Alfven approximation

The Alfvén approximation (after Hannes Alfvén , also drift approximation ) allows a simplified description of the movement of particles in a magnetic field in plasma physics . Under suitable conditions, this movement can be broken down into a gyrating ( gyration ) and a mean, effective ( drift ) part.

condition

The approximation is well applicable when the magnetic field is homogeneous on the order of magnitude of the radius of curvature of the path : ${\displaystyle H}$ ${\displaystyle a}$

${\displaystyle \left|{\frac {\nabla H}{H}}\right|\ll {\frac {1}{a}}}$

with the gradient that describes the inhomogeneity of the magnetic field. ${\displaystyle \nabla H}$

Likewise, only a slight change in the field over time is required.

Approximation

According to the condition, the gyration movement is “small” and fast compared to the other scales of the “magnetic field-particle” system, which allows the movement of the particle to be averaged over a gyration period and thus an effective (drift) movement to be obtained.

The drift speed depends on the inhomogeneity of the magnetic field, the curvature of the magnetic field lines and additionally acting forces.

The radius of the gyration movement is approximate to the Larmor radius , the associated frequency is the cyclotron frequency .

literature

• Willhelm H. Kegel: Plasma Physics: An Introduction . Springer, Berlin / Heidelberg 1998, ISBN 978-3-642-63721-6 .

Individual evidence

1. ↑ F. Hertweck: The movement of charged particles in the magnetic field of a straight wire through which current flows . In: Journal Nature Research Part A . tape 14 , 1959, pp. 47–54 ( thayer.dartmouth.edu [PDF; 552 kB ; accessed on July 1, 2016]).