相关论文: On the singularity of Lie-transform perturbation a…
We introduce a gyro-gauge independent formulation of a simplified guiding-center reduction, which removes the fast time-scale from particle dynamics by Lie-transforming the velocity vector field. This is close to Krylov-Bogoliubov method of…
A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation…
The guiding-center reduction is studied using gyro-gauge-independent coordinates. The Lagrangian 1-form of charged particle dynamics is Lie transformed without introducing a gyro-gauge, but using directly the unit vector of the component of…
It's pointed out that the values of the generators derived by the modern gyrokinetic theory are inappropriately amplified by the pullback transform with the existence of electromagnetic perturbation, and the trajectory equations of the…
The well-known gyrokinetic problem regards the perturbative expansion related to the dynamics of a charged particle subject to fast gyration motion due to the presence of a strong magnetic field. Although a variety of approaches have been…
It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering…
Dr. Brizard's comment on my work is based on a conceived procedure that does not come from my work. The defense of his claim that the modification of the so-called standard Lie's transform theory is unnecessary is also unsupported. This…
This paper pointed out that the usual gyrocenter transform, which implements single-parameter Lie transform perturbation theory on Lagrangian differential 1-form of the orbit of charged particles immersed in a strong magnetic field, is not…
A recent paper by L.~Zheng [Phys. Plasmas, 30, 042515 (2023)] presented a critical analysis of standard Lie-transform perturbation theory and suggested that its application to the problem of charged-particle motion in a magnetic field…
In this paper, to fit the multi-scale perturbations, the single-parameter Lie transform perturbation theory given in [Ann Phys, 151 1 (1983)] is generalized to a multi-parameter case, which provides a formal solution of the new Lagrangian…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
In the Lagrangian theory of guiding center motion, an effective magnetic field $\mathbf{B}^* = \mathbf{B}+(m/e)v_\parallel\nabla \times {\mathbf{b}}$ appears prominently in the equations of motion. Because the parallel component of this…
By abstracting a connection between gauge symmetry and gauge identity on a noncommutative space, we analyse star (deformed) gauge transformations with usual Leibnitz rule as well as undeformed gauge transformations with a twisted Leibnitz…
Singular perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, applying these methods is a subtle art owing to the lack of globally applicable algorithms. Inspired by the fact…
We reconsider gauge-transformation properties in chiral gauge theories on the lattice observing all pertinent information and show that these properties are actually determined in a general way for any gauge group and for any value of the…
Stochastic inference on Lie groups plays a key role in state estimation problems such as; inertial navigation, visual inertial odometry, pose estimation in virtual reality, etc. A key problem is fusing independent concentrated Gaussian…
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…
The Lie claw digraph controls Background Independence and thus the Problem of Time and indeed the Fundamental Nature of Physical Law. This has been established in the realms of Flat and Differential Geometry with varying amounts of extra…
The problem of constructing gauge invariant currents in terms of light-cone bound-state wave functions is solved by utilising the gauging of equations method. In particular, it is shown how to construct perturbative expansions of the…
The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations,…