Higher-order guiding-centre motion in VENUS-LEVIS
Event details
| Date | 18.06.2015 |
| Hour | 10:30 › 11:30 |
| Speaker | Samuel Lanthaler, ETH-Z |
| Location |
PPB 019
|
| Category | Conferences - Seminars |
Starting from the full Lagrangian for a charged particle in a magnetic field, Lie perturbation methods can be used to give a rigorous derivation of Hamiltonian guiding-centre equations which are valid to any desired order in the Larmor radius. This geometric perturbation approach has been used to obtain an analytic derivation of the guiding-centre Lagrangian to second order. Over the past weeks, the resulting equations have been implemented in the VENUS-LEVIS code. The VENUS-LEVIS orbit-solver is designed to investigate fast ions in general 3D magnetic fields. It combines flexibility in the choice of coordinate system with a strict Hamiltonian formulation of guiding-centre and full-orbit equations, switching between the two in the event of strong field variation (gradient, curvature and torsion).
I will show how the consistent use of Lie perturbation methods yields a natural switching between full and guiding-centre orbits. In fact, the availability of both push-forward and pull-back operators would in principle allow for any quantity (e.g. a distribution function) given in terms of full orbit particle coordinates to be transformed to the corresponding quantity in terms of guiding-centre coordinates, and vice versa. The new availability of these operators in VENUS-LEVIS should therefore enhance its flexibility in the future.
Going from first to second order in the guiding-centre approximation has several additional benefits. Among them:
• the coordinate transformation at second order yields an improved switching between full and guiding-centre orbits,
• the inclusion of second order terms, such as the Banos drift, which are important to reproduce matching particle and guiding-centre trajectories,
• improved conservation properties (e.g. invariance of the magnetic moment at second order), which are necessary for the consistency of the guiding-centre approximation,
• the resulting Lagrangian allows for the inclusion of the gyrophase in addition to the guiding-centre position and velocity in a straightforward way.
I will show how the consistent use of Lie perturbation methods yields a natural switching between full and guiding-centre orbits. In fact, the availability of both push-forward and pull-back operators would in principle allow for any quantity (e.g. a distribution function) given in terms of full orbit particle coordinates to be transformed to the corresponding quantity in terms of guiding-centre coordinates, and vice versa. The new availability of these operators in VENUS-LEVIS should therefore enhance its flexibility in the future.
Going from first to second order in the guiding-centre approximation has several additional benefits. Among them:
• the coordinate transformation at second order yields an improved switching between full and guiding-centre orbits,
• the inclusion of second order terms, such as the Banos drift, which are important to reproduce matching particle and guiding-centre trajectories,
• improved conservation properties (e.g. invariance of the magnetic moment at second order), which are necessary for the consistency of the guiding-centre approximation,
• the resulting Lagrangian allows for the inclusion of the gyrophase in addition to the guiding-centre position and velocity in a straightforward way.
Practical information
- Informed public
- Free
Organizer
- Prof. P. Ricci
Contact
- Prof. P. Ricci