The Impedance Budget Toolbox Structure and main concepts - - PowerPoint PPT Presentation

The Impedance Budget Toolbox

Structure and main concepts

Introduction

• Early stages of development
• Outline of general structure
• Based on impedance_toolbox¹ of D. Amorim and IW2D toolbox² of N.

Mounet

• Aims to provide a set of tools for simulating the impedance/wake budget
• f the LHC

¹Study 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 2 4 3 9 4 16 5 25

Z(f) = f²

Hierarchical structure

Component

• 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.

• For example:

○ Zₓᵈᶦᵖ for collimator 18

Component Component Component Component

Element Element

Budget

Hierarchical structure

Element

• Contains a number of components which

together describe the impedance/wake effects of a single physical device in a machine.

• Can also be a useful abstraction for

considering a collection of physical devices

• For example:

○ Collimator 18

Component Component Component Component

Element Element

Budget

Hierarchical structure

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.

plotting.

• For example:

○ The LHC impedance budget

Component Component Component Component

Element Element

Budget

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