scholarly journals Analytical calculation of the orbital spectrum of the guiding centre motion in axisymmetric magnetic fields

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Yannis Antonenas ◽  
Giorgos Anastassiou ◽  
Yannis Kominis
Keyword(s):  
Magnetic Fields ◽  
Analytical Calculation ◽  
Particle Energy ◽  
Hamiltonian Description ◽  
Drift Motion ◽  
Analytical Transformation ◽  
Analytical Formulas ◽  
Particle Resonance ◽  
Energy And Momentum ◽  
Remarkable Agreement

Charged particle motion in axisymmetric toroidal magnetic fields is analysed within the context of the canonical Hamiltonian guiding centre theory. A canonical transformation to variables measuring the drift orbit deviation from a magnetic field line is introduced and an analytical transformation to action-angle variables is obtained, under a zero drift width approximation. The latter is used to provide compact formulas for the orbital spectrum of the drift motion, namely the bounce/transit frequencies as well as the bounce/transit averaged toroidal precession and gyration frequencies. These formulas are shown to have a remarkable agreement with numerically calculated full drift width frequencies and significant differences from standard analytical formulas based on a pendulum-like Hamiltonian description. The analytical knowledge of the orbital spectrum is crucial for the formulation of particle resonance conditions with symmetry-breaking perturbations and the study of the resulting particle, energy and momentum transport.

A reciprocating permanent magnetic actuator for driving magnetic micro robots in fluids

2021 ◽  
pp. 095440622110145
Author(s):  
Chuan Qu ◽  
Yong-Chen Pei ◽  
Qing-Yuan Xin ◽  
Zhen-Xing Li ◽  
Long Xu
Keyword(s):  
Permanent Magnet ◽  
Analytical Calculation ◽  
Magnetic Actuator ◽  
Cross Sectional ◽  
Permanent Magnetic Actuator ◽  
Element Simulation ◽  
Micro Robot ◽  
Analytical Formulas ◽  
Motion Performance ◽  
Motion Characteristics

Magnetic-based driving applications are receiving increasing attention. This study proposed a novel reciprocating permanent magnetic actuator (PMA) to manipulate magnetic micro robots to impact and clear blockages inside fluid pipes in a linear path. The PMA consisted of a cylindrical permanent magnet and a crank slider structure. A straight pipe with a circular cross-sectional area was located in front of the actuator to study the driving performance of PMA. A micro permanent magnet with a cylinder shape was employed as a working robot for manipulation inside the pipe. Firstly, analytical formulas were derived to obtain the magnetic driving force acting on the micro robot and determine the most suitable magnet configuration. The finite element simulation verified the analytical calculation. The developed reciprocating PMA prototype was then introduced, and the PMA and micro robot’s motion performance was analysed. Lastly, preliminary experiments were carried out for evaluating the micro robot’s motion characteristics. Performance tests for different excitation frequencies, flow rates, viscosities, and axial distances, indicating that PMA could manipulate the magnetic micro robot inside the pipe. The results confirmed that the developed PMA could effectively drive the micro robot with the advantage of consecutive magnetic driving. Especially, the micro robot featured good flexibility, rapid response, and a simple structure, suggesting that this micro robot may play an important role in industrial and medical applications, such as blockage elimination and thrombus clearance.

scholarly journals Баллистическое течение двумерных электронов в магнитном поле

2021 ◽  
Vol 55 (7) ◽  
pp. 566
Author(s):  
А.Н. Афанасьев ◽  
П.С. Алексеев ◽  
А.А. Грешнов ◽  
М.А. Семина
Keyword(s):  
Magnetic Fields ◽  
Ballistic Transport ◽  
Ballistic Regime ◽  
Electron Collisions ◽  
Viscosity Effect ◽  
Small Density ◽  
Longitudinal Resistance ◽  
Analytical Formulas ◽  
Sample Width ◽  
Theoretical Results

