scholarly journals Statistical description of coalescing magnetic islands via magnetic reconnection

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Muni Zhou ◽  
David H. Wu ◽  
Nuno F. Loureiro ◽  
Dmitri A. Uzdensky
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Magnetic Reconnection ◽  
Magnetic Energy ◽  
Initial Distribution ◽  
Two Dimensions ◽  
Magnetic Islands ◽  
Plasma Dynamics ◽  
Dirac Delta ◽  
Physical Environments

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

scholarly journals Three-dimensional magnetic reconnection in astrophysical plasmas

2021 ◽  
Vol 477 (2249) ◽  
Author(s):  
Ting Li ◽  
Eric Priest ◽  
Ruilong Guo
Keyword(s):  
Magnetic Reconnection ◽  
Solar Flares ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Particle Energy ◽  
Two Dimensions ◽  
Three Dimensions ◽  
New Paradigm ◽  
Astrophysical Plasmas ◽  
Fundamental Process

Magnetic reconnection is a fundamental process in laboratory, magnetospheric, solar and astrophysical plasmas, whereby magnetic energy is converted into heat, bulk kinetic energy and fast particle energy. Its nature in two dimensions is much better understood than that in three dimensions, where its character is completely different and has many diverse aspects that are currently being explored. Here, we focus on the magnetohydrodynamics of three-dimensional reconnection in the plasma environment of the Solar System, especially solar flares. The theory of reconnection at null points, separators and quasi-separators is described, together with accounts of numerical simulations and observations of these three types of reconnection. The distinction between separator and quasi-separator reconnection is a theoretical one that is unimportant for the observations of energy release. A new paradigm for solar flares, in which three-dimensional reconnection plays a central role, is proposed.

scholarly journals Annihilation of Magnetic Islands at the Top of Solar Flare Loops

2021 ◽  
Vol 923 (2) ◽  
pp. 227
Author(s):  
Yulei Wang ◽  
Xin Cheng ◽  
Mingde Ding ◽  
Quanming Lu
Keyword(s):  
Magnetic Reconnection ◽  
Thermal Conduction ◽  
Large Scale ◽  
Magnetic Energy ◽  
Small Scale ◽  
Magnetic Islands ◽  
Flare Loop ◽  
Flare Loops ◽  
Flare Model ◽  
Magnetic Energy Release

Abstract The dynamics of magnetic reconnection in the solar current sheet (CS) is studied by high-resolution 2.5-dimensional MHD simulation. With the commencing of magnetic reconnection, a number of magnetic islands are formed intermittently and move quickly upward and downward along the CS. Upon collision with the semi-closed flux of the flare loops, the downflow islands cause a second reconnection with a rate comparable with that in the main CS. Though the time-integrated magnetic energy release is still dominated by the reconnection in the main CS, the second reconnection can release substantial magnetic energy, annihilating the main islands and generating secondary islands with various scales at the flare loop top. The distribution function of the flux of the secondary islands is found to follow a power law varying from f ψ ∼ ψ − 1 (small scale) to ψ −2 (large scale), which seems to be independent to background plasma β and thermal conduction (TC). However, the spatial scale and the strength of the termination shocks driven by the main reconnection outflows or islands decrease if β increases or if TC is included. We suggest that the annihilation of magnetic islands at the flare loop top, which is not included in the standard flare model, plays a nonnegligible role in releasing magnetic energy to heat flare plasma and accelerate particles.

scholarly journals Inverse energy transfer in decaying, three dimensional, nonhelical magnetic turbulence due to magnetic reconnection

2020 ◽  
Author(s):  
Pallavi Bhat ◽  
Muni Zhou ◽  
Nuno F Loureiro
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Conserved Quantities ◽  
Magnetic Islands ◽  
Magnetic Turbulence ◽  
Dynamo Effect ◽  
2D And 3D ◽  
The Magnetic Field

Abstract It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, nonhelical, magnetically dominated, magnetohydrodynamic turbulence in 3-dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and the 3D cases, i.e., the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection timescale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse onto one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed.

scholarly journals Magnetic Energy Release, Plasma Dynamics, and Particle Acceleration in Relativistic Turbulent Magnetic Reconnection

2021 ◽  
Vol 919 (2) ◽  
pp. 111
Author(s):  
Fan Guo ◽  
Xiaocan Li ◽  
William Daughton ◽  
Hui Li ◽  
Patrick Kilian ◽  
...  
Keyword(s):  
Particle Acceleration ◽  
Magnetic Reconnection ◽  
Energy Release ◽  
Magnetic Energy ◽  
Plasma Dynamics ◽  
Magnetic Energy Release

scholarly journals Sterile Neutrinos as Dark Matter: Alternative Production Mechanisms in the Early Universe

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 264
Author(s):  
Daniel Boyanovsky
Keyword(s):  
Dark Matter ◽  
Distribution Function ◽  
Kinetic Equation ◽  
Standard Model ◽  
Early Universe ◽  
Quantum Kinetic Equation ◽  
Sterile Neutrinos ◽  
The Standard Model ◽  
Production Mechanisms ◽  
Freeze Out

We study various production mechanisms of sterile neutrinos in the early universe beyond and within the standard model. We obtain the quantum kinetic equations for production and the distribution function of sterile-like neutrinos at freeze-out, from which we obtain free streaming lengths, equations of state and coarse grained phase space densities. In a simple extension beyond the standard model, in which neutrinos are Yukawa coupled to a Higgs-like scalar, we derive and solve the quantum kinetic equation for sterile production and analyze the freeze-out conditions and clustering properties of this dark matter constituent. We argue that in the mass basis, standard model processes that produce active neutrinos also yield sterile-like neutrinos, leading to various possible production channels. Hence, the final distribution function of sterile-like neutrinos is a result of the various kinematically allowed production processes in the early universe. As an explicit example, we consider production of light sterile neutrinos from pion decay after the QCD phase transition, obtaining the quantum kinetic equation and the distribution function at freeze-out. A sterile-like neutrino with a mass in the keV range produced by this process is a suitable warm dark matter candidate with a free-streaming length of the order of few kpc consistent with cores in dwarf galaxies.

scholarly journals A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

scholarly journals Analytical solution of integro-differential equations describing the process of intense boiling of a superheated liquid

2021 ◽  
Author(s):  
Irina Alexandrova ◽  
Alexander Ivanov ◽  
Dmitri Alexandrov
Keyword(s):  
Distribution Function ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Initial Distribution ◽  
Size Distribution Function ◽  
Superheated Liquid ◽  
Balance Equations ◽  
The Laplace Transform ◽  
And Shifts ◽  
Initial Distribution Function

In this article, an approximate analytical solution of an integro-differential system of equations is constructed, which describes the process of intense boiling of a superheated liquid. The kinetic and balance equations for the bubble-size distribution function and liquid temperature are solved analytically using the Laplace transform and saddle-point methods with allowance for an arbitrary dependence of the bubble growth rate on temperature. The rate of bubble appearance therewith is considered in accordance with the Dering-Volmer and Frenkel-Zeldovich-Kagan nucleation theories. It is shown that the initial distribution function decreases with increasing the dimensionless size of bubbles and shifts to their greater values with time.

scholarly journals On hydrodynamics in the presense of strong external potential field

2021 ◽  
Vol 29 (1) ◽  
pp. 21-28
Author(s):  
A. I. Sokolovsky ◽  
S. A. Sokolovsky
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Potential Field ◽  
Chemical Potential ◽  
Local Equilibrium ◽  
Practical Importance ◽  
External Potential ◽  
Equilibrium Distribution Function ◽  
Kinetic Coefficients ◽  
Functional Hypothesis

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.

Sign in / Sign up

Export Citation Format

Share Document