Rotation Field Research Articles

Parker Solar Probe Observations of Magnetic Reconnection Exhausts in Quiescent Plasmas near the Sun

Parker Solar Probe observations are analyzed for the presence of reconnection exhausts across current sheets (CSs) within R < 0.26 au during encounters 4–11. Exhausts are observed with nearly equal probability at all radial distances with a preference for quiescent Tp < 0.80 MK plasmas typical of a slow-wind regime. High Tp > 0.80 MK plasmas of a fast wind characterized by significant transverse fluctuations rarely support exhausts irrespective of the CS width. Exhaust observations demonstrate the presence of local temperature gradients across several CSs with a higher-Tp plasma on locally closed fields and a lower-Tp plasma on locally open field lines for an interchange-type reconnection. A CS geometry analysis directly supports the property that X-lines bisect the magnetic field rotation θ-angle, whether the fields and plasmas are asymmetric or not, to maximize reconnection rates and available magnetic energy. The CS normal width d cs distributions suggest that a multiscale reconnection process through nested layers of bifurcated CSs may be responsible for observed power-law distributions beyond the median d cs ∼ 1000 km with an exponential d cs distribution present for ion kinetic dissipation scales below this median. Magnetic field shear θ-angles are essentially identical at R < 0.26 and 1 au with medians at θ ∼ 55° near the Sun and θ ∼ 65° at 1 au. In contrast, the tangential flow shear distributions are different near and far from the Sun. A bimodal flow shear angle distribution is present near the Sun with strong shear flow magnitudes. This distribution is modified with radial distance toward a relatively flat distribution of weaker flow shear magnitudes.

Effect of the Magnetic Field and Rotation on Peristaltic Flow of A Bingham Fluid in Asymmetric Channel with Porous Medium

In this paper, we investigate the influence of the rotation and magnetic field on the peristaltic flow of the Bingham fluid in an asymmetric channel with a porous medium under the long wavelength and low Reynolds number approximation assumptions. The perturbation method and the Mathematica program for solving nonlinear partial differential equations are used to couple the momentum equations with the rotational and magnetic field equations. The fluid is considered to be subject to a magnetic field and to flow within a porous medium. Graphs are used to display expressions for speed, stress gradient, magnetic subject, current density, rotation impact, and drift function. The findings reveal that the rotation, density, permeability, coupling diversity, and non-dimensional wave amplitude all play significant roles in the phenomenon. The quantities flow has been tested for variant parameters. The impact of the Bingham, Hartman and Darcy numbers are also tested for different values to indicate the effect on the movement of flow fluid. The applications can be seen through many graphics.

Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field

Quantum vortex phases of charged pion condensates induced by rotation in a magnetic field

Magnetocaloric effect at the reorientation of the magnetization in ferromagnetic multilayers with perpendicular anisotropy

We investigate the magnetocaloric effect obtained by the rotation of a magnetic field applied to an exchange-coupled multilayer system composed of two different ferromagnetic (FM) materials. We specifically consider a system in which the two FMs have perpendicular uniaxial anisotropy axes and utilize conditions which yield a reorientation of the total magnetization when compensation between the anisotropies of the two layers occurs. We calculate the consequent entropy change associated with the “artificial” reorientation. By using known parameters from MnBi and Co we predict an entropy change of Δs=0.34 J kg−1 K−1 for perfect coupling. Lastly, we study the behavior of the multilayer under a rotating magnetic field via a micromagnetic model. When the layer thicknesses are of the order of the local domain wall width, the magnetic field-induced entropy change can be obtained with magnetic fields one order of magnitude lower than in the uncoupled case.

