Straight Field Research Articles

Free boundary 3D ideal MHD equilibrium calculations for non-linearly saturated current driven external kink modes in tokamaks

It is shown that free boundary 3D equilibrium calculations in tokamak geometry are capable of capturing the physics of non-linearly saturated external kink modes for monotonic current and q profiles typical of standard (baseline) plasma scenarios. The VMEC ideal MHD equilibrium model exhibits strong flux surface corrugations of the plasma vacuum boundary, driven by the core current profile. A method is presented which conveniently extracts the amplitude of the corrugation in terms of Fourier components in straight field line coordinates. The Fourier spectrum, and condition for non-linear corrugation agrees well with linear simulations, and the saturated amplitude agrees well with non-linear analytic calculations.

Mechanism and Improve Methods of Rudder Lock for Mechanically Controlled Aircraft

Rudder Lock is a threat to flight safety, which should be carefully considered in the airworthiness certification. Since general aircrafts which are equipped with mechanical control system and controlled by unprofessional pilots becomes more and more popular, researches on rudder lock are still necessary. In this paper, a mechanically controlled medium sized transport is studied as an example. By analyzing the steady straight sideslip flight test data and flow field numerical simulation results, the mechanism of rudder lock is analyzed. Two aerodynamic improving methods including double-triangle dorsal fin and reducing set-back hinge balance are proposed. The flow field numerical simulation results show that double triangle dorsal fin can improve the stall characteristic of vertical tail, but the strong vortex will move the center of pressure forward, which worsens the rudder lock. Reducing set-back hinge balance can improve rudder lock effectively, while the hinge moment and rudder force will be increased, therefore the gearing ratio and tab should be carefully designed.

Coronal Jet Collimation by Nonlinear Induced Flows

Abstract Our objective is to study the collimation of solar jets by nonlinear forces corresponding to torsional Alfvén waves together with external forces. We consider a straight, initially non-rotating, untwisted magnetic cylinder embedded in a plasma with a straight magnetic field, where a shear between the internal and external flows exists. By implementing magnetohydrodynamic theory and taking into account the second-order thin flux tube approximation, the balance between the internal nonlinear forces is visualized. The nonlinear differential equation containing the ponderomotive, magnetic tension, and centrifugal forces in the presence of the shear flow is obtained. The solution presents the scale of influence of the propagating torsional Alfvén wave on compressive perturbations. Explicit expressions for the compressive perturbations caused by the forces connected to the torsional Alfvén wave show that, in the presence of a shear flow, the magnetic tension and centrifugal forces do not cancel each other’s effects as they did in its absence. This shear flow plays in favor of the magnetic tension force, resulting in a more efficient collimation. Regarding the ponderomotive force, the shear flow has no effect. The phase relations highlight the interplay of the shear flow and the plasma-β. As the shear flow and plasma-β increase, compressive perturbation amplitudes emerge. We conclude that the jet collimation due to the torsional Alfvén wave highly depends on the location of the jet. The shear flow tightens the collimation as the jet elevates up to the solar corona.

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma

Five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full-$f$discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.

Propagation of Torsional Alfvén Waves from the Photosphere to the Corona: Reflection, Transmission, and Heating in Expanding Flux Tubes

Abstract It has been proposed that Alfvén waves play an important role in the energy propagation through the solar atmospheric plasma and its heating. Here we theoretically investigate the propagation of torsional Alfvén waves in magnetic flux tubes expanding from the photosphere up to the low corona and explore the reflection, transmission, and dissipation of wave energy. We use a realistic variation of the plasma properties and the magnetic field strength with height. Dissipation by ion–neutral collisions in the chromosphere is included using a multifluid partially ionized plasma model. Considering the stationary state, we assume that the waves are driven below the photosphere and propagate to the corona, while they are partially reflected and damped in the chromosphere and transition region. The results reveal the existence of three different propagation regimes depending on the wave frequency: low frequencies are reflected back to the photosphere, intermediate frequencies are transmitted to the corona, and high frequencies are completely damped in the chromosphere. The frequency of maximum transmissivity depends on the magnetic field expansion rate and the atmospheric model, but is typically in the range of 0.04–0.3 Hz. Magnetic field expansion favors the transmission of waves to the corona and lowers the reflectivity of the chromosphere and transition region compared to the case with a straight field. As a consequence, the chromospheric heating due to ion–neutral dissipation systematically decreases when the expansion rate of the magnetic flux tube increases.

