Supercritical Core Research Articles

Convective inhibition with an ocean

Aims.In this work we generalize the notion of convective inhibition to apply it to cases where there is an infinite reservoir of condensible species (i.e., an ocean). We propose a new model for the internal structure and thermal evolution of super-Earths with hydrogen envelopes.Methods.We derive the criterion for convective inhibition in a generalized phase mixture from first principles thermodynamics. We then investigate the global ocean case using a water-hydrogen system, for which we have data, as an example. After illustrating the relevant thermodynamics, we extend our arguments to apply to a system of hydrogen and silicate vapor. We then employ a simple atmospheric model to apply our findings to super-Earths and to make predictions about their internal structures and thermal evolution.Results.For hydrogen envelope masses roughly in the range 10−3−10−1M⊕, convective contact between the envelope and core may shut down because of the compositional gradient that arises from silicate partial vaporization. For envelope hydrogen masses that cause the associated basal pressure to exceed the critical pressure of pure silicate (on the order of a couple kilobars), the base of that envelope and the top of the core lie on the critical line of the two-phase hydrogen-silicate phase diagram. The corresponding temperature is much higher than convective models would suggest. The core is then “supercritical” in the sense that the temperature exceeds the critical temperature for pure silicate. The core then cools inefficiently, with intrinsic heat fluxes potentially comparable to the Earth’s internal heat flux today.Conclusions.This low heat flux may allow the core to remain in a high entropy supercritical state for billions of years, but the details of this depend on the nature of the two-component phase diagram at high pressure, something that is currently unknown. A supercritical core thermodynamically permits the dissolution of large quantities of hydrogen into the core.

Analysis of numerical studies on the thermal-hydraulic and neutronic thermal-hydraulic stability of supercritical water reactors

The paper presents a review of modern studies on the potential types of coolant flow instabilities in the supercritical water reactor core. These instabilities have a negative impact on the operational safety of nuclear power plants. Despite the impressive number of computational works devoted to this topic, there still remain unresolved problems. The main disadvantages of the models are associated with the use of one simulated channel instead of a system of two or more parallel channels, the lack consideration for neutronic feedbacks, and the problem of choosing the design ratios for the heat transfer coefficient and hydraulic resistance coefficient under conditions of supercritical water flow. For this reason, it was decided to conduct an analysis that will make it possible to highlight the indicated problems and, on their basis, to formulate general requirements for a model of a nuclear reactor with a light-water supercritical pressure coolant. Consideration is also given to the features of the coolant flow stability in the supercritical water reactor core. In conclusion, the authors note the importance of further computational work using complex models of neutronic thermal-hydraulic stability built on the basis of modern achievements in the field of neutron physics and thermal physics.

MIGRATION AND GROWTH OF PROTOPLANETARY EMBRYOS. III. MASS AND METALLICITY DEPENDENCE FOR FGKM MAIN-SEQUENCE STARS

ABSTRACT Radial velocity and transit surveys have found that the fraction of FGKM stars with close-in super-Earth(s) (η ⊕) is around 30%–50%, independent of the stellar mass M * and metallicity Z *. In contrast, the fraction of solar-type stars harboring one or more gas giants (η J) with masses M p > 100 M ⊕ is nearly 10%–15%, and it appears to increase with both M * and Z *. Regardless of the properties of their host stars, the total mass of some multiple super-Earths systems exceeds the core mass of Jupiter and Saturn. We suggest that both super-Earths and supercritical cores of gas giants were assembled from a population of embryos that underwent convergent type I migration from their birthplaces to a transition location between viscously heated and irradiation-heated disk regions. We attribute the cause for the η ⊕–η J dichotomy to conditions required for embryos to merge and to acquire supercritical core mass ( ) for the onset of efficient gaseous envelope accretion. We translate this condition into a critical disk accretion rate, and our analysis and simulation results show that it weakly depends on M * and decreases with metallicity of disk gas Z d. We find that embryos are more likely to merge into supercritical cores around relatively massive and metal-rich stars. This dependence accounts for the observed η J–M *. We also consider the dispersed relationship and reproduce the observed η J–Z * correlation.

