Magnetic Field Fluctuations Research Articles

Development of the ion cyclotron emission diagnostic on the HL-2A tokamak

An ion cyclotron emission (ICE) diagnostic, which is based on a B-dot probe, has been recently designed and installed on HL-2A tokamak. The diagnostic is used to study various high-frequency magnetic field fluctuations which can be excited by energetic ions and runaway electrons in the plasma. The ICE diagnostic on HL-2A includes a high-frequency B-dot probe, direct current (DC) block, radio frequency splitters, filter bank and power detectors. The filter bank is composed of 16 channels filters, with the center frequency covering from 10 to 160 MHz, 10 MHz step length and 8 MHz bandwidth. The log detectors with a large dynamic range (from −80 dBm to −20 dBm) are used to detect the bandpass power. Test results of the B-dot probe, filters and power detectors are shown. The signals can also be sampled with a fast analog-to-digital converter with a 14-bit depth, 100 MHz bandwidth and 250 MSample/s sampling rate.

Studying Four Different Permanent Magnet Eddy Currents Heaters with Different Magnet Areas and Numbers to Produce Heat Directly from a Vertical Axis Wind Turbine

Changing the magnetic field on a conductor metal can induce eddy currents, which cause heat generation. In this paper, we use this idea to convert wind energy into thermal energy directly. This system contains a vertical axis wind turbine and an eddy currents heat generator. The eddy currents heat generator has two parts. The first part is a rotor with some permanent magnets causing the magnetic field changes, and the second part is a stator that acts as a conductor. The magnetic field changes in the heat generator play an important role in power output; therefore, we test four different magnet arrangements with different pole numbers on the rotor at different rotational speeds from 100 rpm to 500 rpm to measure the input torque and power needed to rotate each model. Then, based on the measured data, the wind turbine is designed by Qblade software based on the blade element momentum theory. It is shown that compared to the weight of the heat generator and the area of magnetization, designing a proper magnet arrangement for the heat generator can change the output power considerably as it can trigger the magnetic field fluctuation along the direction of rotation. For example, opting for a proper arrangement on the rotor decreases the number of poles from 120 to 24 but increases the power input from 223 W to 1357 W.

Correlations between basal metabolic rate in humans with different age, gender, BMI and local earth magnetic field activity

Daily energy expenditure includes resting metabolism (RMR), endogenous thermogenesis (or thermal effects of food), and energy expenditure associated with exercise. RMR depends on body weight, age, gender, genetic factors, medications used and health status. Every living organism is affected by external factors. Fluctuations in magnetic fields can affect almost every biological system more or less, depending on the characteristics of the particular biological system and magnetic fluctuations. Environmental energy phenomena affect psychophysical processes that can affect people in a variety of ways, depending on their sensitivity, health status, and ability to self-regulate. The aim of this study: to investigate the correlations between basal metabolic rate in humans with different age, gender, BMI and local Earth magnetic field activity. Information on gas metabolism during respiration was obtained by indirect calorimetry where the gas flow was continuously analysed. O2 consumption and CO2 emissions were continuously analysed. The best quality 5 min section was selected from the 15 min recording (automatically selected by the computer). The results were analysed and mean resting metabolic rate (M_RMR) was calculated. Investigations of metabolic rate were performed in Lithuanian, Druskininkai, Medical SPA Center ,,UPA”. Power of spectral density of Local Geo Magnetic field (LGMF) was calculated in 0.32 to 36 Hz frequency range from the Lithuanian (GCI003) magnetometer for East – West direction (E-W). 395 persons were investigated: 116 men and 279 women. All participants were divided into two groups according gender. Women and men groups were divided again into two groups according mean age, the mean was 46 years. Was analysed correlations in women younger (≤ 46 years) and older (> 46 years) groups and the same for men younger (≤ 46 years) and older (> 46 years) groups. On the next step all women and all men, then younger women group, older women group, younger men group and older men group was divided according BMI mean (29), with less than ≤ 29 BMI and with more than > 29 BMI. On the basis of obtained results, we can conclude, that correlations between LGMF and basal metabolic rate features are negative. More expressed negative correlations are seen in persons with smaller BMI. With age negative correlations with LGMF decrease in men group and increase in women group. Sensitivity of persons of different gender to LGMF – differ.

Accommodation of Pulsed Field Gradients with Cascade Field Regulation in Powered Magnets.

