DF Thesis

Theory

Drift Chambers

Typical Construction and Principle of Operation

Drift chambers are charged particle detectors that are designed to measure the trajectory of a particle through a magnetic field and determine its momentum. Typically, drift chambers are constructed using an ionizable gas and planes of wires that establish electric fields used to accelerate the ions resulting in amplification. 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. The anode wires are the sense wires used to collect the liberated electrons and create an electronic signal. That electronic signal propagates along the sense wire in both directions and is read by a pair of coupled timers at either end of the wire.

The "field-shaping" cathode wires within a sense plane are to prevent electrons from being caught roughly in the middle of two anode wires and thus taking a significant amount of time to reach either of them.

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 is 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 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 path of the particle will be tangent to the circle defined by the aforementioned radius for each wire, ultimately giving a 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 as shown below.

<Insert Central Force = Magnetic Force Equation Here>

Clas12

Clas12 is a detector suite built an Jefferson Lab's Hall B. 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 the figure below. There are six chambers in each of three regions which are approximately 2, 3, and 4 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\degree and 45\degree as measured at the target location with respect to the beam axis.

<Insert Image of Regions and Sectors Here>

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\degree. 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 the figure below.

<Insert Image of Layers Here>

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 typical value of 5 Tesla, and it 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 creat 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.

<insert image of magnetic field strengths here>

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 image below.

<Insert CED Image of Lab Coordinate System Here>

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\degree. 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\degree 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

Definition of Terms

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

• Hit
  • A representation of a measurement from an individual wire. This includes a the position of the hit in the tilted sector coordinate system and a distance of closest approach.
• Cluster
  • A representation of groups of physically close hits, i.e. groups of contiguous hits in a superlayer.
• 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.
• Track
  • A representation of a reconstructed path through the detector.