PHENIX TRD Simulation

Introduction

Transition radiation (TR) is emitted when a relativistic particle crosses a boundary between two media with different dielectric constants.

TR becomes useful when particle Lorentz-factor is greater than approxmately 1000. In this case emitted photons are in X-ray range (several keV) and can be detected by, for example, proportional chamber (Time Expansion Chamber (TEC) in the PHENIX experiment). In a very broad range of momenta (from 1 to 100 GeV) transition radiation is emitted only by electrons, which makes it a unique tool for electron/pion separation.

Typical Transition Radiation Detector consists of a radiator (dielectric foils, foam or fibers in gas) and an X-ray detector (e.g. proportional chamber).

Unless explicitly mentioned, simulation was done for gas gain in TEC = 3000 and all 6 TEC planes active.

PHENIX TRD

For the description of the PHENIX Transition Radiation Detector refer to Rob Pisani's TRD page.

TR X-ray spectra

The double differential energy spectrum radiated by a charged particle traversing an interface between two dielectric media is described by the following formula:

For a foil one has to sum up the contributions from the two interfaces:

TR yield from an irregular stack of dielectric layers was first calculated by

G.M.Garibian et al., Sov. Phys. JETP 66 (1974) 552

G.M.Garibian et al., NIM 125 (1975) 133

where I is a factor taking into account interference and absorption. I is a rather complex function, and the reader is refered to the above mentioned references for details.

G.M.Garibian et al. made their calculations assuming that the radiator is in vacuum. Their formulae were generalized for an arbitrary medium by:

M.N.Mazziotta, e-print http://arxiv.org/pdf/physics/9912042 (1999 )

Angular distribution of TR X-rays for different Lorentz-factors (gamma) is shown in the plot below. Theta is the angle between TR X-ray and the direction of the particle.
The distribution depends on X-ray energy and is peaked at approximately 1/gamma.

TR X-ray yield vs energy for different Lorentz-factors, numerically integrated over all theta angles, is shown in the plot below:

Average number of TR X-rays is shown vs Lorentz-factor gamma in the plot below for one TRD/TEC plane in red points. Blue points show the results of the prototype test from PHENIX TRD (1993).
The difference is explained by the fact that only 120 radiator foils were used in this test.

X-ray path length in TEC

Absorption coefficient for X-rays in 0.45 Xe + 0.45 He + 0.1 CH4 gas mixture (density 2.80e-3 g/cm^3) is shown in the plot below. Data points are taken from http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html, and fitted with [0]*exp([1]*pow(x,[2])) function.

Similar plots for other gases:
     0.9 Xe + 0.1 CH4   (density 5.36e-3 g/cm^3)
     Air   (density 1.205e-3 g/cm^3)
     Solid polypropylene (CH2)   (density 0.90 g/cm^3)

The plot below shows the fraction of remaining TR X-rays vs depth in 0.45 Xe + 0.45 He + 0.1 CH4 gas mixture for different X-ray energies:

For 1 GeV/c electron 64% of TR X-rays or 49% of all TR energy are absorbed in 6 TEC planes. In case of 0.9 Xe + 0.1 CH4 gas mixture, 88% of TR X-rays are absorbed (77% of TR energy).

Absorption plot for 0.9 Xe + 0.1 CH4 gas mixture.

Example of an event

The plots below show examples of 1 GeV electron (gamma = 2000) going through 6 TRD/TEC planes. Red histogram shows only ionization losses, black histogram shows sum of ionization and TRD. In the first plane three TR X-rays were produced, one each in third and fourth, and none in second.
The plot was made using mTecSlowSimModule class with gas gain 3000 and 0.9 Xe + 0.1 CH4 gas mixture.

Another example.

e/pi comparison

The plots below show integrated over many events dE vs time bin distributions for pions and electrons with and without transition radiation.

Charge in both plots is in arbitrary unit, but the two plots are normalized relative to each other. As you can see, for Xe/He mixture the signal is more than two times less than for pure Xe.

Pion rejection

The plot below shows pion rejection factor vs dE/dX truncation for different gases with and without TR. Gas gain 3000 and no noise were assumed in this simulation.

Other PID methods

Better pion rejection can be done if two-dimensional cuts are used, as shown in the plot below. It shows total dE/dX vs dE/dX in time bins > 40.

Another method of pion rejection is based on counting number of "clusters", that is, adjacent time bins with amplitude higher than some threshold (see event displays above). This method is supposed to give similar results to using dE/dX.

Useful links

ATLAS Transition Radiation Tracker

Alice TRD

List of TR articles by A.Andronic

Last updated 1/9/2003 by Sasha Lebedev