Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

Abstract

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating a term containing the covariant component $B_{{\Psi }_{\mathrm{P}}}$ of the magnetic field vector with respect to the poloidal flux function ${\Psi }_{\mathrm{P}}$. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency and a single toroidal mode number $n$, we show that simulations using the code ORBIT with and without $B_{{\Psi }_{\mathrm{P}}}$ yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the Appendix), which show that the unabridged GC Lagrangian with $B_{{\Psi }_{\mathrm{P}}}$ retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation, and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) & (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen)modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

10 pages Main + 6 pages Appendix, 16 figures. Submitted

References in corpus (4)

• Toroidal regularization of the guiding center Lagrangian
• On the effect of beating during nonlinear frequency chirping
• On the validity of the guiding-center approximation in a magnetic dipole field
• Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of $\mathbf{E}$ and $\mathbf{B}$

Cited by in corpus (2)

• Kinetic versus Magnetic Chaos in Toroidal Plasmas: A systematic quantitative comparison
• Faithful guiding-center orbits in an axisymmetric magnetic field