Charge transfer considerations of MicroCAT-based detector systems

Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

Charge transfer considerations of MicroCAT-based detector systems$ A. Orthena,*, H. Wagnera, H.J. Bescha, R.H. Menkb, A.H. Walentaa a

Universitat . Siegen, Fachbereich Physik, Emmy-Noether-Campus, Walter-Flex-Str. 3, 57068 Siegen, Germany b ELETTRA, Sincrotrone Trieste, S.S. 14, km 163.5, Basovizza, 34012 Trieste, Italy Received 4 February 2002; received in revised form 3 June 2002; accepted 6 June 2002

Abstract A 3D-field simulation is performed to examine the charge transfer behaviour of the MicroCAT gas gain structures utilised for avalanche charge multiplication in gas-filled radiation detectors. The calculated electron transparency and the ion feedback are compared to experimental results. Further systematic studies are performed to design an optimised gas gain structure for the MicroCAT-detector. r 2002 Elsevier Science B.V. All rights reserved. PACS: 02.60.Cb; 51.10.+y; 51.50.+v; 29.40.Cs Keywords: Hole counter; Parallel plate geometry; MicroCAT; 3D-field simulation; Drift line simulation; Charge transfer; Electron transparency; Ion feedback

1. Introduction Since the introduction of micropattern gas gain devices like GEM [1], MICROMEGAS [2], CAT1 [3] or MicroCAT [4] the application field of gaseous detectors has been widened up tremendously. Especially, the excellent high-rate behaviour predestines these structures for highluminosity experiments as those at the LHC or high-flux synchrotron radiation applications. In

the recent years a wide range of 3D-field simulations were carried out in order to describe the charge transfer behaviour of these microstructures like in the case of GEM [5,6] or MICROMEGAS [7]. Also for the MicroCAT structure the electric field was calculated for a simplified geometry in a 2D-approximation [4]. Since 2D-results only give a rough idea about the field form and therefore the derived charge transfers are very unaccurate we realised a full 3D-model taking the true geometry into account.

$

Work supported by the European Community (contract no. ERBFMGECT980104). *Corresponding author. Tel.: +49 271-740-3563; fax: +49 271-740-3533. E-mail address: [email protected] (A. Orthen). 1 CAT ¼compteur a" trous.

2. Simulation and measurement description The simulation of the charge transfer behaviour of any micropattern device goes along with the

0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 2 ) 0 1 2 7 6 - 7

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

precise description of the electric field in the specified area of interest. Therefore, the charge transfer simulation is subdivided first into the electric field calculation and second into the drift simulation of the involved charges.

2.1. Electric field simulation For an accurate field simulation one has to consider carefully the object’s real geometry. Especially, the comparison to experimental data with respect to electron transparency or ion feedback measurements of the existing MicroCAT structures requires a field simulation taking the object’s physical geometry including more detailed structures into account. For that reason, the particular information about the geometry of the three different MicroCAT types is directly implemented into Ansoft’s MAXWELL 3D-Field Simulator [8], which calculates the electric field for given boundary conditions in a numerical fashion. The scanning electron microscopic photos and the cut through the MicroCAT structure (see Fig. 1) reveal that the hole edges in the MicroCAT mesh are not sharp but rather rounded off due to the production process.2 Furthermore, the hole shapes of the gas gain structure, themselves, conspicuously differ between the upper side and the lower side. All these features have to be considered in the geometric model for the simulation programme. To minimise the calculation effort of the electric field solver, the total simulation area is restricted in x=y-direction to an MCAT basic cell, which fully exploits the existing symmetries. The hexagonal arrangement of holes in the MicroCAT mesh leads to a basic cell definition depicted as area 1 in Fig. 2. The dimensions of the three existing mesh types are listed in Table 1. The type designation of the MicroCAT structures, i.e. MCAT155, corresponds to the number of holes/ in. [4]. By means of the following equation the open area, which is equivalent to the optical 2 The MicroCAT meshes were originally produced for silk screen printing by Stork Screens, The Netherlands.

