[Paper Review] Field integrals for the ATLAS tracking volume

V. Klyukhin, A. Poppleton+1 more|arXiv (Cornell University)|Aug 2, 2018

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper evaluates momentum resolution degradation in the ATLAS inner tracker due to non-uniform magnetic field effects near the solenoid ends. Using field maps from POISSON, it compares the double field integral in the real ATLAS solenoid to an ideal infinite solenoid, finding up to 15% field integral degradation for |η| > 1.8, resulting in a 20–30% worsening of pT resolution compared to ideal conditions.

ABSTRACT

The magnetic field integrals connected with the momentum resolution are calculated for the ATLAS inner tracking volume in a range of pseudorapidity $|η| < 3$ for the cases of `ideal' and inhomogeneous solenoid fields. In the latest case, the magnetic field map is extracted from POISSON calculations with help of an interface program POISGT. The tracking volume is restricted by a length of 6.8 m and by a radius of 1.06 m. The solenoid coil with an active length of 6.3 m and with an inner radius of 1.23 m produces the magnetic flux density of 2 T in the center of the coil.

Motivation & Objective

• To quantify the degradation in magnetic field integral due to the finite length of the ATLAS solenoid, particularly in the forward region (|η| > 1.8).
• To assess the impact of this field inhomogeneity on momentum resolution for high-eta tracks in the ATLAS inner tracker.
• To compare the actual field integral in the ATLAS geometry with that of an ideal infinite solenoid to isolate resolution losses.
• To evaluate whether the extended tracking volume beyond the solenoid end improves momentum resolution in the forward region.
• To determine the sensitivity of momentum resolution to the placement of the last tracking chamber relative to the solenoid end.

Proposed method

• Calculated the double field integral I₂ = ∫∫ B sinθ(dl dr) along particle trajectories in the transverse plane using field maps from the POISSON program package.
• Used the field integral ratio R = I₂(inhomogeneous)/I₂(ideal) to quantify resolution degradation relative to an ideal solenoid.
• Applied the relation Δp/p ∝ 1 − R for impact parameter measurements and Δp/p ∝ 2(1 − R) for sagitta measurements to estimate resolution loss.
• Analyzed field components across radial and longitudinal sections of the tracking volume to visualize field inhomogeneity near solenoid ends.
• Evaluated the dependence of field integral degradation on pseudorapidity η, especially in the forward region (|η| > 1.8).
• Simulated the effect of moving the last tracking chamber inward by 20 cm to assess potential improvements in field integral and resolution.

Experimental results

Research questions

• RQ1 How does the finite length of the ATLAS solenoid affect the magnetic field integral in the forward tracking region (|η| > 1.8)?
• RQ2 To what extent is momentum resolution degraded in the ATLAS tracker due to field inhomogeneity near the solenoid ends compared to an ideal infinite solenoid?
• RQ3 Does the extended tracking volume beyond the solenoid end provide a significant improvement in momentum resolution for forward tracks?
• RQ4 How does the field integral degradation vary with pseudorapidity η, and where does it plateau?
• RQ5 What is the impact of relocating the last tracking chamber 20 cm inward on the field integral and momentum resolution?

Key findings

• The field integral degradation (1 − R) reaches 1% at |η| = 1.1, 5% at |η| = 1.6, and 10% at |η| = 1.8, with a plateau of ~15% for |η| > 1.88.
• For |η| > 1.8, the field integral degradation results in a 20–30% worsening of pT resolution compared to an ideal solenoid, depending on the measurement method.
• The sagitta-based momentum measurement is particularly sensitive, leading to a 30% degradation in Δp/p when R = 0.85.
• The field integral degradation is less pronounced in the real ATLAS field (7%) than in the ideal case (11.4%) when the last chamber is moved inward by 20 cm.
• Despite the rapid drop in field integral magnitude at high |η|, the momentum resolution remains comparable to η = 0 for 1 TeV particles due to the pT dependence via sinθ.
• The current ATLAS geometry provides an effective 2 T field only up to |η| ≈ 0.6, with significant field inhomogeneity beyond |η| ≈ 1.8.