High magnetic fields significantly improve the resolution and sensitivity of nuclear magnetic resonance (NMR) spectroscopy measurements, which presents exciting research opportunities in areas of chemistry, biology, and material science. Powered magnets can provide much higher magnetic fields than persistent mode superconducting magnets but suffer from temporal magnetic field fluctuations due to power supply ripple and variations in cooling water temperature and flow rate which make powered magnets non-viable for high resolution NMR experiments. Previous work has demonstrated that a multi-rate sampled data cascade control system may be used to improve the resolution of NMR experiments in powered magnets. Despite these advances in reducing temporal magnetic field fluctuations, the field regulation design does not accommodate the use of pulsed field gradients, which are necessary in many NMR experiments. This work presents a control topology which accommodates the use of pulsed field gradient signals with the field regulation system. This control approach is verified using NMR measurements.

The Application of Low-Frequency Transition in the Assessment of the Second-Order Zeeman Frequency Shift.

Second-order Zeeman frequency shift is one of the major systematic factors affecting the frequency uncertainty performance of cesium atomic fountain clock. Second-order Zeeman frequency shift is calculated by experimentally measuring the central frequency of the (1,1) or (−1,−1) magnetically sensitive Ramsey transition. The low-frequency transition method can be used to measure the magnetic field strength and to predict the central fringe of (1,1) or (−1,−1) magnetically sensitive Ramsey transition. In this paper, we deduce the formula for magnetic field measurement using the low-frequency transition method and measured the magnetic field distribution of 4 cm inside the Ramsey cavity and 32 cm along the flight region experimentally. The result shows that the magnetic field fluctuation is less than 1 nT. The influence of low-frequency pulse signal duration on the accuracy of magnetic field measurement is studied and the optimal low-frequency pulse signal duration is determined. The central fringe of (−1,−1) magnetically sensitive Ramsey transition can be predicted by using a numerical integrating of the magnetic field “map”. Comparing the predicted central fringe with that identified by Ramsey method, the frequency difference between these two is, at most, a fringe width of 0.3. We apply the experimentally measured central frequency of the (−1,−1) Ramsey transition to the Breit-Rabi formula, and the second-order Zeeman frequency shift is calculated as 131.03 × 10−15, with the uncertainty of 0.10 × 10−15.

Quantum computation protocol for dressed spins in a global field

Spin qubits are contenders for scalable quantum computation because of their long coherence times demonstrated in a variety of materials, but individual control by frequency-selective addressing using pulsed spin resonance creates severe technical challenges for scaling up to many qubits. This individual resonance control strategy requires each spin to have a distinguishable frequency, imposing a maximum number of spins that can be individually driven before qubit crosstalk becomes unavoidable. Here we describe a complete strategy for controlling a large array of spins in quantum dots dressed by an on-resonance global field, namely, a field that is constantly driving the spin qubits, to dynamically decouple from the effects of background magnetic field fluctuations. This approach---previously implemented for the control of single electron spins bound to electrons in impurities---is here harmonized with all other operations necessary for universal quantum computing with spins in quantum dots. We define the logical states as the dressed qubit states and discuss initialization and readout utilizing Pauli spin blockade, as well as single- and two-qubit control in the new basis. Finally, we critically analyze the limitations imposed by qubit variability and potential strategies to improve performance.

Density fluctuations associated with turbulence and waves

Aims.The aim of this work is to demonstrate that the probe-to-spacecraft potential measured by RPW on Solar Orbiter can be used to derive the plasma (electron) density measurement, which exhibits both a high temporal resolution and a high level of accuracy. To investigate the physical nature of the solar wind turbulence and waves, we analyze the density and magnetic field fluctuations around the proton cyclotron frequency observed by Solar Orbiter during the first perihelion encounter (∼0.5 AU away from the Sun).Methods.We used the plasma density based on measurements of the probe-to-spacecraft potential in combination with magnetic field measurements by MAG to study the fields and density fluctuations in the solar wind. In particular, we used the polarization of the wave magnetic field, the phase between the compressible magnetic field and density fluctuations, and the compressibility ratio (the ratio of the normalized density fluctuations to the normalized compressible fluctuations of B) to characterize the observed waves and turbulence.Results.We find that the density fluctuations are 180° out of phase (anticorrelated) with the compressible component of magnetic fluctuations for intervals of turbulence, whereas they are in phase for the circular-polarized waves. We analyze, in detail, two specific events with a simultaneous presence of left- and right-handed waves at different frequencies. We compare the observed wave properties to a prediction of the three-fluid (electrons, protons, and alphas) model. We find a limit on the observed wavenumbers, 10−6 < k < 7 × 10−6m−1, which corresponds to a wavelength of 7 × 106 > λ > 106m. We conclude that it is most likely that both the left- and right-handed waves correspond to the low-wavenumber part (close to the cut-off at ΩcHe + +) of the proton-band electromagnetic ion cyclotron (left-handed wave in the plasma frame confined to the frequency range ΩcHe + + < ω < Ωcp) waves propagating in the outwards and inwards directions, respectively. The fact that both wave polarizations are observed at the same time and the identified wave mode has a low group velocity suggests that the double-banded events occur in the source regions of the waves.

Turbulence and wave transmission at an ICME-driven shock observed by the Solar Orbiter and Wind

Aims.An interplanetary coronal mass ejection (ICME) event was observed by the Solar Orbiter at 0.8 AU on 2020 April 19 and by Wind at 1 AU on 2020 April 20. Futhermore, an interplanetary shock wave was driven in front of the ICME. Here, we focus on the transmission of the magnetic fluctuations across the shock and we analyze the characteristic wave modes of solar wind turbulence in the vicinity of the shock observed by both spacecraft.Methods.The observed ICME event is characterized by a magnetic helicity-based technique. The ICME-driven shock normal was determined by magnetic coplanarity method for the Solar Orbiter and using a mixed plasma and field approach for Wind. The power spectra of magnetic field fluctuations were generated by applying both a fast Fourier transform and Morlet wavelet analysis. To understand the nature of waves observed near the shock, we used the normalized magnetic helicity as a diagnostic parameter. The wavelet-reconstructed magnetic field fluctuation hodograms were used to further study the polarization properties of waves.Results.We find that the ICME-driven shock observed by Solar Orbiter and Wind is a fast, forward oblique shock with a more perpendicular shock angle at the Wind position. After the shock crossing, the magnetic field fluctuation power increases. Most of the magnetic field fluctuation power resides in the transverse fluctuations. In the vicinity of the shock, both spacecraft observe right-hand polarized waves in the spacecraft frame. The upstream wave signatures fall within a relatively broad and low frequency band, which might be attributed to low frequency MHD waves excited by the streaming particles. For the downstream magnetic wave activity, we find oblique kinetic Alfvén waves with frequencies near the proton cyclotron frequency in the spacecraft frame. The frequency of the downstream waves increases by a factor of ∼7–10 due to the shock compression and the Doppler effect.

Evolution of anisotropic turbulence in the fast and slow solar wind: Theory and Solar Orbiter measurements

Aims. Solar Orbiter (SolO) was launched on February 9, 2020, allowing us to study the nature of turbulence in the inner heliopshere. We investigate the evolution of anisotropic turbulence in the fast and slow solar wind in the inner heliosphere using the nearly incompressible magnetohydrodynamic (NI MHD) turbulence model and SolO measurements. Methods. We calculated the two dimensional (2D) and the slab variances of the energy in forward and backward propagating modes, the fluctuating magnetic energy, the fluctuating kinetic energy, the normalized residual energy, and the normalized cross-helicity as a function of the angle between the mean solar wind speed and the mean magnetic field (θUB), and as a function of the heliocentric distance using SolO measurements. We compared the observed results and the theoretical results of the NI MHD turbulence model as a function of the heliocentric distance. Results. The results show that the ratio of 2D energy and slab energy of forward and backward propagating modes, magnetic field fluctuations, and kinetic energy fluctuations increases as the angle between the mean solar wind flow and the mean magnetic field increases from θUB = 0° to approximately θUB = 90° and then decreases as θUB → 180°. We find that solar wind turbulence is a superposition of the dominant 2D component and a minority slab component as a function of the heliocentric distance. We find excellent agreement between the theoretical results and observed results as a function of the heliocentric distance.

Multi-spacecraft observations of the structure of the sheath of an interplanetary coronal mass ejection and related energetic ion enhancement

