MatLab Analysis of RHIC PLL/TF System

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MatLab Analysis of RHIC PLL/TF System

• Carl Schultheiss, Nickolay Malitsky
• Cern PLL Workshop
• June 10-11, 2002

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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

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

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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)

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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.

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MatLab Analysis of RHIC PLL/TF System
MatLab Model
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MatLab Analysis of RHIC PLL/TF System
Beam Simulation Block
?px ?py
x y
Voltage
Voltage
Kicker
UAL
PU
ct
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MatLab Analysis of RHIC PLL/TF System
Beam Simulation Block, Kicker

• Calculate ?px from

Where K is the transverse kicker constant Vk is
the kicker input voltage
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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 Nb(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 xb(t).
• Calculate Vp(t) Zp (Ib(t) xb(t)) where Ib(t)
  Nb(t)e