1. MatLab Analysis of RHIC PLL/TF System Carl Schultheiss, Nickolay Malitsky Cern PLL Workshop June 10-11, 2002

2. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Requirements Beam Simulation Block (BSB) should recreate the beam spectrum including the dynamics. How fast does the tune frequency change when excited by a step change in the quad current? BSB should include chromaticity, both the signal strength reduction due to tune spread, and the interference due to tune frequencies from the other plane.

3. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Requirements (continued) BSB should include coupling, again modeling interference from frequencies due to the other plane. The BSB should be able to simulate the beam at requested reference energies.

4. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Requirements (continued) BSB should be compatible with Simulink. Written as an S- function. Block transfer function should have the voltage to the kicker as input and the voltage from PU as output. This is a time-domain representation. What type of BSB will meet these requirements? A simple frequency representation will not properly represent all the requirements, therefore tracking programs will be probably be required.

5. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Requirements (continued)  Which tracking program?  UAL  Kraken Accelerator Toolbox for MatLab written by A. Terebilo from SLAC.

6. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block Description Run Time Inputs Voltage signal to kicker. Delta strengths (currents) to main vertical and horizontal quad magnets. Delta strengths (currents) to vertical and horizontal sextupole magnets.

7. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block Description (continued)  Run Time Outputs Voltage signal from resonant BPM. Signal is representation of beam spectrum.

8. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block Description (continued) Initial Input Parameters Bunch Description Reference Beam Energy Particle Mass and Charge Number of particles in bunch Number of bunches Bunch Length Energy Spread within the bunch

9. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block Description (continued)  Initial Input Parameters (continued) Accelerator Description Name of SXF RHIC file Names of selected elements

10. 06/11/02 MatLab Analysis of RHIC PLL/TF System S-Function Interface

11. 06/11/02 MatLab Analysis of RHIC PLL/TF System UAL-based Beam Simulation Block (BSB) RHIC Data Source (SXF File) Simulator Model Combination of sector maps and element trackers UAL Collection of C++ accelerator libraries Simulink PLL Model Discrete State S-Function BPM datanumber of turns kicker Quad and sextupole strengths Beam Simulation Block

12. 06/11/02 MatLab Analysis of RHIC PLL/TF System Simulink SimStruct-based Data Exchange Approach Access to local C++ objects : ssGetPWork: access a pointer to the C/C++ object (e.g. accelerator, simulator, etc.) used locally in the S-Function methods (straightforward and perfect) Importing data via Input Port: ssGetInputPortRealSignal : access an array of double elements connected to an input port (straightforward, but primitive) ssGetInputPortSignal : get address to input signals of type other that double (perfect, but needs to be studied)

13. 06/11/02 MatLab Analysis of RHIC PLL/TF System Simulink SimStruct-based Data Exchange Approach (continued) Exporting data via Output Port: ssGetOutputPortRealSignal : access an array of double elements connected to an output port (straightforward, but primitive) ssGetOutputPortSignal : get address to output signals of type other that double (perfect, but needs to be studied)

14. 06/11/02 MatLab Analysis of RHIC PLL/TF System Platform The UAL library compiles on the Linux g++ compiler version 2.95.2. MatLab versions 6.1 and 6.0 are compatible with this compiler. Simulation time is a concern. Linux will allow the simulation to run on a multiprocessor cluster. Selection of the tracking engine will be driven by accuracy, and the time a turn takes to compute.

15. 06/11/02 MatLab Analysis of RHIC PLL/TF System MatLab Model

16. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block KickerUALPU Voltage pxpypxpy xyxy ct

17. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block, Kicker Calculate  p x from: Where K is the transverse kicker constant V k is the kicker input voltage

18. 06/11/02 MatLab Analysis of RHIC PLL/TF System Beam Simulation Block, PU Bin the bunch according to ct; perhaps 10 bins per bunch Count the number of particles in a bin and use to compute the charge in the bin N b (t). Where t is the time of arrival of the center of the bin. Find the average position of the particles in the bin and use as x b (t). Calculate V p (t) = Z p (I b (t) x b (t)) where I b (t) = N b (t)e