Magnetic Coordinates Research Articles

Transfer of the magnetic axis of an undulator to mechanical fiducial marks of a laser tracker system

The exact geometric location of the magnetic centers of sensors or sensor systems using Hall probes or pick-up coils is usually not known with high precision. In order to transfer the high spatial accuracy of magnetic measurements to external mechanic fiducials a device called “Magnetic Landmark” was developed and is described in this report. Its purpose is to establish the exact relation between “magnetic” coordinates used on magnetic measurement systems and “mechanic” coordinates used for alignment.The landmark consists of a permanent magnet configuration, which generates a field distribution with well-defined zero crossings in two orthogonal directions, which can be exactly localized with micrometer precision using magnetic measurement systems. For the “mechanic” measurements several redundant monuments for laser fiducials can be used.Using flip tests for the magnetic as well as mechanic measurements the center positions are determined in magnetic and mechanic coordinates. Using them the relation between the magnetic and surveying coordinates can be established with high accuracy.This report concentrates on the description of the landmark. A thorough analysis on achievable accuracy is presented. The method was developed for the alignment of the 91 undulator segments needed for the European XFEL but can be applied to other magnet systems as well.

Animal Navigation: Birds Have Magnetic Maps

New 'virtual displacement' experiments demonstrate that migrating reed warblers know the magnetic coordinates of their destination, and can set a novel course to their goal with only magnetic-field parameters as a guide.

Method to integrate full particle orbit in toroidal plasmas

It is important to integrate full particle orbit accurately when studying charged particle dynamics in electromagnetic waves with frequency higher than cyclotron frequency. We have derived a form of the Boris scheme using magnetic coordinates, which can be used effectively to integrate the cyclotron orbit in toroidal geometry over a long period of time. The new method has been verified by a full particle orbit simulation in toroidal geometry without high frequency waves. The full particle orbit calculation recovers guiding center banana orbit. This method has better numeric properties than the conventional Runge-Kutta method for conserving particle energy and magnetic moment. The toroidal precession frequency is found to match that from guiding center simulation. Many other important phenomena in the presence of an electric field, such as E×B drift, Ware pinch effect and neoclassical polarization drift are also verified by the full orbit simulation.

A model of high‐latitude thermospheric density

AbstractWe present an empirical model of the high‐latitude air density at 450 km, derived from accelerometer measurements by the CHAllenging Minisatellite Payload and Gravity Recovery and Climate Experiment satellites during 2002–2006, which we call HANDY (High‐Latitude Atmospheric Neutral DensitY). HANDY consists of a quiet model and disturbance model. The quiet model represents the background thermospheric density for “zero geomagnetic activity” conditions. The disturbance model represents the response of the thermospheric density to solar wind forcing at high latitudes. The solar wind inputs used are the following: (1) solar wind electric field ESW, (2) interplanetary magnetic field (IMF) clock angle CSW, and (3) solar wind dynamic pressure PSW. Both quiet and disturbance models are constructed on the basis of spherical harmonic function fitting to the data. Magnetic coordinates are used for the disturbance model, while geographical coordinates are used for the quiet model. HANDY reproduces main features of the solar wind influence on the high‐latitude thermospheric density, such as the IMF By effect that produces a hemispheric asymmetry in the density distribution.

Using Polar‐orbiting Environmental Satellite data to specify the radiation environment up to 1200 km altitude

AbstractData from the Deal dosimeter payload on the Rapid Pathfinder satellite provide daily maps of the radiation environment on a sphere at 1200 km altitude. Through the use of magnetic coordinates, these dosimeter maps can be projected down to lower altitudes, providing valuable information for satellite anomaly resolution for vehicles in low Earth orbit (LEO). Unfortunately, the Deal data are not widely available, and the mission has a limited lifetime. As an alternative, we present a method to estimate the Deal daily maps using belt index data from NOAA's Polar‐orbiting Environmental Satellite (POES) vehicles. The method addresses only trapped radiation but could readily be supplemented with POES's own measurements of solar particle radiation reaching LEO.

