Generation of E × B flow shear by finite orbit width effects from heat sources in tokamaks

We present a possible mechanism for the generation of strong E × B flow shear relevant to internal transport barrier formation in tokamak plasmas. From gyrokinetic calculations, we show that strong E × B flow shear can be generated by finite orbit width (FOW) effects associated with a non-uniform heat source and is sufficient to lead to transport barrier formation in the core region with a moderate power level. Two FOW effects inducing neoclassical polarization are shown to be responsible for this: 1) the radial drift of particle orbit center due to the variation of the heat source within orbit width and 2) the non-uniformly evolved orbit width by the non-uniform heating.

Charged Particles in Near-Earth Space

In this chapter we discuss the concepts that govern the motion of charged particles in the geomagnetic field and the principles how they stay trapped in the radiation belts. The basic particle orbit theory can be found in most plasma physics textbooks. We partly follow the presentation in Koskinen (Physics of space storms, from solar surface to the earth. Springer-Praxis, Heidelberg, 2011). A more detailed discussion can be found in Roederer and Zhang (Dynamics of magnetically trapped particles. Springer, Heidelberg, 2014). A classic treatment of adiabatic motion of charged particles is Northrop (The adiabatic motion of charged particles. Interscience Publishers, Wiley, New York, 1963).

Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic—although possibly incommensurate—motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet—to our knowledge—such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper, we present a closed-form functional relation which allows us to express coordinates of the particle’s orbit without the need to pass through the hourly law of motion.

Closed-Form Solution of Adiabatic Particle Trajectories in Axis-Symmetric Magnetic Fields

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.

Collisionless relaxation of a disequilibrated current sheet and implications for bifurcated structures

Current sheets are ubiquitous plasma structures that play the crucial role of being energy sources for various magnetic phenomena. Although a plethora of current sheet equilibrium solutions have been found, the collisionless process through which a disequilibrated current sheet relaxes or equilibrates remains largely unknown. Here we show, through analyses of phase-space distributions of single-particle orbit classes and particle-in-cell simulations, that collisionless transitions among the orbit classes are responsible for this process. Bifurcated current sheets, which are readily observed in geospace but whose origins remain controversial, are shown to naturally arise from the equilibration process and thus are likely to be the underlying structures in various phenomena; comparisons of spacecraft observations to particle-in-cell simulations support this fact. The bearing of this result on previous explanations of bifurcated structures is also discussed.

Particle orbiting motion in a confined microvortex

Particle motion in viscous fluids is a common and fascinating phenomenon. The hydrodynamics of a trapped finite-size particle recirculating along a stable orbit within a microvortex is still puzzling. Herein we report experimental observations of the orbiting motion of a finite-size particle in a vortex confined in a microcavity. The orbiting particle keeps crossing the streamlines with acute changes in velocity along the orbit, which can be divided into three stages: acceleration, swerving, and following. By examining the relationship between particle orbit and vortex streamlines, we uncover a particle slingshot effect and slip motion. Particle motion and vortex structure in three dimensions are also studied, revealing many new fascinating particle motion phenomena. The results provide new insights into the physics of particle motion in vortices.

Collisionless Relaxation of a Disequilibrated Current Sheet and Implications for Bifurcated Structures

Current sheets are ubiquitous plasma structures that play the crucial role of being energy sources for various magnetic phenomena. Although a plethora of current sheet equilibrium solutions have been found, the collisionless process through which a disequilibrated current sheet relaxes or equilibrates remains largely unknown. Here we show, through analyses of phase-space distributions of single-particle orbit classes and particle-in-cell simulations, that collisionless transitions among the orbit classes are responsible for this process. Bifurcated current sheets, which are readily observed in geospace but whose origins remain controversial, are shown to naturally arise from the equilibration process and thus are likely to be the underlying structures in various phenomena; comparisons of spacecraft observations to particle-in-cell simulations support this fact. The bearing of this result on previous explanations of bifurcated structures is also discussed.