Impedance models for the collider at 3 TeV center of mass #

The first component studied for the collider impedance model is the vacuum chamber. We assume for now that the vacuum chamber is identical for all the accelerator. Also the Twiss beta functions are assumed constant along the ring.

Simple models (single layer of materials, with infinite thickness) were first studied. A study of the minimal chamber radius achievable without beam instability was performed with the these impedance models.

Simple impedance models scans #

Several materials were first investigated for the collider ring impedance

Assumptions for the impedance model #

We assume a circular beam chamber with different radius from 5 mm to 50 mm. Different material are also investigated: Copper at 300 K, Copper at 20 K, Tungsten at 300 K, Tungsten at 80 K. The chamber and material parameters are reported in the tables below.

Chamber geometric parameters:

The materials used have the following properties:

Material resistivity dependency versus temperature is implemented in the impedance toolbox. Copper also includes depedency with magnetic field.

Copper was first chosen as it is a common coating for beam pipe when electrical conductivity is a concern.

Tungsten could be used as a magnet liner to absord muon decay products and avoid excessive heating of the cold bore(see for example N.V. Mokhov et al., 2018, JINST 13 P10024 or M. Green, 1996, Nuclear Physics B, 51 1 pp. 158-167).

Results of the scans #

Several beam pipe radius were scanned, between 5 mm and 40 mm. The results are plotted below for the different materials considered.

Copper chamber at 300 K #

Copper chamber at 20 K #

Tungsten chamber at 300 K #

Tungsten chamber at 80 K #