Context. Sheath regions ahead of coronal mass ejections (CMEs) are large-scale heliospheric structures that form gradually with CME expansion and propagation from the Sun. Turbulent and compressed sheaths could contribute to the acceleration of charged particles in the corona and in interplanetary space, but the relation of their internal structure to the particle energization process is still a relatively little studied subject. In particular, the role of sheaths in accelerating particles when the shock Mach number is low is a significant open research problem. Aims. This work seeks to provide new insights on the internal structure of CME-driven sheaths with regard to energetic particle enhancements. A good opportunity to achieve this aim was provided by multi-point, in-situ observations of a sheath region made by radially aligned spacecraft at 0.8 and ∼1 AU (Solar Orbiter, the L1 spacecraft Wind and ACE, and BepiColombo) on April 19−21, 2020. The sheath was preceded by a weak and slowly propagating fast-mode shock. Methods. We apply a range of analysis techniques to in situ magnetic field, plasma and particle observations. The study focuses on smaller scale sheath structures and magnetic field fluctuations that coincide with energetic ion enhancements. Results. Energetic ion enhancements were identified in the sheath, but at different locations within the sheath structure at Solar Orbiter and L1. Magnetic fluctuation amplitudes at inertial-range scales increased in the sheath relative to the solar wind upstream of the shock, as is typically observed. However, when normalised to the local mean field, fluctuation amplitudes did not increase significantly; magnetic compressibility of fluctuation also did not increase within the sheath. Various substructures were found to be embedded within the sheath at the different spacecraft, including multiple heliospheric current sheet (HCS) crossings and a small-scale flux rope. At L1, the ion flux enhancement was associated with the HCS crossings, while at Solar Orbiter, the ion enhancement occurred within a compressed, small-scale flux rope. Conclusions. Several internal smaller-scale substructures and clear difference in their occurrence and properties between the used spacecraft was identified within the analyzed CME-driven sheath. These substructures are favourable locations for the energization of charged particles in interplanetary space. In particular, substructures that are swept from the upstream solar wind and compressed into the sheath can act as effective acceleration sites. A possible acceleration mechanism is betatron acceleration associated with a small-scale flux rope and warped HCS compressed in the sheath, while the contribution of shock acceleration to the latter cannot be excluded.

The Importance of Electron Landau Damping for the Dissipation of Turbulent Energy in Terrestrial Magnetosheath Plasma

AbstractHeliospheric plasma turbulence plays a key role in transferring the energy of large‐scale magnetic field and plasma flow fluctuations to smaller scales where the energy can be dissipated, ultimately leading to plasma heating. High‐quality measurements of electromagnetic fields and electron velocity distributions by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath present a unique opportunity to characterize plasma turbulence and to determine the mechanisms responsible for its dissipation. We apply the field‐particle correlation technique to a set of 20 MMS magnetosheath intervals to identify the dissipation mechanism and quantify the dissipation rate. It is found that 95% of the intervals have velocity‐space signatures of electron Landau damping that are quantitatively consistent with linear kinetic theory for the collisionless damping of kinetic Alfvén waves. About 75% of the intervals contain asymmetric signatures, indicating a local imbalance of kinetic Alfvén wave energy flux in one direction along the magnetic field than the other. About one‐third of the intervals have an electron energization rate with the same order‐of‐magnitude as the estimated turbulent cascade rate, suggesting that electron Landau damping plays a significant, and sometimes dominant, role in the dissipation of the turbulent energy in these magnetosheath intervals.

Thermally populated versus field-induced triplon bound states in the Shastry-Sutherland lattice SrCu2(BO3)2

The Shastry–Sutherland compound SrCu2(BO3)2 constituting orthogonally coupled dimers harbors an S = 0 singlet ground state. The confluence of strong interdimer interaction and frustration engenders a spectrum of low-energy excitations including localized triplons as well as singlet and triplet bound states. Their dynamics are controlled by an external magnetic field and temperature. Here, we employ high-field Raman spectroscopy to map the field and temperature evolution of such bosonic composite quasiparticles on approaching the 1/8 magnetization plateau. Our study unveils that the magnetic field and thermal fluctuations show remarkably similar effects in melting the singlet bound states, but are disparate in their effects on the fine spectral shapes. This, together with the anti-crossing of two singlet bound states in the intermediate field B = 10 − 16 T, is discussed in terms of the correlated dynamics of frustrated, interacting bosons.

A Solar Source of Alfvénic Magnetic Field Switchbacks: In Situ Remnants of Magnetic Funnels on Supergranulation Scales

