The Impedance Budget Toolbox Structure and main concepts
Introduction ● Early stages of development ● Outline of general structure Based on impedance_toolbox ¹ of D. Amorim and IW2D toolbox² of N. ● Mounet ● Aims to provide a set of tools for simulating the impedance/wake budget of the LHC ¹ Study of the Transverse Mode Coupling Instability in the CERN Large Hadron Collider ²Also called PyZBASE, which is again based on ZBASE by B. Salvant and E. Metral
Impedance/wake functions ● Information about impedance/wake functions stored as actual callable function objects instead of large arrays of wake/impedance data The impedance/wake functions of common elements can occasionally be expressed ○ analytically Allows for arbitrarily fine frequency grid in interesting frequency regions for such functions ○ ○ In cases where analytical expressions cannot be practically obtained and used, the data arrays which define the impedance/wake functions are interpolated to obtain a function ○ Unlike previous toolboxes, the impedance and wake functions belonging to the same component are stored in the same object
Impedance/wake functions Old representation New representation f Z (f) 1 1 Z (f) = f² 2 4 3 9 4 16 5 25
Hierarchical structure Component Budget ● A component contains the wake and/or impedance function in a specific plane for a specific combination of test/source exponents , caused by one device. Element Element ● For example: Z ₓᵈᶦᵖ for collimator 18 ○ Component Component Component Component
Hierarchical structure Element Budget ● Contains a number of components which together describe the impedance/wake effects of a single physical device in a machine. Element Element ● Can also be a useful abstraction for considering a collection of physical devices Component Component Component Component For example: ● ○ Collimator 18
Hierarchical structure Budget Budget ● Contains a number of elements and treats them as one coherent object, looking at the sum of their effects. Contains useful high-level methods for e.g. ● Element Element plotting. For example: ● ○ The LHC impedance budget Component Component Component Component
Test-driven Development ● Allows running a sequence of tests with a single command ● Verify that the program does what you expect it to do ● Confidently make changes to the implementation, knowing that key properties and behavior are preserved
Further work ● Adapting the Fourier transform implementation of IW2D to fit into this framework Generate wake function when only impedance function given, and vice versa ○ ● Implementing function for quickly initializing useful components/elements. ○ Using known formulas with a few given parameters ○ Computing impedance/wake functions from IW2D code ○ E.g. resonators Converting the LHC (and HL-LHC) impedance model into a budget-object ● using the toolbox
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