GEAMAG: GEANT simulation for MAGNEX

GEANT overview

• Provides the means to use experiment-dependent code
  • geometry of the experiment
  • event generators
  • details of digitization
• in an experiment-independent infrastructure
  • tracking & geometrical primitives
  • physics
  • visualisation, etc.

Strictly speaking, GEANT is not a program itself, but a library of routines that are linked together with modules written by the user specific to the problem to be solved. In our case, the compiled program with the geometry for MAGNEX has been named GEAMAG. We started our project before GEANT4 was fully released, so we have used GEANT version 3.21 and the programming is done in Fortran. The effort to convert to GEANT4 would be considerable.

GEAMAG was originally developed on a Unix platform. It was ported to Linux in March 2001.

Geometry

• The target. This has typically been taken as a 61.7µg/cm² mylar foil. The density of mylar being about 1.397 g/cm³, this would normally lead to a thickness of 0.442 µm. However, we have found that the tracking routines in GEANT are sometimes not sensitive to elements in the µm range. To get around this problem, we use an imaginary material of the same composition as mylar, but with a density one-tenth the normal mylar density (0.140 g/cm³), which can then be ten times thicker than the nominal thickness. The origin for the generation of the particles is at the centre of the target (actually, at z = -200). However, particles may be randomly generated at small distances from the origin in order to simulate a finite beam spot size or differences in energy loss effects.
• The position-sensitive start detector (PSD). Only the foil is simulated, and not the generation of electrons and their amplification through the microchannel plate. Instead, ``intrinsic'' resolutions of the position and time signals are generated and folded into the hit coordinates given by GEANT.
  The foil is composed of three elements, the ``sensitive volume'' (in GEANT terminology) of which is a 7 cm diameter mylar foil, of effective thickness 0.5 µm (approx. 69 µg/cm²). A 20 µg/cm² aluminium layer and 0.05 µm CsI coating are the other passive elements. Because of the tracking sensitivity problem mentioned above for the target, all these elements in the program are made of material one-tenth the normal density and ten times thicker than the normal value. The foil is located 15 cm from the target, and tilted at 45^o in the vertical dimension.
• The quadrupole magnet. The construction of the quadrupole field is described below. The magnet itself is 60-cm long cylinder with a 20-cm radius. In addition to this, there are 40 cm-long fringe field extensions at the entrance and exit. Thus the total length of the quadrupole element is 140 cm. The geometrical parameters for the magnet are in fact read from an output file of the ray-tracing program ZGOUBI [2]. A tubular iron yoke, the purpose of which is to block ``stray'' particles, surrounds the magnetic field region.
• The dipole magnet. In shape, this is a 55^o section of a tube, with inner radius 95 cm, outer radius 235 cm and 20 cm height. The positioning of the magnet (and field map) with respect to the central axis from the target is quite critical. The alignment with respect to the central ray from the target is based on trajectories traced back to the entrance field boundary in ZGOUBI. As in the case of the quadrupole, the relevant numbers for the positioning of the magnet are read directly from the same ZGOUBI output file listing that contains the dipole field map.
• The focal plane detector. This is the most complicated element in the simulation, both in geometry (it is a generalised trapezoid) and in construction (it includes four different detection components as well as a gas window and sets of field-defining wires). The focal plane is aligned from a trajectory close to the normal to the dipole exit field boundary. Again, the exact angles and distances are read from the ZGOUBI file.

  In the following description of the focal plane detector, all ``depths'' are taken along the ``trapezoid angle'', which is the angle between normal to the entrance face of the box and a line that joins the midpoints of the entrance and exit faces of the box (it is a few degrees different to the angle of the central ray trajectory with the normal to the entrance face. For the 55° magnet, this trapezoidal angle turns out to be 68.4°. All ``lengths'' are relative to the chosen focal plane length, scaled by the geometry of the trapezoid-shaped box (i.e., the lengths of elements increase the further they are located back in the detector). The focal plane length and height are 105 cm and 21 cm, respectively.

