Computer Simulations of High Voltage Discharge Events in the Deep Underground Neutrino Experiment Particle Detectors
by: William H. Kyle††††††
supervisor: Glenn Horton-Smith, Associate Professor of Physics††††††††
This work is partially funded by the National Science Foundation (NSF) and the Air Force Office of Scientific Research (AFOSR) through NSF grant number PHYS-1461251. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or AFOSR.
Below, I describe the Project Overview, my Research Description, my Research Progress, and will eventually post my Final Presentation. I post my homework assignments from our weekly REU scientific Ethics class, taught by Prof. Bruce Glymour , and my reaction to Prof. Larry Weaver's Lectures. Scroll all the way down to learn more About Me. Finally, I've included some Useful Links.
Project Overview: The Deep Underground Neutrino Experiment is one the most excited new experiments in in physics right now, not only within the physics being done in the US, but also within the international physics community. A large part of what makes it so exciting is that in many different ways, it will be operating in regimes that are well beyond what have commonly, or have ever, been used before. As such, nearly all parts of the design need to go through an extensive process of simulation, testing, prototyping, and modification in order to be sure the final detector system will be able to operate up to standards over a period of decades. For my project this summer, I worked to aid this process by building simulations of how the present designs would behave in one of the most likely of the potential failure scenarios, an electronic discharge of the high voltage components which set up the large internal electric fields which are required. From these simulations, the DUNE collaboration group that is in charge of design requirements can see how these results fit within the necessary standards and therefore make any necessary adjustments that may be indicated. This saves greatly on wasted time and money, as they no longer would need to build them in a scheduled prototype to be able to test how well they will function.
DUNE: THE DEEP UNDERGROUND NEUTRINO EXPERIMENT
††††††††††† DUNE is one of biggest new projects in the works in the field of experimental particle physics. It is a $1.3 Billion project to build the largest yet neutrino detector and will be a 40 kiloton fiducial volume Liquid Argon Time Projection Chamber (LArTPC). The collaboration is set to run over the next 2-3 decades for planning, development, and as different parts of the experiment go up and running. The current reports put the first of the four, 10 kt LArTPCís in operation within 5-10 years. The general layout involves 2 key components: a high wattage neutrino beam which will be running out of Fermi Lab, and the LArTPC detectors which will analyze the characteristics of the beam after it has travelled the 1300 km to their location in South Dakota.
THE LARTPC DETECTORS
††††††††††† My work with has been with the High Voltage Group within the DUNE Collaboration, as has focused on certain aspects of the cathode plate within the detectors. In essence, the way that the detectors work is by functioning as massive capacitors, establishing huge voltages across a dielectric material of liquid argon, to establish a uniform field of 180000 Volts over 3.6 m. This results in a very precisely known value for the drift velocity of any ions within the internal volume of liquid argon. So, by measuring induced currents on the anode and time of drift, we can get the locations of particle interactions, like neutrinos, as they pass through the detector via the charged ions and electrons that these interactions produce. Additionally, the main feature which differentiates the LArTPC setup from just a standard parallel plate capacitor is the implementation of a field cage. The field cage runs all the way around the boundaries of the two capacitive plates, and across the full 3.6 m length between the anode and the cathode. This serves as a way of setting new boundary conditions at the edges which are the same 500V/cm as is desired for the whole volume between the cathode and the anode. This greatly increases the fiducial volume (or volume where physical conditions are known well enough to take data) by essentially eliminating the fringing fields which are the bane of any E&M student.
Model of Current Design for DUNE Prototype of the Liquid Argon Time Projection Chamber
Operation of a Neutrino Detection in a Liquid Argon Time Projection Chamber
MY RESEARCH PROJECT
††††††††††† Due to the extremely high energies and voltages which are being used in DUNEís LArTPC, and the confined area of the cryostat in which it is going to operate, the possibility of sparks and discharge events in the cathode becomes almost inevitable. Therefore, if the experiment is to reach its goal of being able to run continuously over a period of decades, it is extremely important that any such event wonít lead to a capacitive discharge behavior that would be harmful to any parts of the cathode or other elements of the high voltage system; as once the detector is filled with Liquid Argon and starts running, it is no longer possible to have any access to the internal structure to make any changes or repairs. Hence, my research project for the summer was to build a computer simulation of the movement of charge and voltage within the cathode during such an event, and use this simulation for different proposed designs for the geometry of the cathode, to observe approximate shapes and magnitudes of the energy and current which would flow out of the cathode through the High Voltage system.
THE SIMULATION METHOD
††††††††††† To simulate this behavior,
I first needed to derive an equation which would describe the changing voltage
over time at all points across the cathode. Firstly, the two parameters which
describe the material of the cathode, and govern its behavior are the
Resistance and the Capacitance. So, since the cathode is a thin film of
resistive material, we will call it a two dimensional plane of charge, which
means that it will have a sheet resistance defined by Rs
(R per square) and a capacitance of Cs (C per m^2). These values can
be found respectively from the manufacturer, and from the standard formula for
parallel plate capacitance.
††††††††††† Subsequently, the derivation of our equation gives a diffusion equation of the following form:† ††† †(where phi(x,y) = voltage at (x,y))
Using this equation, we can find discrete solutions using the Forward Time Central Space Method. For more detail on this method, here is a link that might be of interest.
