A Review of Lunar and Planetary Magnetic Field Measurements Using Space Probes
Planetary magnetic field boundaries and field interactions with solar wind determined from data obtained by space probes near Moon, Venus and Mars
MAGNETIC DIPOLE↗
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Dynamics of Single Chains of Suspended Ferrofluid Particles
We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.
Cutillas, S.↗
FEA Model and Mechanical Analysis of the Nb 3 Sn 15-T Dipole Demonstrator
Nb$_{3}$Sn magnets with a nominal operation field of ~15 T are being considered for the large hadron collider (LHC) energy upgrade high-energy large hadron collider (HE-LHC) and a post-LHC future circular collider. To demonstrate the feasibility of 15-T accelerator quality dipole magnets, the U.S. magnet development program is developing a single-aperture 15-T Nb$_{3}$Sn dipole demonstrator based on a 4-layer graded cos-theta coil with 60 mm aperture and cold iron yoke. The main design challenges for 15-T accelerator magnets include large Lorentz forces at this field level. To counteract them, an innovative mechanical structure based on a vertically split iron yoke, locked by large aluminum IC-clamps and supported by a thick stainless steel skin, has been developed at Fermilab. To study the performance of the structure, a parametric multiphysics finite element analysis (FEA) model has been set up. This paper describes the numerical model as well as the results of a sensitivity analysis of the effect of geometrical tolerances and assembly parameters.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Exploring the Focusing Mechanism of the NuMI Horn Magnets
Neutrinos at the Main Injector (NuMI) is a project at Fermilab that provides an intense beam of neutrinos used by a number of experiments. NuMI creates a beam of pions that decay into neutrinos, muons, and other particles. Muons are registered by the muon monitors. Magnetic horns are the key elements of the NuMI beam line. This paper uses the muon beam profile observed at the muon monitors to study the NuMI horn focusing mechanism. It is found that the horn magnet generates dipole and quadrupole fields to focus pions. This suggests that the optics of the horn magnet are predominantly linear. Our study shows that the muon beam profile accurately detects the horn current within 0.05%.
43 PARTICLE ACCELERATORS↗
Crystalline membrane morphology beyond polyhedra
Elastic crystalline membranes exhibit a buckling transition from sphere to polyhedron. However, their morphologies are restricted to convex polyhedra and are difficult to externally control. Here we study morphological changes of closed crystalline membranes of superparamagnetic particles. The competition of magnetic dipole-dipole interactions with the elasticity of this magnetoelastic membrane leads to concave morphologies. Interestingly, as the magnetic field strength increases, the symmetry of the buckled membrane decreases from 5-fold to 3-fold, to 2-fold and, finally, to 1-fold rotational symmetry. This gives the ability to switch the membrane morphology between convex and concave shapes with specific symmetry and provides promising applications for membrane shape control in the design of actuatable microcontainers for targeted delivery systems.
36 MATERIALS SCIENCE↗
Geomagnetic eccentric dipole <gemagnitnyy ekstsentrichnyy dipol'<
Geomagnetic eccentric dipole
GEOMAGNETISM↗
Magnetic Shield Design Modeling and Validation for SWOT Spacecraft Ka-Band Extended Interaction Klystron
Two Extended Interaction Klystrons (EIKs) containing strong permanent magnets were modeled magnetically in a representative spacecraft geometry using commercial finite element modeling techniques and were validated against measurements made at varying distances. Initial modeling results for the 63 A-m2 dipole moment magnets showed that magnetic shields would be necessary in order to meet magnetic field requirements for the Surface Water and Ocean Topography (SWOT) spacecraft, which contains components that are susceptible to external DC magnetic fields. JPL and the EIK vendor proposed cold rolled steel and mu-metal as potential shield materials along with proposed thicknesses of 0.5 mm and 1.5 mm. Magnetic shields made from each of these materials were designed and modeled in software, taking highfield saturation into account. Prototype magnetic shields with these parameters were then built, measured with an existing EIK, and compared against modeling results. For single-axis field measurements along the dipole axis, modeling results were within 7 gauss of the measured values at 10 cm from the magnet, and converged to less than 1.5 gauss at distances greater than 14 cm from the magnet. Three-axis field measurements at locations of interest showed that model correlation improved to within 4 gauss at 11 cm and 2 gauss for distances ranging between 15 cm and 36 cm.
Gonzales, Edward↗
Critical Stoermer conditions in quadrupole and double ring-current fields.
