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# LHC Collision rate monitors

The collision rate monitors of LHC (aka Luminosity monitors) BRAN will be used to monitor the rate at which particles collide at the four interaction points of LHC: ATLAS (IP1), ALICE (IP2), CMS (IP5) and LHC-B (IP8).

# Luminosity definition

The luminosity of a collider is defined as the ratio between the rate of a certain event and the cross section for that particular event.

$$L = \frac{\dot{N}_i}{\sigma_i}$$

The luminosity can also be expressed as a function of the parameters of the beams:

$$L=\frac{ N_{b1} N_{b2} f_{rev} k_b}{ 2 \pi \sqrt {(\sigma_{x1}^2 + \sigma_{x2}^2)(\sigma_{y1}^2 + \sigma_{y2}^2)}} \cdot \exp \left[-\frac{(\bar{x}_1-\bar{x}_2)^2}{2(\sigma_{x1}^2 + \sigma_{x2}^2)} -\frac{(\bar{y}_1-\bar{y}_2)^2}{2(\sigma_{y1}^2 + \sigma_{y2}^2)}\right] \cdot \frac{1} {\sqrt{ 1 + (\frac{\phi \sigma_s}{2 \sigma_{x/y}})^2 }}$$

Where N are the bunch populations, f_rev is the revolution frequency, k_b is the number of bunches per beam, $$\sigma_{x/y,1/2}$$ are the beam sizes and the subscripts 1, 2, x and y indicate beam 1, beam 2, horizontal and vertical respectively, $$\sigma_{s}$$ is the bunch length, $$\phi$$ is the total crossing angle and $$\sigma_{x/y}$$ is the transverse beam size in the crossing plane.

For round beams $$\sigma_{x} = \sigma_{y} = \sigma$$ and assuming $$\sigma^2= \beta^{*} \frac{\varepsilon^{*}}{\gamma}$$ we can rewrite it as:

$$L=\frac{ N_{b1} N_{b2} f_{rev} k_b \gamma}{ 4 \pi \beta^{*}\varepsilon^{*} } \cdot \exp \left[- \gamma \frac{(\bar{x}_1-\bar{x}_2)^2 + (\bar{y}_1-\bar{y}_2)^2}{4 \beta^{*}\varepsilon^{*}}\right] \cdot \frac{1} {\sqrt{ 1 + (\frac{\phi \sigma_s}{2 \sigma})^2 }}$$

Calculation of the luminosity from the beam parameters is very difficult as certain parameters can not be directly measured at the collision point and can only be estimated leading to an unacceptable error (the main unknown are the beam sigma).

It is for this reason that dedicated monitors are required.

# Monitors layout

The animation on the left shows the principle of the monitors. When the Proton (or ion) bunches traveling in opposite directions (red and blue dots in the animation) meet at the IP there is a probability that two or more particles will come close enough to interact. In this event a number of collision products will be generated, some will have an electric charge (like pions+/-, protons, etc), other will be neutral (like neutrons, gammas etc.)(small dark dots in the animation). The charged particles will be deflected by the magnet D1 while the neutral particles will continue in a straight line (collinear with the incoming bunches). A detector placed some 140m away and in direct flight path from the IP will thus intercept only the neutral particles. The rate of detections of these events is directly proportional to the machine Luminosity.

The value of the absolute luminosity for the 4 interaction points are quite different. While in ATLAS and CMS the aim is to have the highest possible luminosity, for ALICE and LHC-B the luminosity should be kept at optimal (lower) levels. This means that the number of particles arriving on the BRAN detectors will be very different and as a consequence also the radiation dose to be sustained by these detectors. For this and other reasons two different solutions have been adopted for the BRAN's. At ATLAS and CMS the detector will be a fast ionization chamber, developed by Berkeley lab, and at ALICE and LHC-B the detector will be based on solid state polycrystalline Cadmium-Telluride (CdTe) sensors developed by CSA-LETI Grenoble. While the first option offers the best performance in terms of radiation hardness, the second offers the best performance in terms of sensitivity and speed, still with reasonable resistance to radiation. As reference the dose absorbed by a detector at L= 1034 can be up to 180 MGy/yr

IPMin L (Day 1) [cm-2s-1]Max L (Nominal) [cm-2s-1]
ATLAS2.5 10261.0 1034
ALICE4.4 10263.0 1030
CMS2.5 10261.0 1034
LHC-B4.4 10265.0 1032

Luminosity ranges for the four LHC experiments (@ 7 TeV)

The ionization chamber developed at Berkeley consists of 7 stacked parallel plates with 1mm gaps and about 90x90 mm2. The plates are divided in 4 quadrants so that the center of gravity of the deposited energy can be reconstructed. The detector is inserted inside a pressure vessel that contains the gas mixture (94% Ar and 6% N2) at up to 10 bars. The signals are feed to a front end amplifier sitting near by (about 1 meter away). In order to acquire the signals for each bunch crossing independently (40 MHz) a signal shaper is needed. This device, based on pole-zeros cancellation is installed near the acquisition electronics some 300m away from the detector. The signal is transported there by mean of four 50 Ohm cables (CK50). After the shapers the signals are digitized using the DAB (Digital Acquisition Board) developed by a collaboration between TRIUM and CERN-AB-BI.

A plastic scintillator has been added in front of the BRAN-A detectors (ionization chambers) in order to measure the collision rates at very low luminosity and energies well below 7TeV. The BRAN-A detectors are in fact optimized for 7TeV and 10^34 cm-2s-1 and are at the limits in these low luminosity low energy conditions.

Cherenkov detector studies for IP8.

# Related documents

## annotations

The filling schema for 1 collision in each IP is B1[1, 17851], B2[1, 8911]

B1 B2 1 1 1 8911 1 1 17851 8911

In IP8 B2[26701] would collide with B1[1]