Phase and synchronous detector theory as applied to beam position and intensity measurements
A popular signal processing technique for beam position measurements uses the principle of amplitude-modulation-to-phase-modulation (AM/PM) conversion and phase detection. This technique processes position-sensitive beam-image-current probe-signals into output signals that are proportional to the beam's position. These same probe signals may be summed and processed in a different fashion to provide output signals that are proportional to the peak beam current. This paper derives the transfer functions for the AM/PM beam position and peak beam current processors.
C E~M-POSITION-TRANSFE~ FUNCTIONS USIN CIRCULAR AM-POSITION MONIT
A cylindrical beam-position monitor (BPM) used in many accelerator facilities has four electrodes on which beamimage currents induce bunched-beam signals. These probe-electrode signals are geometrically configured to provide beam-position information about two orthogonal axes. An electronic processor performs a mathematical transfer function (TF) on these BPM-electrode signals to produce output signals whose time-varying amplitude is proportional to the beam's vertical and horizontal position. This paper will compare various beam-position TFs using both pencil beams and will further discuss how diffuse beams interact with some of these TFs. 1 BPM SENSITIVITY BPMs typically have four electrodes on which beam image currents induce bunched-beam signals. These probe signals are initially processed or naturally configured to provide information about the horizontal and vertical axes that describes the beam's position. BPMs may have a variety of cross-sectional shapes, such as circular, rectangular, elliptical, etc. For the circular-cross-section BPM detecting thin beams, sufficient beam position information is contained within Ry . Specifically,
Mathematical Time and Physical Time in the Theory Of Relativity
In the Theory of Relativity time is an imaginary quantity that can not be observed; it is a multiplication of a number that indicates duration of material change and number i that is an imaginary number. i on the square is -1. Time i⁄t is a mathematical time that describes the speed and the duration of material change. In the Universe one can observe physical time only as a stream of material change. It is not that change run in physical time, change itself is physical time.. Distinction between imaginary mathematical time and visible physical time opens some new perspectives into interpretation of Theory of Relativity. c