DF Thesis

Theory

Drift Chambers

The CLAS12 drift chambers are designed to determine the momentum of charged particles moving through them. The following sections are a brief overview of drift chambers in general.

Typical Construction and Principle of Operation

Drift chambers are charged particle detectors that are designed to measure the trajectory of a particle's path through the detector. This is important as it ultimately allows for the measurement of a variety of quantities of scientific interest by means of inverse kinematics.

Typically, drift chambers are constructed out of a chamber filled with an ionizable gas and charged wire planes. The wire planes are arranged to be ideally perpendicular to the particle's direction of motion and come in two alternating types: cathode planes and sense planes. A cathode plane is designed such it creates a nearly-uniform static electric field which will drive electrons towards the sense planes. A sense plane is constructed with alternating anode and cathode guard wires. The anode wires are the sense wires, i.e. where the electrons ultimately end up and create an electronic signal. That electronic signal propagates away from the location of the hit in both directions and is read by a coupled pair of timers at either end of the wire. It is common to have multiple sets of layers which are oriented differently, though still perpendicularly to the direction of motion, to increase the accuracy of the ultimate reconstruction.

The general principle of operation is as follows. A charged particle moves through the detector and ionizes atoms along its path. The electrons, which have been separated from these atoms, are now accelerated towards the anode wires (sense wires). If the anode wire is very thin, the electric field near to it becomes very strong, causing the electrons to pick up a great deal of speed and cause a Townsend avalanche. A Townsend avalanche is a cascading series of ionizations which help to amplify the signal. This signal being a voltage pulse traveling towards either end of the wire from the point where the electrons hit. Using the coupled timers at the ends, it is then possible to use the difference in time of signal propagation to calculate the position along the wire of the hit.

This position along the axis of the wire is only one dimensional information about a particle traveling through 3D space. It is, however, possible to couple the timing information from multiple nearby sense wires and a measurement of the time the liberated electrons take to reach the sense wire to calculate the distance of closest approach (DOCA) to each of them. This then gives a position along the axis of each wire as well as a radius perpendicular to that axis at that point. If all of this information is known perfectly, then the vector component of the path which lies in the plane of a circle defined by the aforementioned radius will be tangent to that circle. Combining that information with the change in hit position along the axis of each wire allows for the ultimate measurement of the particle's path through the detector.

Addition of a Magnetic Field

The inclusion of a magnetic field into a drift chamber allows for the reconstruction of not just the path of the particle, but also the magnitude of its momentum. A uniform magnetic field perpendicular to the particle's direction of motion, for example, would cause the path to bend into some section of a circle, thus changing the expected hit position along the wires of the sense planes. Using these hits, it is then possible to reconstruct the radius of curvature of the path. With the assumption the particle carries the usual elementary charge, it is then possible to back out the particle's momentum by equating the central force and magnetic force as shown in equation \ref{eq:momentumFromForces}.

\begin{equation} \label{eq:momentumFromForces} \frac{mv^2}{r}=qvB\implies{}mv=qBr \end{equation}

Clas12

Clas12 is a detector suite built inside of Hall B at Jefferson Lab. It has been designed to replace the old Clas6 detector in order to take advantage of the recent improvement to Jefferson Lab's electron beam energy, which is now up to 12 GeV.

Clas12's Drift Chamber Construction

The Clas12 Detector's drift chamber is broken up into 18 separate sub-chambers as shown in figure \ref{fig:regionsAndSectors}. There are six chambers in each of three regions which are approximately 2.1, 3.3, and 4.5 meters away from the physics target position. Within each region, the six triangular chambers are arranged to be in symmetric sectors around the beam axis with angular coverage between 5\textdegree{} and 45\textdegree{} as measured at the target location with respect to the beam axis.

\begin{figure} \includegraphics[width=\textwidth]{../ImageRepo/DAF-19-03-24-DC-RegionsAndSectors.png} \caption{The three regions and six sectors per region in the drift chambers} \label{fig:regionsAndSectors} \end{figure}

Within each chamber are two superlayers of wire planes which are arranged such that the axes of the wires in either plane are separated by 12\textdegree{}. Within each super layer are 6 layers of sense wires, each of 112 wires, with a hexagonal arrangement of cathode wires around each of the sense wires as seen in figure \ref{fig:layersInSuperlayers}.

\begin{figure} \includegraphics[width=\textwidth]{../ImageRepo/DAF-19-03-24-DC-LayersInSuperlayers.png} \caption{The six layers per superlayer in the second region.} \label{fig:layersInSuperlayers} \end{figure}

