Radial Currents Research Articles

Two new end members of pyroclastic density currents: Forced convection-dominated and inertia-dominated

A great debate on the flow density of pyroclastic density currents (PDCs) in explosive eruptions has pervaded volcanology over the last decades (Dade and Huppert, 1996, 1997; Wilson, 1997). PDCs consist of gas–particle flows that move for kilometers down the volcano and over the surrounding terrain. They are generated because of vertical collapse of an eruptive column (Woods, 1988; Valentine and Wohletz, 1989), or explosion of a lava dome/overpressure jet (blast) (Esposti Ongaro et al., 2008, 2011), and they flow downstream as radial or unidirectional currents, respectively. Radial currents are also generated because of collapse of an overpressurized (mushroom-like expanded) column (Dellino et al., 2010a), pyroclastic fountaining (Woods and Wohletz, 1991; Clarke et al., 2002), or in ignimbrite-forming eruptions (Fisher et al., 1980; Cas et al., 2011). In this paper, a new subdivision of PDCs, forced convection-dominated and inertia-dominated, is proposed based on flow property. A simple PDC simulation, and field evidences reveal that forced convection-dominated flows may transport own density if they are continuously fed at source, favored by steep volcano, or channelized. Inertia-dominated flows may leak the density floating over topography.

PIC simulation of a thermal anisotropy-driven Weibel instability in a circular rarefaction wave

The expansion of an initially unmagnetized planar rarefaction wave has recently been shown to trigger a thermal anisotropy-driven Weibel instability (TAWI), which can generate magnetic fields from noise levels. It is examined here whether the TAWI can also grow in a curved rarefaction wave. The expansion of an initially unmagnetized circular plasma cloud, which consists of protons and hot electrons, into a vacuum is modelled for this purpose with a two-dimensional particle-in-cell (PIC) simulation. It is shown that the momentum transfer from the electrons to the radially accelerating protons can indeed trigger a TAWI. Radial current channels form and the aperiodic growth of a magnetowave is observed, which has a magnetic field that is oriented orthogonal to the simulation plane. The induced electric field implies that the electron density gradient is no longer parallel to the electric field. Evidence is presented here that this electric field modification triggers a second magnetic instability, which results in a rotational low-frequency magnetowave. The relevance of the TAWI is discussed for the growth of small-scale magnetic fields in astrophysical environments, which are needed to explain the electromagnetic emissions by astrophysical jets. It is outlined how this instability could be examined experimentally.

Instabilities and turbulence in magnetohydrodynamic flow in a toroidal duct prior to transition in Hartmann layers

AbstractFlow of an electrically conducting fluid in a toroidal duct of square cross-section is analysed. The flow is driven by the azimuthal Lorentz force resulting from the interaction between the radial electric currents created by the difference of electric potential maintained between the cylinder walls and the strong magnetic field imposed in the axial direction. The flow geometry and the value of the Hartmann number correspond to the experiment of Moresco & Alboussière (J. Fluid Mech., vol. 504, 2004, pp. 167–181). The purpose of the analysis is to reveal the flow features at Reynolds numbers below the threshold of transition to turbulence in Hartmann layers. We find that the flow experiences a complex evolution. The laminar base flow experiences the first instability at the Reynolds number significantly smaller than that of the threshold. The instability is axisymmetric and oscillatory. Turbulence appears at a slightly higher Reynolds number. Right up to the Hartmann layer instability, the turbulence remains localized in a layer near the outer cylinder wall. It is demonstrated that the turbulence may affect the transition in the Hartmann layers via unsteady forcing of the outer flow.

THE MAXIMUM TORQUE OF SYNCHRONOUS AXIAL PERMANENT MAGNETIC COUPLINGS

Axial permanent magnetic couplings are composed of two discs with a small air-gap in-between. Each disc consists of several segments in the shape of slices of cakes. The segments are polarized in axial direction with alternating polarity. In this work the homogeneous magnetization in the segments is replaced by equivalent currents on the surface of the segments (Amperean model). In a simplifled model we consider only radial currents whereas azimuthal currents along the perimeter of the discs are discarded. This corresponds to the arrangement where one of the discs has much larger diameter than the other disc. Compared to the case of two equal discs it leads to a notable error in the magnetic fleld near the perimeter, yet it has only a small efiect on the torque, especially for the case of optimum couplings. This trick allows for summing up the flelds of all segments in closed form. A concise double integral over the radial magnetic fleld component describes the torque. An investigation of this integral reveals many properties of axial magnetic couplings: A diagram is introduced and areas in this diagram are identifled where the torque shows overshoot, rectangular pulse shape or sinusoidal dependence versus twist angle between both discs. The diagram contains also a curve for maximum torque and one point on this curve is of considerable economic signiflcance: It denotes the global maximum of torque over magnet mass.

