Induced galvanomagnetic effects in copper

1970 ◽  
Vol 48 (15) ◽  
pp. 1806-1816 ◽  
Author(s):  
W. R. Datars
Keyword(s):  
Magnetic Field ◽  
Boundary Value Problem ◽  
Rotating Magnetic Field ◽  
Two Dimensional ◽  
Single Crystal Copper ◽  
One Dimensional ◽  
Open Orbit ◽  
Galvanomagnetic Properties ◽  
Resistivity Tensor ◽  
Galvanomagnetic Effects

The galvanomagnetic properties of copper were studied by observing the torque induced in single-crystal copper by a slowly rotating magnetic field at 1.4 °K. The induced torque varied linearly with the speed of magnet rotation and quadratically with magnetic field. There was large induced torque in high-purity samples from the open orbits in both one-dimensional and two-dimensional regions. In a sample with low ωcτ, there was also a background torque. The induced torque is described by Falicov's solution of the boundary value problem for a sample sphere with a resistivity tensor. The open-orbit torque in an uncompensated metal such as copper is approximately proportional to the transverse resistivity component ρ11. The anisotropy of the open-orbit torques for the (100) and (110) planes of copper is in agreement with that calculated for the magnetoresistance from the Fermi surface of copper. There is anisotropy in the background torque with minima in the region of symmetry directions and for a rotation in a (100) plane.

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

Interaction of a pair of ferrofluid drops in a rotating magnetic field

2018 ◽  
Vol 846 ◽  
pp. 121-142 ◽  
Author(s):  
Mingfeng Qiu ◽  
Shahriar Afkhami ◽  
Ching-Yao Chen ◽  
James J. Feng
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Hydrodynamic Interaction ◽  
Dipole Interaction ◽  
Rotating Magnetic Field ◽  
Viscous Drag ◽  
Planetary Motion ◽  
Two Dimensional ◽  
Initial Separation ◽  
Mutual Induction

We use two-dimensional numerical simulation to study the interaction between a pair of ferrofluid drops suspended in a rotating uniform magnetic field. Numerical results show four distinct regimes over the range of parameters tested: independent spin, planetary motion, drop locking and direct coalescence. These are in qualitative agreement with experiments, and the transition between them can be understood from the competition between magnetophoretic forces and viscous drag. We further analyse in detail the planetary motion, i.e. the revolution of the drops around each other while each spins in phase with the external magnetic field. For drops, as opposed to solid microspheres, the interaction is dominated by viscous sweeping, a form of hydrodynamic interaction. Magnetic dipole–dipole interaction via mutual induction only plays a secondary role. This insight helps us explain novel features of the planetary revolution of the ferrofluid drops that cannot be explained by a dipole model, including the increase of the angular velocity of planetary motion with the rotational rate of the external field, and the attainment of a limit separation between the drops that is independent of the initial separation.

Split Mode Method for the Elliptic 2D Sine-Gordon Equation: Application to Josephson Junction in Overlap Geometry

1998 ◽  
Vol 09 (02) ◽  
pp. 301-323 ◽  
Author(s):  
Jean-Guy Caputo ◽  
Nikos Flytzanis ◽  
Yuri Gaididei ◽  
Irene Moulitsa ◽  
Emmanuel Vavalis
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Josephson Junction ◽  
Gordon Equation ◽  
Splitting Method ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Dimensional Solution ◽  
One Dimensional

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the y-direction with boundary conditions determined by the bias current and a residual which is expanded using modes in the y-direction, the coefficients of which satisfy ordinary differential equations in x with boundary conditions given by the magnetic field. We show by direct comparison with a two-dimensional solution that this method converges and that it is an efficient way of solving the problem. The convergence of the y expansion for the residual is compared for Fourier cosine modes and the normal modes associated to the static one-dimensional sine-Gordon equation and we find a faster convergence for the latter. Even for such large widths as w=10 two such modes are enough to give accurate results.

Parametric instability in the expanding solar wind

2021 ◽  
Author(s):  
Andrea Verdini ◽  
Roland Grappin ◽  
Francesco Malara ◽  
Leonardo Primavera ◽  
Luca Del Zanna
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Parametric Instability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Total Magnetic Field ◽  
One Dimensional ◽  
Preliminary Results ◽  
Dimensional Spectrum ◽  
N Wave

<p>Recent measurments of Parker Solar Probe show that alfvenic fluctuations in the solar wind often appear in the form of swithcback with constant total magnetic field. Our aim is to understand if and how such fluctuations can contribute to the heating or acceleration of the solar wind, via the Parametric Instability. The intability of one dimensional Alfvénic fluctuations has been extensively studied in both homogenoeus plasma and in the expanding solar wind, less so for the two-dimensional case which is closer to expected three-dimensional nature of switchbacks. In this work we study under which condition an Alfvén wave with a two dimensional spectrum (as introduced in Primavera et al ApJ 2019) can decay in the expanding solar wind and we will present preliminary results.</p>

Magnetometric resistivity (MMR) anomalies of two‐dimensional structures

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 947-958 ◽  
Author(s):  
E. Gomez Trevino ◽  
R. N. Edwards
Keyword(s):  
Magnetic Field ◽  
Integral Equation ◽  
Fourier Transform ◽  
Electric Field ◽  
Current Source ◽  
Two Dimensional ◽  
Galvanic Current ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Surface Integrals

An inexpensive, rapid method has been developed for computing all three components of the magnetic field due to galvanic current flow from a point electrode in the vicinity of a conductive subsurface structure of infinite strike‐length and arbitrary cross‐section. For any three‐dimensional (3-D) structure, the magnetic field may be written as a sum of surface integrals over boundaries defining changes in conductivity by a direct modification of the Biot‐Savart law. The integrand of each surface integral includes the components of the electric field tangential to the boundary, which may be evaluated on the boundary using a standard integral equation technique. In the case of a two‐dimensional (2-D) structure, a reformulation of the theory by taking a one‐dimensional Fourier transform along the strike results in the reduction of both the surface integrals necessary to solve the integral equation for the electric field, and the integrals used in computing the magnetic field, to line integrals in wavenumber domain. We evaluate the integrals numerically and solve the integral equation for each of about ten wavenumbers; finally, we obtain the magnetic field in space domain through a concluding one‐dimensional inverse Fourier transform. Type curves and characteristic curves for the simple model of a buried horizontal cylinder beneath a thin layer of conductive overburden are constructed. In the absence of overburden, the half‐width of the anomaly is linearly related to the depth of the cylinder. In the presence of overburden, the form of the anomaly may be predicted in a simple manner from the corresponding anomaly in the absence of overburden, provided the distance from the current source is sufficiently large for most of the available current to have penetrated the overburden.

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