transparency, can be calculated as
 holes 2 p h2 1 open area ¼ 2:54 cm 4 sin 601

161

ð1Þ

where h denotes the hole diameter. In Fig. 3 the simulation model of a double MCAT155 basic cell is shown. However, the total field simulation area consists of both a region below and above the MicroCAT structure. With respect to the cathode distance d between the bottom side of the MicroCAT structure (applied voltage UMCAT ¼ 450 VÞ and the grounded readout anode a typical gap of d ¼ 100 mm is chosen. Since the MicroCAT mesh disturbs the homogeneous drift field only in its immediate neighbourhood it is sufficient to restrict the drift gap in the simulation to 100 mm: A view of the total simulation area is also depicted in Fig. 3. The calculated electric field strength along the symmetry axis of a hole is shown in Fig. 4 for all three MicroCAT structures, applying a drift field of 500 V=cm: It becomes obvious that the transition from the low drift field to the high gas gain field is slower for larger holes and that the restriction of the simulation region to 100 mm above the MCAT is justified. The radial component of the electric field leads to a bunching effect of the electrons into the centre of the holes. 2.2. Drift simulation In order to study the electron and ion drift lines the solutions of the electric field calculations are implemented in Garfield [9], a simulation programme originally developed to describe the characteristics of drift chambers. One can choose between two possibilities to calculate the drift lines: the fast Runge–Kutta (RK) method and the slower but more accurate Monte Carlo (MC) method. Both methods are iterational, but the latter one additionally takes both the longitudinal and the transverse diffusion of the charge carriers into account: a short step length is computed, in which the drift velocity and the diffusion is assumed to be constant. Then, the next position is calculated and the process is repeated, until the charge carrier has reached an electrode.

162

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

Fig. 1. The scanning electron microscopic photos of the upper side (left), lower side (middle) and the vertical cut (right) of an MCAT155 structure reveal the physical geometry.

The gas properties used for the Garfield simulation like the longitudinal and the transverse diffusion or the drift velocities are calculated by the Magboltz programme [10,11], which is included in Garfield. All the simulations and the corresponding measurements are performed with Ar=CO2 ð90=10Þ using a pressure of 1 bar: For all transfer simulations, the charge multiplication in the gas gain region is not considered. It is only considered if the charges pass through the holes of the gas gain structure. Thereby, the electron transparency e is defined as the ratio of the number of starting electrons in the drift region and the number of electrons that reach the anode. The ion feedback d is defined correspondingly. Fig. 2. The hexagonal arrangement of holes forms the MicroCAT structure, whereby l denotes the pitch and h the hole diameter. The single hatched area 1 describes the elementary MCAT basic cell, which is used for the field simulation. The transparency simulation is carried out in the double hatched area 2; corresponding to one half of the basic cell.

Fig. 5 shows a typical Garfield output. The left part of the electron drift lines, which run from the drift cathode at the top towards the anode at the bottom, visualises the RK method, where the bunching effect of the holes is well visible, whereas the right half exemplifies the MC method. The ion drift lines, that are only calculated with the RK method, start at the anode and move upwards. In this graphical output, the density of the plotted drift lines does not correspond to the field strength. The plot is rather useful to illustrate the difference between the two calculation methods and the difference between electron and ion drift lines.

2.3. Charge transfer measurements The experimental determination of the (relative) charge transfer can be realised measuring two of the following three currents at the particular electrodes: Idriftcathode ¼ I0 þ deðG  1ÞI0

ð2Þ

IMCAT ¼ ð1  eÞI0 þ ð1  dÞeðG  1ÞI0

ð3Þ

Ianode ¼ eGI0

ð4Þ

with the incoming current I0 ¼ R

Eg e: W

Thereby, G denotes the gas gain, R the photon rate, Eg the mean energy deposited by the photons in the detector, W the mean ionisation potential of the gas atoms/molecules and e the elementary charge.

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

163

Table 1 Dimensions of the three existing MCAT types Type

Holes/in.

Pitch l

Hole diameter hðmmÞ

Open area%

Thickness ðmmÞ

MCAT155 MCAT215 MCAT305

155 215 305

164 118 83

116 79 45

45.4 40.6 26.5

60 55 55

45

field strength in the centre of a hole as a function of the z-coordinate

40

field strength [kV/cm]

35 30

MCAT155 MCAT215 MCAT305

25 20

upper side of MCAT155

15

lower side of MCAT

10

upper side of MCAT215 and MCAT305

5 0 0

50

100

150

200

250

300

350

distance z from anode [
m]

Fig. 3. The image on the left-hand side (1) shows the simulation model of twice the basic cell (corresponding to the large dashed square in Fig. 2) of an MCAT155 structure. The rather sharp looking edges are only due to the poor rendering of the CAD tool. On the right-hand side (2) the total field simulation area for the MCAT155 structure, consisting of the MicroCAT basic cell, the gas gain region (below the MicroCAT) and the drift region (above the MicroCAT), is depicted.

With the additional requirement of Ianode þ IMCAT þ Idriftcathode ¼ 0 only two of the three unknown variables G; e and d in Eqs. (2)–(4) can be derived, which means that the absolute electron transparency e cannot be determined but only the product eG: Alternatively, it is also possible to measure the signal pulse height (e.g. with a charge sensitive preamplifier) instead of the analysis of the currents in Eqs. (2)–(4).