Plastic Models Designed To Produce Large Height-to-Length Ratio Steady-State Planar and Axisymmetric (Radial) Viscous Liquid Laminar Flow Gravity Currents

Naturally occurring gravity currents include events such as air flowing through an open front door, a volcanic eruption’s pyroclastic flow down a mountainside, and the spread of the Bhopal disaster’s methyl isocyanate gas. Gravity currents typically have a small height-to-distance ratio. Plastic models were designed and constructed with a restricted horizontal liquid flow using a series of connected cells that produced high viscosity laminar liquid flow planar and radial gravity currents. Because these gravity currents had a large height-to-distance ratio, they were easy to observe. Incremental transfer equations were used in spreadsheets to calculate the expected gravity current profiles. The calculated profiles were in good agreement with the liquid heights in the model’s cells at steady state. The steady-state profile for the planar viscous laminar flow gravity current was an x axis parabola.

On the Neoclassical Relationship between the Radial Electric Field and Radial Current in Tokamak Plasmas

The fluid equation is analytically derived in a rigorous manner, stipulating the relationship between the radial electric field and radial current in tokamak plasmas, especially when heated by neutral beam injection. On a very short time scale compared to the decay in poloidal rotation, the polarization current compensates for the non-ambipolar fast-ion radial current, producing a concomitant time change in the radial electric field. This polarization current predominates among the constituents of the radial current that produces the j × B torque. For times comparable to or longer than the decay time, the polarization current is no longer sufficient to compensate for the fast-ion radial current. In a steady state where the radial electric field is constant over time, the polarization current vanishes and the orthogonal conduction current becomes a sole component of the radial current that continues to flow as long as the charge separation occurs due to the neutral beam injection. Analytical work demonstra...

Design study on power flattening to sodium cooled large-scale CANDLE burning core with using thorium fuel

The CANDLE (Constant Axial shape of Neutron flux, nuclide densities and power shape During Life of Energy production) burnup strategy is a unique and new burnup concept. The previous CANDLE cores feature a relatively large peak-to-average power density and discharge burnup distribution. Peaked power and burnup distribution are undesirable, as they deteriorate economical performance. The objective of this paper is to study the feasibility of power flattening of sodium cooled large scale CANDLE reactors toward commercial use by using thorium fuel loading into the inner core zone. If we choose the amount of thorium proper, net radial current of neutrons in the inner core becomes zero in the inner core, and at the boundary between inner and outer core enough neutrons leak from the uranium region and the net radial current is still zero at this point. In the outer region the neutrons leak outward. By this way, we can make the power density distribution flat in the inner core. In the present work, the power density profile is intended flatten for the metallic fuel CANDLE reactors by adding thorium uniformly in the inner core region. We also evaluate that the core radius and height have an effect on power flattening. The maximum axially integrated power density (radial peaking factor) decreases from 1.87 with only uranium fuel to 1.44 with uranium and thorium fuels. The power flattening with loading thorium fuel in the inner core zone creates higher power density and lower coolant velocity that allow higher thermal power and smaller pressure drop.

Instability of magnetohydrodynamic flow in an annular channel at high Hartmann number

Instability of a flow of an electrically conducting fluid in an annular channel is analyzed. Strong constant magnetic field is imposed in the axial direction. Similarly to toroidal duct experiments, the flow is driven by the azimuthal Lorentz force resulting from the interaction between the magnetic field and the radial electric currents created by a difference of electric potential imposed between the cylinders. The instability of the base flow, while clearly of centrifugal nature, is significantly different from the Dean instability detected earlier in hydrodynamic systems and similar MHD systems at low and moderate magnetic fields. Growing perturbations are oscillating and axisymmetric and consist of counter-rotating toroidal vortices arranged side by side in the radial direction and having meridional cross-sections in the form of elongated ellipses oriented slightly obliquely to the axial direction. Simulations of the secondary flow show an interesting feature of periodic transitions between two symmetric solutions.

Quasisymmetric toroidal plasmas with large mean flows

Geometric conditions for quasisymmetric toroidal plasmas with large mean flows on the order of the ion thermal speed are investigated. Equilibrium momentum balance equations including the inertia term due to the large flow velocity are used to show that, for rotating quasisymmetric plasmas with no local currents crossing flux surfaces, all components of the metric tensor should be independent of the toroidal angle in the Boozer coordinates, and consequently these systems need to be rigorously axisymmetric. Unless the local radial currents vanish, the Boozer coordinates do not exist and the toroidal flow velocity cannot take any value other than a very limited class of eigenvalues corresponding to very rapid rotation especially for low beta plasmas.