Distinguishing diapirs from inflated plutons: an integrated rock magnetic fabric and structural study on the Roundstone Pluton, western Ireland

Granitoid plutons account for much of the continental crust and are critical in the generation of several economic resources. Despite over a century of research, the fundamental process by which large felsic bodies intrude remains controversial. Two contrasting models persist: (1) mass ascent and subsequent cooling of magma (diapirism); (2) sheet ascent and subsequent emplacement (laccoliths). The latter hypothesis is different from the former as distinct ascent and emplacement processes must occur and be identifiable; traditional field methods rarely allow this important distinction to be made. We present field, petrographic and anisotropy of magnetic susceptibility data from the Roundstone Pluton, Connemara, western Ireland, which was previously considered a diapiric intrusion. The new data reveal anomalous subvertical magmatic lineations in the core of this circular intrusion as well as a suite of magmatic and submagmatic fabrics that parallel NNW–SSE country rock faults and coeval G2 sheets within the pluton. We deduce that these structures reflect a distinct centralized ascent process along a NNW–SSE conduit. Lateral emplacement and pluton inflation followed, ultimately forming a punched laccolith. We conclude that the combined application of the above techniques provides a unique insight into pluton architecture that removes ambiguity between contrasting diapiric and inflated pluton models. Supplementary material: Complete rock magnetic data tables and sample site coordinates (Irish Grid) are available at http://www.geolsoc.org.uk/SUP18837 .

Tokamak magneto-hydrodynamics and reference magnetic coordinates for simulations of plasma disruptions

This paper formulates the Tokamak Magneto-Hydrodynamics (TMHD), initially outlined by X. Li and L. E. Zakharov [Plasma Science and Technology 17(2), 97–104 (2015)] for proper simulations of macroscopic plasma dynamics. The simplest set of magneto-hydrodynamics equations, sufficient for disruption modeling and extendable to more refined physics, is explained in detail. First, the TMHD introduces to 3-D simulations the Reference Magnetic Coordinates (RMC), which are aligned with the magnetic field in the best possible way. The numerical implementation of RMC is adaptive grids. Being consistent with the high anisotropy of the tokamak plasma, RMC allow simulations at realistic, very high plasma electric conductivity. Second, the TMHD splits the equation of motion into an equilibrium equation and the plasma advancing equation. This resolves the 4 decade old problem of Courant limitations of the time step in existing, plasma inertia driven numerical codes. The splitting allows disruption simulations on a relatively slow time scale in comparison with the fast time of ideal MHD instabilities. A new, efficient numerical scheme is proposed for TMHD.

Optical clock transition in a rare-earth-ion-doped crystal: coherence lifetime extension for quantum storage applications

Atomic clock transitions are desirable for quantum information storage and processing thanks to the protection from decoherence they provide. In the context of rare- earth-ion-doped crystals for quantum information storage, clock Zeeman or hyperfine transitions have been identified and exploited for long-lived storage in spin degrees of freedom. We present a theoretical and experimental analysis on the existence of an optical clock transition in Tm3+:YAG, in view of storage in optical coherences. The combination of a Zeeman-like term and a quadratic electronic Zeeman term in the Hamiltonian, lead to the existence of a magnetic field amplitude (12 mT) for which the derivative of the optical transition energy with respect to the field amplitude vanishes, regardless of the magnetic field orientation. We have verified this prediction through hole-burning spectroscopy experiments. In addition to that, a study of the behavior of the Hamiltonian as a function of the magnetic field orientation yields the direction for which both derivatives with respect to the magnetic field angular coordinates also vanish. The condition for an optical clock transition with three vanishing partial derivatives is met.

Gyrokinetic particle simulation of microturbulence for general magnetic geometry and experimental profiles

Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.

Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics (TMHD), which explicitly reflects the anisotropy of a high temperature tokamak plasma. The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in tokamaks. Free from the Courant restriction on the time step, this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model. At the same time, TMHD requires the use of magnetic field aligned numerical grids. Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented. For the 3-dimensional case of an ergodic magnetic field, this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.

Animal Navigation: Memories of Home

Sea turtles memorize the magnetic coordinates of their natal beach, returning to that combination of parameters to lay eggs decades later. The intervening secular (year-to-year) variation in field intensity and inclination can lead the nesting females to a series of predictably different beaches.

