Related papers: From the orbit theory to a guiding center parametr…
Future nuclear fusion reactors will have to confine plasma with strong kinetic gradients and small fractions of fusion-born energetic particles (EP) that are ~100 times hotter than the thermal ions. In our analysis, we assume the existence…
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly…
We present new tools to establish axisymmetric equilibrium models of the Milky Way. The models we wish to establish are pairs (V,F) where V is the gravitational potential generated by the whole mass distribution including the dark matter,…
A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with arbitrary-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the…
Compact formulas for trapped-particle and passing-particle guiding-center orbits in axisymmetric tokamak geometry are given in terms of the Jacobi elliptic functions and complete elliptic integrals. These formulas can find applications in…
New integral kernels describing the full-wave dielectric response of Maxwellian tokamak plasmas are presented. They realistically account for the rotational transform and for wave dispersion in presence of equilibrium magnetic field…
The excitation of plasmonic nanoparticles by incident electromagnetic waves at frequencies near their subwavelength resonances induces localized heat generation in the surrounding medium. We develop a mathematical framework to rigorously…
The reconstruction of the equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad-Shafranov equation in axisymmetric configuration. The right-hand side of this equation is a nonlinear source, which represents…
Starting with the fractal inspired distribution functions for Maxwell-Boltzmann, Bose-Einstein and Fermi systems, as reported by F. B\"{u}y\"{u}kkili\c{c} and D. Demirhan, we obtain the corresponding probability distributions and study…
We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky's form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-Fokker-Planck…
The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing components. Accurate quantitative modeling and improved qualitative…
This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron…
This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical…
Steady state distribution functions can be used to calculate stability conditions for modes, radiation energy losses, and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true…
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
Neutral-beam-driven, sub-cyclotron compressional (CAE) and global (GAE) \Alfven eigenmodes are routinely excited in spherical tokamaks such as NSTX(-U) and MAST, have been observed on the conventional aspect ratio tokamak DIII-D, and may be…
Turbulent transport near the X-point of a large tokamak is examined using local, gradient-driven simulations that determine the saturated plasma profiles. The distribution of a representative set of particle tracers evolving within these…
In this work we investigate the numerical identification of the diffusion coefficient in elliptic and parabolic problems using neural networks. The numerical scheme is based on the standard output least-squares formulation where the…
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69…
Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma ? and having increased vertical stability. To understand the confinement properties that might be expected in…