СВЧ ЭЛЕКТРОТЕХНОЛОГИЧЕСКАЯ УСТАНОВКА ДЛЯ МИКРОВОЛНОВОЙ ОБРАБОТКИ ПИЛОМАТЕРИАЛОВ И ПОЛИКАПРОАМИДНЫХ НИТЕЙ

Research was carried out to determine the optimal modes for the simultaneous processing of lumber and polycaproamide threads in a hybrid microwave electrotechnological installation. The work was carried out on an installation with a hybrid-type chamber with adjustment of the microwave power level of the magnetrons and the duration of exposure. Two possible designs of a hybrid installation for processing lumber and polycaproamide threads are presented, differing in that in one the lumber was processed inside the chamber, and the polycaproamide threads were pulled through waveguides using bobbins and an electric motor installed outside the chamber, and in the second, both materials were processed inside the installation chamber. The object of research is lumber and polycaproamide threads. Lumber was loaded into the working chamber in the form of a stack, which rotated along its axis, and a structure was examined in which polycaproamide threads were pulled through a waveguide extending from a source of microwave energy outside the chamber. The time of exposure to microwave radiation on lumber and half-caproamide threads was measured using electronic stopwatches; temperature and humidity were measured using a Testo 905T2 thermometer, a Testo 830T1 pyrometer, and a Testo 606-1 digital hygrometer. The use of a hybrid microwave electrotechnological installation reduced the processing time of lumber due to rotation in the microwave field to 15 hours, while ensuring the required quality of the dried material (final moisture content - 7.1%, reduction in chipping and impact bending strength within 5%). The relative breaking elongation of polycaproamide threads increased by 48.2%, and the breaking load – by 27.6%. Thanks to the simultaneous processing of lumber and polycaproamide threads, it is possible to reduce metal consumption and increase the energy efficiency of the installation.

Rotation impact on the radial vibrations of frequency equation of waves in a magnetized poroelastic medium

This research delves into the propagation of radial free harmonic waves in a poroelastic cylinder, conceptualized as a magnetically and rotationaly influenced hollow structure. The primary aim is to elucidate the magnetic field's and rotation impact on the vibrational behavior of such systems. The investigative method encompasses the resolution of motion equations, formulated as partial differential equations, through the application of Lame's potential theory. This analytical process is augmented by the implementation of fitting boundary conditions, culminating in the derivation of a comprehensive expression for the complex dispersion equation, predicated on the premise that the wavenumber embodies a complex entity. The precision of the model is corroborated through a comparative analysis with established literature, underpinned by an exploration of diverse scenarios. The research employed MATLAB for both numerical and graphical assessments, focusing on the dispersion and displacement attributes. Dispersion relations within the poroelastic medium were computed, considering varied magnitudes of magnetic field intensity, rotation and angular velocities. The outcomes are articulated through complex-valued dispersion relations, transcendental formulations, and numerical resolutions employing MATLAB's bisection technique. These insights hold substantial significance for the theoretical advancement in orthopedic research, particularly concerning cylindrical poroelastic media. This study deduces that the radial vibrational patterns and the corresponding frequency equation within a poroelastic medium are profoundly modified by the magnetic field's interference and rotation. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field and rotation.

Limit cycles in a rotated family of generalized Liénard systems allowing for finitely many switching lines

Analytic rotated vector fields have four significant properties: as the rotated parameter $\alpha$ changes, the amplitude of each stable (or unstable) limit cycle varies monotonically, each semi-stable limit cycle bifurcates at most two limit cycles, the isolated homoclinic loop (if exists) disappears while a unique limit cycle with the same stability arises or no closed orbits arise oppositely, and a unique limit cycle arises near the weak focus (if exists). In this paper, we prove that the four properties remain true for a rotated family of generalized Liénard systems having finitely many switching lines. Furthermore, we discuss variational exponent and use it to formulate multiplicity of limit cycles. Then we apply our results to give exact number of limit cycles to a continuous piecewise linear system with three zones and answer to a question on the maximum number of limit cycles in an SD oscillator.

