Rotational transformation
The rotational transformation or twist (small iota) is a geometric parameter for the course of the field lines of a toroidal magnetic field configuration ( tokamak , stellarator ) in the magnetic confinement of plasmas .
It is defined as the ratio of the change in the poloidal magnetic flux to the change in the toroidal magnetic flux :
In the case of toroidal magnetic fields, it is usually assumed that so-called magnetic flux surfaces are present. These are nested toroidal surfaces in which field lines for the magnetic confinement run. The rotation transformation as a characteristic quantity of a river area is to be averaged over such a river.
The concept of flux areas is important for the magnetohydrodynamics of fusion experiments, since it reduces the generally necessary consideration in three-dimensional spatial space to areas. The movement of the plasma particles is shaped by the flow areas.
The integration leading to the magnetic fluxes
in the case of the poloidal / toroidal flow occurs through a surface that captures the poloidal / toroidal component of the field. For the poloidal flow , this area is typically a finite, equatorial ring from the center of the torus with the large radius to a small radius . For the toroidal flow , the integration surface is a poloidal section at the same radius. For the circular torus the integration surface for the toroidal flow is thus a circle.
The size consequently changes with the small torus radius. For a pure torus geometry, as it occurs with the circular tokamak , the rotation transformation is
It can be seen here that the rotation transformation represents the poloidal ( ) offset of a field line after a toroidal ( ) revolution.
The inverse rotation transformation is the safety factor :
An important role for the stability of magnetic configurations is played by the shear , which represents the radial change of the rotational transformation:
Individual evidence
- ↑ F. Wagner, H. Wobig: Magnetic confinement . In: A. Dinklage, T.Klinger, G.Marx, L. Schweikhard (Eds.) Plasma Physics: Confinement, Transport and Collective Effects (= Lecture Notes in Physics , Vol. 670) Springer, Berlin / Heidelberg 2005, ISBN 3 -540-25274-6 , pp. 137-172.