Assessing predictive ability of three auroral precipitation models using DMSP energy flux

AbstractOur study statistically compares the total energy flux outputs of Newell et al.'s () oval variation, assessment, tracking, intensity, and online nowcasting (OVATION) Prime model, Hardy et al.'s () Kp‐based model, and a coupled Space Weather Modeling Framework ring current model to energy flux data obtained from 2198 Defense Meteorological Satellite Program (DMSP) satellite passes in the Northern Hemisphere. Our DMSP data set includes 28 days grouped into continuous 3 and 4 day periods between 2000 and 2008 and encompasses magnetic local times (MLTs) between 04:00 and 21:00. We obtain the most equatorward magnetic latitude coordinate, where a DMSP satellite energy flux measurement exceeds 0.4 erg/cm2/s, and use this point as a proxy for the equatorward boundary of the auroral oval in a particular MLT sector. We then calculate a prediction efficiency (PE) score by comparing the DMSP boundary coordinates to each model, using the same energy flux threshold to obtain a model's boundary location. We find that the PE for the OVATION Prime model is 0.55, and the PE for the Hardy Kp model is 0.51. When we accomplish the same analysis using a higher energy flux threshold equal to 0.6 erg/cm2/s, the OVATION Prime model's PE increases to 0.58, while the Hardy Kp model's score drops to 0.41. Our results indicate that more complex modeling techniques, like those used in OVATION Prime, can more accurately model the auroral oval's equatorward boundary. However, Hardy's discretized Kp model, despite its relative simplicity, is still a competitive and viable modeling option.

Juvenile Osprey Navigation during Trans-Oceanic Migration.

To compensate for drift, an animal migrating through air or sea must be able to navigate. Although some species of bird, fish, insect, mammal, and reptile are capable of drift compensation, our understanding of the spatial reference frame, and associated coordinate space, in which these navigational behaviors occur remains limited. Using high resolution satellite-monitored GPS track data, we show that juvenile ospreys (Pandion haliaetus) are capable of non-stop constant course movements over open ocean spanning distances in excess of 1500 km despite the perturbing effects of winds and the lack of obvious landmarks. These results are best explained by extreme navigational precision in an exogenous spatio-temporal reference frame, such as positional orientation relative to Earth's magnetic field and pacing relative to an exogenous mechanism of keeping time. Given the age (<1 year-old) of these birds and knowledge of their hatching site locations, we were able to transform Enhanced Magnetic Model coordinate locations such that the origin of the magnetic coordinate space corresponded with each bird's nest. Our analyses show that trans-oceanic juvenile osprey movements are consistent with bicoordinate positional orientation in transformed magnetic coordinate or geographic space. Through integration of movement and meteorological data, we propose a new theoretical framework, chord and clock navigation, capable of explaining the precise spatial orientation and temporal pacing performed by juvenile ospreys during their long-distance migrations over open ocean.

The flux-coordinate independent approach applied to X-point geometries

A Flux-Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates, has been introduced in Hariri and Ottaviani [Comput. Phys. Commun. 184, 2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach can efficiently deal with X-point geometries.

Collisionless high energy particle losses in optimized stellarators calculated in real-space coordinates

An approach for the direct computation of collisionless losses of high energy charged particles is developed for stellarator magnetic fields given in real space coordinates. With this approach, the corresponding computations can be performed for magnetic fields with three-dimensional inhomogeneities in the presence of stochastic regions as well as magnetic islands. A code, which is based on this approach, is applied to various stellarator configurations. It is found that the life time of fast particles obtained in real-space coordinates can be smaller than that obtained in magnetic coordinates.

Finite-difference schemes for anisotropic diffusion

In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 1012 times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.

Relationship between foF2 trends and geographic and geomagnetic coordinates

The possibility of presenting parameters k(foF2) and ΔfoF2 characterizing the change over time in the critical frequency of the ionospheric F2 layer in recent decades was considered. These parameters were previously obtained by the authors as functions of geographic coordinates, latitude and longitude. It was shown that there is such a possibility and the corresponding statistical significances of the obtained dependencies lie within the limits from ∼90% to more than 99%. Simultaneously, the dependence of the linear trend k on magnetic coordinates D and I was studied. This dependence should manifest the relation of the trends in foF2 to dynamical processes (horizontal winds) via the vertical drift induced by them and the corresponding change in the F2-layer height.