Assessing the impacts of climate change on crop yields, soil organic carbon sequestration and N2O emissions in wheat–maize rotation systems

Straw retention has been widely implemented to increase soil organic carbon (SOC) sequestration and greenhouse gas (GHG) mitigation for global agriculture. However, the combined effects of long-term straw retention on crop production, SOC sequestration and GHG emissions response to climate change remain unknown. Two nearby wheat–maize rotation field experiments in the North China Plain, combined with local weather, soil and agronomic measurements, were used to evaluate the applicability of the SPACSYS model. The model was then applied to assess the response of crop yield, SOC storage and nitrous oxide (N2O) emissions to three nitrogen fertilizer application levels (100, 200, 400 kg N ha−1) and three representative concentration pathway scenarios (RCP2.6, RCP4.5 and RCP8.5) under straw retention for the wheat–maize rotation systems during 2021–2100. In general, the model was reasonably accurate with R2 and model efficiency (EF) ranging from 0.25 to 0.96 and 0.32–0.94, respectively. Climate change decreased wheat yield by 4–39%, while maize showed a slight increase (3%) under RCP2.6 and a decrease of 1–15% under RCP4.5 and RCP8.5. The SOC storage in the 0–20 cm soil increased at a rate of 73–195 kg C ha−1 yr−1 but decreased within the upper 1 m soil at 280–390 kg C ha−1 yr−1. Climate change reduced the positive effect of SOC sequestration except in RCP2.6 and stimulated substantial N2O emissions ranging from 1–7.5 to 2.9–23.2 kg N ha−1 yr−1, consequently, the global warming potential increased from –79–2555 to 548–9357 kg CO2-eq ha−1 yr−1 under various N fertilizer application levels. This study reveals that the negative feedback under climate change with modelling approach, and extensive efforts are needed to make adaptations to ensure food production and reduce GHG emissions in the future.

Kepler main-sequence solar-like stars: surface rotation and magnetic-activity evolution

While the mission’s primary goal was focused on exoplanet detection and characterization, Kepler made and continues to make extraordinary advances in stellar physics. Stellar rotation and magnetic activity are no exceptions. Kepler allowed for these properties to be determined for tens of thousands of stars from the main sequence up to the red giant branch. From photometry, this can be achieved by investigating the brightness fluctuations due to active regions, which cause surface inhomogeneities, or through asteroseismology as oscillation modes are sensitive to rotation and magnetic fields. This review summarizes the rotation and magnetic activity properties of the single main-sequence solar-like stars within the Kepler field. We contextualize the Kepler sample by comparing it to known transitions in the stellar rotation and magnetic-activity evolution, such as the convergence to the rotation sequence (from the saturated to the unsaturated regime of magnetic activity) and the Vaughan-Preston gap. While reviewing the publicly available data, we also uncover one interesting finding related to the intermediate-rotation gap seen in Kepler and other surveys. We find evidence for this rotation gap in previous ground-based data for the X-ray luminosity. Understanding the complex evolution and interplay between rotation and magnetic activity in solar-like stars is crucial, as it sheds light on fundamental processes governing stellar evolution, including the evolution of our own Sun.

Effects of 3-year biochar application on carbon sequestration, nitrogen retention and nitrate leaching of fluvo-aquic soil profiles in vegetable rotation fields

The impacts of biochar application on the carbon (C) and nitrogen (N) cycles in soil profiles in vegetable fields have rarely been reported. A three-year field experiment (CK, control; BC, biochar; N, nitrogen fertilizer; BCN, biochar and nitrogen fertilizer) was conducted in fluvo-aquic soil with a wild cabbage-Chinese cabbage rotation to investigate biochar effects on soil organic carbon (SOC) sequestration, N retention, and nitrate (NO3−) leaching in the soil profile (topsoil, 0–20 cm; subsoil, 20–50 cm; third-layer soil, 50–100 cm). The results showed that the biochar-induced increase in topsoil SOC under N fertilization was greater for Chinese cabbage season than for wild cabbage season. Excluding biochar-N, biochar application caused an extra increase in topsoil total nitrogen (TN) under N fertilization. Biochar decreased the NO3−-N concentration of third-layer soil solution, particularly under N fertilization, indicating that biochar reduced the potential source of NO3− leaching. Under N fertilization, biochar reduced the abundances of carbon-degrading bacteria (Streptomyces, Bacillus, Mycobacterium, and Sphingomonas) and genes (sga, xylA, lig, and pgu) in the topsoil, as well as the abundances of ammonia-oxidizing bacteria (Nitrosospira and Nitrosomonas) and gene (amoA) in the third-layer soil. However, biochar increased the abundance of ammonia-assimilating bacteria (Rhodococcus) and gene (glnA) in the topsoil. Biochar inhibited the microbial function associated with C degradation by affecting soil TN, thus enhancing topsoil SOC sequestration. Biochar promoted the soil microbial function related to ammonia assimilation by affecting dissolved organic carbon (DOC), subsequently enhancing ammonia assimilation. Moreover, biochar initially inhibited ammonia oxidation in the third-layer soil by increasing soil DOC, subsequently affecting nitrite oxidation and ultimately reducing soil NO3− leaching. Biochar significantly increased the N use efficiency of vegetables in the last two years. This study provides insights into biochar effects on the changes in soil microbial function, which promoted SOC sequestration, enhanced N retention and mitigated nitrate leaching in a vegetable rotation field.

