Euler Potentials

Stern, David P.

doi:10.1119/1.1976373

Cited by 194 publications

(139 citation statements)

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“…The resolutions are essentially 1) compromising the momentum-conserving force slightly in order to attain partial momentum-conservation but stability; 2) formulating dissipation terms for MHD following Monaghan (1997) (see ; 3) deriving the variable smoothing length formulation from a Lagrangian and 4) using prevention not cure by formulating the magnetic field in a divergence free form using the 'Euler potentials' α E and β E such that B = ∇α E × ∇β E . The latter has the further advantage that the Lagrangian evolution of these potentials for ideal MHD is zero, corresponding to the advection of magnetic field lines (Stern 1970), although there are also disadvantages to their use. In practise we add artificial dissipation terms to the Euler potentials' evolution in order to resolve (and dissipate) strong gradients in the magnetic field (see Price and is here applied to star formation problems for the first time.…”

Section: Methodsmentioning

confidence: 99%

The effect of magnetic fields on the formation of circumstellar discs around young stars

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2007

Astrophys Space Sci

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We present first results of our simulations of magnetic fields in the formation of single and binary stars using a recently developed method for incorporating Magnetohydrodynamics (MHD) into the Smoothed Particle Hydrodynamics (SPH) method. An overview of the method is presented before discussing the effect of magnetic fields on the formation of circumstellar discs around young stars. We find that the presence of magnetic fields during the disc formation process can lead to significantly smaller and less massive discs which are much less prone to gravitational instability. Similarly in the case of binary star formation we find that magnetic fields, overall, suppress fragmentation. However these effects are found to be largely driven by magnetic pressure. The relative importance of magnetic tension is dependent on the orientation of the field with respect to the rotation axis, but can, with the right orientation, lead to a dilution of the magnetic pressure-driven suppression of fragmentation.

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Section: Methodsmentioning

confidence: 99%

The effect of magnetic fields on the formation of circumstellar discs around young stars

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2007

Astrophys Space Sci

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“…This knowledge comes from the fact that the magnetic field at the Earth's surface can be assumed to be overwhelmingly due to internal Earth sources [Tsyganenko, 1990]. By only taking into account the highly-dominant dipole term on the Earth's surface, we simply have α ≡ φ on the Earth's surface [e.g., Stern, 1970]. This boundary condition is approximately correct even when we do not extend the domain down to the Earth's surface, but only to a sphere of radius r enveloping the Earth, with r not too large.…”

Section: Inverse Representation; Iterative Computational Methodsmentioning

confidence: 99%

3-D Force-balanced Magnetospheric Configurations

Zaharia

Cheng

Maezawa

2003

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Abstract. The knowledge of plasma pressure is essential for many physics applications in the magnetosphere, such as computing magnetospheric currents and deriving mag-netosphere-ionosphere coupling. A thorough knowledge of the 3-D pressure distribution has however eluded the community, as most in-situ pressure observations are either in the ionosphere or the equatorial region of the magnetosphere. With the assumption of pressure isotropy there have been attempts to obtain the pressure at different locations by either (a) mapping observed data (e.g. in the ionosphere) along the field lines of an empirical magnetospheric field model, or (b) computing a pressure profile in the equatorial plane (in 2-D) or along the Sun-Earth axis (in 1-D) that is in force balance with the magnetic stresses of an empirical model. However, the pressure distributions obtained through these methods are not in force balance with the empirical magnetic field at all locations. In order to find a global 3-D plasma pressure distribution in force balance with the magnetospheric magnetic field we have developed the MAG-3D code, that solves the 3-D force balance equation J × B = ∇P computationally. Our calculation is performed in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials as B = ∇ψ × ∇α. The pressure distribution, P = P (ψ, α), is prescribed in the equatorial plane and is based on satellite measurements. In addition, computational boundary conditions for ψ surfaces are imposed using empirical field models. Our results provide 3-D distributions of magnetic field, plasma pressure as well as parallel and transverse currents for both quiet-time and disturbed magnetospheric conditions.

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“…Each point in the ionosphere is specified using Euler potentials a and b [Northrop and Teller, 1960;Stern, 1970], which are assumed not to vary in time, for a fixed point in the ionosphere. Since the RCM grid is also fixed in the ionosphere, each grid point is characterized by values of a and b that do not change in time.…”

Section: A1 Inductive Electric Fieldsmentioning

confidence: 99%

Rice Convection Model simulation of the substorm‐associated injection of an observed bubble into the inner magnetosphere: 1. Magnetic field and other inputs

et al. 2009

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[1] The objective of this work is a realistic Rice Convection Model (RCM) simulation of a modest substorm that occurred on 22 July 1998 and was observed by the Geotail spacecraft in the inner plasma sheet. It represents the first time the RCM has been used for detailed modeling of an inner magnetospheric event using data from a spacecraft in the inner plasma sheet beyond geosynchronous orbit to drive the model's time-dependent boundary conditions. Since this represents a substantial departure from past practice, we present, in this paper, a detailed account of how model inputs are determined. An accompanying paper presents results and interpretations. Model inputs are adjusted to achieve approximate consistency between RCM-computed values and measurements by Geotail, which was within the RCM modeling region near X GSM = À9 R E , Y GSM = 0. To represent the magnetic field in the growth phase, we utilize a Tsyganenko (1989) statistical magnetic field model, adjusted to agree with Geotail-measured pressure and magnetic field in a new way using analytic solutions to the linear Grad-Shafranov equation. The magnetic field during the expansion phase is represented by adding a substorm current wedge using formulas developed by Tsyganenko. Induction electric fields play a central role in these simulations, because they are large in the vicinity of the substorm injection region. We provide a detailed description of how induction electric fields are included in the RCM as well as a prescription of the electromagnetic gauge condition used in the code.

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Euler Potentials

Abstract: The representation of a magnetic field by the cross product of the gradients of two scalars has recently seen wide use in plasma physics and in the study of energetic particles in space. The properties of such a representation are reviewed and examples of its application are given.

Cited by 194 publications

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The effect of magnetic fields on the formation of circumstellar discs around young stars

The effect of magnetic fields on the formation of circumstellar discs around young stars

3-D Force-balanced Magnetospheric Configurations

Rice Convection Model simulation of the substorm‐associated injection of an observed bubble into the inner magnetosphere: 1. Magnetic field and other inputs

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