Pair Cloud Research Articles

The characteristics of rare earth elements in the main water filling sources of Sunan mining area

This study employs rare earth elements to investigate the features and procedures of water-rock interactions within aquifers of loose strata, sandstone, and limestone in the Sunan mining region of North Anhui, China. Through a comparison of the differential characteristics of rare earth elements across primary water sources, we are able to uncover the influence of water-rock interactions on the transfer and conversion of rare earth elements within various water-sediment systems. Indeed, the normalization of water compositions against host rock concentrations revealed a distinct pattern of rare-earth elements for each group of waters. Not only did the absolute concentrations of the elements in each sampling site change, but also the normalized patterns. In contrast to sediment samples, all water samples exhibit a clear enrichment of MREEs, but they also reveal a trend of HREEs enrichment. This is attributed to the differential adsorption effect of oxides on rare earth elements, which is influenced by pH, and the complexation reactions between rare earth elements and carbonate ions. The significant Ho and Ce anomalies in the water-sediment system are associated with robust water rock interactions, whereas the high Ba content significantly impacts the Eu anomaly. The enrichment of Eu is attributed to the interaction between the water environment and the dissolution of minerals rich in Eu. Furthermore, we utilize decision trees and recursive feature elimination techniques for selecting indices, and create a model that incorporates triangular fuzzy numbers (TFN), CRITIC, D-S evidence theory (DSET), factor space (FS), and set pair cloud model (SPCM) to differentiate, describe, and evaluate three distinct groups of waters with varying hydrofacies. The conclusion drawn is that sandstone and limestone aquifers are the main sources of water inrush, with a mixing ratio exceeding 50%. Moreover, this marks the inaugural attempt to utilize patterns of rare-earth elements for establishing a comparison between various water groups, thereby enabling us to distinguish and differentiate depletion patterns resulting from dilution processes from those resulting from precipitation processes, with the aim of determining the contribution rates of mine water. The findings offer valuable insights for predicting water disasters in the Sunan mining area.

Risk Assessment Mmodel of Karst Tunnel Flood Based on Distance Discriminant Weighting and Set Pair Cloud

Flood has become the main hidden threat to the safety of the karst tunnel. Scientific and reasonable flood classification assessment and prevention measures have also become the main problems to be solved urgently in the construction and operation of tunnels. Aiming at the problems of multiple influencing factors, complex index systems, and linear processing of the connection degree of set pair analysis, a set pair cloud model based on cloud theory eigenvalues is proposed to optimize the connection degree of set pair analysis. Regarding the uncertainty of the evaluation system and the ambiguity of the evaluation grade boundary, firstly, the ridge-type membership function is used to determine the basic probability distribution of each measured index. Secondly, the distance discrimination weighting theory based on the index distance is also established, so that each measured index can assign the dynamic weight of the evaluation system. It can comprehensively determine the weight of the cloud connection degree for the system, and draw the cloud level diagram to determine the tunnel flood risk level. Finally, the proposed model is verified with tunnel flood. The results show that the evaluation results are consistent with other evaluation models and actual tunnel conditions. This model can provide guidance for flood prediction and prevention in karst tunnels.

Three-dimensional structure and stability of discontinuities between unmagnetized pair plasma and magnetized electron-proton plasma

We study with a 3D particle-in-cell simulation discontinuities between an electron–positron pair plasma and magnetized electrons and protons. A pair plasma is injected at one simulation boundary with a speed 0.6c along its normal. It expands into an electron-proton plasma and a magnetic field that points orthogonally to the injection direction. Diamagnetic currents expel the magnetic field from within the pair plasma and pile it up in front of it. It pushes electrons, which induces an electric field pulse ahead of the magnetic one. This initial electromagnetic pulse (EMP) confines the pair plasma magnetically and accelerates protons electrically. The fast flow of the injected pair plasma across the protons behind the initial EMP triggers the filamentation instability. Some electrons and positrons cross the injection boundary and build up a second EMP. Electron-cyclotron drift instabilities perturb the plasma ahead of both EMPs seeding a Rayleigh–Taylor (RT)-type instability. Despite equally strong perturbations ahead of both EMPs, the second EMP is much more stable than the initial one. We attribute the rapid collapse of the initial EMP to the filamentation instability, which perturbed the plasma behind it. The RT-type instability transforms the planar EMPs into transition layers, in which magnetic flux ropes and electrostatic forces due to uneven numbers of electrons and positrons slow down and compress the pair plasma and accelerate protons. In our simulation, the expansion speed of the pair cloud decreased by about an order of magnitude and its density increased by the same factor. Its small thickness implies that it is capable of separating a relativistic pair outflow from an electron-proton plasma, which is essential for collimating relativistic jets of pair plasma in collisionless astrophysical plasma.

