Large-scale flow of collisionless plasmas along the magnetic lines of force: Electric fields and currents parallel to the magnetic field, The stress tensor

Abstract. Two different approaches, referred to as Bu and Ej, can be used to examine the time development of electric fields and currents in space plasmas based on the fundamental laws of physics. From the Bu approach, the required equation involves the generalized Ohm's law with some simplifying assumptions. From the Ej approach, the required equation can be derived from the equation of particle motion, coupled self-consistently with Maxwell's equation, and the definition of electric current density. Recently, some strong statements against the Ej approach have been made. In this paper, we evaluate these statements by discussing (1) some limitations of the Bu approach in solving the time development of electric fields and currents, (2) the procedure in calculating self-consistently the time development of the electric current in space plasmas without taking the curl of the magnetic field in some cases, and (3) the dependency of the time development of magnetic field on electric current. It is concluded that the Ej approach can be useful to understand some magnetospheric problems. In particular, statements about the change of electric current are valid theoretical explanations of change in magnetic field during substorms.

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The path of an electron in combined radial magnetic and electric fields

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1911.0037 ◽

1911 ◽

Vol 85 (578) ◽

pp. 257-262 ◽

Cited By ~ 1

Keyword(s):

Magnetic Field ◽

Electric Field ◽

Electric Fields ◽

Circular Cone ◽

Conic Section ◽

Magnetic Pole ◽

Actual Distribution ◽

A Charge ◽

The Magnetic Field ◽

Lines Of Force

1. In the course of an investigation with a focus tube, in which the anti-cathode was a magnetic pole, some interesting observations were made with regard to the distribution of the fluorescence on the walls of the tube as the magnetic field varied. In order to explain the changes observed, the path of an electron in a radial field was investigated mathematically, and was found to lie on a right circular cone whose vertex coincides with the magnetic pole. If the surface of the cone is developed into a plane the trace of the path is a conic section, with the vertex as focus. This result continues to hold when an electric field, with its lines of force radiating from the same point, is superposed on the magnetic field. Although the actual distribution of electric intensity in a highly exhausted tube must differ widely from that here considered, the investigation sufficiently explains the facts observed. Theoretical . 2. The object is to find the path of a particle of mass m carrying a charge e in combined magnetic and electric fields, when the lines of force are radial and are such as might be due to a single pole of strength μ coincident with an electric charge k .

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Evolution of Large-Scale Coronal Structures

International Astronomical Union Colloquium ◽

10.1017/s0252921100024945 ◽

1994 ◽

Vol 144 ◽

pp. 29-33

Author(s):

P. Ambrož

Keyword(s):

Magnetic Field ◽

Field Line ◽

Large Scale ◽

Coronal Magnetic Field ◽

Source Surface ◽

Solar Cycles ◽

Characteristic Relationship ◽

The Magnetic Field ◽

Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

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An 84-μG Magnetic Field in a Galaxy at Z=0.692?

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308027439 ◽

2008 ◽

Vol 4 (S254) ◽

pp. 95-96

Author(s):

Arthur M. Wolfe ◽

Regina A. Jorgenson ◽

Timothy Robishaw ◽

Carl Heiles ◽

Jason X. Prochaska

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Faraday Rotation ◽

Large Scale ◽

Dynamo Model ◽

Magnetic Field Generation ◽

Interstellar Gas ◽

Splitting Technique ◽

Average Value ◽

The Magnetic Field

AbstractThe magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars (Beck 2005). The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ≈ 3 μG (Han et al. 2006). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars (Kronberg et al. 2008) suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain.Here we report a measurement of a magnetic field of B ≈ 84 μG in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 μG in the neutral interstellar gas of our Galaxy (Heiles et al. 2004). This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past, rather than stronger (Parker 1970).The full text of this paper was published in Nature (Wolfe et al. 2008).

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No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽

10.3390/data6010004 ◽

2021 ◽

Vol 6 (1) ◽

pp. 4

Author(s):

Evgeny Mikhailov ◽

Daniela Boneva ◽

Maria Pashentseva

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Large Scale ◽

Point Of View ◽

Accretion Discs ◽

Wide Range ◽

Astrophysical Objects ◽

Alpha Effect ◽

The Stability ◽

The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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Circumstellar environment of 55 Cancri

Astronomy and Astrophysics ◽

10.1051/0004-6361/201937186 ◽

2020 ◽

Vol 633 ◽

pp. A48 ◽

Cited By ~ 6

Author(s):

C. P. Folsom ◽

D. Ó Fionnagáin ◽

L. Fossati ◽

A. A. Vidotto ◽

C. Moutou ◽

...

Keyword(s):

Magnetic Field ◽

Stellar Wind ◽

Large Scale ◽

Rotation Axis ◽

Doppler Imaging ◽

Magnetic Pole ◽

Average Strength ◽

Detailed Understanding ◽

The Magnetic Field ◽

Circumstellar Environment

Context. 55 Cancri hosts five known exoplanets, most notably the hot super-Earth 55 Cnc e, which is one of the hottest known transiting super-Earths. Aims. Because of the short orbital separation and host star brightness, 55 Cnc e provides one of the best opportunities for studying star-planet interactions (SPIs). We aim to understand possible SPIs in this system, which requires a detailed understanding of the stellar magnetic field and wind impinging on the planet. Methods. Using spectropolarimetric observations and Zeeman Doppler Imaging, we derived a map of the large-scale stellar magnetic field. We then simulated the stellar wind starting from the magnetic field map, using a 3D magneto-hydrodynamic model. Results. The map of the large-scale stellar magnetic field we derive has an average strength of 3.4 G. The field has a mostly dipolar geometry; the dipole is tilted by 90° with respect to the rotation axis and the dipolar strength is 5.8 G at the magnetic pole. The wind simulations based on this magnetic geometry lead us to conclude that 55 Cnc e orbits inside the Alfvén surface of the stellar wind, implying that effects from the planet on the wind can propagate back to the stellar surface and result in SPI.