On the validity of the guiding-center approximation in the presence of strong magnetic gradients

The motion of a charged particle in a nonuniform straight magnetic field with a constant magnetic-field gradient is solved exactly in terms of elliptic functions. The connection between this problem and the guiding-center approximation is discussed. It is shown that, for this problem, the predictions of higher-order guiding-center theory agree very well with the orbit-averaged particle motion and hold well beyond the standard guiding-center limit ϵ≡ρ/L≪1, where ρ is the gyromotion length scale and L is the magnetic-field gradient length scale.

Phase mixing of Alfvén waves propagating in non-reflective magnetic plasma configurations

The ability of phase mixing to provide efficient damping of Alfven waves even in weakly dissipative plasmas made it a popular mechanism for explaining the solar coronal heating. Initially it was studied in the equilibrium configurations with the straight magnetic field lines and the Alfven speed only varying in the direction perpendicular to the magnetic field. Later the analysis of the Alfven wave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller than the characteristic scale of the background quantity variation. This assumption enabled using the Wentzel, Kramers, and Brillouin (WKB) method. When it is not satisfied the study was only carried out numerically. In general, even the wave propagation in a one-dimensional inhomogeneous equilibrium can be only studied numerically. However there is one important exception, so-called non-reflective equilibria. In these equilibria the wave equation with the variable phase speed reduces to the Klein-Gordon equation with constant coefficients. In this paper we apply the theory of non-reflective wave propagation to studying the Alfven wave phase mixing in two-dimensional planar magnetic plasma equilibria. Using curvilinear coordinates we reduce the equation describing the Alfven wave phase mixing to the equation that becomes a one-dimensional wave equation in the absence of dissipation. This equation is further reduced to the equation which is the one-dimensional Klein-Gordon equation in the absence of dissipation. Then we show that this equation has constant coefficients when a particular relation between the plasma density and magnetic field magnitude is satisfied. Using the derived Klein-Gordon-type equation we study the phase mixing in various non-reflective equilibria. We emphasise that our analysis is valid even when the wavelength is comparable with the characteristic scale of the background quantity variation. In particular, we study the Alfven wave damping due to phase mixing in an equilibrium with constant plasma density and exponentially divergent magnetic field lines. We confirm the result previously obtained in the WKB approximation that there is enhanced Alfven wave damping in this equilibrium with the damping length proportional to ln(Re), where Re is the Reynolds number. Our theoretical results are applied to heating of coronal plumes. We show that, in spite of enhanced damping, Alfven waves with periods of the order of one minute can be efficiently damped in the lower corona, at the height about 200 Mm, only if the shear viscosity is increased by about 6 orders of magnitude in comparison with its value given by the classical plasma theory. We believe that such increase of the shear viscosity can be provided by the turbulence.

Estimation of wind-driven soil erosion of a loess-like sediment and its implications for the occurrence of archaeological surface and subsurface finds – An example from the environs of Corneşti-Iarcuri, western Romania