Theoretical Derivation and Calculation of Electron Charge

In this paper, we propose an assumption of which the relation between electron and phonon is discussed and investigated based on the experiment of γ photon and electric interconverting with each other. We calculated the charge of a particular standing wave topology with Maxwell’s equation rotated in accordance space with the SO3 transformation. The derived charge value is 1.6299 × 10−19 around 1.73% different from the experimental data, indicating the proposal is a promising theory to explain the origin of charge and spin of electron particle. Electron spin angular momentum comes from the orbital angular momentum of photon rotation (electromagnetic field rotation), and electron charge comes from photon, that is, the space-time rotation effect of electromagnetic wave.

Electric Field Characteristics of Rotating Permanent Magnet Stimulation.

Neurostimulation devices that use rotating permanent magnets are being explored for their potential therapeutic benefits in patients with psychiatric and neurological disorders. This study aims to characterize the electric field (E-field) for ten configurations of rotating magnets using finite element analysis and phantom measurements. Various configurations were modeled, including single or multiple magnets, and bipolar or multipolar magnets, rotated at 10, 13.3, and 350 revolutions per second (rps). E-field strengths were also measured using a hollow sphere (r=9.2 cm) filled with a 0.9% sodium chloride solution and with a dipole probe. The E-field spatial distribution is determined by the magnets' dimensions, number of poles, direction of the magnetization, and axis of rotation, while the E-field strength is determined by the magnets' rotational frequency and magnetic field strength. The induced E-field strength on the surface of the head ranged between 0.0092 and 0.52 V/m. In the range of rotational frequencies applied, the induced E-field strengths were approximately an order or two of magnitude lower than those delivered by conventional transcranial magnetic stimulation. The impact of rotational frequency on E-field strength represents a confound in clinical trials that seek to tailor rotational frequency to individual neural oscillations. This factor could explain some of the variability observed in clinical trial outcomes.

Resonances of Supernova Neutrinos in Twisting Magnetic Fields.

We investigate the effect of resonant spin conversion of the neutrinos induced by the geometrical phase in a twisting magnetic field. We find that the geometrical phase originating from the rotation of the transverse magnetic field along the neutrino trajectory can trigger a resonant spin conversion of Dirac neutrinos inside the supernova, even if there were no such transitions in the fixed-direction field case. We have shown that, even though resonant spin conversion is too weak to affect solar neutrinos, it could have a remarkable consequence on supernova neutronization bursts where very intense magnetic fields are quite likely. We demonstrate how the flavor composition at Earth can be used as a probe to establish the presence of non-negligible magnetic moments, potentially down to 10^{-15}μ_{B} in upcoming neutrino experiments like the Deep Underground Neutrino Experiment and the Hyper-Kamiokande. Possible implications are analyzed.

