Machine Learning Applications to Maintain the NuMI Neutrino Beam Quality at Fermilab

: The NuMI target facility at Fermilab produces an intense muon neutrino beam for NOvA


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Neutrinos at the Main Injector (NuMI) beamline [1][2][3] at the Fermi National Accelerator 13 Laboratory in Illinois has been designed to deliver an intense muon neutrino beam to 14 NuMI neutrino experiments. Protons of 120 GeV from the main injector collide with a 15 fixed graphite target to produce the neutrino beam for experiments. The charged particles 16 produced from the proton interactions with the target nuclei are focused on a 675 m long, 17 2 m diameter cylindrical decay pipe by using two focusing horns systems which operate 18 with 200 kA horn current. The mesons may decay into neutrinos and muons before they are 19 absorbed through the hadron absorber which is located after the decay volume. Some of 20 the high-energy muons produced from the meson decay may pass through muon monitors 21 that are located after the hadron absorber.

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The muon monitors are an array of helium gas ionization chambers [4]. Each muon 23 monitor has been built with 81 parallel plate ionization chambers with an electrode spacing 24 of 3 mm. Every charged particle ionizes the helium gas to produce ions and electrons when 25 they pass through the ionizing chambers. Muon Monitors are sensitive to the primary 26 beam changes and horn current variations. Unique responses of muon monitors are useful 27 to build machine learning applications to monitor the quality of the NuMI neutrino beam. 28 After the MINOS detector shut down since February 2019, the muon monitors provide 29 useful information to monitor the beam quality, target health, horn performance and 30 identify issues with the beamline alignment. Our goal is to improve and monitor the 31 performance of neutrino beam delivery for neutrino experiments by applying modern 32 artificial intelligence and machine learning techniques.

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Three muon monitors have unique response to the proton beam variables. In this 35 paper, we report the muon monitor responses to the proton beam position changes at the 36 target as an example. The data has been recorded by moving the proton beam horizontally 37 and vertically for selected horn current settings. The beam positions at the target has been 38 extrapolated by using two set of horizontal and vertical beam position monitors (BPM) in 39 the upstream to the target. 40 We report the correlation of the muon monitor centroid measurement as a function of 41 the beam position at the target. The response of the muon flux centroid to the horizontal 42 and vertical beam variations for 200 kA horn current settings are shown in Fig. 1. The 43 correlation of muon monitor centroid to the proton beam position has been fitted to a linear 44 function. The study shows that three muon monitors are responding differently to the 45 proton beam variations. According to the vertical scan, the non-linear response of the muon 46 flux centroid is visible at the upper and lower limits of the proton beam.

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In this study, we present a machine learning approach to predict the proton beam 49 position at the target, beam intensity and the focusing horn current by taking into account 50 the downstream muon monitor signals. The responses of the individual pixels in the muon 51 monitoring system to the beam and horn current variations have been taken into account 52 to train a ML model. The data samples have been collected from the spill-by-spill time series measurements 55 of devices in the NuMI beamline for beam settings and horn current settings. The pedestal 56 subtracted signal measurements of 241 pixels 1 of three muon monitors were taken as input 57 variables for the ML model. The randomly sampled training (70%) and validation (30%) 58 data samples were selected from the target scan data collected on 2019-12-12 and few hours 59 of selected normal operation data The ML model architecture is defined as fully connected multilayered artificial neural 62 network (ANN) with multiple hidden layers. The output of the each nodes in the layers 63 are calculated by an appropriate "activation function". The ANN is designed by taking 64 into account 241 pixel measurements of three muon monitors as input nodes and multiple 65 hidden layers and four output nodes to predict the proton beam position (horizontal 66 and vertical), beam intensity and horn current. ANN has been optimized by using a 67 hyperparameter tuning process to obtain the optimal architecture. The hyperparameter 68 tuning is done by searching the best combination of the number of hidden layers, number 69 of nodes, batch size, learning rate and the activation functions.  to obtain the best weights to predict the network output by minimizing an appropriate 73 loss function. The best optimized ANN structure that we have achieved from our network 74 optimization is described in Tab. 1 with four hidden layers, the learning rate η = 10 −5 and 75 the batch size 32.
Layer Shape Parameters Activation   1  480  116160  tanh  2  130  62530  sigmoid  3  135  17685  sigmoid  4  11  1496  sigmoid  5  4 48 linear Table 1. The optimized ANN model with the number of hidden layers, parameters and the associated activation functions. Each node in the first layer has been connected to 243 inputs from the muon monitor signals and the output layer is predicting the beam position, beam intensity and the horn current.

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A comparison of the model predictions of four output variables on the validation data 77 are shown in Fig. 3. The top left and top right plots in Fig. 3 shows the proton beam position 78 horizontal and vertical predictions. The beam intensity and the horn current predictions 79 are shown in the bottom left and right plots in Fig. 3. The model has been tested with 80 randomly selected data sets for the normal beam operations.

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In this section, we describe the efforts to build ML models by using simulation data. 83 This effort may help to understand some of the rare "anomaly" scenarios such as horn tilt or 84 slip, target tilt, target deterioration, density effects. The simulation data for ML applications 85 is generated by using NuMI beamline simulation (G4NuMI) which is based on geant4 86 simulation tools [5].

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Uniform beam simulation technique is being used to generate significant amount 88 of Monte Carlo data samples for machine learning applications by varying the incident 89 beam parameters and horn current settings. In this technique, we generate a uniformly 90 distributed single simulation data sample for the selected beam variable range. The 91 uniformly distributed sample is then used to generate Gaussian beam profiles for the 92 selected beam positions and widths.

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A linear regression model has been tested to predict the horizontal proton beam 94 position and the horn current from simulation data. In this study, we take account 243 95   Both models have a good fitting with high prediction accuracy because our simulation 107 data samples describe more ideal conditions than real beam data. Unlike simulation data, 108 real beam data is noisy and has background effects on measurements from known and 109 unknown sources.

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In this paper, we summarize the progress of machine learning applications by taking 112 into account the downstream muon monitor signals. These ML predictions give an extra 113 monitoring of the beam and horn current behaviours. This will be helpful to monitor the 114 beam performance and developing trends or issues during the regular beam operations. 115 ML model building with simulation data is useful to predict rare incidents and anomalies.