Critical Stormer pass points for quadrupole field and double-ring-current field with parallel or antiparallel dipole moments
GEOMAGNETICALLY TRAPPED PARTICLE↗
Magnetic Shield Design Modeling and Validation for SWOT Spacecraft Ka-Band Extended Interaction Klystron
Two Extended Interaction Klystrons (EIKs) containing strong permanent magnets were modeled magnetically in a representative spacecraft geometry using commercial finite element modeling techniques and were validated against measurements made at varying distances. Initial modeling results for the 63 A-m2 (amperes per square meter) dipole moment magnets showed that magnetic shields would be necessary in order to meet magnetic field requirements for the Surface Water and Ocean Topography (SWOT) spacecraft, which contains components that are susceptible to external DC (Direct Current) magnetic fields. JPL (Jet Propulsion Laboratory) and the EIK vendor proposed cold rolled steel and mu-metal as potential shield materials along with proposed thicknesses of 0.5 millimeters and 1.5 millimeters. Magnetic shields made from each of these materials were designed and modeled in software, taking high-field saturation into account. Prototype magnetic shields with these parameters were then built, measured with an existing EIK, and compared against modeling results. For single-axis field measurements along the dipole axis, modeling results were within 7 gauss of the measured values at 10 centimeters from the magnet, and converged to less than 1.5 gauss at distances greater than 14 centimeters from the magnet. Three-axis field measurements at locations of interest showed that model correlation improved to within 4 gauss at 11 centimeters and 2 gauss for distances ranging between 15 centimeters and 36 centimeters.
Gonzales, Edward↗
The Effects of Localized Thermal Pressure on Equilibrium Magnetic Fields and Particle Drifts in The Inner Magnetosphere
Localized injections of hot anisotropic plasma sheet particles into the inner magnetosphere can significantly deform the quiet time dipole–like magnetic field and thus disturb electron and ion's drift paths and scattering rates. Although many details of magnetic field deformation can be inferred from empirical models, roles of different characteristics of injected plasma on the structure of such deformation require further investigation. In this study, we use the 2–D axisymmetric equilibrium model to calculate self–consistent magnetic field in force balance with a Gaussian thermal pressure distribution characterized by four input parameters: the ratio between plasma pressure and magnetic pressure ( β ) at the pressure peak β 0 , the radial location of the pressure peak L 0 , the width of the half peak pressure σ 0 , and the equatorial pressure anisotropy A e . Using the modeled magnetic field, we find that the magnetic field perturbation increases with increasing β 0 and decreasing σ 0 while the magnetic curvature perturbation increases with increasing A e , β 0 , and σ 0 and decreasing L 0 . For energetic particles the change of magnetic gradient drift motion is much greater than that of curvature drift motion. The magnetic dip structure formation requires a critical β value that increases with increasing σ 0 and decreasing L 0 . Despite the unavailability of observations in the existing literatures to check the condition of magnetic dip formation, such condition will be checked against observations as a future study. Lastly, we also use 3–D ring current–atmosphere interactions model with self–consistent magnetic field model to illustrate the effect of azimuthal pressure distribution, which is relevant to asymmetric ring current.
79 ASTRONOMY AND ASTROPHYSICS↗
Emergent chirality in the electric polarization texture of titanate superlattices
Significance Many natural structures exhibit chirality that is essential to their functional interactions, yet the chiral electronic structures found in condensed matter systems have been primarily limited to magnetic materials. Notably, the electric dipole equivalent of magnetic skyrmions has remained conspicuously elusive. However, recent theoretical predictions and experimental observations of the continuous rotation of electric polarization in titanate superlattices suggests that such complex oxide nanocomposites are ideal candidates for realizing chiral electric dipole configurations. Here we present the results from superlattices of PbTiO 3 and SrTiO 3 using a combination of resonant soft X-ray diffraction and second-principles simulations. We observe chiral arrays of polar line defects, spontaneously formed by the complex interactions in these artificial superlattices constructed from two nonchiral lattices.
36 MATERIALS SCIENCE↗
Quench-Back Management for Fast Decaying Currents in SHMS Superconducting Magnets at Jefferson Lab
The Super High Momentum Spectrometer (SHMS) of Hall C, part of the 12-GeV upgrade at Jefferson Lab, was successfully commissioned in 2017. Early operation demonstrated that fast current dumps decays of the SHMS Q2/Q3 and dipole superconducting magnets triggered quenches, causing some level of operational difficulty. Tests and detailed assessments suggest that nonquench induced fast current decay could result in substantial ac loss in the conductor and subsequently trigger a quench-back effect. The OPERA/ELECTRA software package was used to calculate the amount of heat deposited in the copper stabilizer from a fast current decay. The resistances of external energy dump resistors were lowered to slow the fast dumping of the magnet's current to reduce or eliminate the quench-back effect. A worst-case adiabatic quench scenario was analyzed, assuming no external dump resistor and no liquid helium surrounding the coil, to ensure the safety of the magnets. The stress levels in the coil imposed by winding, collaring preload, Lorentz force, and temperature gradient during a quench were also examined. The Tsai-Wu material failure criterion was used to determine the acceptable combined stress level. Linear orthotropic analysis of the coil indicates that the magnets can be operated safely with appropriately sized dump resistors. Fast dump tests with the modified dump resistors have been planned to verify the performance and suitability.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A method for the measurement of extremely feeble torques on massive bodies.
