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In this paper, the magnetic flux density was studied using a mathematical model and different inner radius has been used for the iron free coil. The maximum value of magnetic field and the magnetic scalar potential was calculated. The paraxial ray can be studied using rung Kutta to solve the differential equation in the infinite and zero magnification condition, all results are determined using MATLAB program.

In the current research was to benefit from the potential of the two cylindrical electric lenses to be used in the product a mathematical model from which, one can determine the magnetic field distribution of the charged particle objective lens. With aid of simulink in matlab environment, some simulink models have been building to determine the distribution of the target function and their related axial functions along the optical axis of the charged particle lens. The present study showed that the physical parameters (i.e., the maximum value, Bmax, and the half width W of the field distribution) and the objective properties of the charged particle lens have been affected by varying the main geometrical parameter of the lens named the bore radius R.

Huygens’ metasurfaces demonstrate almost arbitrary control over the shape of a scattered beam; however, its spatial profile is typically fixed at the fabrication time. The dynamic reconfiguration of this beam profile with tunable elements remains challenging, due to the need to maintain the Huygens’ condition across the tuning range. In this work, we experimentally demonstrate that a time-varying metadevice which performs frequency conversion can steer transmitted or reflected beams in an almost arbitrary manner, with fully dynamic control. Our time-varying Huygens’ metadevice is made of both electric and magnetic meta-atoms with independently controlled modulation, and the phase of this modulation is imprinted on the scattered parametric waves, controlling their shapes and directions. We develop a theory which shows how the scattering directionality, phase, and conversion efficiency of sidebands can be manipulated almost arbitrarily. We demonstrate novel effects including all-angle beam steering and frequency-multiplexed functionalities at microwave frequencies around 4 GHz, using varactor diodes as tunable elements. We believe that the concept can be extended to other frequency bands, enabling metasurfaces with an arbitrary phase pattern that can be dynamically tuned over the complete2πrange.

Alongside magnetic reconnection, turbulence is another fundamental nonlinear plasma phenomenon that plays a key role in energy transport and conversion in space and astrophysical plasmas. From a numerical, theoretical, and observational point of view there is a long history of exploring the interplay between these two phenomena in space plasma environments; however, recent high-resolution, multi-spacecraft observations have ushered in a new era of understanding this complex topic. The interplay between reconnection and turbulence is both complex and multifaceted, and can be viewed through a number of different interrelated lenses - including turbulence acting to generate current sheets that undergo magnetic reconnection ( turbulence-driven reconnection ), magnetic reconnection driving turbulent dynamics in an environment ( reconnection-driven turbulence ) or acting as an intermediate step in the excitation of turbulence, and the random diffusive/dispersive nature of the magnetic field lines embedded in turbulent fluctuations enabling so-called stochastic reconnection . In this paper, we review the current state of knowledge on these different facets of the interplay between turbulence and reconnection in the context of collisionless plasmas, such as those found in many near-Earth astrophysical environments, from a theoretical, numerical, and observational perspective. Particular focus is given to several key regions in Earth’s magnetosphere – namely, Earth’s magnetosheath, magnetotail, and Kelvin-Helmholtz vortices on the magnetopause flanks – where NASA’s Magnetospheric Multiscale mission has been providing new insights into the topic.

Atomic-resolution electron microscopes utilize high-power magnetic lenses to produce magnified images of the atomic details of matter. Doing so involves placing samples inside the magnetic objective lens, where magnetic fields of up to a few tesla are always exerted. This can largely alter, or even destroy, the magnetic and physical structures of interest. Here, we describe a newly developed magnetic objective lens system that realizes a magnetic field free environment at the sample position. Combined with a higher-order aberration corrector, we achieve direct, atom-resolved imaging with sub-Å spatial resolution with a residual magnetic field of less than 0.2 mT at the sample position. This capability enables direct atom-resolved imaging of magnetic materials such as silicon steels. Removing the need to subject samples to high magnetic field environments enables a new stage in atomic resolution electron microscopy that realizes direct, atomic-level observation of samples without unwanted high magnetic field effects. Electron microscopy typically requires strong magnetic lenses in order to reach atomic resolution, prohibiting the possibility to measure magnetic materials. The authors here present a lens design that enables atomic-resolution electron microscopy of magnetic materials by providing a field-free sample region.

