Kein Folientitel

1
Theory of Field Lines
Variational principle ----gt Differential
equation
Equivalence to Hamiltonian mechanics
Definition of magnetic surface ?(x) const
Mechanical analogue Integral surface
2
Magnetic surface
Magnetic surfaces are densily covered by
magnetic field lines
3
Magnetic surfaces
Problems When do magnetic surfaces exist? How
to compute magnetic surfaces? What is the effect
of field perturbations?
4
Field Lines
Poincaré surface of section
Field line integration provides an
flux- conserving map of the poloidal plane onto
itself
5
Magnetic Surface Wendelstein 7-AS
Poincaré Plot
Rational surface
Rotational Transform
q
Closed field lines i rational
6
Wendelstein 7-ASPoincaré Plot
i 0.48
i 0.51
i 1/2
Magnetic islands
7
Examples of magnetic surfaces
HSR5/22
HSR3/15
Major radius m 15 18 22 Minor radius
m 2.26 2.1 2.05 Aspect ratio 6.6 8.5 10.7 Iota(
0) 0.63 0.83 0.87 Iota(a) 0.75 1.0 1.0 ltjpar/j
perpgt 1.25 0.74 0.74
HSR4/18
8
Divertor
Magnetic islands at the plasma boundary are
utilised for divertor action.
9
Summary
Nested magnetic surfaces exist in
configurations with symmetry Symmetry breaking
perturbations create magnetic islands and
stochastic regions Islands arise on rational
surfaces, the separatrix is stochastic For good
plasma confinement magnetic islands must be
avoided