††††††††††† For this project, the main goal that I was given by my mentor was to test the hypothesis of the DUNE High Voltage group that splitting the cathode into three pieces would decrease the average current being output during a discharge. As such, this is the configuration I tested in my simulations, as well as a fully connected single piece cathode as my comparison. Also, since this was mainly for preproduction modifications to the next scheduled prototype detector to be built, ProtoDUNE, I used the specs for that designís cathode plane. That design is for a cathode that is 6m x 1.15m. Below are a few images of the distribution of voltage across the cathode at different time steps during the discharge simulation:
T = 0 seconds
T = 40 microseconds
T = 100 microseconds
T = 200 microseconds
T = 400 microseconds
T = 1 millisecond
Here are the resulting graphs of current and stored energy as compared between One Connection (3 piece segmented cathode, only connected at the edges) and All Connections (1 piece non-segment cathode)
Comparing Results of Both Cathode Geometries
ADDING THE FIELD CAGE
††††††††††† After I had developed my simulation to the point where I had obtained the results shown above, I was asked by Dr. Horton-Smith to present my findings to the DUNE High Voltage Working Group that he leads. Aside from obtaining some feedback from them, the main product of the meeting was getting a new goal of using my previous code as a base to build a new simulation that instead models the Current and Energy behavior of the field cage during discharge. Due to the current designs for how the HV lines feed into the different parts of the detector, the field cage is electrically isolated from the cathode plane, and can therefore be modeled separately. Then, by adding together all the products of the two simulations, we can see the total signal being input into the high voltage system. Additionally, since each bar of the field cage is constructed out of conductive aluminum, as opposed to the resistive film of the cathode, we donít have to worry about the sorts of diffusion effects within each field cage element and instead model it as a standard circuit of resistors and capacitors. After making the necessary adjustments to my simulation, these are the results I obtained for the discharge out of the field cage, where Iíve modeled one side of the field cage for each of the width and height dimensions of the cathode. As such, the total field cage is made up of two of each of these sides to connect the cathode to the anode along all four CPA/APA edges, and therefore the total signal into the HV system would be twice the sum of the following two simulations.
1.15m Field Cage Element Length
6.0m Field Cage Element Length
Combined Signal for Total Field Cage
ELECTRIC FIELDS, INDUCED CHARGES, AND THE ANODE PLANE
††††††††††† As the final step of this research project, I needed to find a way to use my existing results for the distribution of voltages in the rest of the system through the course of a discharge to try and build the changing electric fields, and therefore induced currents, that would be occurring at the anode plane. This aspect of the of the discharge behavior is also of most interest to the DUNE collaboration, and the people in charge of modifying and finalizing the designs for future prototype, and final, detector designs. This is because while the cathode contains massive voltages and energies, itís only absolute requirement for a properly functioning detector is that it must be able to reach, and maintain, the proper voltage of 180 kV. As such, there are a plethora of methods and modifications that can be made to limit its possible behavior for different worst case scenarios that wonít result in hindering the performance of the system in its highest function as a detector. However, the anode plane serves its main purpose as the detector of charged ions and electrons throughout the detector, and so is experimentally required to be a grid of wires that are connected to extremely sensitive detection systems through essentially no electronic shielding or safeguarding. As such, any sort of induced current from a cathode discharge cannot be eliminated because that would also be eliminating the same sorts of induction signals that are how particle interactions can be located. Unfortunately, while being so important, this is also a ridiculously more complicated process to simulate with anywhere near the level of accuracy I could achieve in my previous simulations. Therefore, our aim was to instead simulate some approximate results using a simplified system, and treat any output more as an order of magnitude type of result, and only as a very rough starting answer to whether or not it would be necessary to either do experimental tests of the design, or discuss possible modifications to improve the operational stability of the detector.
††††††††††† The Method Can be Broken Down Into the Following Steps
(1) Use the Voltage in each discrete grid element at a given time to get a value of electric charge for that element from its capacitance
(2) Use a monopole approximation for each element, i.e. place a point charge of the calculated magnitude at the center of each discrete element
(3) Find the resulting voltages from these charges in the region around the anode plane
(4) Take derivatives of the voltage perpendicular to the anode plane on both faces to get the induced charge via equations for electromagnetic boundary conditions
(5) Sum the charge over the area of each wire in the anode plane to get the total charge on each wire at a given time step
(6) Measure the change in this total charge between each time step to get the current out of each wire
(7) Output the current output of only the wire with the largest signals, and therefore the worst case scenario that must be able to be accounted for
(8) Plot these results over both the long term discharge, and for a short period right at the start of the discharge
This allows us to also see the magnitude of the current spike produced at the start of the discharge
Here are some more detailed presentations that breakdown the simulation methods and the theoretical basis of my work
Final Presentation: Click here to download my final presentation for this research project: PowerPoint or pdf
About Me: †I am from Downstate New York, specifically the town of Nyack NY in Rockland County. I attend Kenyon College in Gambier, Ohio, and am currently entering my fourth year as a physics major there. Iím also interested in sociology and philosophy, and have used the opportunities available at a liberal arts school like Kenyon to study them in addition to physics.† I had always been interested in the STEM fields up through High School, but during my first semester at Kenyon, I decided to give the physics department a try and take a Classical Physics class. I completely fell in love with the subject, as well as the other people who were also involved in the subject, and Iíve been hooked ever since.
I have found the following links particularly informative or useful: