Choice of the list of BLMs

In order to avoid this phenomenon, the value of the offset (1.8·10⁻⁷Gy/s for RS09) is systematically removed from all monitors when constructing the vectors, before normalisation.

4.2 Choice of the list of BLMs

This section will present the selection of them BLMs from IR7 composing the coordi- nates of the transversal loss vectors expressed in them-vector space. The selection of monitors of IR3 will be presented separately.

4.2.1 Problem

In this work, each coordinate of the loss vectors corresponds to the signal of one BLM.

They must be selected following specific criteria. Beforehand, these criteria themselves must be established.

The influence of each BLM signal — each vector coordinate — on the whole vector depends only on the intensity of the loss, and BLMs with high losses will have a higher weight in the decomposition. In addition, the point of this work is to separate different loss vectors (loss scenarios). From this point of view, there are three main types of monitors:

1. BLMs that have a low signal in all loss scenarios;

2. BLMs that have a high signal in all loss scenarios;

3. BLMs that have different signals in different loss scenarios.

It is obvious that the most interesting BLMs, when discriminating between scenar- ios, will be the BLMs of the third type.

BLMs with low signal in all scenarios

When calculating one of the vector decompositions, the BLMs of the first type have no influence. They do not carry information on the nature of the loss: if added to the vectors, they only “dilute” this information. If they are included, the vector will have a higher dimension for the same information.

4. IMPLEMENTATION OF VECTOR DECOMPOSITION

It is better to ignore these BLMs. Tests on simple examples show that they don’t drastically change the result of a decomposition. Typically, for SVD, one of the left eigenvectors will have zeros everywhere, and a one at the position of the BLM: it will be a vector of the canonical basis. The corresponding singular value will be very low, or there will be no singular value associated to that vector: the index of the vector will be higher thann. The vector will either be ignored or have only a negligible contribution.

This was checked by running the SVD with all monitors in IR7, then plotting all the left singular vectors of matrixU (cf. § 3.2).

BLMs with high signal in all scenarios

The case opposite to BLMs of the first type are the BLMs that show, in every case, a signal higher than most other BLMs of the vectors. This case is more critical because such BLMs, even if they cannot be used for discriminating between loss scenarios, have a strong influence on the decomposition: the higher the signal of the BLM relative to the others, the higher the influence on the decomposition. Only a small variation on the contribution of such BLMs can be bigger than the signal of some other BLMs, and lead to a change in the recomposition result.

If possible, such BLMs should be removed from the list, as they do not carry dis- criminating information: their signal is high in all scenario. They could lead to wrong decomposition. The concept of the decomposition is to match vectors. Between all coordinates, the highest ones have the highest influence on the decomposition. Match- ing such a coordinate (even if it carries no information) to the detriment of a another smaller coordinate (which could carry information) will lead to a smaller error on the decomposition for the wrong information. The vector would have been matched to the

“wrong” coordinate.

BLMs that have different signals in different scenarios

This third case is the most relevant one. These BLMs can be used for simple discrimi- nation “by eye” between scenarios. They are the BLMs carrying the information about the differences between the loss scenarios.

The selected BLMs were the ones that were at the same time in the list of BLMs with highest signals, and in the list of BLMs with the highest variations from one loss

4.2 Choice of the list of BLMs

scenario to another. The ways to evaluate this variation are presented in the next section.

4.2.2 Selection technique

The list of chosen BLMs, selected after sorting by different criteria, was produced by following several steps.

Distributions of the signal of each BLM

For the BLM selection, all loss scenarios were considered together. All the occurrences (loss maps) of all the loss scenarios were gathered. Each loss map is a verification measurement of collimation cleaning. These measurements are done on a regular basis in the LHC, meaning that several are available.

The average signal and the standard deviation of each BLM were calculated consid- ering all loss maps of all scenarios together, after normalisation. The standard deviation gives a quantification of the variation of the signal from one loss scenario to another.

Beforehand, the check was made that the signal of one BLM doesn’t change much between loss maps of the same scenario (cf. § 4.1.1). The standard deviation of the signal of a BLM within one loss scenario is small: less than 5% of the average signal, for 2010 and 2011 loss maps. Conversely, the standard deviation between scenarios is big (cf. fig. 4.3): same order of magnitude as the average; that is, much bigger than the standard deviation within one scenario.

Variations of BLM signal between scenarios

The first way to evaluate the variation of one BLM signal from one scenario to another was to calculate the difference between the highest and the lowest signal for all loss maps. However, this doesn’t take into account all loss maps, only the two loss maps with highest and lowest signal. The way to consider all loss maps is to use standard deviation.

However, both the standard deviation and the difference between minimum and maximum signals are proportional to the mean value of the signal. When ordering the monitors by decreasing standard deviation, the results are extremely similar as a simple “ordering by signal”(cf. tab. 5.1). The relevant quantities here are theRelative

4. IMPLEMENTATION OF VECTOR DECOMPOSITION

Figure 4.3: Distributions of all BLMs of point 7 when considering all loss scenarios at the same time, for the loss maps of 2010. Averages and standard deviations are calculated for all 28 measurements (4 scenarios ×7 dates) at the same time. These specific loss maps are not used in the decomposition, but the selection is the same. BLMs are displayed with the same relative order as they have in the LHC, but DCUM is not respected. The BLMs showing the bigger error bars are the most relevant ones.

Standard Deviation (RSD); and the min/max ratio, which corresponds to the “length of the error bar” in log scale (cf. fig. 4.3).

These two quantities gave very similar results, and the monitors with the highest values were selected (cf. tab. 4.2).

Symmetry beam 1 / beam 2

The physical implementation of components and instruments in the LHC is nearly always symmetric for beam 1 and beam 2 around the interaction points. It is the case for the collimators in point 3 and 7. In order to follow this symmetry, every time a monitor was selected for one beam, the symmetric monitor was added to the list as well. This is validated by the fact that in most cases, both monitors were already in the selection.

The results are presented in tab. 4.2.