Fuel Assembly Design for Supercritical Water-Cooled Reactor

The supercritical water-cooled reactor (SWCR) has been selected as one of the most promising reactors for Generation IV nuclear reactors due to its higher thermal efficiency and more simplified structure compared to the state-of-the-art light water reactors (LWRs). However, there are a large number of potential problems that must be addressed, particularly the fuel assembly design of the SCWR. SCWRs are a kind of high-temperature, high-pressure, water-cooled reactor that operates above the thermodynamic critical point of water (374°C, 22.1 MPa). Corrosion and degradation of materials used in supercritical water environments are determined by several environment- and material-dependent factors. In particular, irradiation-induced changes in microstructure and microchemistry are major concerns in a nuclear reactor. Many structural materials including alloys and ceramics have been proposed for use as SCWR components or materials for applying protective coatings in SCWRs. In this paper, the present status of supercritical fuel assembly design at home and abroad is reported. According to the special requirements of supercritical core design, a kind of configuration design of fuel assembly with two-flow core and using SiC as cladding material are proposed. The analysis results have shown that the design basically meets the requirements of fuel assembly design, which has good feasibility and performance.

Dynamic transition in supercritical iron.

Recent advance in understanding the supercritical state posits the existence of a new line above the critical point separating two physically distinct states of matter: rigid liquid and non-rigid gas-like fluid. The location of this line, the Frenkel line, remains unknown for important real systems. Here, we map the Frenkel line on the phase diagram of supercritical iron using molecular dynamics simulations. On the basis of our data, we propose a general recipe to locate the Frenkel line for any system, the recipe that importantly does not involve system-specific detailed calculations and relies on the knowledge of the melting line only. We further discuss the relationship between the Frenkel line and the metal-insulator transition in supercritical liquid metals. Our results enable predicting the state of supercritical iron in several conditions of interest. In particular, we predict that liquid iron in the Jupiter core is in the “rigid liquid” state and is highly conducting. We finally analyse the evolution of iron conductivity in the core of smaller planets such as Earth and Venus as well as exoplanets: as planets cool off, the supercritical core undergoes the transition to the rigid-liquid conducting state at the Frenkel line.

THE COLLAPSE OF TURBULENT CORES AND RECONNECTION DIFFUSION

For a molecular cloud clump to form stars some transport of magnetic flux is required from the denser, inner regions to the outer regions of the cloud, otherwise this can prevent the collapse. Fast magnetic reconnection which takes place in the presence of turbulence can induce a process of reconnection diffusion (RD). Extending earlier numerical studies of reconnection diffusion in cylindrical clouds, we consider more realistic clouds with spherical gravitational potentials and also account for the effects of the gas self-gravity. We demonstrate that within our setup RD is efficient. We have also identified the conditions under which RD becomes strong enough to make an initially subcritical cloud clump supercritical and induce its collapse. Our results indicate that the formation of a supercritical core is regulated by a complex interplay between gravity, self-gravity, the magnetic field strength and nearly transonic and trans-Alfv\'enic turbulence, confirming that RD is able to remove magnetic flux from collapsing clumps, but only a few of them become nearly critical or supercritical, sub-Alfv\'enic cores, which is consistent with the observations. Besides, we have found that the supercritical cores built up in our simulations develop a predominantly helical magnetic field geometry which is also consistent with observations. Finally, we have evaluated the effective values of the turbulent reconnection diffusion coefficient and found that they are much larger than the numerical diffusion, especially for initially trans-Alfv\'enic clouds, ensuring that the detected magnetic flux removal is due to to the action of the RD rather than to numerical diffusivity.