Single-axis meter design and development for measuring feeble torques on massive bodies, discussing calibration, testing results, evaluation of static dipole moments and spacecraft spin-rate control moments
SPACECRAFT PERFORMANCE↗
Development of Design for the STS Extraction Magnet System
The Oak Ridge National Laboratory STS Project will enhance the Spallation Neutron Source by adding a new neutron source. The upgrade includes a 30% increase in beam energy and a 50% boost in beam current, doubling the accelerator's power capability to 2.8 MW. The Ring-to-Second-Target Beam Transport (RTST) system is vital in directing high-energy proton beams to the new second target station. New magnets have to fit into a restricted space within the existing beamline to add the new extraction line. New, fast kicker magnets (Pulsed Dipole), a focusing quad with an aperture for both beamlines (Large Quad) and the replacement of existing 21Q40 Quads with 'Narrow Quads' having identical fields as the existing design are Fermilab's responsibility. The design of these magnets poses unique challenges, as in addition to the high requirements on the quality of magnetic fields, they are subject to major restrictions related to their dimensions.
Chernenok, V. [Fermilab] (ORCID:0009000778148215)↗
Global MHD Simulation of Mesoscale Structures at the Magnetospheric Boundary
We have continued our modeling of the solar wind/magnetosphere interaction for steady solar Wind conditions by carrying out a series of 3 D global magneto-hydrodynamics (MHD) simulations using a set of predetermined solar wind parameters as input to the code. With the results from the simulations that we ran last year for two other dipole tilts (0 and 35 deg), we have 36 data sets to study the dynamics of mesoscale structures at the magnetospheric boundary. We have started the analysis of these runs to investigate geometrical properties and the topology of the magnetic and electric fields for the different solar wind regimes and orientations considered. Preliminary results indicate that merging sites are consistent with patterns proposed for antiparallel merging at the dayside magnetopause. Another goal of this investigation is to establish the displacement of the cusp region as a function of the solar wind dynamic pressure, IMF direction and magnetic field dipole tilt. One of the difficulties of that study is to locate precisely the cusp in the simulation results. We have used several case studies to establish a series of criteria in to permit a routine identification of that location. We need now to process the rest of the simulation results using these criteria to obtain statistical results.
Berchem, Jean↗
Saturn's magnetic field and magnetosphere
Results of Pioneer Saturn vector helium magnetometer measurements of the magnetic field and magnetosphere of Saturn are reported. The detection of a bow shock at 23.7 Saturn radii and the magnetosphere crossing at 17.4 Saturn radii suggest an equatorial surface field of 0.3 gauss, which is similar to that of the earth, and the polarity of the field is observed to be similar to that of Jupiter and opposite to the earth's. An increase of magnetic field strength with decreasing radius indicates the dipole nature of the magnetic field, which modified by the compression of the magnetosphere by the solar wind and the presence of a ring current in the middle magnetosphere. Inversions of the field measurements to obtain equivalent dipole source vectors reveal that the tilt angle between the magnetic dipole and the rotation axis is less than 1 deg, and spherical harmonic analysis of the data indicates that the magnetic field is more uniform than those of the earth and Jupiter, consistent with a small Saturn core. An apparent hydromagnetic wake associated with Titan was also observed.
Smith, E. J.↗
Quantum phases for point-like charged particles and for electrically neutral dipoles in an electromagnetic field
We point out that the known quantum phases for an electric/magnetic dipole moving in an electromagnetic (EM) field must be presented as the superposition of more fundamental quantum phases emerging for elementary charges. Using this idea, we find two new fundamental quantum phases for point-like charges, next to the known electric and magnetic Aharonov–Bohm (A–B) phases, named by us as the complementary electric and magnetic phases, correspondingly. We further demonstrate that these new phases can indeed be derived via the Schrödinger equation for a particle in an EM field, where however the operator of momentum is re-defined via the replacement of the canonical momentum of particle by the sum of its mechanical momentum and interactional field momentum for a system “charged particle and a macroscopic source of EM field”. The implications of the obtained results are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Probing the Consequences of Cubic Particle Shape and Applied Field on Colloidal Crystal Engineering with DNA
In a magnetic field, cubic Fe 3 O 4 nanoparticles exhibit assembly behavior that is a consequence of a competition between magnetic dipole-dipole and ligand interactions. In most cases, the interactions between short hydrophobic ligands dominate and dictate assembly outcome. To better tune the face-to-face interactions, cubic Fe3O4 nanoparticles were functionalized with DNA. Their assembly behaviors were investigated both with and without an applied magnetic field. Upon application of a field, the tilted orientation of cubes, enabled by the flexible DNA ligand shell, led to an unexpected crystallographic alignment of the entire superlattice, as opposed to just the individual particles, along the field direction as revealed by small and wide-angle X-ray scattering. This observation is dependent upon DNA length and sequence and cube dimensions. Taken together, these studies show how combining physical and chemical control can expand the possibilities of crystal engineering with DNA.
36 MATERIALS SCIENCE↗