Anode Design for a Picosecond Time-of-Flight Detector
September 25, 2004
Abstract
While it has been shown that the use of Cherenkov photons produced by energetic particles can be used to achieve fast time-of-flight measurements, the physical realities of this system present complications. I propose a design for such a system which reduces timing uncertainty and improves resolution. By using equal length transmission lines to collect an electrical signal generated by a Cherenkov shower, path length uncertainty is minimized. Monte Carlo simulations indicate that timing resolutions on the order of 1 picosecond can be achieved with existing technology. Such a system would dramatically improve particle identification in large accelerators.
Anode Design for a Picosecond Time-of-Flight Detector
September 25, 2004
In experimental high energy physics, particle identification plays an important role in gathering data. When two particles collide in an accelerator, the energy of the collision allows new particles to be formed. Correctly reconstructing the events of a collision allows experimentalists to examine phenomenon and provide data for new physics. For this purpose, the collision vertex is surrounded by a cylindrical array of instruments which allow researchers to observe the thousands of events occurring each second. These detectors record energy, time, and position for particles passing through them. A large solenoidal magnet causes charged particles to travel in curved paths, allowing a calculation of their momentum.
In several cases, distinguishing between particles which behave in similar ways can be difficult. The charged hadrons π, K, and p, for example, all commonly produced in collisions, are not easily differentiated. The best way to separate the three is an accurate measurement of mass, which is calculated from a measurement of both velocity and momentum. While a momentum calculation can be made for a charged particle after observing a curved track, the generally accepted method for determining velocity relies on measuring the time required for a particle to travel from the collision vertex to some other point. This is the purpose of a time-of-flight (TOF) system. A TOF detector a fixed distance from the collision vertex records the time as a particle passes though it. After a time has been measured for enough particles resulting from one collision, it is possible to determine an accurate fit for the time of collision. This calculation facilitates the computation of the time interval, the velocity, and most importantly the mass of the incident particle.
Figure 1: This image shows the difference in the time it takes for the hadrons of a given momentum to travel 1.5 meters. Δt gives an idea of the timing resolution necessary to for a TOF system to distinguish the two particles.
Current time-of-flight systems achieve a time resolution of approximately 100 picoseconds. In the most common design, particles pass through scintillator bars, exciting photons which travel down the bar to a photomultiplier tube which amplifies the signal for a reading. A test system at Fermi National Accelerator Laboratory used 20 rectangular bars of scintillator, each 4x4x130 centimeters and an average of 1.40 centimeters from the particle beam [1]. In such a system, the resolution is limited by uncertainty in the path length of photons bouncing down the scintillator. The target resolution for the Fermilab system was 125 picoseconds [1].
Figure 2: Photons emitted by a passing particle can take very different paths. This difference in path length results in significant timing uncertainty.
Schroll [2] proposes a new type of TOF system, one in which Cherenkov photons (see Appendix I) are produced in a window directly above the photodetector. In this setup, a particle passes through a window, producing Cherenkov radiation. These photons hit a photocathode, which releases electrons. The electrons are then accelerated into a micro-channel plate (MCP), where they pass through an array of cylindrical channels. If a large voltage is applied across the MCP, this process can result in a gain around 2*105 [3]. This signal is then deposited on an anode to be converted into data. Because the entire device is only millimeters thick and particles are passing directly through, variation in path length is limited and time resolution is improved.
Figure 3: Photons excited by a passing particle can take very different paths. This difference in path length results in significant timing uncertainty.
Through Monte Carlo simulation of this design, Schroll showed that time resolution on the order of 1 picosecond might be possible. First, the maximum time difference of photons arriving at the photocathode was analytically derived as:
(1)
where T is the thickness of the window, n the refractive index of the window, β the speed of the particle in terms of c, and c the speed of light. Since a particle must be traveling faster than light waves propagate in a given medium to produce Cherenkov radiation, the approximation β=1 is a valid one. Schroll also estimates how much deviation from this approximation might affect results. However, since the particles being considered are highly energetic, this is a safe assumption. After considering factors such as the quantum efficiency of the photocathode, the possibility of photons being absorbed in the window, and the uncertainty inherent in the MCP, it became apparent both that a sufficiently large signal would be detected on the anode and that resolution much better than 100 picoseconds was possible.
Figure 4: The number of photons, the time of the first signal to be deposited on the anode, and the average time a signal arrives on the anode are plotted for 1000 Monte Carlo simulations of particles passing through the window.
However, there are still significant problems in the design to be worked out. Schroll models his detector on micro-channel plate photomultiplier tubes made by Hamamatsu, which are generally several inches across [4]. This introduces the possibility for a great deal of timing uncertainty; the signal must be collected from a single point along the anode, but will arrive at different places. Even if the signal is collected from the center of the anode, the timing uncertainty arising from differences in path length is calculated to be at least as severe as 24 picoseconds. The difficulty arises from the fact that on a picosecond time scale, tiny electrical effects become major issues. In this case, the signal deposited can only travel across the anode at 300 μ per picosecond, a tremendously slow rate when the anode is several tens of thousands of microns across.
The difficult question, then, is how to construct the anode to eliminate this problem. The solution proposed here begins by dividing the surface of a 2 inch square anode into four 1 inch square regions, each with a separate readout. Each of these areas is then divided into an array of 100 small pads, each 2.5 millimeters wide. The signal incident on each pad is then routed to a central collector through a transmission line. Signals propagate through transmission lines with a characteristic time delay that depends only the materials and the length of line. If the transmission lines for the pads are all one fixed length, then the signals passing through them will experience an identical delay. This allows the electrical signal deposited on the anode to propagate through the anode to a collection point without adding significant uncertainty.