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Large scale magnetic anomalies over western Canada and the Arctic: a discussion

Canadian Journal of Earth Sciences ◽

10.1139/e76-082 ◽

1976 ◽

Vol 13 (6) ◽

pp. 790-802 ◽

Cited By ~ 37

Author(s):

R. L. Coles ◽

G. V. Haines ◽

W. Hannaford

Keyword(s):

Magnetic Field ◽

Large Scale ◽

Elevated Temperatures ◽

Magnetic Anomalies ◽

The Arctic ◽

Evolutionary Development ◽

Magnetic Feature ◽

Western Canada ◽

Arctic Regions ◽

The Magnetic Field

A contoured map of vertical magnetic field residuals (relative to the IGRF) over western Canada and adjacent Arctic regions has been produced by amalgamating new data with those from previous surveys. The measurements were made at altitudes between 3.5 and 5.5 km above sea level. The map shows the form of the magnetic field within the waveband 30 to 5000 km. A magnetic feature of several thousand kilometres wavelength dominates the map, and is probably due in major part to sources in the earth's core. Superimposed on this are several groups of anomalies which contain wavelengths of the order of a thousand kilometres. The patterns of the short wavelength anomalies provide a broad view of major structures and indicate several regimes of distinctive evolutionary development. Enhancement of viscous magnetization at elevated temperatures may account for the concentration of intense anomalies observed near the western edge of the craton.

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The development of magnetic field line wander by plasma turbulence

Journal of Plasma Physics ◽

10.1017/s0022377817000617 ◽

2017 ◽

Vol 83 (4) ◽

Cited By ~ 5

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.

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Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

Annales Geophysicae ◽

10.5194/angeo-34-55-2016 ◽

2016 ◽

Vol 34 (1) ◽

pp. 55-65 ◽

Cited By ~ 4

Author(s):

A. D. M. Walker ◽

G. J. Sofko

Keyword(s):

Magnetic Field ◽

Steady State ◽

Electric Field ◽

Electric Fields ◽

Magnetic Field Line ◽

Geomagnetic Field ◽

Geomagnetic Field Models ◽

Spatial Derivatives ◽

Field Lines ◽

The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

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Constraint on ion–neutral drift velocity in the Class 0 protostar B335 from ALMA observations

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732195 ◽

2018 ◽

Vol 615 ◽

pp. A58 ◽

Cited By ~ 6

Author(s):

Hsi-Wei Yen ◽

Bo Zhao ◽

Patrick M. Koch ◽

Ruben Krasnopolsky ◽

Zhi-Yun Li ◽

...

Keyword(s):

Magnetic Field ◽

Drift Velocity ◽

Large Scale ◽

Ambipolar Diffusion ◽

Neutral Drift ◽

Neutral Gas ◽

Mhd Simulations ◽

Ambipolar Drift ◽

Velocity Drift ◽

The Magnetic Field

Aims. Ambipolar diffusion can cause a velocity drift between ions and neutrals. This is one of the non-ideal magnetohydrodynamics (MHD) effects proposed to enable the formation of large-scale Keplerian disks with sizes of tens of au. To observationally study ambipolar diffusion in collapsing protostellar envelopes, we compare here gas kinematics traced by ionized and neutral molecular lines and discuss the implication on ambipolar diffusion. Methods. We analyzed the data of the H13CO+ (3–2) and C18O (2–1) emission in the Class 0 protostar B335 obtained with our ALMA observations. We constructed kinematical models to fit the velocity structures observed in the H13CO+ and C18O emission and to measure the infalling velocities of the ionized and neutral gas on a 100 au scale in B335. Results. A central compact (~1′′–2′′) component that is elongated perpendicular to the outflow direction and exhibits a clear velocity gradient along the outflow direction is observed in both lines and most likely traces the infalling flattened envelope. With our kinematical models, the infalling velocities in the H13CO+ and C18O emission are both measured to be 0.85 ± 0.2 km s−1 at a radius of 100 au, suggesting that the velocity drift between the ionized and neutral gas is at most 0.3 km s−1 at a radius of 100 au in B335. Conclusions. The Hall parameter for H13CO+ is estimated to be ≫1 on a 100 au scale in B335, so that H13CO+ is expected to be attached to the magnetic field. Our non-detection or upper limit of the velocity drift between the ionized and neutral gas could suggest that the magnetic field remains rather well coupled to the bulk neutral material on a 100 au scale in this source, and that any significant field-matter decoupling, if present, likely occurs only on a smaller scale, leading to an accumulation of magnetic flux and thus efficient magnetic braking in the inner envelope. This result is consistent with the expectation from the MHD simulations with a typical ambipolar diffusivity and those without ambipolar diffusion. On the other hand, the high ambipolar drift velocity of 0.5–1.0 km s−1 on a 100 au scale predicted in the MHD simulations with an enhanced ambipolar diffusivity by removing small dust grains, where the minimum grain size is 0.1 μm, is not detected in our observations. However, because of our limited angular resolution, we cannot rule out a significant ambipolar drift only in the midplane of the infalling envelope. Future observations with higher angular resolutions (~0. ′′1) are needed to examine this possibility and ambipolar diffusion on a smaller scale.

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