scholarly journals A Monte Carlo simulation of magnetic field line tracing in the solar wind

2001 ◽  
Vol 8 (3) ◽  
pp. 151-158 ◽  
Author(s):  
P. Pommois ◽  
G. Zimbardo ◽  
P. Veltri
Keyword(s):  
Magnetic Field ◽  
Monte Carlo Simulation ◽  
Solar Wind ◽  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Field Line ◽  
Magnetic Field Line ◽  
Magnetic Turbulence ◽  
Field Lines ◽  
The Magnetic Field

Abstract. It is well known that the structure of magnetic field lines in solar wind can be influenced by the presence of the magnetohydrodynamic turbulence. We have developed a Monte Carlo simulation which traces the magnetic field lines in the heliosphere, including the effects of magnetic turbulence. These effects are modelled by random operators which are proportional to the square root of the magnetic field line diffusion coefficient. The modelling of the random terms is explained, in detail, in the case of numerical integration by discrete steps. Furthermore, a proper evaluation of the diffusion coefficient is obtained by a numerical simulation of transport in anisotropic magnetic turbulence. The scaling of the fluctuation level and of the correlation lengths with the distance from the Sun are also taken into account. As a consequence, plasma transport across the average magnetic field direction is obtained. An application to the propagation of energetic particles from corotating interacting regions to high heliographic latitudes is considered.

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 A comparison between FUV remote sensing of magnetotail stretching and the T01 model during quiet conditions and growth phases

2007 ◽  
Vol 25 (1) ◽  
pp. 161-170 ◽  
Author(s):  
C. Blockx ◽  
J.-C. Gérard ◽  
V. Coumans ◽  
B. Hubert ◽  
M. Meurant
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Field Line ◽  
Time History ◽  
Field Configuration ◽  
Growth Phases ◽  
Theoretical Position ◽  
Proton Precipitation ◽  
Field Lines ◽  
The Magnetic Field

Abstract. In a previous study, Blockx et al. (2005) showed that the SI12 camera on board the IMAGE spacecraft is an excellent tool to remotely determine the position of the isotropy boundary (IB) in the ionosphere, and thus is able to provide a reasonable estimate of the amount of stretching of the magnetic field lines in the magetotail. By combining an empirical model of the magnetospheric configuration with Sergeev's criterion for non-adiabatic motion, it is also possible to obtain a theoretical position of IB in the ionosphere, for known conditions in the solar wind. Earlier studies have demonstrated the inadequacy of the Tsyganenko-1989 (T89) model to quantitatively reproduce the field line stretching, particularly during growth phases. In this study, we reexamine this question using the T01 model which considers the time history of the solar wind parameters. We compare the latitude of IB derived from SI12 global images near local midnight with that calculated from the T01 model and the Sergeev's criterion. Observational and theoretical results are found to frequently disagree. We use in situ measurements of the magnetic field with the GOES-8 satellite to discriminate which of the two components in the calculation of the theoretical position of the IB (the T01 model or Sergeev's criterion) induces the discrepancy. For very quiet magnetic conditions, we find that statistically the T01 model approximately predicts the correct location of the maximum proton precipitation. However, large discrepancies are observed in individual cases, as demonstrated by the large scatter of predicted latitudes. For larger values of the AE index, the model fails to predict the observed latitude of the maximum proton intensity, as a consequence of the lack of consideration of the cross-tail current component which produces a more elongated field configuration at the location of the proton injection along the field lines. We show that it is possible to match the observed location of the maximum proton precipitation by decreasing the current sheet half-thickness D parameter. We thus conclude that underestimation of the field line stretching leads to inadequately prediction of the boundary latitude of the non-adiabatic proton precipitation region.

Peripheral Stochasticity in Tokamaks.The Martin-Taylor Revisited

1992 ◽  
Vol 47 (9) ◽  
pp. 941-944 ◽  
Author(s):  
R. L. Viana ◽  
I. L. Caldas
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Theoretical Analysis ◽  
Field Line ◽  
Magnetic Field Line ◽  
Current Model ◽  
Large Aspect Ratio ◽  
Magnetic Surfaces ◽  
Field Lines ◽  
The Magnetic Field

Abstract We analyse the effect of an Ergodic Magnetic Limiter on the magnetic field line dynamics in the edge of a large aspect-ratio Tokamak. We model the limiter action as an impulsive perturbation and use a peaked-current model for the Tokamak equilibrium field. The theoretical analysis is made through the use of invariant flux functions describing magnetic surfaces. Results are compared with a numerical mapping of the field lines

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Sofiane Bourouaine ◽  
Gregory G. Howes
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Plasma Turbulence ◽  
Turbulent Plasma ◽  
Nonlinearity Parameter ◽  
Time Interval ◽  
Weak Turbulence ◽  
Field Lines ◽  
The Magnetic Field

The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time $t_{2}$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time $t\lesssim t_{2}$ for strong turbulence, and at $t\gtrsim t_{2}$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval $t_{2}<t\leqslant 13t_{2}$. Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form $\langle (\unicode[STIX]{x1D6FF}r)^{2}\rangle =A(z/L_{\Vert })^{p}$ ($L_{\Vert }$ is the correlation length parallel to the magnetic background field $\boldsymbol{B}_{\mathbf{0}}$, $z$ is the distance along $\boldsymbol{B}_{\mathbf{0}}$ direction), providing functional forms of the amplitude coefficient $A$ and power-law exponent $p$ as a function of the nonlinearity parameter.