In order to design an anode which allows the routing of transmission lines, several layers were needed. The design of the device resembles a multilayer circuit board, and existing processes can be used in manufacturing it [5,6]. To accommodate the equal length routing, the anode consists of five electrical layers separated by four layers of nonconducting material. The top layer is the pad surface which receives the signal. Below that are two pairs of routing layer and ground plane which allow the signal to propagate though transmission lines. A pin collecting all transmission lines allows the signal to be collected from the back of the anode. In the current design, the RMS error in the length of the lines is reduced to 5.9 microns.
Figure 5: A schematic of one of the routing layers of the anode. 200 25 μ thick lines are all routed so that their lengths are equal. The other routing layer immediately below uses the same design flipped horizontally.
In order to assess the resolution possible with such a design, it was no longer sufficient for a Monte Carlo simulation to address only the timing of the photons. To evaluate the new system, the location of the signal arriving on the pads needed to be known as well. As derived in Appendix II, the location of a photon emitted by the particle a distance D away from exiting the window will have x and y position
(2)
(3)
where x and y are relative to the location at which the particle exits the window, φ is the angle between the particle’s path and the window’s normal vector, ψ is a random variable between 0 and 2π indicating the direction of emission, and θC is the Cherenkov angle given by
(4)
The fact that
(5)
where N is the number of photons emitted, Z is the charge in multiples of e, and α is the fine structure constant [7,8] allows for the path of the particle to be split into a small grid. At each point in the grid the number δ2N/δxδλ was calculated and multiplied by the grid size δx*δλ. If a random number on (0,1] was smaller than this probability, a photon was emitted and its time and position after leaving the window were recorded. The program written for this Monte Carlo also corrected for the quantum efficiency (the probability that an incident photon will excite an electron) of the photocathode and probability of absorption in the window.
After simulating the shape and timing of the Cherenkov showers, the electrical properties of the MCP and the anode were simulated using Mentor Graphics electrical engineering programs. The data concerning the nature of each shower was fed into programs which simulated the physical characteristics and electric properties of the design. Although the pulse arriving at the collector typically lasted for approximately 100 picoseconds, the RMS error in the rise time for the pulses was only .8 picoseconds.
Figure 6: This graph shows the average shape of a pulse arriving at the back edge of the window. 100 pulses were simulated and the number of photons in each 200 micron square bin was counted.
Figure 7: In order to simulate the effect of a pulse on each individual pad, the number of photons arriving at each pad was counted. Above is one sample pulse.
Though the evidence suggests strongly that such a system would drastically improve time-of-flight measurements, there are still issues to be resolved. One possibility which may introduce uncertainty is the behavior of the detector inside the strong magnetic field around the collision vertex. Though conceivably possible to locate the detector outside the solenoidal coil, this might allow interactions with the coil itself and introduce greater uncertainty. However, the effect of the magnetic field is expected to be minimal [9].
Another issue which still remains is the design of electronics to collect the signal and convert it to digital data. While this process may incur additional uncertainty, the accuracy of the signal exiting the anode should facilitate accurate timing.
If the prototype detector being developed is successfully tested, the potential of such a device would be impressive. Greater accuracy in particle identification would allow for a better understanding of the physics at work in an accelerator. Additionally, a time-of-flight detector accurate to picosecond resolution could be used to associate photons to a specific collision vertex when several events happen in close proximity.
Appendix I
Cherenkov light is produced by an energetic charged particle when its velocity in a medium exceeds the speed at which electromagnetic waves propagate in that medium.
Figure 8: In a sufficient large radiator, Cherenkov light is produced in a coherent conical wavefront.
Cherenkov photons are emitted at the characteristic Cherenkov angle θC to the path of the particle.
(6)
Appendix II
At some distance D from the point where it exits the window, a particle traveling at an angle φ to the normal of the window emits a Cherenkov photon at the Cherenkov angle θC.This photon’s path is rotated about the path of the particle at a random angle ψ.
If the point at which the particle exits the window is taken to be the origin, and the point at which it emits a photon is taken to t=0, then the coordinates of the particle are given by:
(7)
The coordinates of the emitted photon must then be
(8)
Since (A,B,C) is a unit vector, we use geometry to determine
(9)
By solving z=0 we obtain
(10)
Subsequently plugging in t to determine the values of x and y when the photon exits the window gives us
(11)
(12)
Using this result, we can easily simulate the location of Cherenkov photons produced as well as their time behavior. Since the probability of emission of a Cherenkov photon depends on the wavelengths considered and the path of the particle, the Monte Carlo simulation divides the path and the emission spectrum into a grid. The number of photons emitted in a given section of the spectrum is randomly determined according to this probability for each small piece of the particle’s path. Since the photons can be rotated with respect to the path of the particle, ψ is given a uniform random distribution. The time and position between the particle and the photon leaving the window are then calculated. This information was fed into a simulation of the electrical characteristics of the photocathode, MCP, and anode.
References
[1] S. Geer et al, Time-of-Flight Test System Performance, Fermi National Accelerator Laboratory, Batavia (1996).
[2] R. Schroll, Picosecond Timing with Cherenkov Light in a “Head-on” Geometry, University of Chicago, Chicago (2004).
[3] Hamamatsu Corporation, Technical Information. NIR MCP-PMT, http://usa.hamamatsu.com/assets/applications/ETD/Nir
_mcp_pmt.pdf
[4] Hamamatsu Corporation, Microchannel Plate – Photomultiplier Tube (MCP-PMTs) R3809U-50 Series, http://usa.hamamatsu.com/assets/pdf/parts_R/R3809U-50.pdf
[5] H. Sanders, private communications
[6] F. Tang, private communications
[7] K. Kleinknecht, Detectors for Particle Radiation, 2nd Edition, University Press, Cambridge (1998).
[8] W. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer-Verlag, New York (1994).
[9] P. Hink, private communications
11