Clas12's Magnetic Fields

The Clas12 detector has two magnetic fields, one solenoidal field at the target and one toroidal field centered around the second region. The solenoidal field points primarily in the direction of the beamline with a nominal value of 5 Tesla, and is designed to provide a "phi-kick", or rotation about the beam axis, to any particle coming off at angle from the beamline. The toroidal field is actually the result of six smaller coils, one in each sector, which all contribute to create a field which is primarily in the phi (azimuthal about the beam line) direction. This is designed to bend particles either into or away from the beam line throught the drift chambers which allows for the reconstruction of the particle's momentum. See figure \ref{fig:magneticFields}.

\begin{figure} \includegraphics[width=\textwidth]{../ImageRepo/DAF-19-03-24-DC-MagneticFieldMagnitude.png} \caption{The strength of both the solenoidal (left) and toroidal (center) magnetic fields.} \label{fig:magneticFields} \end{figure}

Coordinate Systems

The collaboration has defined two coordinate systems in addition to the lab system to reduce the complexity of the reconstruction process within the drift chamber. The lab coordinate system is defined by a right-handed system such that the positive y-direction is upwards, against the pull of gravity and the positve z-direction is down the beam line. This results in the positve x-direction bisecting what is known as sector one as shown in the figure \ref{fig:labCoordinateSystem}.

\begin{figure} \includegraphics[width=\textwidth]{../ImageRepo/DAF-19-03-24-DC-LabCoordinateSystem.png} \caption{The lab coordinate system and sectors as seen when looking down the beam line.} \label{fig:labCoordinateSystem} \end{figure}

The sector coordinate system is defined by rotating the sector of interest into the position of sector one. This rotation will naturally be some multiple of 60\textdegree{}. The image below shows a typical representaion of this coordinate system with the y-direction being perpendicular to the paper.

<Insert Image of Sector Coordinate System Here>

The tilted sector coordinate system take the sector coordinate system and rotates it about the y-axis by 25\textdegree{} such that the z-direction is now perpendicular to the plane of the drift chambers. See the image below.

<Insert Image of Tilted Sector Coordinate System Here>

Clas12 Event Reconstruction

The following sections describe the two current methods used to reconstruct the particle's path through the detector. Hit Based Tracking only uses the position information, no timing information, and Time Based Tracking uses the output of Hit Based Tracking and the timing information.

Definition of Terms

There are several terms which must be understood before reading further:

• Hit
  • A representation of a measurement from an individual wire.
• Cluster
  • A representation of groups of physically close hits.
• Segment
  • A representation of a linear fit to a cluster.
• Cross
  • A representation of a position and momentum vector of the particle's trajectory at the midplane between two superlayers as reconstructed from the segments of both superlayers.
• Track
  • A representation of a reconstructed path through the detector.
• Swimmer
  • A programatic tool utilizing a fourth order Runge-Kutta approximation to step, or "swim", a particle's trajectory through the detector.

Hits to Clusters

Beginning with the Hit Based reconstruction, the raw hits are all initially sorted into clumps. Clumps are the rawest form of cluster as they are are created by independently taking each superlayer in each sector and adding the hits found therein to the clump. The clump is then processed to remove hits caused by noise. This is determined by whether or not the DOCA for that hit is greater than the size of the cell. The list of clumps is then processed int a list of clusters by removing any clumps which have less than four total hits within them. The clusters are then split into multiple clusters if neccesary by means of checking the \textchi{}\textsuperscript{2} of a linear fit to the hits. Following that step, the program updates the raw hits with various additional information and stores them as well as the clusters.

The Time Based reconstruction takes the clusters from the Hit Based Reconstruction and further refines them. First, for each cluster the algorithm removes secondary hits, which are defined as hits that lie within the same layer as another hit and fail a test comparing the relative DOCA's. The clusters are then refit with the aforementioned \textchi{}\textsuperscript{2} test if necessary to ensure that the most accurate clusters have been found. Next, the algorithm attempts to resolve the left-right ambiguity in the cluster's linear fit, i.e. determine on which side of which wires the particle passed. Finally, the clusters and associated hits are updated with this new information.

Clusters to Segments

The Hit Based reconstruction builds the segments by first excluding any clusters with more than fourteen hits from consideration. Then, for each remaining cluster, the information from the linear fit is taken from the tests already done in the previous step and set in the segment accordingly.

The Time Based reconstruction first takes each cluster and subjects it to a test wherein the average DOCA of the hits within the cluster is calculated and then compared to the average cell size of the cells where those hits were recorded. Clusters which fail this test are culled. The clusters then undergo the same process as the Hit Based clusters.