Method for producing a stationary wave field of arbitrary shape comprising the steps of defining at least one volume being limited in the direction of the axis of propagation of a beam, of the type 0≦z≦L; defining an intensity pattern within the said region 0≦z≦L by a function F(z), describing the said localized and stationary intensity pattern, which is approximated by means of a Fourier expansion or by a similar expansion in terms of (trigonometric) orthogonal functions; providing a generic superposition of Bessel or other beams highly transversally confined; calculating the maximum number of superimposed Bessel beams the amplitudes, the phase velocities and the relative phases of each Bessel beam of the superposition, and the transverse and longitudinal wavenumbers of each Bessel beam of the superposition.

Method and apparatus for producing stationary intense wave fields of arbitrary shape

A method is provided that includes transmitting an alternating current along a wire placed along a given axis relative to a magnetic element producing a magnetic field having an axis. The wire may be stretched such that the wire has an audible fundamental frequency. Additionally or alternatively, the alternating current may be a continuous alternating current. The method also includes in at least one instance, detecting a vibration of the wire thereby indicating that a transverse component of the magnetic field is coupled with the alternating current. And in the respective instance(s), the method includes adjusting a position of the wire or magnetic element to at least reduce the vibration of the wire thereby indicating increased alignment of the given axis and magnetic-field axis.

System and method of aligning a magnetic element

Methods and apparatus are provided for modifying a free electron laser (FEL) to produce a non-diverging laser beam. A relativistic electron beam is converted to a Bessel beam in an FEL resonator with conical end mirrors, and the Bessel beam is coupled to the optical field within the laser resonator. The resultant laser beam is propagated with minimal divergence, and is wave corrected at the resonator output to produce a uniform intensity circular beam. The laser beam can be of smaller diameter than that of a conventional resonator due to its diffractionless propagation, which enables the magnetic structure gap within the resonator to be smaller, thus producing a higher optical gain.

Robert R. Rice

Papers

Bessel free electron laser device