Simulation study on rotor speed of combined rotary separator in coal pneumatic conveying

The separator is a key component of coal pneumatic conveying systems, which plays an important role in improving particle collection efficiency and reducing dust pollution. In this paper, a combined rotary separator was designed. Based on the traditional cyclone separator, the rotor blades were installed and matched with the guide vanes to increase the material separation and collection performance. The influence of rotor speed on the characteristics of the separator was studied by computational fluid dynamics simulation, and the flow field velocity and pressure distribution and the particle trajectory and separation degree were obtained. The results showed that the flow field tangential velocity plays a dominant role in the separation process and is approximately symmetrically distributed with the rotor axis as the center. The velocity of the flow field in the inner rotor is approximately positively correlated with the rotor speed, and the tangential velocity gradually decreases with the increase in the flow field height. The static pressure of the flow field is approximately axisymmetric along the rotor axis, and there is a pressure gradient from the outer separation cone to the rotor axis. The particles in the separator show a separation phenomenon based on the different sizes, and the change trend of the separation degree under different rotor speeds is similar. When the rotor speed is 160 rpm, the particles maintain the highest integrity. The rotor speed of 320 rpm has a protective effect on coarse particles above 1000 µm.

A theory for the emission of infrasound from Tornadoes

Tornadoes have been shown to radiate infrasound to great distances, however convincing fundamental sound mechanisms are still absent. After using vortex sound theory to study sound generated by two numerical tornadoes, we found that there is a significant low-frequency signal between 0.1 Hz and 1 Hz. The sound is closely related to rotation of the non-axisymmetric vorticity field and its frequency depends on the rotational frequency. The non-axisymmetric vorticity field is represented by a Kirchhoff vortex-like flow in baseline tornado model and by multiple-vortex flow in eddy injection tornado model. Interestingly, there also exist high-frequency components in the later model which are hypothesized to originate from vortex merging process. Field detection data of tornado infrasound provides some support for the low-frequency sound.

Heating uniformity improvement of the intermittent microwave drying for carrot with simulations and experiments

AbstractHeating uniformity is always a concern in microwave drying for foodstuff, where unsatisfied product quality could be caused by over‐ or inadequate‐heating. To deal with this concern, multi‐physics field rotation simulation models and intermittent microwave drying modes were designed and evaluated in this study. Four drying modes with different intermittent time ratios (R1/2, R1/3, R1/4, and R1/5) were first applied in drying experiments. Their effects on temperature distribution, drying characteristics, and quality aspects (chromatic aberration, rehydration ratio, vitamin C content, and sensory evaluation) for carrot samples were compared and analyzed. The results revealed that the carrot quality in R1/4 mode drying was increased by up to 64% in comparison with the other three modes. The root‐mean‐square error of the moisture ratio was maintained at a lower value, and a better consistency was also achieved in R1/4 mode. To further improve the drying performance and efficiency, a novel stage intermittent‐time control strategy was attempted, that is, an appropriate strategy was used in each drying stage. With this method, the best drying effect could be obtained. The above work can promote a deeper understanding of the drying kinetic and provide novel operation strategies in the microwave drying of food products.Practical applicationsA multi‐physics field rotational simulation model (MFRSM) coupled with an intermittent microwave drying process, including electromagnetic heating, heat, and mass transfer, was developed to characterize the drying process of rotating samples in an intermittent microwave dryer. The MFRSM was helpful to analyze the continuous microwave drying process of the sample and deepen the understanding of the internal heat and mass transfer process of the sample. Four modes with different intermittent schedules were designed, and simulation models were also established. The drying characteristics in different modes were analyzed; a long intermittent time could affect the drying efficiency on account of the driving force, while a short intermittent time would reduce the product quality because of the continuous high temperature. R1/4 mode was founded in terms of drying efficiency and drying quality. An optimized stage intermittent‐time control strategy (R‐IO mode) was designed. The drying time in the three stages was shortened by 25% in total compared with R1/4 mode. Meanwhile, the vitamin C retention, the taste quality of the dried products were improved. These works are expected to provide benefits for the understanding of the intermittent microwave drying modes on drying kinetic using the MFRSM. It can also be useful in the development of an IMD for food materials.

