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VERSION:2.0
CALSCALE:GREGORIAN
PRODID:UW-Madison-Physics-Events
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SEQUENCE:0
UID:UW-Physics-Event-3477
DTSTART:20141006T170000Z
DTEND:20141006T180000Z
DTSTAMP:20240328T131027Z
LAST-MODIFIED:20140917T211959Z
LOCATION:2535 Engineering Hall
SUMMARY:Chaotic coordinates for the Large Helical Device\, Plasma Phys
ics (Physics/ECE/NE 922) Seminar\, Stuart Hudson\, Princeton Plasma Ph
ysics Laboratory
DESCRIPTION:
\nThe study of dynamical systems is facilitated b
y a coordinate framework with coordinate surfaces that coincide with i
nvariant structures of the dynamical flow. For integrable (e.g. axisym
metric) systems\, a continuous family of invariant surfaces is guarant
eed and action-angle (straight-fieldline) coordinates may be construct
ed. For non-integrable systems\, e.g. stellarators and perturbed tokam
aks\, this continuous family is broken. Nevertheless\,action-angle-lik
e coordinates can still be constructed that simplify the description o
f the dynamics\, where
\npossible. The Poincare-Birkhoff theorem\,
the Aubry-Mather theorem\, and the KAM theorem show that there are im
portant structures that are invariant under the perturbed dynamics\; n
amely the periodic orbits\, the cantori\,and the irrational flux surfa
ces. Coordinates adapted to these invariant sets\, which we call chaot
ic coordinates\,provide substantial advantages. The regular motion bec
omes straight\, and the irregular motion is bounded by\, and dissected
by\, coordinate surfaces that coincide with surfaces of locally-minim
al magnetic-fieldline flux. Chaotic coordinates are based on almost-in
variant surfaces. The theory of quadratic-flux-minimizing (QFM)surface
s is reviewed\, and the numerical techniques that allow high-order QFM
surfaces to be
\nconstructed for chaotic magnetic fields of exper
imental relevance are described. As a practical example\, the chaotic
edge of the
\nmagnetic field as calculated by HINT2 code in the La
rge Helical Device (LHD) is examined. The theoretical and numerical te
chniques for finding the boundary surface are implemented\, and a coor
dinate system based on a selection of QFM surfaces is constructed that
simplifies the description of the magnetic field\; so that\, to a goo
d approximation\, the flux surfaces (including the last closed flux su
rface) become straight and the islands become ‘square’.
URL:https://www.physics.wisc.edu/events/?id=3477
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