scholarly journals Relative magnetic field line helicity

2019 ◽  
Vol 624 ◽  
pp. A51 ◽  
Author(s):  
K. Moraitis ◽  
E. Pariat ◽  
G. Valori ◽  
K. Dalmasse
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Solar Physics ◽  
Magnetic Helicity ◽  
Geometrical Complexity ◽  
Wide Range ◽  
Field Lines ◽  
Definition Of ◽  
The Magnetic Field

Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of magnetic helicity is given by the field line helicity, which expresses the amount of helicity associated to individual field lines rather than in the full analysed volume. Aims. Magnetic helicity is not a gauge-invariant quantity in general, unless it is computed with respect to a reference field, yielding the so-called relative magnetic helicity. The field line helicity corresponding to the relative magnetic helicity has only been examined under specific conditions so far. This work aims to define the field line helicity corresponding to relative magnetic helicity in the most general way. In addition to its general form, we provide the expression for the relative magnetic field line helicity in a few commonly used gauges, and reproduce known results as a limit of our general formulation. Methods. By starting from the definition of relative magnetic helicity, we derived the corresponding field line helicity, and we noted the assumptions on which it is based. Results. We checked that the developed quantity reproduces relative magnetic helicity by using three different numerical simulations. For these cases we also show the morphology of field line helicity in the volume, and on the photospheric plane. As an application to solar situations, we compared the morphology of field line helicity on the photosphere with that of the connectivity-based helicity flux density in two reconstructions of an active region’s magnetic field. We discuss how the derived relative magnetic field line helicity has a wide range of applications, notably in solar physics and magnetic reconnection studies.

Magnetic Field Line Diffusion at the Onset of Stochasticity

1987 ◽  
Vol 42 (10) ◽  
pp. 1181-1192
Author(s):  
K. Elsässer ◽  
P. Deeskow
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficient ◽  
Field Line ◽  
Magnetic Field Line ◽  
Time Integration ◽  
Kinetic Equations ◽  
Theoretical Formula ◽  
Stochasticity Threshold ◽  
Field Lines ◽  
Line Diffusion

The Hamiltonian equations of a particle in a random set of waves just above the stochasticity threshold are considered both theoretically and numerically. First we derive the diffusion coefficient and the autocorrelation time perturbatively without using the thermodynamic limit, and we discuss the relevance of the H am iltonian problem for particle acceleration and magnetic field line flow. Then we integrate the equations for an ensemble of magnetic field lines numerically for a model problem [15] and show the time evolution of moments and correlations. Twice above the threshold we observe diffusive behaviour from the beginning, but the diffusion coefficient includes also the non-resonant modes. Just at threshold we find first a short phase o f free acceleration, later a diffusion which is slower than predicted by the theoretical formula. The best way to analyze the problem is in terms of cumulants, but a reliable com parison with any theory requires also a time integration of the corresponding kinetic equations.

Fast magnetic field line reconnection

1977 ◽  
Vol 284 (1325) ◽  
pp. 369-417 ◽  
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Fluid Velocity ◽  
Magnetic Reynolds Number ◽  
Diffusion Region ◽  
Mathematical Basis ◽  
Similarity Type ◽  
Field Lines ◽  
The Magnetic Field

Petschek (1964) has given a qualitative model for fast magnetic field line reconnection, at speeds up to a significant fraction of the Alfven speed. It is supposed that an electrically conducting fluid is permeated by an almost uniform magnetic field which reverses direction across a plane of symmetry parallel to the field lines. An almost uniform stream flows steadily towards the plane of symmetry and is maintained by pressure forces. Magnetic field line reconnection occurs at the origin inside a small central diffusion region. The reconnected magnetic field is swept away rapidly in two thin jets aligned with the plane of symmetry. The inflow and outflow regions are separated by discontinuities at which the tangential components of the magnetic field and fluid velocity suffer abrupt changes. Sonnerup (1970) and Yeh & Axford (1970), on the other hand, have given alternative solutions for the incompressible case which include a second set of discontinuities. Their solutions are of similarity type, valid over some length scale which is much less than the overall distance between the magnetic field sources but is much greater than the size of the central diffusion region. The second set of discontinuities is, however, unacceptable for an astrophysical plasma, since they need to be generated at corners in the flow rather than at the central diffusion region. This paper presents other solutions for the incompressible case, which are locally self-similar, without discontinuities or singular behaviour at a second set of discontinuities. The solutions are valid everywhere outside the central diffusion region when the inflow Alfven Mach number M 1 (see (2.3) below) is much less than unity and are valid at large distances from the diffusion region when M 1 = 0(1). The analysis has been summarized by Priest & Soward (1976). It puts Petschek’s mechanism on a sound mathematical basis and shows that the discontinuities are not in general straight but curve away from the incoming flows. Our estimate of the maximum reconnection rate M e,max (see (10.9) below) depends weakly on the value of the magnetic Reynolds number R m,e (see (10.7) below). It decreases from 0.2 when R m,e > = 10 to 0.03 when R m,e = 10 6 .

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