Conservation equations and calculation of mean flows in gyrokinetics

Conservation equations are derived for the gyrocenter toroidal momentum density and the polarization field. These equations are derived from the gyrokinetic model as it is implemented in simulation codes. In view of predicting the toroidal rotation in future fusion devices such as ITER, where external momentum input will be small, accurate simulations of momentum transport are crucial. The evolution equation for gyrocenter toroidal momentum density involves the divergence of the off-diagonal components of the Reynolds and generalized Maxwell stress, while the source term is the radial current of gyrocenters. The time evolution of the polarization field is the opposite of the gyrocenter current. Hence, an evolution equation for the total momentum density, i.e., the sum of gyrocenter and polarization field toroidal momentum density can be written. The force balance equation and the toroidal momentum conservation equations have been numerically tested with the gysela code. They are satisfied with a high level of accuracy.

Energy and angular momentum storage in a rotating magnet

We consider a cylindrical metallic magnet that is set into rotation about a horizontal axis by a falling mass. In such a system the magnetic field causes a radial current which is non-solenoidal. The current leads to charge accumulation and a partial attenuation of the radial current. The magnetic field acting on the radially flowing current slows down the acceleration. We evaluate the angular velocity and displacement using Newtonian dynamics. We show that the electromagnetic angular momentum must be taken into account to calculate the change in the angular momentum due to the external torque on the system. The loss in the potential energy of the falling mass can be explained only by taking into consideration the electrostatic energy and the Joule loss.

Momentum balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas

We have investigated the influence of symmetry properties of toroidal magnetic configurations on the mechanisms used for determining the radial electric field such as the momentum balance and the ambipolar particle transport. Both neoclassical and anomalous transport of particles, heat and momentum in axisymmetric and nonaxisymmetric toroidal systems are taken into account. Generally, in nonaxisymmetric systems, the radial electric field is determined by the neoclassical ambipolarity condition. For axisymmetric systems with up–down symmetry and quasisymmetric systems with stellarator symmetry, it is shown using a novel parity transformation that the particle fluxes are automatically ambipolar up to and the determination of the radial electric field Es requires solving the momentum balance equations, where δ denotes the ratio of the thermal gyroradius to the characteristic equilibrium scale length. In axisymmetric systems with large E × B flows on the order of the ion thermal velocity vTi, the radial fluxes of particles, heat and toroidal momentum are dependent on Es and its radial derivative while the time evolution of the Es profile is governed by the toroidal momentum balance equation. In nonaxisymmetric systems, E × B flows of are not generally allowed even in the presence of quasisymmetry because the nonzero radial current is produced by the large flow term in the equilibrium force balance for which the Boozer and Hamada coordinates cannot be constructed.

OHMIC DISSIPATION IN THE ATMOSPHERES OF HOT JUPITERS

Hot Jupiter atmospheres exhibit fast, weakly-ionized winds. The interaction of these winds with the planetary magnetic field generates drag on the winds and leads to ohmic dissipation of the induced electric currents. We study the magnitude of ohmic dissipation in representative, three-dimensional atmospheric circulation models of the hot Jupiter HD 209458b. We find that ohmic dissipation can reach or exceed 1% of the stellar insolation power in the deepest atmospheric layers, in models with and without dragged winds. Such power, dissipated in the deep atmosphere, appears sufficient to slow down planetary contraction and explain the typically inflated radii of hot Jupiters. This atmospheric scenario does not require a top insulating layer or radial currents that penetrate deep in the planetary interior. Circulation in the deepest atmospheric layers may actually be driven by spatially non-uniform ohmic dissipation. A consistent treatment of magnetic drag and ohmic dissipation is required to further elucidate the consequences of magnetic effects for the atmospheres and the contracting interiors of hot Jupiters.

