Click on   for the abstract/outline of the chapter           Click on   for the full postal aadress           Click on   for personal Web page.

List of chapters and authors. Updated 10 June 2003

TITLE OF CHAPTER	AUTHOR(s)
1.  Introduction to magnetic helicity	Mitchell A. Berger [London, UK]   m.berger@ucl.ac.uk  Gunnar Hornig [Bochum, D]   gh@tp4.ruhr-uni-bochum.de
2.  Higher-order link invariants	Mitchell A. Berger [London, UK]   m.berger@ucl.ac.uk  Gunnar Hornig [Bochum, D]   gh@tp4.ruhr-uni-bochum.de
3.  Magnetic helicity and conservation laws in MHD	Antonio Ferriz Mas [Vigo, E]   antonio.ferriz@oulu.fi
4.  Magnetic helicity -- a useful tool in dynamo theory	Axel Brandenburg [Copenhagen, DK]   brandenb@nordita.dk
5.  The role of helicity flux through boundaries	Wolfgang Dobler [Freiburg, D]   Wolfgang.Dobler@kis.uni-freiburg.de
6.  Solar Observations and their relevance to magnetic                 helicity	Dana Longcope [Bozeman, USA]   dana@physics.montana.edu  Alexei Pevtsov [Sac Peak, USA]   apevtsov@nso.edu

• 1. Definition of helicity, gauge invariance
  

• 2. Definition of helicity, gauge invariance
  

• 3. Cross helicity
  

• 4. Interpretation of the integral    (relation to the linking number/asymptotic linking number)

• 5. Magnetic helicity under Reconnection    (2D Reconnection: strict conservation of helicity)

• 6. Magnetic helicity under Reconnection    (3D- Reconnection, estimates of helicity production for 3D reconnection)

• 7. Magnetic helicity under Reconnection    (Helicity separation by reconnection)

• 8. Helicity conservation on the Sun    (simple example of how to measure helicity in a real plasma)

• 9. Covariant helicity

• 10. Helicity in a periodic domain    (counter example)

• 1. Motivation

• 2. 3rd-order invariant

• 3. 4th-order invariant

• 4. Recursive definition of higher-order invariants

• 5. Higher-order invariants under reconnection

• 1. Kinematical aspects. Transport theorem for a material curve.

• 2. The magnetic induction equation.

• 3. Evolution equation for the magnetic helicity density.

• 4. Hydrodynamic and magnetohydrodynamic equations written in "conservation form".

• 5. Alfvén's theorem and related results.

• 6. Conservation of magnetic helicity: Eulerian and Lagrangian approaches.

• 1. Introduction

• 2. Magnetic helicity conservation: Limits on the rate of change of magnetic helicity; generalization of Berger's bound.

• 3. Helical turbulence: prototype of an alpha-effect; inverse cascade or alpha-effect?

• 4. Open boundaries: Preferential loss of large scale field; quantitative treatment.

• 5. Connection with alpha-quenching: Dynamical alpha-quenching is consistent with magnetic helicity conservation. Comparison of different algebraic quenching formulae.

• 1. Helicity flux density and net helicity flux

• 2. Gauge issues and ambiguities concerning the helicity flux

• 3. The spatially periodic case

• 4. Dynamo simulations with open boundaries 4.1 Normal-field boundary condition 4.2 Perfect-conductor boundary condition 4.3 Magnetic buoyancy

• 5. Fast helicity separation by shear

• 1. Measurement techniques (how we can measure helicity on the Sun and interplanetary medium):

  • Direct measurement of relative helicity (hypothetical prospects and predicted limitations).

  • Measurements of relative helicty flux --- the time rate of change formula.

    • i. advection term - emergence of pre-twisted fields

    • ii. braiding term - motion of p-spheric flux. using assumed velocity, i.e. diff. rotation measured the velocity

  • Helicity Proxies and their reliability.

    • i. remote: alpha-best, , chirality alpha-best - alpha-corona correlation

    • ii. In-situ: solar wind turbulence, magnetic clouds

• 2. Observed helicity/chirality patterns

  • a. Latitudinal variation and Hemispheric dependance sunspots, AR magnetic fields, filaments, sigmoids, large-scale magnetic field, IMF, magnetic clouds

  • b. Solar cycle variation (none)

  • c. Large-scale patterns helicity nests, coronal flux systems, transequatorial loops

  • d. Small-scale pattern (inside a single polarity sunspot, modeling (flux tube bifurcation during rise)

  • e. Quiet Sun (weak field) helicity (helicity "test" of surface dynamo, calculations of Rossby number for different convection scales).

• 3. 3. Interpretation and possible implications

  • a. Critical review of different mechanisms of helicity generation and how they compare with observations

  • b. Helicity/Chirality continuity through solar atmosphere (e.g., alpha-best - alpha-corona correlation ARs tilt-twist correlation (?) helicity in magnetic

  • c. Helicity evolution (helicity loading, reconnection of twisted flux tubes, (lack of) gradual build-up of helicity, helicity balance in ARs, AR emergence and helicity evolution).

Comments about this page to: Antonio Ferriz Mas

Last modified: 10 June 2003

  Top of page