The influence of the spent electron beam parameters on possibilities multistage energy recovery in prototype gyrotron developed for DEMO project is determined. characteristics electrodes and magnetic coils a collector with four-stage were optimized considering distributions electrons' coordinates velocities obtained as result calculating electron-wave interaction cavity. In trajectory analysis ...

We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This exists for magnetic fields with nested toroidal flux surfaces} provided $ \oint\mathrm{d}l/B\:(\mathbf{j}\cdot\nabla\psi)=0$, where symbols have their usual meaning, and integral is taken along closed field lines. All quasisymmetric fields, regardless associated form equilibria, must s...

the tenacity of a graph g, t(g), is dened by t(g) = min{[|s|+τ(g-s)]/[ω(g-s)]}, where the minimum is taken over all vertex cutsets s of g. we dene τ(g - s) to be the number of the vertices in the largest component of the graph g - s, and ω(g - s) be the number of components of g - s.in this paper a lower bound for the tenacity t(g) of a graph with genus γ(g) is obtained using the graph's...

Abstract. Error fields and resistive magnetohydrodynamic (MHD) modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. The broken toroidal symmetry leads to enhanced neoclassical toroidal plasma viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal plasma viscosity also results in a steady s...

Progress on gyrokinetic-ion drift-fluid-electron hybrid simulation is reported. Simulation results are shown from a threedimensional toroidal electromagnetic simulation using field-line-following coordinates. It is found that for β & 1.5% there is strong destabilization of Alfvénic ion-temperature-gradient (ITG) driven instabilities. Nonlinear results show a corresponding increase in the the io...

The standard approach for computing the trace of the inverse of a very large, sparse matrix A is to view the trace as the mean value of matrix quadratures, and use the Monte Carlo algorithm to estimate it. This approach is heavily used in our motivating application of Lattice QCD. Often, the elements of A−1 display certain decay properties away from the non zero structure of A, but random vecto...

We solve the problem of a resistive toroid carrying a steady azimuthal current. We use standard toroidal coordinates, in which case Laplace’s equation is R-separable. We obtain the electric potential inside and outside the toroid, in two separate cases: 1) the toroid is solid; 2) the toroid is hollow (a toroidal shell). Considering these two cases, there is a difference in the potential inside ...

The toroidal dipole is a localized electromagnetic excitation, distinct from the magnetic and electric dipoles. While the electric dipole can be understood as a pair of opposite charges and the magnetic dipole as a current loop, the toroidal dipole corresponds to currents flowing on the surface of a torus. Toroidal dipoles provide physically significant contributions to the basic characteristic...

Theories for the toroidal momentum confinement in tokamaks have been developed. It is shown that the logarithmic gradient of the toroidal flow is a linear combination of logarithmic gradients of the plasma pressure and the temperature in neoclassical quasilinear theory. The fluctuation-induced toroidal stress consists of a diffusion flux, a convective flux, and a residual flux. The effects of a...

Lattice formulations of gravity can be used to study non-perturbative aspects quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model that has been in this way. It built-in time foliation but coordinate-independent the spatial directions. The higher-order phase transitions observed may define continuum limit theory. Some are better studied when topology space toroidal rather t...