DR 21(OH): A HIGHLY FRAGMENTED, MAGNETIZED, TURBULENT DENSE CORE

We present high-angular-resolution observations of the massive star forming core DR21(OH) at 880 mum using the Submillimeter Array (SMA). The dense core exhibits an overall velocity gradient in a Keplerian-like pattern, which breaks at the center of the core where SMA 6 and SMA 7 are located. The dust polarization shows a complex magnetic field, compatible with a toroidal configuration. This is in contrast with the large, parsec-scale filament that surrounds the core, where there is a smooth magnetic field. The total magnetic field strengths in the filament and in the core are 0.9 and 2.1 mG, respectively. We found evidence of magnetic field diffusion at the core scales, far beyond the expected value for ambipolar diffusion. It is possible that the diffusion arises from fast magnetic reconnection in the presence of turbulence. The dynamics of the DR 21(OH) core appear to be controlled energetically in equal parts by the magnetic field, magneto-hydrodynamic (MHD) turbulence and the angular momentum. The effect of the angular momentum (this is a fast rotating core) is probably causing the observed toroidal field configuration. Yet, gravitation overwhelms all the forces, making this a clear supercritical core with a mass-to-flux ratio of ~6 times the critical value. However, simulations show that this is not enough for the high level of fragmentation observed at 1000 AU scales. Thus, rotation and outflow feedback is probably the main cause of the observed fragmentation.

Numerical Study on the Heat Transfer Characteristics of Supercritical Water in Enhanced Sub-Channels in Reactors

The characteristics of heat transfer enhancement and deterioration in supercritical water reactor core is essential to the reactor efficiency and security. At present, there exists deficiency in the study of core enhanced channels. Two different fins arrangements of the enhanced channels are designed in present paper, which are long-strip fins and equal-distance short fins. At the conditions of the supercritical pressure of 25MPa, the inlet temperature of 350°C and different inlet velocities, the heat transfer enhancement and deterioration characteristics of water flowing in the two different fins arrangements of the enhanced channels were studied and comparatively analyzed. The results show that the heat transfer is enhanced in the channels with fins. The heat transfer enhancement is better in the channel with equal-distance short fins when lower input velocity, better in the channel with long-strip fins when high input velocity. The surface heat transfer coefficients increase with the velocity increases; the surface heat transfer coefficients in equal-distance short fins is two to three times than that in the channel without fins. There exists heat transfer deterioration when the input velocity is lower in the channel without fins and with long-strip fins, no deterioration occurs in the channel with equal-distance short fins. The channel with equal-distance short fins is a relatively reasonable of the three channels.

The non-isothermal stage of magnetic star formation - II. Results

In a previous paper we formulated the problem of the formation and evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in axisymmetric geometry, accounting for the effects of ambipolar diffusion and Ohmic dissipation, grain chemistry and dynamics, and radiative transfer. Here we present results of star formation simulations that accurately track the evolution of a protostellar fragment over eleven orders of magnitude in density (from 300 cm^-3 to \approx 10^14 cm^-3), i.e., from the early ambipolar-diffusion--initiated fragmentation phase, through the magnetically supercritical, dynamical-contraction phase and the subsequent magnetic decoupling stage, to the formation of a protostellar core in near hydrostatic equilibrium. As found by Fiedler & Mouschovias (1993), gravitationally-driven ambipolar diffusion leads to the formation and subsequent dynamic contraction of a magnetically supercritical core. Moreover, we find that ambipolar diffusion, not Ohmic dissipation, is responsible for decoupling all the species except the electrons from the magnetic field, by a density \approx 3 x 10^12 cm^-3. Magnetic decoupling precedes the formation of a central stellar object and ultimately gives rise to a concentration of magnetic flux (a `magnetic wall') outside the hydrostatic core --- as also found by Tassis & Mouschovias (2005a,b) through a different approach. At approximately the same density at which Ohmic dissipation becomes more important than ambipolar diffusion (\gtrsim 7 x 10^12 cm^-3), the grains carry most of the electric charge as well as the electric current. The prestellar core remains disclike down to radii ~ 10 AU, inside which thermal pressure becomes important. The magnetic flux problem of star formation is resolved for at least strongly magnetic newborn stars by this stage of the evolution, i.e., by a central density \approx 10^14 cm^-3. The hydrostatic core has radius \approx 2 AU, density \approx 10^14 cm^-3, temperature \approx 300 K, magnetic field strength \approx 0.2 G, magnetic flux \approx 5 x 10^18 Wb, luminosity ~ 10^-3 L_\odot, and mass ~ 10^-2 M_\odot.

