Ksenia R. Samokhvalova

Analytical and numerical calculations of the dispersion characteristics of two-dimensional dielectric photonic band gap structures

An exact analytical dispersion relation is derived for transverse-magnetic modes with kz=0 in a particular two-dimensional rectangular photonic band gap structure. The dispersion relation is analyzed, and the dispersion characteristics are determined. Analytical results are compared with results from the Massachusetts Institute of Technology Photonic Band Gap Structure Simulator (PBGSS) code. The error tolerance in the PBGSS code is established. Finally, the attenuations of modes with frequencies in global band gaps are computed analytically.

Warm-fluid equilibrium theory of a thermal charged-particle beam in a periodic solenoidal focusing field

A warm-fluid equilibrium theory is presented which describes a new thermal equilibrium of a rotating charged-particle beam in a periodic solenoidal focusing field. Warm-fluid equations are solved in the paraxial approximation. The rms beam envelope, the density and flow velocity profiles, and the self-consistent Poisson equations are derived. Density profiles are calculated numerically for high-intensity and low-intensity beams. Temperature effects in such beams are investigated. Radial confinement of the beam is discussed.

Adiabatic thermal equilibrium theory for periodically focused axisymmetric intense beam propagation

An adiabatic equilibrium theory is presented for an intense, axisymmetric charged-particle beam propagating through a periodic solenoidal focusing field. The thermal beam distribution function is constructed based on the approximate and exact invariants of motion, i.e., a scaled transverse Hamiltonian and the angular momentum. The approximation of the scaled transverse Hamiltonian as an invariant of motion is validated analytically for highly emittance-dominated beams and highly space-charge-dominated beams, and numerically tested to be valid for cases in between with moderate vacuum phase advances (σv<90°). The beam root-mean-square (rms) envelope equation is derived, and the self-consistent nonuniform density profile is determined. Other statistical properties such as flow velocity, temperature, total emittance and rms thermal emittance, equation of state, and Debye length are discussed. Numerical examples are presented, illustrating the effects of the beam perveance, emittance, and rotation on the beam...

Simulation of the bulk and surface modes supported by a diamond lattice of metal wires

We present a numerical study of the electromagnetic properties of the three-dimensional metallic wire lattices operating at microwave frequencies with applications to advanced accelerating structures and microwave sources. The metallic lattices can be considered as “artificial plasmas” because they demonstrate the properties of plasmas with a negative dielectric constant. Bulk modes in a diamond lattice of metal wires and surface modes on its interface are calculated. It is shown that the lattice can be modeled as an anisotropic medium with spatial dispersion. In contrast to a simple cubic lattice, the diamond lattice allows the existence of three different interfaces—one isotropic and two anisotropic. The surface modes supported by these interfaces are affected by spatial dispersion, in sharp contrast with the surface mode on an isotropic vacuum/plasma interface. For particle accelerator applications, we identify the electromagnetic mode confined by a plasmonic waveguide formed as a defect in a diamond lattice. All deleterious higher order modes excited as wakefields from the accelerating particle are found to be leaky. The diamond lattice is also useful as a research tool for studying particle radiation in media with spatial dispersion.

Warm‐Fluid Equilibrium Theory of a Charged Particle Beam in a Periodic Solenoidal Focusing Field

A warm‐fluid equilibrium theory is presented which describes a new thermal rigid‐rotor equilibrium of a charged particle beam in a periodic solenoidal focusing field. Warm‐fluid equations are solved in the paraxial approximation. The rms beam envelope and self‐consistent Poisson equations are derived. Density profiles are calculated numerically for high‐intensity beams. Temperature effects in such beams are investigated.

Thermal Rigid-rotor Equilibrium of Intense Beam Propagation through a Periodic Solenoidal Focusing Field

A new thermal rigid‐rotor Vlasov equilibrium is obtained for an intense, axisymmetric charged‐particle beam with nonuniform thermal density in the radial direction propagating through a periodic solenoidal focusing field. The thermal beam distribution function is constructed and the beam envelope equation is derived, and examples of periodically focused rigid‐rotor thermal equilibria are presented. Statistical properties and possible applications of the present beam equilibrium are discussed.

Adiabatic warm-fluid equilibrium theory of thermal charged-particle beams in alternating-gradient focusing fields

An adiabatic warm-fluid equilibrium theory for a thermal charged-particle beam in an alternating-gradient focusing field is presented. Warm-fluid equilibrium equations are solved in the paraxial approximation. The theory predicts that the four-dimensional rms thermal emittance of the beam is conserved, but the two-dimensional rms thermal emittances are not constant. The rms beam envelope equations and the self-consistent Poisson equation, governing the beam density and potential distributions, are derived. Although the presented rms beam envelope equations have the same form as the previously known rms beam envelope equations, the evolution of the rms emittances in the present theory is given by analytical expressions. The density does not have the simplest elliptical symmetry, but the constant-density contours are ellipses, and the aspect ratio of the elliptical constant-density contours decreases as the density decreases along the transverse displacement from the beam axis. For high-intensity beams, the beam density profile is flat in the center of the beam and falls off rapidly within a few Debye lengths, and the rate at which the density falls is approximately isotropic in the transverse directions.

Warm-fluid equilibrium theory of an intense charged-particle beam propagating through a Periodic solenoidal focusing channel

A warm-fluid theory of a thermal equilibrium for a rotating charged-particle beam in a periodic solenoidal focusing magnetic field is presented. The warm-fluid equilibrium equations are solved in the paraxial approximation. It is shown that the flow velocity for the thermal equilibrium corresponds to periodic rotation and radial pulsation. The equation of state for the thermal equilibrium is adiabatic. The beam envelope equation and self-consistent Poissons equation are derived. The comparison between analytically computed density profiles and the recent experimental results from University of Maryland Electron Ring (UMER) is presented. Temperature effects in the beam equilibria are investigated. The radial confinement of the beam is discussed.

Analytical and Numerical Calculations of 2D Dielectric Photonic Band Gap Structures

Dielectric photonic band gap structures have many promising applications for optical devices, microwave generation, and laser acceleration. We present the results of our recent work on analytical calculations of 2D photonic band gap structures with kz=0. We compare the analytical results with computer simulation results from MIT Photonic Band Gap Structure Simulator (PBGSS) code. We also discuss the convergence of the computer simulation results to the analytical results.