This study introduces an easy-to-apply approach to studying historic landscape development and tillage-induced wind-driven soil erosion of a loess-like sediment. It discusses the implications of these processes for the preservation of cultural remains in the environs of the largest known European ground monument – Corneşti-Iarcuri. This Late Bronze Age enclosure is located in the loess-covered, undulating plains of western Romania and consists of four earth-filled wooden ramparts. Interpretation of historic and modern maps is combined with the study of written sources to qualitatively record historic landscape development. It is shown that major changes in the natural environment, including the intensification of arable farming and the regular establishment of straight field paths, occurred in the study area between c. 1770 and c. 1865. The amount of surface lowering due to wind-driven soil erosion is estimated using a combination of systematic feature extraction from the historic and modern maps, high resolution modeling of the topography based on LiDAR data, subsurface compaction measurements and grain size analyses. The surface lowering on the arable fields of the high plain since c. 1865 totals between 10 and 40cm. This, together with the actual plowing depth of c. 30cm, implies that archaeological structures must have penetrated the subsurface to between 40 and 70cm in order to be preserved in the present-day subsurface. Thus, this study shows that a considerable portion of the cultural heritage has presumably been lost. Moreover, the still intact lower-lying stratigraphy is threatened by the destructive impact of plowing that successively reaches greater depths due to ongoing tillage-induced wind-driven soil erosion on the arable fields. However, bioturbation causing distortion of the systemic context of the cultural remains cannot be excluded, as Luvic Phaeozems and Luvic Chernozems prevail in the study area.

Negative viscosity from negative compressibility and axial flow shear stiffness in a straight magnetic field

Negative compressibility ion temperature gradient (ITG) turbulence in a linear plasma device controlled shear de-correlation experiment can induce a negative viscosity increment. However, even with this negative increment, we show that the total axial viscosity remains positive definite, i.e., no intrinsic axial flow can be generated by pure ITG turbulence in a straight magnetic field. This differs from the case of electron drift wave turbulence, where the total viscosity can turn negative, at least transiently. When the flow gradient is steepened by any drive mechanism, so that the parallel shear flow instability (PSFI) exceeds the ITG drive, the flow profile saturates at a level close to the value above which PSFI becomes dominant. This saturated flow gradient exceeds the PSFI linear threshold, and grows with ∇Ti0 as |∇V∥|/|k∥cs|∼|∇Ti0|2/3/(k∥Ti0)2/3. This scaling trend characterizes the effective stiffness of the parallel flow gradient.

Torsional wave propagation in solar tornadoes

Aims. We investigate the propagation of torsional waves in coronal structures together with their collimation effects in the context of magnetohydrodynamic (MHD) theory. The interplay of the equilibrium twist and rotation of the structure, e.g. jet or tornado, together with the density contrast of its internal and external media is studied to shed light on the nature of torsional waves.Methods. We consider a rotating magnetic cylinder embedded in a plasma with a straight magnetic field. This resembles a solar tornado. In order to express the dispersion relations and phase speeds of the axisymmetric magnetohydrodynamic waves, the second-order thin flux tube approximation is implemented for the internal medium and the ideal MHD equations are implemented for the external medium.Results. The explicit expressions for the phase speed of the torsional wave show the modification of the torsional wave speed due to the equilibrium twist, rotation, and density contrast of the tornado. The speeds could be either sub-Alfvenic or ultra-Alfvenic depending on whether the equilibrium twist or rotation is dominant. The equilibrium twist increases the phase speed while the equilibrium rotation decreases it. The good agreement between the explicit versions for the phase speed and that obtained numerically proves adequate for the robustness of the model and method. The density ratio of the internal and external media also play a significant role in the speed and dispersion. Conclusions. The dispersion of the torsional wave is an indication of the compressibility of the oscillations. When the cylinder is rotating or twisted, in contrast to when it only possesses a straight magnetic field, the torsional wave is a collective mode. In this case its phase speed is determined by the Alfven waves inside and outside the tornado.

Wave function properties of a single and a system of magnetic flux tube(s) oscillations

AbstractIn this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero‐β approximation. A single three‐dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high‐resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube ( ), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.

Canonical straight field line magnetic flux coordinates for tokamaks

New global straight field line coordinates are introduced for a toroidal plasma configuration. The new coordinate system provides a canonical description of particle guiding center motion while maintaining the straight field line feature. These coordinates are convenient for combining MHD calculations with kinetic modeling of energetic particles. We demonstrate how the new coordinate system can be constructed by transforming the poloidal and toroidal angles. Numerical examples show comparison of the new coordinates with various non-canonical coordinates for the same equilibrium configuration.

