Guiding Center Dynamics Research Articles

Reduction and approximation in guiding-center dynamics

The guiding-center and gyrocenter formulations of plasmas in strong magnetic fields aim at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. At each finite level of a perturbative treatment these formulations are approximations to the true dynamics. Here we discuss the conditions under which guiding-center dynamics may become an exact operation in the framework of reduction of dynamical systems with symmetry.

Covariant gyrokinetic description of relativistic plasmas

A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of magnetized rel- ativistic plasmas in intense gravitational fields, such as in accretion disks around compact gravitating bodies. The goal of this paper is to formulate a gyrokinetic description for a Vlasov-Maxwell plasma within the framework of general relativity. A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and corresponding expres- sions for the four-current density, is derived for an arbitrary four-dimensional coordinate system. General relativity effects are taken into account via the tetrad formalism. The guiding-center dynamics of charged particles and the gyrokinetic transforma- tion are obtained accurate to the second order of the ratio of the Larmor radius to the nonuniformity scale length. The wave terms with arbitrary wavelength (kρL ∼ 1) are described in the second-order (nonlinear) approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged Maxwell equations. The derivation is based on the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. Its results improve on existing limitations of the gyrokinetic theory.

Covariant descriptions of the relativistic guiding-center dynamics

The relativistic guiding center dynamics of charged particles is described in terms of noncanonical variables. The gyrokinetic transformation is obtained using the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. It is shown that the definition of the ignorable gyrophase (as well as those of the magnetic moment and the gyrocenter energy) is not unique, and allows for several free functions in the gyrokinetic transformation. This freedom can be interpreted as a choice of the reference frame. One of these frames, namely that moving with the relativistic version of the E_×B_-drift velocity, generates the simplest and intuitive description.

Relativistic guiding-center dynamics in the presence of strong flows

A Lagrangian approach to relativistic particle guiding-center dynamics in strongly magnetized plasmas, based on a covariant formulation, is presented, proving that a four-dimensional transformation is required in order to define the correct relativistic gyrophase-averaged Lagrangian. Comparisons with previous approaches show that these become potentially inconsistent, particularly for magnetoplasmas exhibiting relativistic mass-flow velocities and/or deeply relativistic particles, causing the paradox of hyper-relativistic guiding-center velocities. To avoid this inconvenience, the relativistic velocity addition law is adopted to describe the particle motion with respect to the reference frame locally at rest with the fluid. Based on the adoption of the relativistic Hamilton principle, new expressions are determined for the relativistic guiding-center velocity transformation, the relativistic magnetic moment and the relativistic gyrokinetic equations of motion.

Probability of orbit transition in asymmetric toroidal plasma

Trapped particles in stellarators and tokamaks can be either locally trapped in the ripple wells or toroidally trapped by the 1/R variation of the magnetic field strength. Transitioning particles make transitions back and forth between these two states. The transition probability gives the relative rate of toroidally trapped particles to become locally trapped. In this paper the transition probably is uniquely defined, and an improved analytical calculation of the transition probability is given. It is then calculated numerically by following the full guiding-center dynamics. Comparison with the numerical results shows that the present calculation is more accurate than those previously presented.

Finite force-free pulsar atmosphere models

Models of cold plasma atmospheres in a dipole magnetic field which are both force-free, rho/sub q/(ExB)=0, and finite in extent are studied. These models satisfy the local force-free condition which is necessary for a minimum energy state and have the required continuous electric field at the plasma-vacuum surface. By Pilipp's theorem it is known that such atmospheres cannot rigidly rotate. The nature of this differential rotation of the plasma is determined for several models. It is noted that all finite models may allow for corotational, toroidal regions about the equatorial plane, characterized by the fact that these magnetic field lines do not extend into the vacuum region. For all models examined, the charge density has only one sign on all magnetic surfaces which extend into the vacuum. Since all models have an arbitrary scaling factor, any corotating portion of the magnetosphere may, or may not, have only one charge sign on magnetic surfaces. All models are apparently stable to guiding center perturbations, but obviously cannot all have the desired minimum configurational energy, which is one of the future refinements needed to select a realistic model. These models indicate that any current loop which might result from the cross-field breakdown ofmore » guiding center dynamics, due to E/sub perpendicular/>B, would occur near the juncture of the plasma-vacuum surface and the equatorial plane. Such currents would flow from a ring around the poles rather than directly from over the poles.« less