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It is argued that the relativistic Vlasov–Maxwell equations of the kinetic theory of plasma approximately describe a relativistic system of N charged point particles interacting with the electromagnetic Maxwell fields in a Bopp–Landé–Thomas–Podolsky (BLTP) vacuum, provided the microscopic dynamics lasts long enough. The purpose of this work is not to supply an entirely rigorous vindication, but to lay down a conceptual road map for the microscopic foundations of the kinetic theory of special-relativistic plasma, and to emphasize that a rigorous derivation seems feasible. Rather than working with a BBGKY-type hierarchy of n -point marginal probability measures, the approach proposed in this paper works with the distributional PDE of the actual empirical 1-point measure, which involves the actual empirical 2-point measure in a convolution term. The approximation of the empirical 1-point measure by a continuum density, and of the empirical 2-point measure by a (tensor) product of this continuum density with itself, yields a finite- N Vlasov-like set of kinetic equations which includes radiation-reaction and nontrivial finite- N corrections to the Vlasov–Maxwell–BLTP model. The finite- N corrections formally vanish in a mathematical scaling limit N → ∞ in which charges ∝ 1 / √ N . The radiation-reaction term vanishes in this limit, too. The subsequent formal limit sending Bopp’s parameter ϰ → ∞ yields the Vlasov–Maxwell model.

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-centre trajectories of plasma particles undergoing $\\boldsymbol {E}\\times \\boldsymbol {B}$ drift motion, considering that the electric field has a stationary non-monotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a non-monotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the safety factor profile parameters, the appearance and breakup of these shearless curves are observed. The shearless curve's successive breakup and recovery are explained using concepts from bifurcation theory. We also present bifurcation sequences associated with the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study the transport dependence on the perturbation amplitudes, relative phase, and spatial-mode choice. Using particle transmissivity as a confinement criterion, identical-mode pairs exhibit phase-controlled behavior: anti-phase waves produce destructive interference and strong confinement while in-phase waves add constructively and drive chaotic transport. Mode-mismatched pairs produce richer phase-space structure with higher-order resonances and sticky regions; the transmissivity boundaries become geometrically complex. Box-counting dimensions quantify this: integer dimension smooth boundaries for identical modes versus non-integer fractal-like dimension for distinct modes, demonstrating that phase and spectral content of waves jointly determine whether interference suppresses or promotes transport.

A canonical procedure transforming the unitary evolution group Ut in a contracting semigroup Wt for phase-space ensembles has been developed for Kolmogorov dynamical systems in a series of recent papers. This paper investigates the physical meaning of this transformation. We stress that, for sufficiently unstable dynamical systems in which phase-space points are identified with an arbitrary but finite precision, one must take into account the undiscernibility of trajectories having the same asymptotic behavior in the future. The fundamental objects of our description are thus bundles of converging trajectories. We show that such an ensemble, corresponding to initial conditions whose support has finite measure, is then represented by a distribution function (called a Boltzmann ensemble) that evolves to equilibrium under the action of a markovian semigroup. The usual Gibbs-Koopman ensembles satisfying the Liouville equation are recovered as a singular limit. This work validates Boltzmann's intuition for a class of unstable dynamical systems and appears as a step toward the derivation of equations exhibiting irreversibility at a microscopic level.

The ExB electron drift instability, present in many plasma devices, is an important agent in cross-field particle transport. In presence of a resulting low frequency electrostatic wave, the motion of a charged particle becomes chaotic and generates a stochastic web in phase space. We define a scaling exponent to characterise transport in phase space and we show that the transport is anomalous, of super-diffusive type. Given the values of the model parameters, the trajectories stick to different kinds of islands in phase space, and their different sticking time power-law statistics generate successive regimes of the super-diffusive transport.

In tokamak-confined plasmas, particle transport can be reduced by modifying the radial electric field. In this paper, we investigate the influence of both a well-like and a hill-like shaped radial electric field profile on the creation of shearless transport barriers (STBs) at the plasma edge, which are a type of barrier that can prevent chaotic transport and are related to the presence of extreme values in the rotation number profile. For that, we apply an ExB drift model to describe test particle orbits in large aspect-ratio tokamaks. We show how these barriers depend on the electrostatic fluctuation amplitudes and on the width and depth (height) of the radial electric field well-like (hill-like) profile. We find that, as the depth (height) increases, the STB at the plasma edge becomes more resistant to fluctuations, enabling access to an improved confinement regime that prevents chaotic transport. We also present parameter spaces with the radial electric field parameters, indicating the STB existence for several electric field configurations at the plasma edge, for which we obtain a fractal structure at the barrier/non-barrier frontier, typical of quasi-integrable Hamiltonian systems.

A model calculation is presented to characterize the anomalous cross-field transport of electrons in a Hall thruster geometry. The anomalous nature of the transport is attributed to the chaotic dynamics of the electrons arising from their interaction with fluctuating unstable electrostatic fields of the electron cyclotron drift instability that is endemic in these devices. Electrons gain energy from these background waves leading to a significant increase in their temperature along the perpendicular direction \\(T_\\perp / T_\\parallel \\sim 4\\) and an enhanced cross-field electron transport along the thruster axial direction. It is shown that the wave-particle interaction induces a mean velocity of the electrons along the axial direction, which is of the same order of magnitude as seen in experimental observations.

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-center trajectories of plasma particles undergoing ExB drift motion, considering that the electric field has a stationary nonmonotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a nonmonotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the parameters of the safety factor profile, the appearance, and breakup of these shearless curves are observed. The successive shearless curves breakup and recovering is explained using concepts from bifurcation theory. We also present bifurcation sequences associated to the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless invariant curves that act as transport barriers in the phase space. Although reported in numerical investigations, the shearless bifurcation, i.e., the emergence scenario of multiple shearless curves, is not well understood. In this work, we derive an area-preserving map as a local approximation of a particle transport model for confined plasmas. Multiple shearless curves are found in this area-preserving map, with the same shearless bifurcation scenario numerically observed in the original model. Due to its symmetry properties and simple functional form, this map is proposed as a model to study shearless bifurcations.

We investigate the influence of the finite Larmor radius on the dynamics of guiding-center test particles subjected to an \\(\\mathbf{E} \\times \\mathbf{B}\\) drift in a large aspect-ratio tokamak. For that, we adopt the drift-wave test particle transport model presented by W. Horton [Physics of Plasmas \\textbf{5}, 3910 (1998)] and introduce a second-order gyro-averaged extension, which accounts for the finite Larmor radius effect that arises from a spatially varying electric field. Using this extended model, we numerically examine the influence of the finite Larmor radius on chaotic transport and the formation of transport barriers. For non-monotonic plasma profiles, we show that the twist condition of the dynamical system, i.e.,\\ KAM theorem's non-degeneracy condition for the Hamiltonian, is violated along a special curve, which, under non-equilibrium conditions, exhibits significant resilience to destruction, thereby inhibiting chaotic transport. This curve acts as a robust barrier to transport and is usually called shearless transport barrier. While varying the amplitude of the electrostatic perturbations, we analyze bifurcation diagrams of the shearless barriers and escape rates of orbits to explore the impact of the finite Larmor radius on controlling chaotic transport. Our findings show that increasing the Larmor radius enhances the robustness of transport barriers, as larger electrostatic perturbation amplitudes are required to disrupt them. Additionally, as the Larmor radius increases, even in the absence of transport barriers, we observe a reduction in the escape rates, indicating a decrease in chaotic transport.