Stellarator Particle Orbits

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(go to low aspect ratio stellarator gallery)

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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.

Quicktime Movie of passing orbit trajectory (1.1 Mb)

Quicktime Movie of trapped orbit trajectory (0.9Mb)


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: