Measurement of the bowing and thermal stability

In order to study the correlation to the temperature of the size of the IBL distortion, cosmic-ray events were collected in March 2015 at different temperatures: 15 C,7 C,0 C, 10 C, 15 C and 20 C. To quantify the size of the IBL distortion, track-based alignment cor-rections [59] were applied to determine the positions of the IBL modules as well as their ge-ometrical distortions relative to the nominal geometry. More than 5⇥10⁵ cosmic-ray events were taken at each temperature with both the toroid field and the solenoid field on. The trigger for cosmic-ray events was the Fast-OR trigger of the TRT, a hardware-based logical OR of the TRT wires having a hit along a likely muon-track path. The trigger efficiency was above 90% [60] and the average aquisition rate 4.84Hz. Tracks were reconstructed from hits measured by three subdetectors: the Pixel Detector (including the IBL), the SCT, and the TRT. 17% of Fast-OR triggered events were used in the distortion studies after a series of track quality cuts:

• NP ixel+NSCT 4: at least four silicon hits;

• NT RT 25: at least 25 hits in the TRT;

• pT trk 2GeV: 2 GeV threshold of the transverse momentum.

The pTtrk 2GeV is applied in order to reduce the impact of multiple scattering in the traversed material. The unbiased track-to-hit residual vector, #»

rres = #»

rhit

#»rexp, is used to quantify the distortion of the IBL, where #»

rhit is the vector of measurements of the hit position in the module and #»

rexp is the expected position according to the track fit. Both are defined in the local coordinate system² of the module registering the hit. The residuals were unbiased, since the hits on a certain module were removed from the track fit before computing the track-to-hit residual. To demonstrate the distortion effect due to temperature variation, a set of initial alignment constants with the ideal geometry for flat staves was used as the reference constant set for the track reconstruction. There was also a global alignment for the whole IBL as a rigid body, to account for global displacements of the IBL with respect to the other ID sub-detectors; there were a total of 3 degrees of translation and 3 degrees of rotation for the IBL. This initial alignment corrections [59] were derived from the cosmic-ray data collected in February 2015. Using cosmic-ray data collected in March 2015, the magnitude of the distortion was found to depend linearly on the operating temperature of the IBL, with a gradient of 10µm K ¹. For a quantitative estimate of the temperature gradient, a set of module-level alignment correction was calculated using the data collected at 20 C. The module-level alignment takes each individual IBL module as the basic element for the geometry correction. Three possible translations, and one rotation around the local-z axis are allowed. The measured residual after this alignment correction at 20 C is shown in Figure 5.12. It is consistent with zero, which shows that the distortion of the IBL can be corrected by the alignment algorithm. The y-residual shows no temperature dependence within20µm uncertainty. The FEA simulation calculates that the averaged local-x residuals,

2In the IBL module frame, the x and y axes are defined in the detector plane with the x-axis pointing along the most precise measurement direction. The x-axis is oriented along the transverse plane in the ATLAS coordinate system. The y-axis points along the beam direction.

(a) (b)

Figure 5.12: The track-to-hit residual mean in the (a) local-x and (b) the local-y direction.

The residual mean is averaged over all hits of modules at the same global-z positon. The alignment corrections derived at 20 C are applied to the local positions in the module frames. For local-x, each data set is fitted to a parabola which is constrained to match to the baseline B = 0 at z = z0 = 366.5mm.

xL, is expected to be parabolic. Therefore a fitting function to describe xL, is parametrized with the following parabolic function:

x_L(z) = B M

z₀²(z² z₀²) (5.1)

wherez is the global z position of the module, z0 =366.5mm is the fixing point of the stave at both ends,B is the baseline which describes the overall translation of the whole stave and M is the magnitude of the distortion at the center of the stave. Bis set to a common constant for all temperature points because the end-blocks of each stave are fixed mechanically. M is the free parameter in the fit and it can be used to quantify the size of the distortion.

The above parametrization function describes the distortion shape of each temperature, as presented in Figure 5.12a. Figure 5.13 shows the magnitude of the distortion as function the operating temperature. A linear dependence on the temperature of the magnitude of the distortion is observed. The temperature gradient of the magnitude of the distortion, M, is fit as:

dM

dT = 10.6±0.7µm K ¹ (5.2)

The uncertainty on the above gradient is estimated by comparing to a fit performed with-out constraining the baseline B in addition to the statistical uncertainty. The observation supports the hypothesis that the distortion is driven by the mismatch of the coefficient of thermal expansion.

