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Lorentz forces on the dust in Jupiter's ring
The paths of dust particles in the Jovian ring are investigated using a numerical integration program, including the acceleration due to gravity and the Lorentz and drag accelerations arising from the motions of the charged dust through the Jovian plasma. It is determined that the orbit of a 2.5 micron radius spherical dust particle with a density of 2 g/cu cm -10V will become significantly perturbed. The ring will tend to warp northwards near 130-160 deg longitude, with the maximum excursion of the Jupiter ring grains equalling about 0.1 deg (consistent with a distance of 220 km above the equatorial plane). It is found that either the particles are larger or the voltages on them less than what has been determined by previous investigators, while the plasma near the ring may be considerably cooler than was estimated. Calculations show that particles of 0.3 micron with -10 V potentials are spread from 1.68-1.98 of the radius of Jupiter and inclined up to 7 deg out of the equatorial plane. The paths of these particles do not follow Keplerian orbits, and the particle positions are not symmetric about the equatorial plane. Particles of 0.4 micron radius have less asymmetric orbits than 0.3 micron particles, while particles less than 0.2 micron are perturbed into Jupiter cloudtops within a few tens of hours.
Electromagnetic coil optimization for reduced Lorentz forces
Abstract The reduction of magnetic forces on electromagnetic coils is an important consideration in the design of high-field devices such as the stellarator or tokamak. Unfortunately, these forces may be too time-consuming to evaluate by conventional finite element modeling within an optimization loop. Although mutual forces can be computed rapidly by approximating large-bore coils as infinitely thin, this approximation does not hold for self-forces as it leads to an unphysical divergence. Recently, a novel reduced model for the self-field, self-force, and self-inductance of electromagnetic coils based on filamentary models was rigorously derived and demonstrated to be highly accurate and numerically efficient to evaluate (Hurwitz et al 2024 IEEE Trans. Magn. 60 7001614). In this paper, we present an implementation of the reduced self-force model employing automatic differentiation within the simsopt stellarator design software and use it in derivative-based coil optimization for a quasi-axisymmetric stellarator. We show that it is possible to significantly reduce point-wise forces throughout the coils, though this comes with trade-offs to fast particle losses and the minimum distance between coils and the plasma surface. The trade-off between magnetic forces and coil-surface distance is mediated by the minimum coil–coil distance for coils near the inboard side of the ‘bean’ cross-section of the plasma. The relationship between forces and fast particle losses is mediated by the normal field error. Coil forces can be lowered to a threshold with minimal deterioration to losses. Importantly, the magnet optimization approach here can be used also for tokamaks, other fusion concepts, and applications outside of fusion.
Simulated Lorentz Force Detuning Compensation With A Double Lever Tuner On A Dreassed ILC/1.3 GHz Cavity At Room Temperature [Poster]
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Lorentz Force Accelerator Technology Investigated
The NASA Glenn Research Center is developing Lorenz force accelerators (LFAs) for a wide variety of space applications. These range from the precision control of formation-flying spacecraft to the primary propulsion system for very high power interplanetary spacecraft. The specific thruster technologies being addressed are pulsed plasma thrusters (PPT) and magnetoplasmadynamic (MPD) thrusters.
Erratum: “Abrupt Changes in the Photospheric Magnetic Field, Lorentz Force, and Magnetic Shear during 15 X-class Flares” (2019, ApJS, 240, 11)
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Lorentz Body Force Induced by Traveling Magnetic Fields
The Lorentz force induced by a traveling magnetic field (TMF) in a cylindrical container has been calculated. The force can be used to control flow in dectrically conducting melts and the direction of the magnetic field and resulting flow can be reversed. A TMF can be used to partially cancel flow driven by buoyancy. The penetration of the field into the cylinder decreases as the frequency increases, and there exists an optimal value of frequency for which the resulting force is a maximum. Expressions for the Lorentz force in the limiting cases of low frequency and infinite cylinder are also given and compared to the numerical calculations.