Two-dimensional particle simulation of the boundary between a hot pair plasma and magnetized electrons and protons: Out-of-plane magnetic field

By means of a particle-in-cell (PIC) simulation, we study the interaction between a uniform magnetized ambient electron–proton plasma at rest and an unmagnetized pair plasma, which we inject at one simulation boundary with a mildly relativistic mean speed and temperature. The magnetic field points out of the simulation plane. The injected pair plasma expels the magnetic field and piles it up at its front. It traps ambient electrons and drags them across the protons. An electric field grows, which accelerates protons into the pair cloud's expansion direction. This electromagnetic pulse separates the pair cloud from the ambient plasma. Electrons and positrons, which drift in the pulse's nonuniform field, trigger an instability that disrupts the current sheet ahead of the pulse. The wave vector of the growing perturbation is orthogonal to the magnetic field direction and magnetic tension cannot stabilize it. The electromagnetic pulse becomes permeable for pair plasma, which forms new electromagnetic pulses ahead of the initial one. A transition layer develops with a thickness of a few proton skin depths, in which protons and positrons are accelerated by strong electromagnetic fields. Protons form dense clumps surrounded by a strong magnetic field. The thickness of the transition layer grows less rapidly than we would expect from the typical speeds of the pair plasma particles and the latter transfer momentum to protons; hence, the transition layer acts as a discontinuity, separating the pair plasma from the ambient plasma. Such a discontinuity is an important building block for astrophysical pair plasma jets.

Collisionless Rayleigh–Taylor-like instability of the boundary between a hot pair plasma and an electron–proton plasma: The undular mode

We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron–positron cloud from a cooler electron–proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an x-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron–proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which is carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collisionless instability similar to a Rayleigh–Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

Risk evaluation of dam-break environmental impacts based on the set pair analysis and cloud model

Many dams have been constructed around the world. Compared with the potential losses of life and economy, the environmental impacts caused by dam breach were less analyzed. As a systematic theory, the set pair analysis method deals with both the certainty and uncertainty of a system or process as a whole. But when dealing with the analysis of environmental impacts with obvious uncertainty, the fuzziness feature of the indices was not considered comprehensively. Hence, this paper introduced the connection degree of set pair analysis in five grades, and the cloud model-based weight calculation method to improve the evaluation. The proposed method was applied to the case study of Qianping Reservoir, Henan Province, China, showing that the comprehensive environmental impacts caused by the potential dam breach were medium. The results of the study indicate that the proposed method is applicative and provides reliability for environmental impacts evaluation of dam breach.

Collisionless tangential discontinuity between pair plasma and electron–proton plasma

We study with a one-dimensional particle-in-cell simulation the expansion of a pair cloud into a magnetized electron–proton plasma as well as the formation and subsequent propagation of a tangential discontinuity that separates both plasmas. Its propagation speed takes the value that balances the magnetic pressure of the discontinuity against the thermal pressure of the pair cloud and the ram pressure of the protons. Protons are accelerated by the discontinuity to a speed that exceeds the fast magnetosonic speed by the factor of 10. A supercritical fast magnetosonic shock forms at the front of this beam. An increasing proton temperature downstream of the shock and ahead of the discontinuity leaves the latter intact. We create the discontinuity by injecting a pair cloud at a simulation boundary into a uniform electron–proton plasma, which is permeated by a perpendicular magnetic field. Collisionless tangential discontinuities in the relativistic pair jets of x-ray binaries (microquasars) are in permanent contact with the relativistic leptons of their inner cocoon, and they become the sources of radio synchrotron emissions.