New 237Np Burning Strategy in a Supercritical CO2-Cooled Fast Reactor Core Attaining Zero Burnup Reactivity Loss

A new 237Np burning strategy in a supercritical CO2-cooled fast reactor core has been proposed: consuming 237Np as fuel and burnable poison to attain zero burnup reactivity loss. Addition of 237Np at content of 6.5 wt% in fuel engenders nearly zero burnup reactivity loss of 0.02% Δk/k during 10 yr. The burning rate of 237Np in the core is ~69 kg/yr, which is equivalent to the quantity produced in a year from about 20 light water reactors of equivalent electrical output. The zero burnup reactivity loss enables reduction of the control rod number to half that of a typical sodium-cooled mixed-oxide fuel MONJU core without added 237Np and no need for rod operation with fuel burning to compensate for the burnup reactivity loss. Void reactivity is 0.72% Δk/kk’, which is three-fourths that of a typical Na-cooled core, although 237Np is added and the active core length is elongated to 1.2 m. The power density is reduced to ~20% of that in a Na-cooled core. The hot-spot temperature of cladding is below its maximum permissible temperature of 700°C.

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment. III. A Parameter Study

In two previous papers we formulated and solved, for a fiducial set of free parameters, the problem of the formation and evolution of a magnetically supercritical core inside a magnetically subcritical parent cloud. In this paper we present a parameter study to assess the sensitivity of the results (1) to the density at which the equation of state becomes adiabatic; (2) to the initial mass-to-flux ratio of the parent cloud; and (3) to ionization by radioactive decay of different nuclei (40K and 26Al) at high densities (number density > 10^12 particles per cubic cm). We find that (1) the results depend only slightly on the density at which the onset of adiabaticity occurs; (2) memory of the initial mass-to-flux ratio is completely lost at late times, which emphasizes the relevance of this work, idependently of the adopted theory of core formation; and (3) the precise source of radioactive ionization alters the degree of attachment of the electrons to the field lines (at high densities), and the relative importance of ambipolar diffusion and Ohmic dissipation in reducing the magnetic flux of the protostar. The value of the magnetic field at the end of the runs is insensitive to the values of the free parameters and in excellent agreement with meteoritic measurements of the protosolar nebula magnetic field. The magnetic flux problem of star formation is resolved for at least strongly magnetic newborn stars. A complete detachment of the magnetic field from the matter is unlikely. The formation of a "magnetic wall" (with an associated magnetic shock) is independent of the assumed equation of state, although the process is enhanced and accelerated by the formation of a central hydrostatic core.

The Origin of Episodic Accretion Bursts in the Early Stages of Star Formation

We study numerically the evolution of rotating cloud cores, from the collapse of a magnetically supercritical core to the formation of a protostar and the development of a protostellar disk during the main accretion phase. We find that the disk quickly becomes unstable to the development of a spiral structure similar to that observed recently in AB Aurigae. A continuous infall of matter from the protostellar envelope makes the protostellar disk unstable, leading to spiral arms and the formation of dense protostellar/protoplanetary clumps within them. The growing strength of spiral arms and ensuing redistribution of mass and angular momentum creates a strong centrifugal disbalance in the disk and triggers bursts of mass accretion during which the dense protostellar/protoplanetary clumps fall onto the central protostar. These episodes of clump infall may manifest themselves as episodes of vigorous accretion (≥10-4 M☉ yr-1), as is observed in FU Orionis variables. Between these accretion bursts, the protostar is characterized by a low accretion rate (<10-6 M☉ yr-1). During the phase of episodic accretion, the mass of the protostellar disk remains less than the mass of the protostar.