  • The entrance window and support grid. The entrance window is the same length and height as the focal plane. It is made of 2.5 µm mylar. The support grid is a mesh of 100 µm diameter vertical and horizontal plastic wires. The spacing between adjacent wires is 1 cm.
  • The front field shaping wires. These are 0.5 cm behind the window. Their material is steel, their diameter is 100 µm and the separation between adjacent wires is 1 cm. Each wire is 7 cm longer than the focal plane.
  • The first Drift Chamber (DC₁). This position-sensitive element begins 0.05 cm behind the front field-shaping wires and is 3 cm deep. For each event in the focal plane, a record of the track ``hits'' in coordinate space is stored in an array, as well as the accumulated energy loss. At the end of the event, the mean horizontal position along the depth of the drift chamber is calculated to obtain the base value for x<sub>foc</sub>. The smallest value of the vertical hits is taken for the base value of the y<sub>foc</sub> signal. These raw numbers are then ``smeared'' by adding randomly-generated numbers with distributions corresponding firstly to the ``intrinsic'' resolution of the counters, and secondly to the effect of the spreading of the electron cloud. Note that no assumption has been made as to the actual construction of the ``Drift Chambers''. They could have, for example, individual anode strip readout, or resistive wire readout, or any other method of obtaining a position signal from the ionization track. Only the ``intrinsic'' resolution of the counter should be specified depending on the actual type it is desired to simulate.
  • The Ionization Chamber. An accumulative energy-loss signal is recorded for particles transversing this volume. This signal would be used in an experiment to help identify the particle type by atomic number. The chamber is 18 cm deep and begins 0.05 cm after DC₁.
  • The second Drift Chamber (DC₂). This position-sensitive element is similar to the first Drift chamber, except that it is longer. It is used together with DC₁ to obtain the focal plane angles. It is 3 cm deep and located 0.05 cm after the end of the Ionization Chamber.
  • The rear field shaping wires. These are 0.05 cm behind the second Drift Chamber. They are of the same material, diameter and spacing as the front field shaping wires, but are longer (9 cm longer than the second Drift Chamber).
  • The silicon array is the last element in the focal plane detector (not counting the aluminium back wall to the detector box). The array follows the exit field shaping wires by a short distance. It is composed of vertical columns of detectors arranged along the back of the detector box. The number of elements in a column is determined by the size of the individual detectors and the height of the focal plane. The number of columns is based on the length of DC₂. Further details on the geometry of the silicon array may be found in [3].
    From the silicon array one obtains two basic data: the residual energy (stopping energy) of the particle and a time relative to the start of the event. The silicon time record can be used in conjunction with the time record from the PSD start detector to construct a simulated an experimental time-of-flight signal.

  The detector gas used in the ``full'' simulations discussed here is isobutane, typically at a pressure of 10 mbar. The gas material or pressure (density) can be changed in the program. To study the ``bare'' optical resolution of the spectrometer, the counter can be "emptied" of gas, except necessarily for the two Drift Chambers.
  To prevent spurious particle tracks from entering or exiting the counter from the sides, 5-mm thick aluminium ``walls'' have been added to the exterior of the detector. An aluminium frame similarly surrounds the entrance window.

Layout of the elements in the GEAMAG simulation. The dipole and quadrupole magnetic fields are not shown. In the focal plane element, the chamber walls, window support mesh and field defining wires have been removed for clarity.

Magnetic field

Detector intrinsic resolutions

One should note that the detector intrinsic resolutions (PSD and focal plane) used here are taken from the expected improvement in resolution after modifications, rather than those actually measured in the detector test runs in May 1997 [3]. A future study could investigate the final energy resolution obtainable for the full system with the experimentally measured values. For the PSD, the values used here are for the microchannel plate with magnetic field and are given in the following table:

In the case of the focal plane detector, the values are for the modified GANIL drift chambers, with the value for the vertical position resolution reported in ref. [5]. and are given in the table below:

Spreading from vertical drift of electrons

where e_T is the transverse characteristic electron drift energy, which depends on the gas type. For pure isobutane, we take e_T as 0.2 eV [7]. For helium + 16% butane, Schmidt and Martens [6] indicate a value of e_T of 0.28 eV. The number of electrons in the swarm, N_pair, is obtained from dividing the energy loss underneath DC₁ by the energy to create an ion pair in the gas. For isobutane, this is 23 eV, for helium it is 41 eV. The reduced field is the value required to be in the ``plateau'' region of the drift velocity vs E_red curve. For isobutane, this is about 3 kV/cm at 1 atm, or 30 V/cm at 10 mbar pressure. For helium, the number is about 12.5 V/cm at 10 mbar. The estimation of the contribution to the vertical position signal is similar to that for the horizontal, except that e_T should be replaced by e_L in the above formula, where e_L is in general smaller than e_T. Schmidt and Martens [6] give e_L = 0.12 eV for helium with 16% isobutane. Assuming the same L/T ratio for pure isobutane, one obtains e_L approx 0.1 eV (since the electron drift contribution is always small for isobutane, this assumption is not critical).

Bibliography

[1] GEANT: Detector description and simulation tool (version 3.21), CERN Program Library Long Writeup W5013, Applications Software Group, CERN, Geneva, Switzerland (1997).

[2] F. Meot and S. Valero, ZGOUBI Users' Guide, Version 3, SATURNE, LNS/GT/93-12 (1996).

[3] A. Cunsolo, M. Aliotta, A. Bonaccorso, F. Cappuzzello, E. Costanzo, D. Ficarra, A. Foti, M. Lattuada, M. Re, S. Romano, V. Shchepunov, C. Spitaleri, A. Tumino, D. Vinciguerra, S. Cherubini, P. Roussel-Chomaz, W. Mittig, O. Malishev, A. Popeko, H. Savajols, C. Stephan, L. Tassan-Got and A Yeremin, MAGNEX: a large acceptance magnetic spectrometer for EXCYT, INFN-LNS report, 1998.

[4] W. Munch and B. Schorr, Routine NORBAS, (Normalised Basic Splines) CERN MATHLIB library routine E210.

[5] A.C.C. Villari, Nucl. Instrum. Methods A 281 (1989) 240.

[6] B. Schmidt and K. Martens, Nucl. Instrum. Methods A 317 (1992) 148.

[7] G. Charpak and F. Sauli, reprinted in "Experimental techniques in high-energy nuclear and particle physics", ed. Th. Ferbel (World Scientific, 1991).

 

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