Structure of a collisionless pair jet in a magnetized electron–proton plasma: flow-aligned magnetic field

Aims. We study the effect a guiding magnetic field has on the formation and structure of a pair jet that propagates through a collisionless electron–proton plasma at rest. Methods. We model with a particle-in-cell (PIC) simulation a pair cloud with a temperature of 400 keV and a mean speed of 0.9c (c - light speed). Pair particles are continuously injected at the boundary. The cloud propagates through a spatially uniform, magnetized, and cool ambient electron–proton plasma at rest. The mean velocity vector of the pair cloud is aligned with the uniform background magnetic field. The pair cloud has a lateral extent of a few ion skin depths. Results. A jet forms in time. Its outer cocoon consists of jet-accelerated ambient plasma and is separated from the inner cocoon by an electromagnetic piston with a thickness that is comparable to the local thermal gyroradius of jet particles. The inner cocoon consists of pair plasma, which lost its directed flow energy while it swept out the background magnetic field and compressed it into the electromagnetic piston. A beam of electrons and positrons moves along the jet spine at its initial speed. Its electrons are slowed down and some positrons are accelerated as they cross the head of the jet. The latter escape upstream along the magnetic field, which yields an excess of megaelectronvolt positrons ahead of the jet. A filamentation instability between positrons and protons accelerates some of the protons, which were located behind the electromagnetic piston at the time it formed, to megaelectronvolt energies. Conclusions. A microscopic pair jet in collisionless plasma has a structure that is similar to that predicted by a hydrodynamic model of relativistic astrophysical pair jets. It is a source of megaelectronvolt positrons. An electromagnetic piston acts as the contact discontinuity between the inner and outer cocoons. It would form on subsecond timescales in a plasma with a density that is comparable to that of the interstellar medium in the rest frame of the latter. A supercritical fast magnetosonic shock will form between the pristine ambient plasma and the jet-accelerated plasma on a timescale that exceeds our simulation time by an order of magnitude.

Cocoon formation by a mildly relativistic pair jet in unmagnetized collisionless electron-proton plasma

By modelling the expansion of a cloud of electrons and positrons with the temperature of 400 keV which propagates at the mean speed of 0.9c (c: speed of light) through an initially unmagnetized electron-proton plasma with a particle-in-cell simulation, we find a mechanism that collimates the pair cloud into a jet. A filamentation (beam-Weibel) instability develops. Its magnetic field collimates the positrons and drives an electrostatic shock into the electron-proton plasma. The magnetic field acts as a discontinuity that separates the protons of the shocked ambient plasma, known as the outer cocoon, from the jet's interior region. The outer cocoon expands at the speed of 0.15c along the jet axis and at 0.03c perpendicularly to it. The filamentation instability converts the jet's directed flow energy into magnetic energy in the inner cocoon. The magnetic discontinuity cannot separate the ambient electrons from the jet electrons. Both species rapidly mix and become indistinguishable. The spatial distribution of the positive charge carriers is in agreement with the distributions of the ambient material and the jet material predicted by a hydrodynamic model apart from a dilute positronic outflow that is accelerated by the electromagnetic field at the jet's head.

Expansion of a mildly relativistic hot pair cloud into an electron-proton plasma

The expansion of a charge-neutral cloud of electrons and positrons with the temperature 1 MeV into an unmagnetized ambient plasma is examined with a 2D particle-in-cell simulation. The pair outflow drives solitary waves in the ambient protons. Their bipolar electric fields attract electrons of the outflowing pair cloud and repel positrons. These fields can reflect some of the protons, thereby accelerating them to almost an MeV. Ion acoustic solitary waves are thus an efficient means to couple energy from the pair cloud to protons. The scattering of the electrons and positrons by the electric field slows down their expansion to a nonrelativistic speed. Only a dilute pair outflow reaches the expansion speed expected from the cloud's thermal speed. Its positrons are more energetic than its electrons. In time, an instability grows at the front of the dense slow-moving part of the pair cloud, which magnetizes the plasma. The instability is driven by the interaction of the outflowing positrons with the protons. These results shed light on how magnetic fields are created and ions are accelerated in pair-loaded astrophysical jets and winds.

One-dimensional thermal pressure-driven expansion of a pair cloud into an electron-proton plasma

Recently, a filamentation instability was observed when a laser-generated pair cloud interacted with an ambient plasma. The magnetic field it drove was strong enough to magnetize and accelerate the ambient electrons. It is of interest to determine if and how pair cloud-driven instabilities can accelerate ions in the laboratory or in astrophysical plasma. For this purpose, the expansion of a localized pair cloud with the temperature 400 keV into a cooler ambient electron-proton plasma is studied by means of one-dimensional particle-in-cell simulations. The cloud's expansion triggers the formation of electron phase space holes that accelerate some protons to MeV energies. Forthcoming lasers might provide the energy needed to create a cloud that can accelerate protons.

