties of quantum rings (QRs) in monolayer and bilayer graphene under a uniform external magnetic field. To this goal, we first employ a simplified model to obtain energy eigenvalues of monolayer and bilayer graphene quantum rings. Then, by applying the Shannon and Tsallis formalisms, we have calculated the entropy, specific heat, magnetization, and magnetic susceptibility of monolayer and bilayer graphene. Our results show that thermodynamic quantities in the Shannon formalism have oscillation behaviors with increasing external magnetic fields. Unlike the Shannon formalism, the obtained properties by the Tsallis formalism show a peak structure. Also, the peak location depends on the number of graphene layers.

Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is static spherical symmetric, it is integrable. However, the spherical symmetry and the integrability are destroyed when the black hole is immersed in an external asymptotic uniform magnetic field and the particle is charged. Although the magnetized modified Schwarzschild spacetime is nonintegrable and inseparable, it allows for the application of explicit symplectic integrators when its Hamiltonian is split into five explicitly integrable parts. Taking one of the proposed explicit symplectic integrators and the techniques of Poincaré sections and fast Lyapunov indicators as numerical tools, we show that the charged particle can have chaotic motions under some circumstances. Chaos is strengthened with an increase of the modified gravity parameter from the global phase space structures. There are similar results when the magnetic field parameter and the particle energy increase. However, an increase of the particle angular momentum weakens the strength of chaos.

Magnetically Controlled Modular Cubes With Reconfigurable Self-Assembly and Disassembly

Reconfigurable modular robots, which can actively assemble and disassemble on command, offer the possibility of mesoscale (milliscale and microscale) manufacturing with robustness and controllability. In this study, we present a design of a scalable modular subunit with embedded permanent magnets in a 3-D printed cubic body. The subunit can be wirelessly controlled by an external uniform magnetic field. We also present controlled assembly–disassembly techniques for these subunits. Our modular robotic platform is highly reconfigurable and can create programmable, predetermined patterns based on open-loop control. The 2-D motion planner computes all reachable polyomino shapes from an arbitrary initial configuration and provides the shortest movement sequences to form each shape. Experimental results match computational modeling, demonstrating robust and reproducible behavior of the modular robotic platform that is promising for mesoscale manufacturing applications. Two cube sizes were tested: 10-mm edge lengths and 2.8-mm edge lengths.