Abstract One of the striking observations from the Parker Solar Probe (PSP) spacecraft is the prevalence in the inner heliosphere of large amplitude, Alfvénic magnetic field reversals termed switchbacks. These δ B R / B ∼  ( 1 ) fluctuations occur over a range of timescales and in patches separated by intervals of quiet, radial magnetic field. We use measurements from PSP to demonstrate that patches of switchbacks are localized within the extensions of plasma structures originating at the base of the corona. These structures are characterized by an increase in alpha particle abundance, Mach number, plasma β and pressure, and by depletions in the magnetic field magnitude and electron temperature. These intervals are in pressure balance, implying stationary spatial structure, and the field depressions are consistent with overexpanded flux tubes. The structures are asymmetric in Carrington longitude with a steeper leading edge and a small (∼1°) edge of hotter plasma and enhanced magnetic field fluctuations. Some structures contain suprathermal ions to ∼85 keV that we argue are the energetic tail of the solar wind alpha population. The structures are separated in longitude by angular scales associated with supergranulation. This suggests that these switchbacks originate near the leading edge of the diverging magnetic field funnels associated with the network magnetic field—the primary wind sources. We propose an origin of the magnetic field switchbacks, hot plasma and suprathermals, alpha particles in interchange reconnection events just above the solar transition region and our measurements represent the extended regions of a turbulent outflow exhaust.

Transmission of an ICME Sheath Into the Earth's Magnetosheath and the Occurrence of Traveling Foreshocks

AbstractThe transmission of a sheath region driven by an interplanetary coronal mass ejection into the Earth's magnetosheath is studied by investigating in situ magnetic field measurements upstream and downstream of the bow shock during an ICME sheath passage on 15 May 2005. We observe three distinct intervals in the immediate upstream region that included a southward magnetic field component and are traveling foreshocks. These traveling foreshocks were observed in the quasi‐parallel bow shock that hosted backstreaming ions and magnetic fluctuations at ultralow frequencies. The intervals constituting traveling foreshocks in the upstream survive transmission to the Earth's magnetosheath, where their magnetic field, and particularly the southward component, was significantly amplified. Our results further suggest that the magnetic field fluctuations embedded in an ICME sheath may survive the transmission if their frequency is below ∼0.01 Hz. Although one of the identified intervals was coherent, extending across the ICME sheath and being long‐lived, predicting ICME sheath magnetic fields that may transmit to the Earth's magnetosheath from the upstream at L1 observations has ambiguity. This can result from the strong spatial variability of the ICME sheath fields in the longitudinal direction, or alternatively from the ICME sheath fields developing substantially within the short time it takes the plasma to propagate from L1 to the bow shock. This study demonstrates the complex interplay ICME sheaths have with the Earth's magnetosphere when passing by the planet.

Whistler waves observed by Solar Orbiter/RPW between 0.5 AU and 1 AU

Context. Solar wind evolution differs from a simple radial expansion, while wave-particle interactions are assumed to be the major cause for the observed dynamics of the electron distribution function. In particular, whistler waves are thought to inhibit the electron heat flux and ensure the diffusion of the field-aligned energetic electrons (Strahl electrons) to replenish the halo population. Aims. The goal of our study is to detect and characterize the electromagnetic waves that have the capacity to modify the electron distribution functions, with a special focus on whistler waves. Methods. We carried out a detailed analysis of the electric and magnetic field fluctuations observed by the Solar Orbiter spacecraft during its first orbit around the Sun, between 0.5 and 1 AU. Using data from the Search Coil Magnetometer and electric antenna, both part of the Radio and Plasma Waves (RPW) instrumental suite, we detected the electromagnetic waves with frequencies above 3 Hz and determined the statistical distribution of their amplitudes, frequencies, polarization, and k-vector as a function of distance. Here, we also discuss the relevant instrumental issues regarding the phase between the electric and magnetic measurements as well as the effective length of the electric antenna. Results. An overwhelming majority of the observed waves are right-handed circularly polarized in the solar wind frame and identified as outwardly propagating quasi-parallel whistler waves. Their occurrence rate increases by a least a factor of 2 from 1 AU to 0.5 AU. These results are consistent with the regulation of the heat flux by the whistler heat flux instability. Near 0.5 AU, whistler waves are found to be more field-aligned and to have a smaller normalized frequency (f/fce), larger amplitude, and greater bandwidth than at 1 AU.

Complexity of Magnetic-field Turbulence at Reconnection Exhausts in the Solar Wind at 1 au

Abstract Magnetic reconnection is a complex mechanism that converts magnetic energy into particle kinetic energy and plasma thermal energy in space and astrophysical plasmas. In addition, magnetic reconnection and turbulence appear to be intimately related in plasmas. We analyze the magnetic-field turbulence at the exhaust of four reconnection events detected in the solar wind using the Jensen–Shannon complexity-entropy index. The interplanetary magnetic field is decomposed into the LMN coordinates using the hybrid minimum variance technique. The first event is characterized by an extended exhaust period that allows us to obtain the scaling exponents of higher-order structure functions of magnetic-field fluctuations. By computing the complexity-entropy index we demonstrate that a higher degree of intermittency is related to lower entropy and higher complexity in the inertial subrange. We also compute the complexity-entropy index of three other reconnection exhaust events. For all four events, the B L component of the magnetic field displays a lower degree of entropy and higher degree of complexity than the B M and B N components. Our results show that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in magnetic-field turbulence.

