Toroidal regularization of the guiding center Lagrangian
- Courant Inst. of Mathematical Sciences, New York, NY (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, the Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- Grant/Contract Number:
- AC52-07NA27344; FG02-86ER53223; AC05-06OR23100; AC52-07NA2734
- OSTI ID:
- 1424084
- Alternate ID(s):
- OSTI ID: 1409875
- Report Number(s):
- LLNL-JRNL-737871; TRN: US1801902
- Journal Information:
- Physics of Plasmas, Vol. 24, Issue 11; ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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