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__Stellarator Particle Orbits__

(go to
high aspect ratio stellarator gallery)
(go to
low aspect ratio stellarator gallery)
(return
to Main MHD visualization page)

Understanding particle orbits in stellarators is fundamental in
assessing their confinement and transport properties. The orbit
trajectory equations are derived from Hamiltonian dynamics and are
typically lead to ordinary differential equations in terms of four
canonical conjugate momentum and position variables. These are then
often rewritten in terms of 3 spatial coordinates and one
velocity-like variable before being solved numerically. In the
equilibrium magnetic field structure of the stellarator the energy
and magnetic moment are conserved quantities. Since the magnetic
field strength varies along the particle orbit, the parallel and
perpendicular components of velocity will vary along the trajectory
and trapping regions can be present where the parallel velocity
component goes to zero. In the following pictures, we show orbits in
white for a low aspect ratio stellarator for 3 different values of
initial pitch angle (the angle between the particle's velocity and
the magnetic field). The first two rows of figures show orbits which
experience trapping along their trajectories while the third row of
pictures shows orbits which have no trapping. We have also included
links to separate pages which have quicktime movies of time-dependent
orbit trajectories.

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__Deeply Trapped Orbit (large pitch angle):__

__Shallowly Trapped (transitional) Orbit - moderate
pitch angle:__

__Passing Orbit (this also is close to the structure
of the magnetic field lines) - small pitch angle:__