For a correct operation of the IBL detector a stable temperature is therefore required. The sources of temperature instability are the intrinsic stability of the cooling system as well as the environment and the variation in power consumption of the FEs. Since the thermal capacity of the cooling system is much larger than the module’s power consumption, the cool-ing pipe temperature stability is assumed to be decoupled from the variation of the power consumption. The stability of the temperature of the IBL cooling system was investigated

Figure 5.13: The magnitude of the distortion as a function of the temperature. Each data point is a best fit of a parabola to the local-x residual mean as a function of the global-z of the module position. The alignment corrections derived at 20 C are applied to the local positions in the module frames.

using the temperature sensor monitoring system during the same cosmic-ray run studied in the previous section. There are 10 negative temperature coefficient (NTC) thermistors for each stave. They are composed of one NTC for every four FE chips (eight in total per stave) and one NTC for each of the inlet and outlet sides of the cooling pipe at z'±700mm. The precision of the NTC sensors on modules and the sensors on the cooling pipe is estimated to be ⇠ 0.02K. The IBL employs a bi-phase CO2 cooling system [61]. The coolant, CO2, is liquid at the inlet and it transits to bi-phase (gas and liquid) as it absorbs the heat dissi-pated in the stave. The actual position of transition varies by staves. Therefore the outlet side is considered to represent a more accurate reference for the temperature of the coolant than the inlet side. On the other hand, the NTC sensors on modules are used to evaluate the temperature stability at the modules. For each sensor i of each run k, the temperature value is read out N_i^(k) times in the detector control system, while each run is a block of the data-taking period. The standard deviation and the peak-to-peak values of each sensor i of each run k are defined as:

Standard deviation: T^(k)i = r

1 N_i^(k)

P

j(T_i^(k)[j] < T_i^(k) >)² Peak to peak: T_i^(k) =max(j)(T_i^(k)[j]) min(j)(T_i^(k)[j]).

(5.3) whereT_i^(k)[j])is each temperature readout and< T_i^(k) >represents the average temperature readout. For the cooling pipe outlet, there are 14 sensors in total. The standard deviation of T_i^(k)[j] over 14 sensors, denoted as:

( T^(k)) = s 1

14 X

i

( T_i^(k) < T^(k) >)², (5.4) where < T^(k) > represents the average of T_i^(k) over 14 sensors. Figure 5.14a shows the results of the stability study using the cooling outlet-pipe temperature sensors. Each bar represents a run. There are two kinds of bars denoted as RM S and "peak-to-peak". The vertical range of the RMS bar for each run k is defined as:

RMS: [< T^(k) > ( T^(k)), < T^(k) >+ ( T^(k))], (5.5)

Date

2015-Mar-12 2015-Mar-19 2015-Mar-26

Temperature Variation [K]

Cool. Pipe Peak to Peak excursion

ATLAS Preliminary

(a)

Date

2015-Mar-12 2015-Mar-19 2015-Mar-26

Temperature Variation [K]

Figure 5.14: Stability of the outlet of the (a) cooling pipe temperature and (b) module tem-perature sensors of the IBL during the comic-ray data-taking in the commissioning phase.

Each bar represents the block of data taking period called runs. The width of each bar rep-resents the duration of the data-taking of the run. For each module temperature sensor, the RMS and the peak-to-peak values of the temperature readout during the run are calculated.

The "RMS’ bar in the figure represents the variance of the RMS values of the 112 tempera-ture sensors with indicating±1RMS range around the average RMS. The "peaktopeak" bar represents the variance of the peak-to-peak values of the 112 temperature sensors indicating the maximum and the minimum peak-to-peak values among the 112 temperature sensors.

and the vertical range of the peak-to-peak bar is defined as:

peak to peak: [mini( T_i^(k)), maxi( T_i^(k))]. (5.6) The width of each bar represents the duration of the corresponding run. As seen in the plot, the RMS bar of the temperature during a run is well within 0.05K while the peak-to-peak bar is within 0.2K.

The same description of the stability is performed for 112 NTC sensors on the modules, and the result is shown in Figure 5.14b. For most of the runs the peak-to-peak value is within 0.25K, which is not significantly larger than the stability of the outlet cooling pipe of0.2K. The maximum peak-to-peak values in some of the runs are close to0.4K. These excess values are recorded by the sensors which are the closest to the inlet cooling pipe. It is considered that the temperature fluctuation at this position is caused by the bi-phase transition of the CO2 coolant. Such a local temperature fluctuation is expected to have small impact to the global distortion of the stave. The fact that the variation of module temperature is not very deviated from the cooling output pipe temperature stability indicates that the dominant source of the module temperature variation could be considered to be from the stability of the cooling system and environment.