Related papers: General formulation of impedance in Frenet-Serret …
The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic…
The concepts of wake fields and impedance are introduced to describe the electromagnetic interaction of a bunch of charged particles with its environment in an particle accelerator. The wake fields can act back on the beam and lead to…
This note gives an introduction to the theories of impedances and wakes in particle accelerators. The standard formulation assumes that the beam is traveling along a straight orbit with constant velocity $\vec{v}=v\vec{e}_z$. On this note,…
The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a "fiducial observer." We find that a relativistically complete and…
The motion of test particles along circular orbits in the vacuum $C$ metric is studied in the Frenet-Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.
The dynamic impedance of a sphere oscillating in an elastic medium is considered. Oestreicher's formula for the impedance of a sphere bonded to the surrounding medium can be expressed simply in terms of three lumped impedances associated…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as…
The coherent deflection of charged particles bunch in the field of an counter-propagating bunch is considered. Bunches collide at non-zero crossing angle and they have different energies. Charge distributions in both colliding bunches are…
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for…
Acceleration is a fundamental concept in physics which is taught in mechanics at all levels. Here, we discuss some challenges in teaching this concept effectively when the path along which the object is moving has a curvature and…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
A comparative analysis of a description of spin dynamics in the cylindrical and Frenet-Serret coordinate systems is carried out. An equivalence of these two systems is shown. A possibility of efficient use of the cylindrical coordinate…
The spin-dependent inertial force in an accelerating system under the presence of electromagnetic fields is derived from the generally covariant Dirac equation. Spin currents are evaluated by the force up to the lowest order of the…
We consider the interaction between an electrically polarizable atom in its fundamental state and a wedge constituted by two semi-infinite perfectly conducting plates. Using a formalism based on a master equation, we compute the dispersion…
Theory of the ac spin injection from a ferromagnetic electrode into a normal conductor through a tunnel or Schottky contact is developed. Diffusion and relaxation of non-equilibrium spins results in a frequency dependent complex impedance…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard…
The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for…