A Novel Method for Estimating the Intrinsic Magnetic Field Spectrum of Kinetic-Range Turbulence

Understanding plasma turbulence below the ion characteristic scales is one of the key open problems of solar wind physics. The bulk of our knowledge about the nature of the kinetic-scale fluctuations comes from the high-cadence measurements of the magnetic field. The spacecraft frame frequencies of the sub-ion scale fluctuations are frequently around the Nyquist frequencies of the magnetic field sampling rate. Thus, the resulting ‘measured’ time series may significantly differ from the ‘true’ ones. It follows that second-order moments (e.g., power spectral density, PSD) of the signal may also be highly affected in both their amplitude and their slope. In this paper, we focus on the estimation of the PSD slope for finitely sampled data and we unambiguously define a so-called local slope in the framework of Continuous Wavelet Transform. Employing Monte Carlo simulations, we derive an empirical formula that assesses the statistical error of the local slope estimation. We illustrate the theoretical results by analyzing measurements of the magnetic field instrument (MFI) on board the Wind spacecraft. Our analysis shows that the trace power spectra of magnetic field measurements of MFI can be modeled as the sum of PSD of an uncorrelated noise and an intrinsic signal. We show that the local slope strongly depends on the signal-to-noise (S/N) ratio, stressing that noise can significantly affect the slope even for S/N around 10. Furthermore, we show that the local slopes below the frequency corresponding to proton inertial length, 5≳kλpi>1, depend on the level of the magnetic field fluctuations in the inertial range (Pin), exhibiting a gradual flattening from about −11/3 for high Pin toward about −8/3 for low Pin.

Space Weather Observations With InSight

AbstractSolar activity, in the form of coronal mass ejections and corotating interaction regions, results in changes in the solar wind that propagate out through the solar system and interact with the magnetic field environments of planets. Such phenomena have been observed to affect the magnetic field and plasma around Mars as seen from orbit. However, no surface observations have previously been possible because of the absence of ground‐based instrumentation. Here, for the first time, we observe the effects of increased solar activity with the magnetometer on the InSight mission in December 2020. We find several days of increased activity including magnetic field fluctuations at periods of minutes to hours. Although only the flanks of this relatively weak coronal mass ejection hit Mars, the observed effects provide insight into how solar activity alters magnetic fields at the surface.

Nuclear relaxation rate enhancement by a 14N quadrupole nucleus in a fluctuating electric-field gradient.

We consider the longitudinal quadrupole relaxation rate enhancement (QRE) of a 1H nucleus due to the time fluctuations of the local dipolar magnetic field created by a close quadrupole 14N nucleus, the electric-field gradient (EFG) Hamiltonian of which changes with time because of vibrations/distortions of its chemical environment. The QRE is analytically expressed as a linear combination of the cosine Fourier transforms of the three quantum time auto-correlation functions GAA(t) of the 14N spin components along the principal axes A = X, Y, and Z of the mean (time-averaged) EFG Hamiltonian. Denoting the three transition frequencies between the energy levels of this mean Hamiltonian by νA, the functions GAA(t) oscillate at frequencies νA + sA/(2π) with mono-exponential decays of relaxation times τA, where the frequency dynamic shifts sA and the relaxation times τA are closed expressions of the magnitude of the fluctuations of the instantaneous EFG Hamiltonian about its mean and of the characteristic fluctuation time. Thus, the theoretical QRE is the sum of three Lorentzian peaks centered at νA + sA/(2π) with full widths at half maxima 1/(πτA). The predicted peak widths are nearly equal. The predicted dynamic shifts of the peaks are much smaller than their widths and amazingly keep proportional to the transition frequencies νA for reasonably fast EFG fluctuations. The theory is further improved by correcting the transition frequencies by the 14N Zeeman effects of second order. It is successfully applied to reinterpret the QRE pattern measured by Broche, Ashcroft, and Lurie [Magn. Reson. Med. 68, 358 (2012)] in normal cartilage.

Oscillation Characteristics of HTS Maglev Under Strong Magnetic Field Fluctuations

Oscillation Characteristics of HTS Maglev Under Strong Magnetic Field Fluctuations