Geostrophic to magnetically-damped turbulence in liquid metal rotating magnetoconvection
Understanding planetary core convection dynamics requires the study of convective flows in which the Coriolis and Lorentz forces attain a leading-order, so-called magnetostrophic balance. Experimental investigations of rotating magnetoconvection (RMC) in the magnetostrophic regime are therefore essential to broadly characterize the properties of local-scale planetary core flow. Toward this end, we present here the first thermovelocimetric measurements of magnetostrophic, liquid metal convection, which are made using liquid gallium as the working fluid, at moderate rotation rates (Ekman numbers 10 -4 ≤ Ek ≤ 10 -5 ) and in the presence of dynamically strong magnetic fields (Elsasser number Λ = 1). Complementary rotating convection (RC) experiments are performed at the same rotation rates to serve as reference cases. Our RMC velocity measurements adequately follow a geostrophic turbulent scaling for cases in which local-scale convective inertial forces exceed the Lorentz forces in the fluid bulk. In cases where Lorentz forces exceed local-scale inertia (local or convective interaction parameter N ℓ or N C ≳ 3), the root-mean-square RMC velocities are magnetically damped, yielding values below the geostrophic turbulent RC scaling prediction. An enhancement in heat transfer is observed, which we attribute to the increased coherence of vertically aligned magnetostrophic convective flow. Finally, our results and comparisons to dynamo simulations suggest that the system is in the strong-field regime, where convection-scale flows are magnetically damped with N C ≳ 3).
FARGO3D: A NEW GPU-ORIENTED MHD CODE
We present the FARGO3D code, recently publicly released. It is a magnetohydrodynamics code developed with special emphasis on the physics of protoplanetary disks and planet–disk interactions, and parallelized with MPI. The hydrodynamics algorithms are based on finite-difference upwind, dimensionally split methods. The magnetohydrodynamics algorithms consist of the constrained transport method to preserve the divergence-free property of the magnetic field to machine accuracy, coupled to a method of characteristics for the evaluation of electromotive forces and Lorentz forces. Orbital advection is implemented, and an N-body solver is included to simulate planets or stars interacting with the gas. We present our implementation in detail and present a number of widely known tests for comparison purposes. One strength of FARGO3D is that it can run on either graphical processing units (GPUs) or central processing units (CPUs), achieving large speed-up with respect to CPU cores. We describe our implementation choices, which allow a user with no prior knowledge of GPU programming to develop new routines for CPUs, and have them translated automatically for GPUs.
A kinetic model of friction in strongly coupled strongly magnetized plasmas
Plasmas that are strongly magnetized in the sense that the gyrofrequency exceeds the plasma frequency exhibit novel transport properties that are not well understood. As a representative example, we compute the friction force acting on a massive test charge moving through a strongly coupled and strongly magnetized one-component plasma using a generalized Boltzmann kinetic theory. Recent works studying the weakly coupled regime have shown that strong magnetization leads to a transverse component of the friction force that is perpendicular to both the Lorentz force and velocity of the test charge, in addition to the stopping power component aligned antiparallel to the velocity. Recent molecular dynamics simulations have also shown that strong Coulomb coupling in addition to strong magnetization gives rise to a third component of the friction force in the direction of the Lorentz force. Here, we show that the generalized Boltzmann kinetic theory captures these effects and generally agrees well with the molecular dynamics simulations over a broad range of Coulomb coupling and magnetization strength regimes. The theory is also used to show that the “gyro” component of the friction in the direction of the Lorentz force arises due to asymmetries associated with gyromotion during short-range collisions. Computing the average motion of the test charge through the background plasma, the transverse force is found to strongly influence the trajectory by changing the gyroradius and the gyrofriction force is found to slightly change the gyrofrequency of the test charge resulting in a phase shift.
Force law in material media, hidden momentum and quantum phases
We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.
Force balance in the magnetospheres of Jupiter and Saturn
Spacecraft measurements of the plasma populations and magnetic fields near Jupiter and Saturn have revealed that large magnetospheres surround both planets. Magnetic field measurements have indicated closed field line topologies in the dayside magnetospheres of both planets while plasma instruments have shown these regions to be populated by both hot and cold plasma components convected azimuthally in the sense of planetary rotation. By using published data from the Voyager Plasma Science (PLS), Low Energy Charged Particle (LECP), and Magnetometer (MAG) instruments, it is possible to investigate the validity of the time stationary MHD momentum equation in the middle magnetospheres of Jupiter and Saturn. At Saturn, the hot plasma population is negligible in the dynamic sense and the centrifugal force of the cold rotating plasma appears to balance the Lorentz force. At Jupiter, the centrifugal force balances about 25 percent of the Lorentz force. The remaining inward Lorentz force is balanced by pessure gradients in the hot, high-beta plasma of the Jovian magnetodisk.