Analytical and numerical study on cooling flow field designs performance of PEM fuel cell with variable heat flux

In PEM fuel cells, during electrochemical generation of electricity more than half of the chemical energy of hydrogen is converted to heat. This heat of reactions, if not exhausted properly, would impair the performance and durability of the cell. In general, large scale PEM fuel cells are cooled by liquid water that circulates through coolant flow channels formed in bipolar plates or in dedicated cooling plates. In this paper, a numerical method has been presented to study cooling and temperature distribution of a polymer membrane fuel cell stack. The heat flux on the cooling plate is variable. A three-dimensional model of fluid flow and heat transfer in cooling plates with 15 cm × 15 cm square area is considered and the performances of four different coolant flow field designs, parallel field and serpentine fields are compared in terms of maximum surface temperature, temperature uniformity and pressure drop characteristics. By comparing the results in two cases, the constant and variable heat flux, it is observed that applying constant heat flux instead of variable heat flux which is actually occurring in the fuel cells is not an accurate assumption. The numerical results indicated that the straight flow field model has temperature uniformity index and almost the same temperature difference with the serpentine models, while its pressure drop is less than all of the serpentine models. Another important advantage of this model is the much easier design and building than the spiral models.

Quantum-control-landscape structure viewed along straight paths through the space of control fields

The dynamics of closed quantum systems may be manipulated by using an applied field to achieve a control objective value for a physical goal. The functional relationship between the applied field and the objective value forms a quantum control landscape, and the optimization process consists of a guided climb up the landscape from the bottom to the top. Two classes of landscape features are important for understanding the ease of finding an optimal control field. The first class of topological landscape features has been proven to be especially simple in that no suboptimal local maxima exist (upon satisfaction of certain assumptions), which partially accounts for the ease of finding optimal fields. Complementary to the topology, the second class of features entails the landscape structure, characterizing the sinuous nature of the paths leading to an optimal control field. Previous work found that the landscape structure is also particularly simple, as excursions up the landscape guided by a gradient algorithm correspond to nearly straight paths through the space of control fields. In this paper we take an alternative approach to examining landscape structure by constructing, and then following, exactly straight trajectories in control space. Each trajectory starts at a corresponding point on the bottom of the landscape and ends at an associated point on the top, with the observable values taken either as the state-to-state transition probability, the expectation value of a general observable, or the distance from a desired unitary transformation. In some cases the starting point is at a suboptimal critical-point saddle, with the goal, again, of following a straight field path to the optimal objective yield or another suboptimal critical point. We find that the objective value almost always rises monotonically upon following a straight control path from one critical point to another, which shows that landscape structure is very simple, being devoid of rough bumps and gnarled ``twists and turns''. An analysis reveals that the generally featureless nature of quantum control landscapes can be understood in terms of the occurrence of many interfering quantum pathways contributing while traversing the landscape, essentially smoothing out the terrain. These results also provide a basis for further studies to seek a new efficient algorithm to discover optimal fields by means of taking into account the inherently smooth landscape structure.

Effects of Straight and Serpentine Flow Field Designs on Temperature Distribution in Proton Exchange Membrane (PEM) Fuel Cell

Proton exchange membrane fuel cells or sometimes called as polymer electrolyte membrane (PEM) fuel cells is a device for energy transformation in a changing process from one form of energy to another form of energy. It became as an alternative especially for future use in stationary and vehicular applications. PEM fuel cells provide high efficiency and power density with null emission, low operating temperature, quickly start and long life. One of the aspects that are crucial in optimizing the PEM fuel cells performance is a flow field geometry. In this paper, a simulation case of PEM fuel cells was simulated to determine effects of a straight and serpentine flow field on temperature distribution in PEM fuel cells. ANSYS Fluent software was used to simulate 3-dimensional models of single PEM fuel cells in order to determine the effects of changes in the geometry flow field on temperature distributions. Results showed that the serpentine flow field design produces a better temperature distribution along the membrane. The simulation result shows a good agreement with the experiment, thus boost a higher confidence in the results to determine the effectiveness of the flow field design in PEM fuel cells.

