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.
An RF Beam Position Measurement Module for the Fermilab Energy Doubler
This paper describes the design, realization and performance of the RF Beam Position Measurement Module designed for the Fermilab Energy Doubler. This module measures beam off-axis position and intensity over a 60db dynamic range. For 20 or more contiguous 53MHz beam bunches, the unit will derive a position signal for 108 to 1011 protons per bucket with a position accuracy of ±0.5 mm. Also, the unit will measure the position of 1010 or more protons in a single isolated rf bunch. A beam intensity signal is also generated for triggering purposes. Since 220 of these modules are to be built, cost and performance were optimized. The entire unit is housed in a 1-wide NIM module.
The General Theory of Relativity
THE WORD “SPECIAL” IN “SPECIAL THEORY OF RELATIVITY” means that the theory is restricted to those frames of reference for which the law of inertia holds, that is, inertial frames of reference.* Einstein sometimes referred to them as Galilean frames of reference. At first glance, it does not seem reasonable to expect that the principle of relativity can be extended to non-inertial frames. The reasons are fairly obvious. The principle of relativity that we have been using states that the laws of physics have the same form in all frames of reference to which the principle applies. In other words there should be no way to determine by an experiment which of two frames of reference is in motion relative to the other.