Fig. 4. Calculated electric field strength along the symmetry axis of a hole as a function of the distance z from the anode for all three MicroCAT structures. The spacer gap between MCAT and anode amounts to 100 mm; the voltage of the gas gain structure amounts to 450 V; and a drift field of 500 V=cm is applied. For this calculation, the drift gap is exceptionally chosen to 200 mm:

For larger gas gains Gb1 the ion feedback reads Idriftcathode  I0 eG d¼ Idriftcathode þ IMCAT eðG  1Þ Idriftcathode  I0 E : ð5Þ Idriftcathode þ IMCAT The absolute accuracy of the current measurements is estimated to be far better than 30%.

3. Electron transparency simulations and measurements In case of a small electron transparency e only a small fraction of electrons produced in the conversion region reaches the multiplication

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

164

region. The knowledge of the absolute transparency eabs is needed when, for example, single electrons shall be detected. Furthermore, a large e is the basis of a high effective gas gain Geff ¼ eG; because the real gas gain G is limited for reliable detector operation. The influence of the drift field on G in the investigated field range 100 V=cmpEdrift p3000 V=cm; which has been determined by the calculation of the gas gain with Garfield, amounts to less than 4% for the MCAT155 structure (worst case) and is neglected.

drift towards the anode. For symmetry reasons, only one half of the basic cell is taken into account for this calculation (see area 2 in Fig. 2), hence saving simulation time. Each calculated transparency considers 2000 electron drift lines. Several transparency measurements with a prototype detector have been carried out, using values for the MCAT-voltage UMCAT ; the cathode distance d or the drift field Edrift which differ from those used for the field simulation because of technical reasons. But regarding the boundary conditions of the MicroCAT-detector’s geometry, the charge transfer behaviour can only depend on the ratio of the electric fields in the conversion and the avalanche region Z ¼ jEdrift =Egain j ¼ jEdrift ðUMCAT =dÞ1 j; if one neglects charge diffusion effects. In this respect, Egain ¼ UMCAT =d; which denotes the field in the gas gain region, is approximated to be constant. In order to test the quality of the simulation and to examine if the electron transfer’s dependence on the ratio Z is also valid, when charge diffusion is taken into account (MC method), a simulation series is carried out for the MCAT215 and the MCAT305 structures changing the drift field Edrift and the cathode distance d but keeping the quotient Z ¼ 1=90 constant applying a cathode voltage of UMCAT ¼ 450 V: The result (see Fig. 6) shows that the electron transparency only depends on the ratio Z of the fields for each simulation method, whereby the electron transparency calculated with the RK method defines an upper limit because the diffusion process is not considered in contrast to the MC method. The fluctuations from the mean value can be ascribed to numeric variations, caused by the finite number of electron drift lines. The fact that the charge transfer only depends on Z enables the comparison of the simulation to transparency measurements with different Edrift ; UMCAT and d:

3.1. General considerations

3.2. Examination of the three existing MCAT types

For the electron transparency simulation, uniformly distributed starting points of the electron drift lines are chosen. All electrons start at a height of 100 mm above the MicroCAT structure and

The electron transparencies as a function of Z for all three MCAT types have been calculated using both the RK and the MC methods. The simulated transparency as a function of the drift

*10

-3

Vertical cut of the MCAT215 structure

Gas: Ar 90%, CO2 10%, T=300 K, p=1 atm

24 22 20 z-Axis [cm]

18 16 14 12 10 8 6 4 2 z

0 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 Viewing plane: x=-0.0051391 y-Axis [cm]

8 10 12 14 -3 *10

Fig. 5. Charge drift lines in a typical Garfield plot (here for a cut through an MCAT215 structure with a cylindrical hole shape, indicated by the black region). The drift field amounts to 400 V=cm: Both drift line calculation methods are shown as an example for electron drift lines, which run from the top to the bottom along the slightly lighter plotted drift lines: the RK method on the left-hand side and the MC method on the righthand side. The ions move upwards along the darker plotted drift lines, which are only calculated by the RK method, from the anode at the bottom towards the drift cathode.

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177 100

Runge-Kutta method MCAT215 Monte-Carlo method MCAT215

80

1000

800

70 60

Edrift [V/cm]

electron transparency [%]

90

600

50 40

Runge-Kutta method MCAT305 Monte-Carlo method MCAT305

drift field

400

30 20

200

10 0

0 0

50

100

150

200

250

300

350

cathode distance [
m]

Fig. 6. Simulation of the electron transparency of the MCAT215 and the MCAT305 structure as a function of the cathode distance d for a constant ratio Z ¼ jEdrift ðUMCAT =dÞ1 j ¼ 1=90: The transparencies are calculated using both, the RK and the MC methods. Additionally, the applied drift fields for the particular cathode distances are shown.