Neutron-kinetic code validation against measurements in the Moscow V-1000 zero-power facility

Measurements carried out in an original-size VVER-1000 mock-up (V-1000 facility, Kurchatov Institute, Moscow) were used for the validation of three-dimensional neutron-kinetic codes, designed for VVER safety calculations. The significant neutron flux tilt measured in the V-1000 core, which is caused only by radial-reflector asymmetries, was successfully modeled. A good agreement between calculated and measured steady-state powers has been achieved, for relative assembly powers and inner-assembly pin power distributions. Calculated effective multiplication factors exceed unity in all cases. The time behaviour of local powers, measured during two transients that were initiated by control rod moving in a slightly super-critical core, has been well simulated by the neutron-kinetic codes.

Does Magnetic Levitation or Suspension Define the Masses of Forming Stars?

We investigate whether magnetic tension can define the masses of forming stars by holding up the subcritical envelope of a molecular cloud that suffers gravitational collapse of its supercritical core. We perform an equilibrium analysis of the initial and final states assuming perfect field freezing, no rotation, isothermality, and a completely flattened configuration. The sheet geometry allows us to separate the magnetic tension into a levitation associated with the split monopole formed by the trapped flux of the central star and a suspension associated with curved field lines that thread the static pseudodisk and envelope of material external to the star. We find solutions where the eigenvalue for the stellar mass is a fixed multiple of the initial core mass of the cloud. We verify the analytically derived result by an explicit numerical simulation of a closely related three-dimensional axisymmetric system. However, with field freezing, the implied surface magnetic fields much exceed measured values for young stars. If the pinch by the central split monopole were to be eliminated by magnetic reconnection, then magnetic suspension alone cannot keep the subcritical envelope (i.e., the entire model cloud) from falling onto the star. We argue that this answer has general validity, even if the initial state lacked any kind of symmetry, possessed rotation, and had a substantial level of turbulence. These findings strongly support a picture for the halt of infall that invokes dynamic levitation by YSO winds and jets, but the breakdown of ideal magnetohydrodynamics is required to allow the appearance in the problem of a rapidly rotating, centrifugally supported disk. We use these results to calculate the initial mass function and star formation efficiency for the distributed and clustered modes of star formation.

Binary and Multiple Star Formation in Magnetic Clouds: Bar Growth and Fragmentation

We study the non-axisymmetric evolution of magnetized clouds, using a 2D MHD code based on the physically motivated thin-disk approximation. We found that such clouds become unstable to non-axisymmetric perturbations after the supercritical cores are formed due to ambipolar diffusion. We show that for a wide range of initial cloud parameters, the $m=2$ mode grows nonlinearly into a bar during the isothermal collapse after the supercritical core formation. The supercritical core can break up into fragments during or after the isothermal phase of cloud evolution. The outcome of fragmentation depends on the initial cloud conditions, such as the magnetic field strength, rotation rate, amount of cloud mass and mass distribution. It is classified into three different types: (1) separate core formation, (2) bar fragmentation, and (3) disk fragmentation. These three types of fragmentation loosely correspond to the empirical classification of embedded binary and multiple systems of Looney, Mundy, & Welch, based on millimeter dust continuum observations. The well-studied starless core, L1544, appears to belong to the bar fragmentation type. We expect it to produce a highly elongated, opaque bar at the center in the future, which should break up into fragments of initial masses in the substellar regime.

On the Timescale for the Formation of Protostellar Cores in Magnetic Interstellar Clouds