Linear MHD Wave Propagation in Time-Dependent Flux Tube

In this article, we evaluate the time-dependent wave properties and the damping rate of propagating fast magneto-hydrodynamic (MHD) waves when energy leakage into a magnetised atmosphere is considered. By considering a cold plasma, initial investigations into the evolution of MHD wave damping through this energy leakage will take place. The time-dependent governing equations have been derived previously in Williamson and Erdelyi (2014a, Solar Phys.289, 899 – 909) and are now solved when the assumption of evanescent wave propagation in the outside of the waveguide is relaxed. The dispersion relation for leaky waves applicable to a straight magnetic field is determined in both an arbitrary tube and a thin-tube approximation. By analytically solving the dispersion relation in the thin-tube approximation, the explicit expressions for the temporal evolution of the dynamic frequency and wavenumber are determined. The damping rate is, then, obtained from the dispersion relation and is shown to decrease as the density ratio increases. By comparing the decrease in damping rate to the increase in damping for a stationary system, as shown, we aim to point out that energy leakage may not be as efficient a damping mechanism as previously thought.

The universal instability in general geometry

The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.

Linear stability studies including resistive wall effects with the CASTOR/STARWALL code

CASTOR/STARWALL is a code package for linear stability studies consisting of the CASTROR_3DW code, the STARWALL code, and a hybrid version of both codes named CASTOR3D that is currently under development. The latter solves an extended eigenvalue problem consisting of the plasma part defined by the weak form of the perturbed single-fluid MagnetoHydroDynamic (MHD) equations, and a vacuum part which is derived from an energy functional. This new code can describe wall resistivity and plasma inertia simultaneously. Furthermore, besides the so far used straight field line coordinates, additionally, general flux coordinates are implemented which are more appropriate for the description of instabilities located close to the separatrix (e.g. Edge Localized Modes (ELMs)). The formulation of the eigenvalue problem in the new coordinates is not limited to axisymmetric equilibria, so that, finally, stability studies of resistive and rotating, 3D equilibria should be possible. In this paper we will sketch the theory, report on the progress of the code development, and present first results.

CONSTRAINING THE PHYSICAL CONDITIONS IN THE JETS OF γ-RAY FLARING BLAZARS USING CENTIMETER-BAND POLARIMETRY AND RADIATIVE TRANSFER SIMULATIONS. I. DATA AND MODELS FOR 0420–014, OJ 287, AND 1156+295

To investigate parsec-scale jet flow conditions during GeV gamma-ray flares detected by the Fermi Large Angle Telescope, we obtained centimeter-band total flux density and linear polarization monitoring observations from 2009.5 through 2012.5 with the 26-meter Michigan radio telescope for a sample of core-dominated blazars. We use these data to constrain radiative transfer simulations incorporating propagating shocks oriented at an arbitrary angle to the flow direction in order to set limits on the jet flow and shock parameters during flares temporally associated with gamma-ray flares in 0420-014, OJ 287, and 1156+295; these AGN exhibited the expected signature of shocks in the linear polarization data. Both the number of shocks comprising an individual radio outburst (3-4) and the range of the compression ratios of the individual shocks (0.5-0.8) are similar in all three sources; the shocks are found to be forward-moving with respect to the flow. While simulations incorporating transverse shocks provide good fits for 0420-014 and 1156+295, oblique shocks are required for modeling the OJ~287 outburst, and an unusually-low value of the low energy cutoff of the radiating particles' energy distribution is also identified. Our derived viewing angles and shock speeds are consistent with independent VLBA results. While a random component dominates the jet magnetic field, as evidenced by the low fractional linear polarization, to reproduce the observed spectral character requires that a significant fraction of the magnetic field energy is in an ordered axial component. Both straight and low pitch angle helical field lines are viable scenarios.

Coronal heating and nanoflares: current sheet formation and heating

Aims. Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona.Methods. A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed.Results. For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained.