scholarly journals A family of Vlasov–Maxwell equilibrium distribution functions describing a transition from the Harris sheet to the force-free Harris sheet

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
T. Neukirch ◽  
F. Wilson ◽  
O. Allanson
Keyword(s):  
Equilibrium Distribution ◽  
Distribution Functions ◽  
Smooth Transition ◽  
Slight Variation ◽  
Astrophysical Plasmas ◽  
Magnetic Field Profile ◽  
Guide Field ◽  
Alternative Approach ◽  
Potential Applications ◽  
The Magnetic Field

We discuss a family of Vlasov–Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution functions had been briefly discussed by Harrison & Neukirch (Phys. Rev. Lett., vol. 102, (2009a), 135003), but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will be suggested that avoids the problem. This is achieved by considering a slight variation of the magnetic field profile, which allows a smooth transition between the Harris and force-free Harris sheet cases.

Dependence of the a-Si:H Defect Density of States on the Magnetic Field Profile of an Electron Cyclotron Resonance Microwave Plasma

1992 ◽  
Vol 258 ◽  
Author(s):  
F.S. Pool ◽  
J.M. Essick ◽  
Y.H. Shing ◽  
R.T. Mather
Keyword(s):  
Magnetic Field ◽  
Density Of States ◽  
Cyclotron Resonance ◽  
Electron Cyclotron Resonance ◽  
Microwave Plasma ◽  
Defect Density ◽  
Electron Cyclotron ◽  
Field Profile ◽  
Magnetic Field Profile ◽  
The Magnetic Field

ABSTRACTThe magnetic field profile of an electron cyclotron resonance (ECR) microwave plasma was systematically altered to determine subsequent effects on a-Si:H film quality. Films of a-Si:H were deposited at pressures of 0.7 mTorr and 5 mTorr with a H2/SiH4 ratio of approximately three. The mobility gap density of states ND, deposition rate and light to dark conductivity were determined for the a-Si:H films. This data was correlated to the magnetic field profile of the plasma, which was characterized by Langmuir probe measurements of the ion current density. By variation of the magnetic field profile ND could be altered by more than an order of magnitude, from 1×1016 to 1×1017 at 0.7 mTorr and 1×1016 to 5×1017 at 5 mTorr. Two deposition regimes were found to occur for the conditions of this study. Highly divergent magnetic fields resulted in poor quality a-Si:H, while for magnetic field profiles defining a more highly confined plasma, the a-Si:H was of device quality and relatively independent of the magnetic field configuration.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

scholarly journals Diffusion at the Earth magnetopause: enhancement by Kelvin-Helmholtz instability

2007 ◽  
Vol 25 (1) ◽  
pp. 271-282 ◽  
Author(s):  
R. Smets ◽  
G. Belmont ◽  
D. Delcourt ◽  
L. Rezeau
Keyword(s):  
Magnetic Field ◽  
Distribution Functions ◽  
Larmor Radius ◽  
Simple Analytical Model ◽  
Helmholtz Instability ◽  
Field Reversal ◽  
Finite Larmor Radius ◽  
The Earth ◽  
Specific Distribution ◽  
The Magnetic Field

Abstract. Using hybrid simulations, we examine how particles can diffuse across the Earth's magnetopause because of finite Larmor radius effects. We focus on tangential discontinuities and consider a reversal of the magnetic field that closely models the magnetopause under southward interplanetary magnetic field. When the Larmor radius is on the order of the field reversal thickness, we show that particles can cross the discontinuity. We also show that with a realistic initial shear flow, a Kelvin-Helmholtz instability develops that increases the efficiency of the crossing process. We investigate the distribution functions of the transmitted ions and demonstrate that they are structured according to a D-shape. It accordingly appears that magnetic reconnection at the magnetopause is not the only process that leads to such specific distribution functions. A simple analytical model that describes the built-up of these functions is proposed.

An Alternative Approach to the Asymptotic Theory of Spurious Regression, Cointegration, and Near Cointegration

1993 ◽  
Vol 9 (1) ◽  
pp. 36-61 ◽  
Author(s):  
Katsuto Tanaka
Keyword(s):  
Asymptotic Theory ◽  
Distribution Functions ◽  
Present Approach ◽  
Local Power ◽  
Limiting Distributions ◽  
Spurious Regression ◽  
Alternative Approach

An alternative approach is taken to the asymptotic theory of cointegration. The present approach gives a different expression for the limiting distributions of statistics associated with cointegration, which enables us to compute accurately the distribution functions. Alternative interpretations of cointegration are given and a notion of near cointegration is introduced. We then devise tests which take cointegration as the null and discuss the limiting local power under the alternative of near cointegration.

Disequilibrium Adjustment and Economic Outcomes

2016 ◽  
Author(s):  
Alan Kirman ◽  
Rajiv Sethi
Keyword(s):  
Economic Theory ◽  
Social Interactions ◽  
Equilibrium Selection ◽  
Economic Outcomes ◽  
Central Theme ◽  
Equilibrium Method ◽  
Alternative Approach ◽  
Potential Applications

A central organizing principle in contemporary economic theory is the notion of equilibrium: all individuals make plans that are optimal, given beliefs that are mutually consistent. The equilibrium method is effective in generating sharp predictions, but it sidesteps important questions about how equilibrium can be attained, optimality assessed, and available alternatives enumerated. This chapter describes an alternative approach in which the process of adjustment is a central theme. Individuals adapt to changes in their environment by making incremental changes in their behavior. These changes alter the environment faced by others, which leads to further dynamic adjustments. Trajectories may eventually converge to an equilibrium, but this is not inevitable. Even when convergence does occur, it may be to one of several conceivable equilibria, so that the dynamics operate as an equilibrium selection device. These ideas are explored primarily through the example of homophily in social interactions, with other potential applications also briefly considered.

scholarly journals Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Alessandro Geraldini ◽  
F. I. Parra ◽  
F. Militello
Keyword(s):  
Magnetic Field ◽  
Fluid Model ◽  
Boltzmann Distribution ◽  
Distribution Functions ◽  
Magnetized Plasma ◽  
Electron Mass ◽  
Ion Temperature ◽  
Ion Distribution ◽  
Ionic Charge ◽  
The Magnetic Field

The magnetic presheath is a boundary layer occurring when magnetized plasma is in contact with a wall and the angle $\unicode[STIX]{x1D6FC}$ between the wall and the magnetic field $\boldsymbol{B}$ is oblique. Here, we consider the fusion-relevant case of a shallow-angle, $\unicode[STIX]{x1D6FC}\ll 1$ , electron-repelling sheath, with the electron density given by a Boltzmann distribution, valid for $\unicode[STIX]{x1D6FC}/\sqrt{\unicode[STIX]{x1D70F}+1}\gg \sqrt{m_{\text{e}}/m_{\text{i}}}$ , where $m_{\text{e}}$ is the electron mass, $m_{\text{i}}$ is the ion mass, $\unicode[STIX]{x1D70F}=T_{\text{i}}/ZT_{\text{e}}$ , $T_{\text{e}}$ is the electron temperature, $T_{\text{i}}$ is the ion temperature and $Z$ is the ionic charge state. The thickness of the magnetic presheath is of the order of a few ion sound Larmor radii $\unicode[STIX]{x1D70C}_{\text{s}}=\sqrt{m_{\text{i}}(ZT_{\text{e}}+T_{\text{i}})}/ZeB$ , where e is the proton charge and $B=|\boldsymbol{B}|$ is the magnitude of the magnetic field. We study the dependence on $\unicode[STIX]{x1D70F}$ of the electrostatic potential and ion distribution function in the magnetic presheath by using a set of prescribed ion distribution functions at the magnetic presheath entrance, parameterized by $\unicode[STIX]{x1D70F}$ . The kinetic model is shown to be asymptotically equivalent to Chodura’s fluid model at small ion temperature, $\unicode[STIX]{x1D70F}\ll 1$ , for $|\text{ln}\,\unicode[STIX]{x1D6FC}|>3|\text{ln}\,\unicode[STIX]{x1D70F}|\gg 1$ . In this limit, despite the fact that fluid equations give a reasonable approximation to the potential, ion gyro-orbits acquire a spatial extent that occupies a large portion of the magnetic presheath. At large ion temperature, $\unicode[STIX]{x1D70F}\gg 1$ , relevant because $T_{\text{i}}$ is measured to be a few times larger than $T_{\text{e}}$ near divertor targets of fusion devices, ions reach the Debye sheath entrance (and subsequently the wall) at a shallow angle whose size is given by $\sqrt{\unicode[STIX]{x1D6FC}}$ or $1/\sqrt{\unicode[STIX]{x1D70F}}$ , depending on which is largest.

scholarly journals Filaments and striations: anisotropies in observed, supersonic, highly magnetized turbulent clouds

2019 ◽  
Vol 492 (1) ◽  
pp. 668-685 ◽  
Author(s):  
James R Beattie ◽  
Christoph Federrath
Keyword(s):  
Magnetic Field ◽  
Column Density ◽  
Three Dimensional ◽  
High Density ◽  
Systematic Analysis ◽  
Guide Field ◽  
Degree Of Anisotropy ◽  
Mach Numbers ◽  
Magnetohydrodynamic Simulations ◽  
The Magnetic Field

ABSTRACT Stars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$) and turbulent Mach numbers ($\operatorname{\mathcal {M}}=2{\!-\!20}$), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\operatorname{\mathcal {M}_{\text{A}}}\lt 1$, and $\operatorname{\mathcal {M}}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\operatorname{\mathcal {M}}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\operatorname{\mathcal {M}}$ that determine which kind of anisotropy dominates the morphology of a cloud.

scholarly journals Observations of diffusion in the electron halo and strahl

2016 ◽  
Vol 34 (12) ◽  
pp. 1175-1189 ◽  
Author(s):  
Chris Gurgiolo ◽  
Melvyn L. Goldstein
Keyword(s):  
Magnetic Field ◽  
Energy Range ◽  
Lower Energy ◽  
Three Dimensional ◽  
Distribution Functions ◽  
Electron Velocity ◽  
Electron Velocity Distribution ◽  
Velocity Distribution Functions ◽  
The Magnetic Field ◽  
Solar Wind Electron

Abstract. Observations of the three-dimensional solar wind electron velocity distribution functions (VDF) using ϕ–θ plots often show a tongue of electrons that begins at the strahl and stretches toward a new population of electrons, termed the proto-halo, that exists near the projection of the magnetic field opposite that associated with the strahl. The energy range in which the tongue and proto-halo are observed forms a “diffusion zone”. The tongue first appears in energy generally near the lower-energy range of the strahl and in the absence of any clear core/halo signature. While the ϕ–θ plots give the appearance that the tongue and proto-halo are derived from the strahl, a close examination of their density suggests that their source is probably the upper-energy core/halo electrons which have been scattered by one or more processes into these populations.

scholarly journals Multi-point observations of intermittency in the cusp regions

2007 ◽  
Vol 14 (4) ◽  
pp. 525-534 ◽  
Author(s):  
M. M. Echim ◽  
H. Lamy ◽  
T. Chang
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Haar Wavelet ◽  
Distribution Functions ◽  
Statistical Properties ◽  
Coarse Grained ◽  
Haar Wavelet Transform ◽  
Intermittent Behavior ◽  
Field Fluctuations ◽  
The Magnetic Field

Abstract. In this paper we investigate the statistical properties of magnetic field fluctuations measured by the four Cluster spacecraft in the cusp and close to the interface with the magnetospheric lobes, magnetopause and magnetosheath. At lower altitudes along the outbound orbit of 26 February 2001, the magnetic field fluctuations recorded by all four spacecraft are random and their Probability Distribution Functions (PDFs) are Gaussian at all scales. The flatness parameter, F – related to the kurtosis of the time series, is equal to 3. At higher altitudes, in the cusp and its vicinity, closer to the interface with the magnetopause and magnetosheath, the PDFs from all Cluster satellites are non-Gaussian and show a clear intermittent behavior at scales smaller than τG≈ 61 s (or 170 km). The flatness parameter increases to values greater than 3 for scales smaller than τG. A Haar wavelet transform enables the identification of the "events" that produce sudden variations of the magnetic field and of the scales that have most of the power. The LIM parameter (i.e. normalized wavelet power) indicates that events for scales below 65 s are non-uniformly distributed throughout the cusp passage. PDFs, flatness and wavelet analysis show that at coarse-grained scales larger than τG the intermittency is absent in the cusp. Fluctuations of the magnetic energy observed during the same orbit in the magnetosheath show PDFs that tend toward a Gaussian at scales smaller than τG found in the cusp. The flatness analysis confirms the decreasing of τG from cusp to magnetosheath. Our analysis reveals the turbulent cusp as a transition region from a non-intermittent turbulent state inside the magnetosphere to an intermittent turbulent state in the magnetosheath that has statistical properties resembling the solar wind turbulence. The observed turbulent fluctuations in the cusp suggests a phenomenon of nonlinear interactions of plasma coherent structures as in contemporary models of space plasma turbulence.

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