Large Anomalous Hall Effect at Room Temperature in a Fermi‐Level‐Tuned Kagome Antiferromagnet

AbstractThe recent discoveries of surprisingly large anomalous Hall effect (AHE) in antiferromagnets have attracted much attention due to their promising use in spintronics devices. However, such AHE‐hosting antiferromagnetic materials are rare in nature. Herein, it is demonstrated that Mn2.4Ga, a Fermi‐level‐tuned kagome antiferromagnet, has a large anomalous Hall conductivity of ≈150 Ω−1 cm−1 at room temperature that surpasses the usual high values (i.e., 20–50 Ω−1 cm−1) observed so far in two outstanding kagome antiferromagnets, Mn3Sn and Mn3Ge. Although the triangular spin structure of Mn2.4Ga shows a weak net magnetic moment of ≈0.05 µB per formula unit, it guarantees a nonzero Berry curvature in the kagome plane. Moreover, the anomalous Hall conductivity exhibits a sign reversal with the rotation of a small magnetic field that can be ascribed to the field‐controlled chirality of the spin triangular structure. This theoretical calculations further suggest that the large AHE in Mn2.4Ga originates from a significantly enhanced Berry curvature associated with the tuning of the Fermi level close to the Weyl points. These properties, together with the ability to manipulate moment orientations using a moderate external magnetic field, make Mn2.4Ga extremely exciting for future antiferromagnetic spintronics.

Intelligent fuzzy back-stepping observer design based induction motor robust nonlinear sensorless control

Introduction. The control algorithm of Induction Motor (IM) is massively dependent on its parameters; so, any variation in these parameters (especially in rotor resistance) gives unavoidably error propagates. To avoid this problem, researches give more than solution, they have proposed Variable Structure Control (VSC), adaptive observers such as Model Reference Adaptive System, Extended Luenberger Observer (ELO) and the Extended Kalman Filter (EKF), these solutions reduce the estimated errors in flux and speed. As novelty in this paper, the model speed observer uses the estimated currents and voltages as state variables; we develop this one by an error feedback corrector. The Indirect Rotor Field Oriented Control (IRFOC) uses the correct observed value of speed; in our research, we improve the observer’s labour by using back-stepping Sliding Mode (SM) control. Purpose. To generate the pulse-width modulation inverter pulses which reduce the error due of parameters variations in very fast way. Methods. We develop for reach this goal an exploration of two different linear observers used for a high performance VSC IM drive that is robust against speed and load torque variations. Firstly, we present a three levels inverter chosen to supply the IM; we present its modelling and method of control, ending by an experiment platform to show its output signal. A block diagram of IRFOC was presented; we analyse with mathematic equations the deferent stages of modelling, showed clearly the decoupling theory and the sensorless technique of control. The study described two kinds of observers, ELO and EKF, to estimate IM speed and torque. By the next of that, we optimize the step response using the fuzzy logic, which helps the system to generate the PI controller gains. Both of the two observers are forward by SM current controller, the convergence of SM-ELO and SM-EKF structures is guaranteed by minimizing the error between actual and observed currents to zero. Results. Several results are given to show the effectiveness of proposed schemes.

Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity

Abstract In this study, we investigated the effect of a rotation field and magnetic field on a homogeneous photo-thermoelastic nonlocal material and how its thermal conductivity changes as a result of a linearly distributed thermal load. The thermal conductivity of an interior particle is supposed to increase linearly with temperature under the impact of laser pulses. Microelastic (microelements distribution), non-local semiconductors are used to model the problem under optoelectronic procedures, as proposed by the thermoelasticity theory. According to the microelement transport processes, the micropolar-photo-thermoelasticity theory accounts for the medium’s microelongation properties. This mathematical model is solved in two dimensions using the harmonic wave analysis. Non-local semiconductor surfaces can generate completely dimensionless displacement, temperature, microelongation, carrier density, and stress components with the appropriate boundary conditions. The effects of thermal conductivity, thermal relaxation times, magnetic pressure effect, laser pulses, and rotation parameters on wave propagation in silicon (Si) material are investigated and graphically displayed for a range of values.

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.