Application of Cloud Theory and Set Pair Analysis Coupled Model for Evaluating Environmental Carrying Capacity in Tianjin

Following the development of national economy, environmental pollution and ecological hazards has been resulted from the pollutant discharge and reclamation etc. So it is very important for evaluating the environmental carrying capacity for guiding the environmental management and control. In this paper, a systematic assessment model with detailed procedure for environmental carrying capacity is proposed, based on the combination of set pair analysis method and cloud theory. The membership degree function obtained from bell function in cloud theory is used for connection degree function in set pair analysis method. The normalization means of membership degree has advantageous of improving the reasonability of membership space. The calibration results of case study work well in Tianjin Binhai New District. This shows the coupled model has advantages of concision, easy-operation and high precision of set pair analysis method, and the randomness and ambiguity of assessment indexes’ membership can be reflected in the assessment procedure by using the cloud theory, so the assessment results are reliable and practical significance.

Collisionless reconnection: magnetic field line interaction

Abstract. Magnetic field lines are quantum objects carrying one quantum Φ0 = 2πh/e of magnetic flux and have finite radius λm. Here we argue that they possess a very specific dynamical interaction. Parallel field lines reject each other. When confined to a certain area they form two-dimensional lattices of hexagonal structure. We estimate the filling factor of such an area. Anti-parallel field lines, on the other hand, attract each other. We identify the physical mechanism as being due to the action of the gauge potential field, which we determine quantum mechanically for two parallel and two anti-parallel field lines. The distortion of the quantum electrodynamic vacuum causes a cloud of virtual pairs. We calculate the virtual pair production rate from quantum electrodynamics and estimate the virtual pair cloud density, pair current and Lorentz force density acting on the field lines via the pair cloud. These properties of field line dynamics become important in collisionless reconnection, consistently explaining why and how reconnection can spontaneously set on in the field-free centre of a current sheet below the electron-inertial scale.

Nonlinear Dynamics in the Relativistic Plasma of Astrophysical High‐Energy Sources

Relativistic plasmas are interesting media for particle acceleration, especially when their kinetic pressure is in rough equipartition with the magnetic pressure. Indeed, when in rough equipartition, these relativistic plasmas have generalized Alfven waves that propagate at velocities close to the velocity of light, which makes the acceleration process more efficient than usual. With this in mind, we have investigated some properties that are of interest to several issues in high-energy astrophysics, such as the source of high-energy cosmic rays, the origin of the high-energy emission of blazars and microquasars, the synchrotron radiation of jets, and the gamma-ray bursts of cosmic fireballs. Three types of relativistic plasmas are considered: plasma dominated by the relativistic proton component (high-energy cosmic rays), plasma dominated by highly relativistic electrons (the protons being nonrelativistic), and plasma dominated by relativistic electron-positron pairs. Electron or pair-dominated plasmas are interesting on the one hand because of their fast dynamics, and on other hand because the energy of magnetic perturbations goes directly into the radiative particles. The energy transfer from the electromagnetic perturbations to the particles depends on the nonlinear dynamics. We derive the nonlinear systems that govern the dynamics of these relativistic plasmas close to equipartition. We discuss the possibility of self-modulation instability and soliton formation and demonstrate the existence of a transition at equipartition that has remarkable mathematical properties. We show that particle acceleration in a pair plasma is efficient only when the plasma pressure is below the equipartition value. We give intuitive arguments that this would also be true for the other plasmas, but we do not yet have firm proof. Thus, a pair plasma has a regulation mechanism toward equipartition, since radiation cooling is not efficiently balanced above equipartition. This is an interesting issue for nonthermal radio sources. We have also devised a new kind of collisionless quasi-parallel relativistic shock when a relativistic pair cloud pervades an ambient medium. The proton backstream in the relativistic front drives a monochromatic wave responsible for strong nonlinearities that heat the relativistic plasma. The instability is quenched when the relativistic plasma has been sufficiently heated.