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During beam injection from the Alternating Gradient Synchrotron (AGS) to the Relativistic Heavy Ion Collider (RHIC), the beam parameters (βx,y ,α x,y) of the AGS to RHIC (ATR) transfer line [1,2,3,4] at the RHIC injection point, should “match” those of the RHIC synchrotron at the same point. A good beam “matching” requires the knowledge of the optics of the ATR transfer line, which depends partly on the beam parameters (βx,y ,α x,y) at the origin of the ATR transfer line. These beam parameters were originally determined with theoretical calculations [5] (before the installation of the ATR line), and presently, (after the completion of the ATR line) can be determined experimentally. This note addresses the following tasks: a) Outlines the theory of a method which is currently used to obtain the beam parameters (βx,y, α x,y) and the transverse beam emittance (εx,y) at any given point along the ATR line. b) Provides a description of the computer code which uses an algorithm based on the theory described in (a) above, to calculate these beam parameters. c) Presents values of the emittance and beam parameters that have been calculated by using measured beam profiles as input data in the computer code mentioned in (b) above, and compares the beam parameters with theoretically calculated ones. d) Provides suggestions on future improvements of the computer code and on data collection methods which will enable the experimental determination of the dispersion functions ( y x, η , ' ,y x η ). Theoretical Formalism of the Method for the Measurement of Beam Emittance and Beam parameters in a Beam Transfer Line The method which is applied to measure the beam parameters/emittance is based upon two main assumptions. First the beam transport is accomplished with zeroth order (drift space, and dipole) and first order (quadrupole) magnetic elements, and second, the particle distribution within the beam is “normal” (Gaussian) in any of its phase-space coordinates. The first assumption is expressed by the relation

A Computer code to measure the Beam Emittance and Beam Parameters of the ATR Line