Measurements of Transmembrane Potential and Magnetic Field at the Apex of the Heart

We studied the transmembrane potential and magnetic fields from electrical activity at the apex of the isolated rabbit heart experimentally using optical mapping and superconducting quantum interference device microscopy, and theoretically using monodomain and bidomain models. The cardiac apex has a complex spiral fiber architecture that plays an important role in the development and propagation of action currents during stimulation at the apex. This spiral fiber orientation contains both radial electric currents that contribute to the electrocardiogram and electrically silent circular currents that cannot be detected by the electrocardiogram but are detectable by their magnetic field, B z . In our experiments, the transmembrane potential, V m , was first measured optically and then B z was measured with a superconducting quantum interference device microscope. Based on a simple model of the spiral structure of the apex, V m was expected to exhibit circular wave front patterns and B z to reflect the circular component of the action currents. Although the circular V m wave fronts were detected, the B z maps were not as simple as expected. However, we observed a pattern consistent with a tilted axis for the apex spiral fiber geometry. We were able to simulate similar patterns in both a monodomain model of a tilted stack of rings of dipole current and a bidomain model of a tilted stack of spiraled cardiac tissue that was stimulated at the apex. The fact that the spatial pattern of the magnetic data was more complex than the simple circles observed for V m suggests that the magnetic data contain information that cannot be found electrically.

HF Radar Performance in a Low-Energy Environment: CODAR SeaSonde Experience on the West Florida Shelf*

AbstractThree long-range (5 MHz) Coastal Ocean Dynamics Application Radar (CODAR) SeaSonde HF radars overlooking an array of as many as eight moored acoustic Doppler current profilers (ADCPs) have operated on the West Florida Shelf since September 2003 for the purpose of observing the coastal ocean currents. HF radar performance on this low-energy (currents and waves) continental shelf is evaluated with respect to data returns, the rms differences between the HF radar and the ADCP radial currents, bearing offsets, and radial velocity uncertainties. Possible environmental factors affecting the HF radar performance are discussed, with the findings that both the low-energy sea state and the unfavorable surface wave directions are the main limiting factors for these HF radar observations of currents on the WFS. Despite the challenge of achieving continuous backscatter from this low-energy environment, when acquired the data quality is good in comparison with the ADCP measurements. The rms differences range from 6 to 10 cm s−1 for hourly and from 3 to 6 cm s−1 for 36-h low-pass-filtered radial currents, respectively. Bearing offsets are in the range from −15° to +9°. Coherent variations of the HF radar and ADCP radial currents are seen across both tidal and subtidal frequency bands. By examining the HF radar radial velocities at low wave energy, it is found that the data returns decrease rapidly for significant wave heights smaller than 1 m, and that the rms differences between the HF radar and ADCP radials are degraded when the significant wave height is smaller than 0.3 m.

Magnetosphere‐ionosphere coupling at Jupiter: Effect of field‐aligned potentials on angular momentum transport

We present a time‐independent model of Jupiter's rotation‐driven aurora based on angular momentum conservation, including the effects of a field‐aligned potential () and an ionospheric conductivity that is modified by precipitating electrons. We argue that arises from a limit to field‐aligned current at high latitudes, and hence, we apply a current‐voltage relation, which takes into account the low plasma densities at high latitudes. The resulting set of nonlinear equations that govern the behavior of angular momentum transfer is underconstrained and leads to a set of solutions, including those derived in earlier work. We show that solutions with high angular momentum transfer, large radial currents, and small mass transport rates ( ≤ 1000 kg/s) exist. Our set of solutions can reproduce many of the observed characteristics of Jupiter's main auroral oval, including the energy of the precipitating electrons, the energy flux into the ionosphere, the width of the aurora at the ionosphere, and net radial current across the field for a radial mass transport value of ∼500 kg/s.

Estimation and Assessment of Errors Related to Antenna Pattern Distortion in CODAR SeaSonde High-Frequency Radar Ocean Current Measurements

Abstract A simulation-based investigation of errors in HF radar–derived, near-surface ocean current measurements is presented. The simulation model is specific to Coastal Ocean Dynamics Application Radar (CODAR) SeaSonde radar systems that employ a compact, collocated antenna geometry. In this study, radial current retrievals are obtained by processing simulated data using unmodified CODAR data processing software. To avoid limiting the results to specific ocean current and wind wave scenarios, the analyses employ large ensembles of randomly varying simulated environmental conditions. The effect of antenna pattern distortion on the accuracy of retrievals is investigated using 40 different antenna sensitivity patterns of varying levels of distortion. A single parameter is derived to describe the level of the antenna pattern distortion. This parameter is found to be highly correlated with the rms error of the simulated radial currents (r = 0.94) and therefore can be used as a basis for evaluating the severity of site-specific antenna pattern distortions. Ensemble averages of the subperiod simulated current retrieval standard deviations are found to be highly correlated with the antenna pattern distortion parameter (r = 0.92). Simulations without distortions of the antenna pattern indicate that an rms radial current error of 2.9 cm s−1 is a minimum bound on the error of a SeaSonde ocean radar system, given a typical set of operating parameters and a generalized ensemble of ocean conditions.