In conductors with a very small density of defects, electrons at low temperatures collide predominantly with a sample edges. Therefore, the ballistic regime of charge and heat transport is realized. The application of a perpendicular magnetic field substantially modifies the character of ballistic transport. For the case of two-dimensional (2D) electrons in the magnetic fields corresponding to the diameter of the cyclotron trajectories smaller than the sample width a hydrodynamic transport regime is formed. In the latter regime, the flow is mainly controlled by rare electron–electron collisions, which determine the viscosity effect. In this work, we study the ballistic flow of 2D electrons in long samples in magnetic fields up to the critical field of the transition to the hydrodynamic regime. From solution of the kinetic equation, we obtain analytical formulas for the profiles of the current density and the Hall electric field far and near the ballistic-hydrodynamic transition as well as for the longitudinal and Hall resistances in these ranges. Our theoretical results, apparently, describe the observed longitudinal resistance of pure graphene samples in the diapason of magnetic fields below the ballistic-hydrodynamic transition.

scholarly journals Analytical calculation of time of reaching specific values based on visibility loss during a fire

2018 ◽  
Vol 193 ◽  
pp. 03007 ◽  
Author(s):  
Sergei Kolodyazhniy ◽  
Vladimir Kozlov
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Ventilation System ◽  
Analytical Calculation ◽  
Critical Time ◽  
Original Data ◽  
Critical Value ◽  
Time Intervals ◽  
Evacuation Time ◽  
Analytical Formulas

Using an integral mathematical model of a fire considering the assumptions typical of a starting stage of a fire, analytical dependencies were obtained for determining the time of reaching a critical value of the density of a smoke screen in a premises with a fire epicenter and adjoining premises. By means of analytical formulas for determining critical evacuation time intervals based on visibility loss, table values for different parameters that are included in the original equations were obtained. Simple engineering analytical solutions that describe the dynamics of smoke formation in premises in case of a fire when used in a certain combination are presented. The obtained dependencies allow one to identify the critical time of evacuation with no use of special PC software as well as to obtain original data without calculating an anti-smoke ventilation system.

Simplified Analytical Calculation and Modification of the Crushing Forces of Intersection Units in Vessel-Bridge Collisions

2020 ◽  
Author(s):  
Yin Faqiang ◽  
Pan Jin ◽  
Huang Shiwen ◽  
Xu Mingcai
Keyword(s):  
Small Angle ◽  
Large Angle ◽  
Analytical Formula ◽  
Analytical Calculation ◽  
Typical Structure ◽  
Analytical Formulas ◽  
Ship Collision ◽  
Collision Force ◽  
Inclined Angle ◽  
The Impact

Abstract Because of the increasingly busy maritime trade, the number of bridges damaged by ship-bridge collision also increases. In order to reduce the serious losses caused by ship-bridge collision incidents, it is necessary to make a rapid estimation of ship collision forces. The simplified analytical formulas can be used to rapidly evaluate the collision force in ship collision accidents, but it is found that the existing simplified formulas are only applicable to bulb structures including small-angle inclined elements and not suitable for large-angle inclined elements which exist in ship-bridge collision. In this paper, the quasi-static crushing simulation of the bulbous structure with small-angle inclined angle elements is carried out, and the applicability of the simplified analytical formula of the intersection unit to the typical structure is verified. By comparing the simplified analytical results of the bow with the quasi-static simulation results and the ratio of the strength reduction factor to the effective crushing distance, it is found that the inclined angle of the inclined element will affect the impact force of the simplified analytical calculation. Then, finite element analysis of the truncated-type intersection structure with different element inclination angles are carried out, and the results show that the existing simplified analytical formula is no longer suitable for the calculation of collision force when the inclined angle is greater than 40°. For this reason, the existing simplified analytical formulas are modified for the large-angle inclined elements, and it can provide a certain reference calculation value for the collision force of vessel-bridge collision which includes large-angle inclined elements.

scholarly journals Particle Acceleration and Radiation in Magnetospheres of Collapsing Stars

2000 ◽  
Vol 195 ◽  
pp. 403-406
Author(s):  
V. Kryvdyk
Keyword(s):  
Magnetic Fields ◽  
Energy Distribution ◽  
Power Law ◽  
Charged Particles ◽  
Particle Dynamics ◽  
Initial Energy ◽  
Particle Energy ◽  
Radiation Fluxes ◽  
Nonthermal Emission ◽  
Initial Power

Particle dynamics and nonthermal emission therefrom in the magnetospheres of collapsing stars with initial dipole magnetic fields and a certain initial energy distribution of charged particles (power-law, relativistic Maxwell, and Boltzmann distributions) are considered. The radiation fluxes are calculated for various collapsing stars with initial dipole magnetic fields and an initial power-law particle energy distribution in the magnetosphere. The effects can be observed by means of modern instruments.

scholarly journals Our dynamic sun: 2017 Hannes Alfvén Medal lecture at the EGU

2017 ◽  
Vol 35 (4) ◽  
pp. 805-816 ◽  
Author(s):  
Eric Priest
Keyword(s):  
Magnetic Fields ◽  
Magnetic Energy ◽  
Active Regions ◽  
Particle Energy ◽  
Space Environment ◽  
Small Scale ◽  
The Sun ◽  
Strong Shear ◽  
Outer Atmosphere ◽  
Mass Ejection

Abstract. This lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A small-scale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic fine-scale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fast-particle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.

scholarly journals Modeling heat transfer process in soils

2018 ◽  
Vol 251 ◽  
pp. 02048 ◽  
Author(s):  
Ian Ofrikhter ◽  
Alexander Zaharov ◽  
Andrey Ponomaryov ◽  
Natalia Likhacheva
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Thermal Conductivity ◽  
Analytical Calculation ◽  
Accurate Method ◽  
Heat Transfer Process ◽  
Preliminary Evaluation ◽  
Soil Base ◽  
Undisturbed Sample ◽  
Analytical Formulas

In this paper, a new model is presented for calculating the thermal conductivity of soils, and the main provisions for the derivation of analytical formulas are given. The presented model allows taking into account the density, moisture content and temperature of the soil base. The technique presented in the paper makes it possible to dispense with laborious experiments to estimate the thermal conductivity of the soil. The method of analytical calculation is step by step presented in the paper. Two variants of using the method are proposed: 1) Less accurate method, for preliminary evaluation, without the need to take probe and conduct experiments. 2) More accurate method, with at least one experiment with a disturbed or undisturbed sample. The results of comparison of calculated values of thermal conductivity and experimental data are presented.

Direct measurements of two-way wave-particle energy transfer in a collisionless space plasma

Science ◽  
2018 ◽  
Vol 361 (6406) ◽  
pp. 1000-1003 ◽  
Author(s):  
N. Kitamura ◽  
M. Kitahara ◽  
M. Shoji ◽  
Y. Miyoshi ◽  
H. Hasegawa ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Particle Energy ◽  
Magnetic Field Direction ◽  
Particle Interactions ◽  
Momentum Exchange ◽  
Quantitative Evidence ◽  
Ion Distributions ◽  
Wave Particle Interactions ◽  
Electromagnetic Ion Cyclotron Waves ◽  
Energy And Momentum

Particle acceleration by plasma waves and spontaneous wave generation are fundamental energy and momentum exchange processes in collisionless plasmas. Such wave-particle interactions occur ubiquitously in space. We present ultrafast measurements in Earth’s magnetosphere by the Magnetospheric Multiscale spacecraft that enabled quantitative evaluation of energy transfer in interactions associated with electromagnetic ion cyclotron waves. The observed ion distributions are not symmetric around the magnetic field direction but are in phase with the plasma wave fields. The wave-ion phase relations demonstrate that a cyclotron resonance transferred energy from hot protons to waves, which in turn nonresonantly accelerated cold He+ to energies up to ~2 kilo–electron volts. These observations provide direct quantitative evidence for collisionless energy transfer in plasmas between distinct particle populations via wave-particle interactions.

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