The Bearingless Electrical Machine
Electromagnetic bearings allow the suspension of solids. For rotary applications, the most important physical effect is the force of a magnetic circuit to a high permeable armature, called the MAXWELL force. Contrary to the commonly used MAXWELL bearings, the bearingless electrical machine will take advantage of the reaction force of a conductor carrying a current in a magnetic field. This kind of force, called Lorentz force, generates the torque in direct current, asynchronous and synchronous machines. The magnetic field, which already exists in electrical machines and helps to build up the torque, can also be used for the suspension of the rotor. Besides the normal winding of the stator, a special winding was added, which generates forces for levitation. So a radial bearing, which is integrated directly in the active part of the machine, and the motor use the laminated core simultaneously. The winding was constructed for the levitating forces in a special way so that commercially available standard ac inverters for drives can be used. Besides wholly magnetic suspended machines, there is a wide range of applications for normal drives with ball bearings. Resonances of the rotor, especially critical speeds, can be damped actively.
The magnetic furnace: intense core dynamos in B stars
The dynamo action achieved in the convective cores of main-sequence massive stars is explored here through three-dimensional (3D) global simulations of convective core dynamos operating within a young 10 M{sub ⊙} B-type star, using the anelastic spherical harmonic code. These simulations capture the inner 65% of this star by radius, encompassing the convective nuclear-burning core (about 23% by radius) and a portion of the overlying radiative envelope. Eight rotation rates are considered, ranging from 0.05% to 16% of the surface breakup velocity, thereby capturing both convection that barely senses the effects of rotation and other situations in which the Coriolis forces are prominent. The vigorous dynamo action realized within all of these turbulent convective cores builds magnetic fields with peak strengths exceeding a megagauss, with the overall magnetic energy (ME) in the faster rotators reaching super-equipartition levels compared to the convective kinetic energy (KE). The core convection typically involves turbulent columnar velocity structures roughly aligned with the rotation axis, with magnetic fields threading through these rolls and possessing complex linkages throughout the core. The very strong fields are able to coexist with the flows without quenching them through Lorentz forces. The velocity and magnetic fields achieve such a state by being nearly co-aligned, and with peak magnetic islands being somewhat displaced from the fastest flows as the intricate evolution proceeds. As the rotation rate is increased, the primary force balance shifts from nonlinear advection balancing Lorentz forces to a magnetostrophic balance between Coriolis and Lorentz forces.
The Role of Magnetic Reconnection in the Structure and Dynamics of Fast Coronal Mass Ejections
Both observations and models of flare-associated coronal mass ejections (CMEs) suggest that magnetic reconnection in an ejection's wake substantially increases the net, outward Lorentz force accelerating the CME. A stronger outward force can cause a feedback loop, driving further magnetic reconnection in a "reconnective instability." The flux accretion model captures this by relating reconnected flux, ∆ rec , and magnetic field strength, B CME , to increased outward Lorentz force, ∆F r . To better understand reconnection's role in CME dynamics, we analyze two snapshots from a 2.5D, MHD simulation of a breakout eruption. Outward Lorentz forces increase substantially as reconnection proceeds, caused primarily by "flank currents," which flow just inside the boundary of the rising ejection's wake and parallel to its axis. This model's reconnection jet also alters the ejection's internal structure, an effect that could be sought in observations. Analyzing reconnection-induced Lorentz forces in 3D simulations could provide additional insights into CME dynamics.
An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems
An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).
Phonon Hall Viscosity of Ionic Crystals
When time-reversal symmetry is broken, the low-energy description of acoustic lattice dynamics allows for a dissipationless component of the viscosity tensor, the phonon Hall viscosity, which captures how phonon chirality grows with the wave vector. In this work, we show that, in ionic crystals, a phonon Hall viscosity contribution is produced by the Lorentz forces on moving ions. We calculate typical values of the Lorentz force contribution to the Hall viscosity using a simple square lattice toy model, and we compare it with literature estimates of the strengths of other Hall-viscosity mechanisms.
Macroscopic kinematics of the Hall electric field under influence of carrier magnetic moments
The relativistic effect on electromagnetic forces yields two types of forces which depend on the velocity of the relevant particles: (i) the usual Lorentz force exerted on a moving charged particle and (ii) the apparent Lorentz force exerted on a moving magnetic moment. In sharp contrast with type (i), the type (ii) force originates due to the transverse field induced by the Hall effect (HE). This study incorporates both forces into a Drude-type equation with a fully spin-polarized condition to investigate the effects of self-consistency of the source and the resultant fields on the HE. We also examine the self-consistency of the carrier kinematics and electromagnetic dynamics by simultaneously considering the Drude type equation and Maxwell equations at low frequencies. Thus, our approach can predict both the dc and ac characteristics of the HE, demonstrating that the dc current condition solely yields the ordinary HE, while the ac current condition yields generation of both fundamental and second harmonic modes of the HE field. When the magnetostatic field is absent, the simultaneous presence of dc and ac longitudinal currents generates the ac HE that has both fundamental frequency and second harmonic.