First results of operational ionospheric dynamics prediction for the Brazilian Space Weather program

It is shown the development and preliminary results of operational ionosphere dynamics prediction system for the Brazilian Space Weather program. The system is based on the Sheffield University Plasmasphere–Ionosphere Model (SUPIM), a physics-based model computer code describing the distribution of ionization within the Earth mid to equatorial latitude ionosphere and plasmasphere, during geomagnetically quiet periods. The model outputs are given in a 2-dimensional plane aligned with Earth magnetic field lines, with fixed magnetic longitude coordinate. The code was adapted to provide the output in geographical coordinates. It was made referring to the Earth’s magnetic field as an eccentric dipole, using the approximation based on International Geomagnetic Reference Field (IGRF-11). During the system operation, several simulation runs are performed at different longitudes. The original code would not be able to run all simulations serially in reasonable time. So, a parallel version for the code was developed for enhancing the performance. After preliminary tests, it was frequently observed code instability, when negative ion temperatures or concentrations prevented the code from continuing its processing. After a detailed analysis, it was verified that most of these problems occurred due to concentration estimation of simulation points located at high altitudes, typically over 4000km of altitude. In order to force convergence, an artificial exponential decay for ion–neutral collisional frequency was used above mentioned altitudes. This approach shown no significant difference from original code output, but improved substantially the code stability. In order to make operational system even more stable, the initial altitude and initial ion concentration values used on exponential decay equation are changed when convergence is not achieved, within pre-defined values. When all code runs end, the longitude of every point is then compared with its original reference station longitude, and differences are compensated by changing the simulation point time slot, in a temporal adjustment optimization. Then, an approximate neighbor searching technique was developed to obtain the ion concentration values in a regularly spaced grid, using inverse distance weighting (IDW) interpolation. A 3D grid containing ion and electron concentrations is generated for every hour of simulated day. Its spatial resolution is 1° of latitude per 1° of longitude per 10km of altitude. The vertical total electron content (VTEC) is calculated from the grid, and plotted in a geographic map. An important feature that was implemented in the system is the capacity of combining observational data and simulation outputs to obtain more appropriate initial conditions to the ionosphere prediction. Newtonian relaxation method was used for this data assimilation process, where ionosonde data from four different locations in South America was used to improve the system accuracy. The whole process runs every day and predicts the VTEC values for South America region with almost 24h ahead.

Thrust and efficiency model for electron-driven magnetic nozzles

A performance model is presented for magnetic nozzle plasmas driven by electron thermal expansion to investigate how the thrust coefficient and beam divergence efficiency scale with the incoming plasma flow and magnetic field geometry. Using a transformation from cylindrical to magnetic coordinates, an approximate analytical solution is derived to the axisymmetric two-fluid equations for a collisionless plasma flow along an applied magnetic field. This solution yields an expression for the half-width at half-maximum of the plasma density profile in the far-downstream region, from which simple scaling relations for the thrust coefficient and beam divergence efficiency are derived. It is found that the beam divergence efficiency is most sensitive to the density profile of the flow into the nozzle throat, with the highest efficiencies occurring for plasmas concentrated along the nozzle axis. Increasing the expansion ratio of the magnetic field leads to efficiency improvements that are more pronounced for incoming plasmas that are not concentrated along the axis. This implies that the additional magnet required to increase the expansion ratio may be worth the added complexity for plasma sources that exhibit poor confinement.

A multichannel magnetic probe system for analysing magnetic fluctuations in helical axis plasmas

The need to understand the structure of magnetic fluctuations in H-1NF heliac [S. Hamberger et al., Fusion Technol. 17, 123 (1990)] plasmas has motivated the installation of a sixteen former, tri-axis helical magnetic probe Mirnov array (HMA). The new array complements two existing poloidal Mirnov arrays by providing polarisation information, higher frequency response, and improved toroidal resolution. The helical placement is ideal for helical axis plasmas because it positions the array as close as possible to the plasma in regions of varying degrees of favourable curvature in the magnetohydrodynamic sense, but almost constant magnetic angle. This makes phase variation with probe position near linear, greatly simplifying the analysis of the data. Several of the issues involved in the design, installation, data analysis, and calibration of this unique array are presented including probe coil design, frequency response measurements, mode number identification, orientation calculations, and mapping probe coil positions to magnetic coordinates. Details of specially designed digitally programmable pre-amplifiers, which allow gains and filters to be changed as part of the data acquisition initialisation sequence and stored with the probe signals, are also presented. The low shear heliac geometry [R. Jiménez-Gómez et al., Nucl. Fusion 51, 033001 (2011)], flexibility of the H-1NF heliac, and wealth of information provided by the HMA create a unique opportunity for detailed study of Alfvén eigenmodes, which could be a serious issue for future fusion reactors.