# Magnetic helicity

﻿
Magnetic helicity

In plasma physics, magnetic helicity is the extent to which a magnetic field "wraps around itself". It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines).

If magnetic field lines follow the strands of a twisted rope, this configuration would have nonzero magnetic helicity; left-handed ropes would have negative values and right-handed ropes would have positive values.[clarification needed]

Formally,

$H = \int {\mathbf A}\cdot{\mathbf B}\,d^3{\mathbf r}$

where

${\mathbf B}$ is the magnetic field strength
${\mathbf B}=\nabla\times{\mathbf A}$;
$\mathbf A$ is the vector potential of ${\mathbf B}$

Magnetic helicity is a conserved quantity. It is conserved in electromagnetic fields, even when magnetic reconnection dissipates energy. The concept is useful in solar dynamics and in hydromagnetic dynamo theory.[1] Magnetic helicity is a gauge-dependent quantity, because $\mathbf A$ can be redefined by adding a gradient to it (gauge transformation). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity is gauge invariant. A gauge-invariant relative helicity has been defined for volumes with non-zero magnetic flux on their boundary surfaces[2] If the magnetic field is turbulent and weakly inhomogeneous a magnetic helicity density and its associated flux can be defined in terms of the density of field line linkages.[3]

## References

1. ^ Brandenburg, A. (2009). "Hydromagnetic Dynamo Theory". Scholarpedia 2 (3): 2309. doi:10.4249/scholarpedia.2309. rev #73469.
2. ^ Berger, M.A. (1999). "Introduction to magnetic helicity". Plasma Physics and Controlled Fusion 41 (12B): 167. Bibcode 1999PPCF...41..167B. doi:10.1088/0741-3335/41/12B/312.
3. ^ Subramanian, K.; Brandenburg, A. (2006). "Magnetic helicity density and its flux in weakly inhomogeneous turbulence". The Astrophysical Journal Letters 648: L71–L74. arXiv:astro-ph/0509392. Bibcode 2006ApJ...648L..71S. doi:10.1086/507828.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Helicity (fluid mechanics) — this page is about helicity in fluid mechanics. For helicity of magnetic fields, see magnetic helicity. For helicity in particle physics, see helicity (particle physics). In fluid mechanics, helicity is the extent to which corkscrew like motion… …   Wikipedia

• Helicity — The term helicity has several meanings in physics, all referring (perhaps obliquely) to a phenomenon that resembles a helix. See:*helicity (fluid mechanics) *helicity (particle physics) *magnetic helicity *circular dichroismIn biochemistry,… …   Wikipedia

• Magnetic field — This article is about a scientific description of the magnetic influence of an electric current or magnetic material. For the physics of magnetic materials, see magnetism. For information about objects that create magnetic fields, see magnet. For …   Wikipedia

• Madison Symmetric Torus — Infobox Magnetic Fusion Device name = Madison Symmetric Torus dev type=Reversed field pinch loc=Madison, Wisconsin, USA rad maj = 1.50 m rad min = 52 cm aspect = 2.88|The Madison Symmetric Torus (MST) is a reversed field pinch (RFP) physics… …   Wikipedia

• Taylor state — A Taylor state is the minimum energy state of a plasma satisfying the constraint of conserving magnetic helicity. [cite book author = Paul M. Bellan year = 2000 title = Spheromaks: A Practical Application of Magnetohydrodynamic dynamos and plasma …   Wikipedia

• Trisops — was an experimental machine for the study of magnetic confinement of plasmas with the ultimate goal of producing fusion power. The configuration was a variation of a compact toroid, a toroidal (doughnut shaped) structure of plasma and magnetic… …   Wikipedia

• Sustained Spheromak Physics Experiment — The Sustained Spheromak Physics Experiment is a program at Lawrence Livermore National Laboratory in the United States to investigate spheromak plasma. [ [http://www.mfescience.org/sspx/ Sustained Spheromak Physics Experiment SSPX] MFEScience.… …   Wikipedia

• Conservation law — For the legal aspects of environmental conservation, see conservation movement. In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. One particularly… …   Wikipedia

• Magnetohydrodynamic turbulence — Magnetohydrodynamics (MHD) deals with what is a quasi neutral fluid with very high conductivity. The fluid approximation implies that the we focus at macro length and time scales which are much larger than the collision length and collision time… …   Wikipedia

• Automatic calculation of particle interaction or decay — The automatic calculation of particle interaction or decay is part of the computational particle physics branch. It refers to computing tools that help calculating the complex particle interactions as studied in high energy physics, astroparticle …   Wikipedia