We revisit the problem of the formation of dense protostellar cores due to ambipolar diffusion within magnetically supported molecular clouds, and derive an analytical expression for the core formation timescale. The resulting expression is similar to the canonical expression ≃ � 2 ff /�ni ∼ 10�ff (whereff is the free-fall time andni is the neutral-ion collision time), except that it is multiplied by a numerical factor C(µc0), where µc0 is the initial central mass-to-flux ratio normalized to the critical value for gravitational collapse. C(µc0) is typically ∼ 1 in highly subcritical clouds (µc0 ≪ 1), although certain conditions allow C(µc0) ≫ 1. For clouds that are not highly subcritical, C(µc0) can be much less than unity, with C(µc0) → 0 for µc0 → 1, significantly reducing the time required to form a supercritical core. This, along with recent observations of clouds with mass-to-flux ratios close to the critical value, may reconcile the results of ambipolar diffusion models with statistical analyses of cores and YSO's which suggest an evolutionary timescale ∼ 1 Myr for objects of mean density ∼ 10 4 cm −3 . We compare our analytical relation to the results of numerical simulations, and also discuss the effects of dust grains on the core formation timescale. Subject headings: diffusion — dust, extinction — ISM: abundances — ISM: clouds — ISM: magnetic fields — MHD — plasmas — stars: formation

Consistency of Ambipolar Diffusion Models with Infall in the L1544 Protostellar Core

Recent high-resolution studies of the L1544 protostellar core by Tafalla et al. and Williams et al. reveal the structure and the kinematics of the gas. The observations of this prestellar core provide a natural test for theoretical models of core formation and evolution. Based on their results, the above authors claim a discrepancy with the implied infall motions from ambipolar diffusion models. In this paper, we reexamine the earlier ambipolar diffusion models and conclude that the L1544 core can be understood to be a magnetically supercritical core undergoing magnetically diluted collapse. We also present a new ambipolar diffusion model specifically designed to simulate the formation and evolution of the L1544 core. This model, which uses reasonable input parameters, yields mass and radial density distributions, as well as neutral and ion infall speed profiles, that are in very good agreement with physical values deduced by observations. The lifetime of the core is also in good agreement with mean prestellar core lifetimes estimated from statistics of an ensemble of cores. The observational input can act to constrain other currently unobserved quantities, such as the degree of ionization and the background magnetic field strength and orientation near the L1544 core.

Magnetic Braking, Ambipolar Diffusion, and the Formation of Cloud Cores and Protostars. II. A Parameter Study

The formulation of the problem of the formation of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds was presented in a previous paper, where detailed numerical simulations for two different model clouds were also discussed. In this paper, we study the effect of varying five dimensionless free parameters: the ratio <SUP>∼</SUP>p of external density and central density in a reference state (which is related simply to an initial equilibrium state), the initial radial length scale l<SUP>∼</SUP><SUB>ref</SUB> of the column density of the cloud, the central angular velocity of the reference state <SUP>∼</SUP>Ω<SUB>c,ref</SUB>, the central neutral-ion collision time in the reference state <SUP>∼</SUP>τ<SUB>ni,ref</SUB> (which is inversely proportional to the collapse retardation factor V<SUB>ff</SUB> ≡ τ<SUB>ff</SUB>/τ<SUB>ni</SUB>) and the exponent k in the relation between the ion and neutral densities n<SUB>i</SUB> ∝ n<SUP>k</SUP><SUB>n</SUB>. In addition to the models previously presented, seven more models are investigated here. Different values (1/1000 to 1/100) of the initial magnetic-braking efficiency parameter <SUP>∼</SUP>p(&gt;0) do not significantly affect the evolution; magnetic braking remains effective during the quasistatic phase and ineffective during the (dynamic) collapse of the magnetically and thermally supercritical core. The initially very effective magnetic braking also means that the solution is insensitive to values of <SUP>∼</SUP>Ω<SUB>c,ref</SUB>. Different values of l<SUP>∼</SUP><SUB>ref</SUB> yield qualitatively similar evolution, with smaller cloud sizes leading to slightly smaller core sizes. Increasing the value of τ<SUB>ni,ref</SUB> leads to a more rapid evolution and larger, more rapidly rotating cores. A smaller k leads to relatively more rapid evolution in the core and a better core-envelope separation. We also give an analytical explanation of the previously presented result, that the gravitational field acting on an infalling mass shell in the central region of a nonhomologously contracting thin disk increases as 1/r<SUP>3</SUP><SUB>m</SUB>, where r<SUB>m</SUB> is the Lagrangian radius of the shell.