Kalman Filter Update 3

I recently finished up the final stages of applying the Kalman filter, and obtained estimates of the test-beam particles’ momentum errors, which was the main purpose of this project. I have discussed in previous posts how I propagated the Kalman filter through the beamline, and hinted in my last post that I had finally taken momentum errors into account. The method to do this was iterative in nature; I first applied the Kalman filter through the beamline and obtained values for the directional errors at wirechambers 2 and 3. These could be used to obtain the error in the measured bend angle, and this could be used to find a momentum error. We then ran the filter again, but used this new bend error to obtain improved errors in the wirechamber 3 directional error. We then found an improved bend and momentum error, etc. This process was repeated 3 or 4 times, by which point the further iterations made almost no improvement on the values obtained.

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Kalman Filter Update 2

As noted in my previous post, I have now updated my filter to store the slope of the particle’s path in the y-z plane (this is the plane in which the magnet will bend the particle’s path) instead of the angle at which it is travelling. This allows for better accuracy in tracking the particle. I was able to finish applying this to the magnet-off data sample (as the name implies, the magnet was turned off, so that the particle should just travel in a straight line) and obtained good agreement between data and prediction.

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Kalman Filter Stage 1

My direction of research has changed slightly since the start of summer. My new goal is to apply a Kalman filter to the MINERvA testbeam. One of the purposes of this testbeam is to determine the momenta of the incoming particles, which is accomplished by setting up a pairs of wire chambers before and after a magnet. These pairs of wire chambers enable us to determine the direction of the particle’s motion before and after passage through the magnetic field, and, from this change in direction, we can determine the particle’s momentum. However, the wire chambers have some degree of error in determining the particle’s position which translates to errors in the particle’s direction and momentum.

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Abstract: Analysis and Modelling of Test-Beam Data from the MINERvA Experiment

One of the most interesting areas of study in physics today is the study of neutrinos, very weakly interacting particles that are produced in certain nuclear reactions. The MINERvA experiment has been set up to study these particles. Other experiments, such as MINOS, wish to study neutrino energies. However, the energy collected in their detectors depends not only on the energy and flux of the neutrinos, but also on a quantity called “cross-section,” which is a measure of a neutrino’s probability of interacting while passing through a given material. Since it is not possible to detect neutrinos directly, we observe the particles produced when neutrinos interact with nuclei, and, from their behavior, are able to gain information about the neutrinos themselves. To detect these resultant particles, we are able to look at their energy depositions in detectors. Each particle has some characteristic pattern for depositing its energy, which would allow us to identify it quite readily. However, it is first necessary to match up these patterns with the particles and figure out the probability that a certain pattern is caused by a given particle. In order to do this, we have a separate test-beam experiment to understand the detected patterns. We fire particles through a magnetic field and measure the angle by which they bend. Based on the angle of bending of the particle’s path, we are able to determine the momentum of the particle. We then send them into detectors where we can measure the time it takes them to pass between two points (which we call the time-of-flight measurement), giving us the particle’s velocity. From these quantities, we are able to determine the particle’s mass, allowing us to determine its identity. However, we also see its energy deposition pattern in the detector, allowing us to match the deposition with the particle in the main experiment. During my research this summer, my goal is to help to improve models of particle interactions. I would use the Geant4 software package to look at such factors in the track as its length and distribution of the energy deposition and then adjust parameters in models of the particle’s behavior to improve models of the particle interactions. This would allow us to determine from the particle track alone what the chances are that it was caused by a certain particle, which could be applied back to the main part of the MINERvA experiment to improve our understanding of neutrino interactions.