Validation of results: Centers of Mass

4. IMPLEMENTATION OF VECTOR DECOMPOSITION

depend linearly ofc:

c= a−b

S and b=S−a therefore:

a= S

2 ·c+S 2 forb, the result is:

b=−S

2 ·c+S 2

This shows that for a fixed (or normalised) total lossS, each signal depends linearly on the center of mass if the other one is fixed: the center of mass gives the relative proportion of the signals.

The centers of mass also have the advantage to be able to be combined: a and b can be any combination of signals that we want to compare against each other. For instance, acan be the sum of the signals at the vertical collimators, andb the sum of the signals at the horizontal collimators.

4.5.2 Implementation and verifications

The values used for the centers of mass are the combinations of the signals at the four primary collimators(cf. tab. 4.6).

Expert name Beam & plane BLM index Loss TCP.D6L7.B1 B1 vertical 18 v₁ TCP.C6L7.B1 B1 horizontal 19 h1

TCP.C6R7.B2 B2 horizontal 114 h₂ TCP.D6R7.B2 B2 vertical 113 v₂

Table 4.6: List of primary collimators of IP7 used in the Centers of Mass.

The centers of mass used for discrimination between beam 1 and beam 2 is:

CoM_1|2 ≡ (h₂+v₂)−(h₁+v₁) h1+v1+h2+v2

(4.1) It always varies between −1 and +1. In this case, −1 means that the measured loss profile is made only of beam 1 scenarios, and +1 means that the measured loss profile is made only of beam 2 scenarios. A center of mass of 0 means that both beams give the same contribution to the overall loss.

4.5 Validation of results: Centers of Mass

Figure 4.15: Distributions of the results of CoM1|2 (cf. eq. 4.1). Each one of the 4 plots corresponds to a loss scenario (known before the calculation), given in the title of each plot.

There are 7 different loss maps for each scenario (28 in total). The results of the centers of mass match perfectly the type of every single vector. This is because the primary collimators for beam 1 are installed far away from the collimators for beam 2, and the signals at the corresponding BLMs are well separated: onfig. 4.1, the primary collimator for beam 1 are around index 20, whereas the ones for beam 2 are at index 116.

For horizontal and vertical cases, the center of mass is:

CoM_H|V ≡ (v₁+v₂)−(h₁+h₂)

h₁+v₁+h₂+v₂ (4.2)

In this case, the center of mass varies between −1 when it is dominated by signal from the horizontal collimators and +1 when it is dominated by the signal from the vertical collimators. Again, a center of mass of 0 shows that the losses from both planes are equal.

In order to evaluate the correctness of the centers of mass, they were first calculated for all 28 loss maps of 2010 (4 scenarios×7 dates). The results are presented infig. 4.15.

For beam discrimination, they match exactly the dominating beam (1 or 2) of every single vector.

However, the results for the centers of mass are not as good for the separation between horizontal and vertical loss maps (cf. fig. 4.16). They are separated, but do

4. IMPLEMENTATION OF VECTOR DECOMPOSITION

Figure 4.16: Distributions of the results of CoMH|V (cf. eq. 4.2). Each one of the 4 plots corresponds to a scenario (known before the calculation), given in the title. There are 7 different loss maps for each scenario (28 in total). The centers of mass have different values depending on the scenarios, but they vary between−1 and−0.5, instead of varying between−1 and 1.

not give the expected results: instead of varying between −1 and 1, the results vary between −1 and−0.5. This could be reproduced with the selected loss maps of 2011 used in the decomposition, and with all loss maps of 2011 for statistics (cf. fig. 4.17).

TheCoM_1|2, giving always correct results (all values are +1 or−1), are not represented.

In addition to varying in an interval smaller than expected, some of the 2011 loss maps give a “wrong” (opposite to the expected value knowing the associated loss sce- nario), e.g. −0.5 instead of −1 for some of the B1H loss maps of 2011 (cf. fig. 4.17, right column, third plot down). This is not an issue: these loss maps were not selected and are not used in the decomposition. Again, no loss map gives a CoM_H|V bigger than zero.

This is due to the relative position of the corresponding collimators: the horizon- tal collimators sits downstream and next to the vertical one. The secondary shower produced when the protons hit the vertical collimator will also be detected by the hor- izontal collimator: part of the signal seen by the horizontal collimator comes from the vertical one.

4.5 Validation of results: Centers of Mass

Figure 4.17: Distributions of the results of CoMH|V (cf. eq. 4.2). Each one of the 8 plots corresponds to one scenario (known before the calculation), given in the title; in each distribution, there is one entry per loss map of the considered scenario. Top 4: loss maps of 2011 used in the decomposition. There are 4 loss maps per scenario, given intab. 4.1. The results of the centers of mass are separated and vary between−1 and−0.5. Bottom 4: all loss maps of 2011. Most of the entries for B1V and B2V are above−0.5; the lower values indicate “wrong” loss maps.

4. IMPLEMENTATION OF VECTOR DECOMPOSITION

Several corrections were considered, such as subtracting the signal of the vertical collimator from the horizontal one, or stretching the variation interval.

Implementing the first method showed that a factor of roughly two times the vertical signal had to be subtracted in order to get a correct variation interval; but this created a pole for the function (h, v) 7→ (h−α ·v, v), i.e. a value for which the function would diverge to infinity. Arbitrarily stretching the variation interval, corresponding to the precedent method with no pole and a correction factor of higher value, led to the problem of some values of the centers of mass being higher than one, in cases where the cross-talk between the two monitors is overestimated.

Eventually, the choice was made to keep the centers of mass uncorrected, knowing that the horizontal/vertical one would vary between −1 and −0.5.