Microscopy and crystallography are two essential experimental methodologies for advancing modern science. They complement one another, with microscopy typically relying on lenses to image the local structures of samples, and crystallography using diffraction to determine the global atomic structure of crystals. Over the past two decades, computational microscopy, encompassing coherent diffractive imaging (CDI) and ptychography, has advanced rapidly, unifying microscopy and crystallography to overcome their limitations. Here, I review the innovative developments in CDI and ptychography, which achieve exceptional imaging capabilities across nine orders of magnitude in length scales, from resolving atomic structures in materials at sub-ångstrom resolution to quantitative phase imaging of centimetre-sized tissues, using the same principle and similar computational algorithms. These methods have been applied to determine the 3D atomic structures of crystal defects and amorphous materials, visualize oxygen vacancies in high-temperature superconductors and capture ultrafast dynamics. They have also been used for nanoscale imaging of magnetic, quantum and energy materials, nanomaterials, integrated circuits and biological specimens. By harnessing fourth-generation synchrotron radiation, X-ray-free electron lasers, high-harmonic generation, electron microscopes, optical microscopes, cutting-edge detectors and deep learning, CDI and ptychography are poised to make even greater contributions to multidisciplinary sciences in the years to come. This review highlights transformative advancements in computational microscopy, encompassing coherent diffractive imaging and ptychography, which unify microscopy and crystallography to achieve unparalleled resolution, precision, and large fields of view, enabling diverse applications and driving breakthroughs across multidisciplinary sciences.

The possibilities to accelerate vortex electrons with orbital angular momentum (OAM) to relativistic energies and to produce vortex ions, protons, and other charged particles crucially depend on whether the OAM is conserved during the acceleration and on how phase space of the wave packet evolves. We show that both the OAM and a mean emittance of the packet, the latter obeying the Schrödinger uncertainty relation, are conserved in axially symmetric fields of electric and magnetic lenses, typical for accelerators and electron microscopes, as well as in Penning traps. Moreover, a linear approximation of weakly inhomogeneous fields works much better for single packets than for classical beams. We analyze quantum dynamics of the packet’s rms radius ⟨ ρ 2 ⟩, relate this dynamics to a generalized form of the van Cittert–Zernike theorem, applicable at arbitrary distances from a source and for non-Gaussian packets, and adapt the Courant–Snyder formalism to describe the evolution of the packet’s phase space. The vortex beams can therefore be accelerated, focused, steered, trapped, and even stored in azimuthally symmetric fields and traps, somewhat analogously to the classical angular-momentum-dominated beams. We also give a quantum version of the Busch theorem, which states how one can produce vortex electrons with a magnetized cathode during either field- or photoemission, as well as vortex ions and protons by using a magnetized stripping foil employed to change a charge state of ions. Spatial coherence of the packets plays a crucial role in these applications and we provide the necessary estimates for particles of different masses.

A computer-aided design (CAD) has been carried out to investigate the properties of the magnetic electron mirror design. The work has been focused on suggesting a mathematical formula to represent the radial displacement. The function that has been taken into consideration was suggested to give rise to the mirror action. A numerical solution is carried out for solving the Paraxial-ray equation for determining the optical properties such as the focal length, the spherical and chromatic aberration coefficients and the excitation of the mirror. The pole shape of the mirror has been determined in two dimensions. In the present work, the profile of the mirror determined from the suggested trajectory is the single-pole types. The coefficients of the chromatic and spherical aberrations of the magnetic mirror are determined and normalized in terms of the focal length. The operational requirements are determining the choice of the mirror.

As a non-invasive innovative diagnosis platform, advanced flexible contact lenses can dynamically monitor vital ocular indicators, spot abnormalities and provide biofeedback guidance for real-time diagnosis and rehabilitation tracking of chronic eye diseases. However, most of the state-of-the-art reported contact lenses either can only monitor a single indicator at a time or realize multifunctional integration based on multiple materials. Herein, we developed a flexible multifunctional contact lens based on inorganic γ-Fe 2 O 3 @NiO magnetic oxide nanosheets, which can be attached conformally and seamlessly to the eyeball to simultaneously monitor glucose level in tears, eyeball movement, and intraocular pressure. The optimized contact lens has a reliable glucose detection limit (0.43 μmol), superior eye movement measurement accuracy (95.27%) and high intraocular pressure sensitivity (0.17 MHz mmHg − 1 ). This work presents a concept in the biochemical and biophysical integrated sensing of ocular signals using contact lens via an innovative material, and provides a personalized and efficient way for health management. Graphical Abstract