Validation of Surface Current Measurements in the Northern Adriatic Sea from High-Frequency Radars

Abstract The performances of a shore-based high-frequency (HF) radar network deployed along the coast of the Venice lagoon (northern Adriatic Sea) are discussed based on a comparison with a single bottom-mounted ADCP deployed in the shallow-water area offshore of the lagoon for a 40-day period in August–September 2005. The analyses, carried out using currents representative of the first meter for the HF radars and 2.5 m for the ADCP, gave rms differences of radial currents in the range of 8.7–14.7 cm s−1 (correlation 0.37– 0.82) for the ideal pattern and 8.4–20.5 cm s−1 (correlation 0.14–0.84) for the measured pattern. Good correlation was found between surface current vectors and moored data (scalar correlation up to R = 0.83, vector correlation ρ = 0.78, veering angle 6°). Comparison metrics were improved for the low-passed currents. Angular offsets ranged between +6° and +11°. Differences depended primarily on the geophysical variability within the water column. Bearing offsets also contributed because they lead to comparisons with radial velocities at erroneous angular sectors. Radar performances were severely affected by strong northeasterly wind pulses in their early stages. An increased broadband noise, spread over the entire Doppler spectrum across all ranges to the antennas, masked the Bragg peaks and determined the loss in radar coverage, introducing gross underestimations of both radial velocities and total currents.

High energy density plasmas generated by radial foil explosions

High energy density (HED) plasmas, produced by diverse techniques, such as lasers or pulsed power generators, can help scientists to better understand extreme states of matter as well as astrophysical phenomena. While fast Z-pinches are the most common approach to generating HED plasmas in the pulsed power community, radial foil configurations can yield plasma pressures on the order of 0.5 Mbar on a 1 MA, 100 ns current rise time generator, similar to wire array configurations producing Z-pinches. In this experimental setup, a thin metallic foil stretched onto a circular anode connects to a very small ‘pin’ cathode at the center. Radial currents flow in the foil then down the pin cathode, thereby generating an axi-symmetric toroidal magnetic field under the foil. Initial experimental results (Gourdain et al 2010 Phys. Plasmas 17 012706) showed that the foil current interacts with this field and the resulting J × B force lifts the foil upward. Very rapidly the foil plasma turns into a bubble-shaped cavity above the central pin, and that bubble expands at 300 km s−1, until instabilities destroy the axial symmetry, bursting the bubble open. This paper complements these initial results by using time-integrated x-ray pin-hole cameras and a focusing spectrometer with spatial resolution. In addition to laser interferometry, these new data help to provide a better estimate of the plasma electron density inside the bubble, above 1020 cm−3, and of the electron temperature, between 300 and 400 eV inside the central plasma column. We also discovered the presence of ‘bright’ spots in the plasma, with densities larger than 5 × 1021 electrons cm−3 and temperatures above 1 keV. Finally laser interferometry gives a precise mapping of the initial plasma jet and bubble areal densities.

Jovian magnetosphere–ionosphere current system characterized by diurnal variation of ionospheric conductance

We developed a new numerical model of the Jovian magnetosphere–ionosphere coupling current system in order to investigate the effects of diurnal variation of ionospheric conductance. The conductance is determined by ion chemical processes that include the generation of hydrogen and hydrocarbon ions by solar EUV radiation and auroral electrons precipitation. The model solves the torque equations for magnetospheric plasma accelerated by the radial currents flowing along the magnetospheric equator. The conductance and magnetospheric plasma then change the field-aligned currents (FACs) and the intensity of the electric field projected onto the ionosphere. Because of the positive feedback of the ionospheric conductance on the FAC, the FAC is the maximum on the dayside and minimum just before sunrise. The power transferred from the planetary rotation is mainly consumed in the upper atmosphere on the dayside, while it is used for magnetospheric plasma acceleration in other local time (LT) sectors. Further, our simulations show that the magnetospheric plasma density and mass flux affect the temporal variation in the peak FAC density. The enhancement of the solar EUV flux by a factor of 2.4 increases the FAC density by 30%. The maximum density of the FAC is determined not only by the relationship between the precipitating electron flux and ionospheric conductance, but also by the system inertia, i.e., the inertia of the magnetospheric plasma. A theoretical analysis and numerical simulations reveal that the FAC density is in proportion to the planetary angular velocity on the dayside and to the square of the planetary angular velocity on the nightside. When the radial current at the outer boundary is fixed at values above 30 MA, as assumed in previous model studies, the peak FAC density determined at latitude 73°–74° is larger than the diurnal variable component. This result suggests large effects of this assumed radial current at the outer boundary on the system.