100

real hole geometry Runge-Kutta method Monte-Carlo method

electron transparency [%]

90 80 70 60 50 40

optical transparency

30 20

cylindrical hole geometry Runge-Kutta method Monte-Carlo method

MCAT155

10 0 0

500

1000

1500

2000

2500

3000

drift field [V/cm]

Fig. 7. Simulated electron transparency for the MCAT155 structure with a realistic approximation of the geometry (corresponding to Figs. 1 and 3) and, for comparison, with a cylindrical hole shape. Both, the RK- and the MC-transparency calculation methods are applied.

field for the MCAT155 structure is shown in Fig. 7. Concerning the influence of the object’s geometry two kinds of models are presented for this transparency simulation: first, the realistic model (corresponding to Fig. 3), depicted in the upper two transparency curves, and second, for

165

comparison, a structure consisting of cylindrical holes with sharp edges (model not depicted), visible in the lower two transparency curves. A large deviation in the electron transparencies of both geometries becomes obvious. This fact stresses the importance of a proper realisation of the basic MCAT cell’s geometry to achieve a good accordance with experimental results. In the following, only the realistic geometries are further considered. The shape of the transparency curve in Fig. 7 can be explained as follows: for small drift fields ðEdrift p600 V=cmÞ the transparency forms a plateau of about 100%, which means that every electron, started in the drift region at least 100 mm above from the MCAT, reaches the gas gain region and finally the subjacent anode. With increasing drift fields more and more electrons are forced to move to the gas gain structure itself. As a consequence, the electron transparency decreases. For very large ratios Z; the electron transparency even falls below the optical transparency, which is shown for example at Edrift > 2500 V=cm for the MCAT155 structure (optical transparency of 45:4 %) with a cylindrical hole shape. Over the whole simulated drift field range the MC method yields lower transparencies than the RK method: by diffusion processes in the gas volume the drifting electrons can move to regions where some drift lines—very close (some mm) to the surface of the MicroCAT structure—end on the mesh. These electrons will not reach the anode and therefore the transparency decreases. Experimentally, not the absolute but only the relative electron transparency emeas-rel is determined by the measurement of the relative signal pulse heights (p absolute electron transparency emeas-abs ), which are taken from the MicroCAT structure and amplified by a charge sensitive preamplifier/shaper system. As mentioned above, the gas gain G is estimated to be constant. In order to compare simulation and measurement the measured relative pulse heights emeas-rel (see Fig. 8) have to be renormalised using the simulations’ results as will be explained in the following: in Fig. 8 the measured relative pulse height rises to maximum with an increasing drift

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

166

100

electron transparency/pulse height [%]

1.0

MCAT155

0.9

relative pulse height

0.8 0.7 0.6 0.5 0.4

measured relative pulse height

0.3 0.2 0.1 0.0 0

500

1000

1500

2000

2500

drift field [V/cm]

Fig. 8. Measured relative pulse height emeas-rel as a function of the drift field for the MCAT155 structure, using an 8 keV photon beam, a gas pressure of 1 bar Ar=CO2 ð90=10Þ; an MCAT voltage of 1170 V and a cathode distance of 225 mm:

field in the range of Edrift E300 V=cm: The signal loss for smaller drift fields can be explained by attachment and recombination of the primary produced electrons (8 keV photons in argon correspond to Nprim E300 primary electrons) with ions in the conversion region. For drift fields Edrift \300 V=cm the recombination is negligible. The measured relative pulse height for the MCAT155 structure then reaches a plateau, which can also be found in both simulated electron transparency curves (see Fig. 7). At this point the important assumption is made that the simulation results, yielded by the MC method, provide the true electron transparencies. Therefore, the renormalised pulse height emeas-renorm ðZÞ is calculated by the following equation: emeas-renorm ðZÞ ¼ n  emeas-rel ðZÞ

ð6Þ

with n¼

esim-MC ðZ0 Þ emeas-rel ðZ0 Þ

ð7Þ

adapting the relative pulse height emeas-rel for Edrift;0 ¼ 300 V=cm; according to Z0 ¼ jEdrift;0 ðUMCAT =dÞ1 j ¼ 5:8  103 ; to the simulated MC electron transparency esim-MC ðZ0 Þ: In the case of the MCAT155 structure, the measurement matches the simulated value of 100% and

90

MCAT155

80 70 60 50 renormalised measured rel. pulse height simulation (RK method) simulation (MC method)

40 30 20 10 0 0.00

charge losses due to recombination at low drift fields 0.01

0.02

0.03

0.04

0.05

0.06

0.07

η

Fig. 9. Comparison between the (renormalised) measured pulse heights and the simulated electron transparency for the MCAT155 structure.

therefore the normalisation factor is n ¼ 1: Because of the good consistency in this case, the same procedure is carried out for all MCAT structures. The comparison of the MCAT155 electron transparency simulation to the experiment (see Fig. 9) shows a good agreement within the 100%transparency plateau. Up to ZE3  102 the simulated MC curve fits well to the measured transparency, whereas the RK curve always yields too high a transparency. Still higher drift fields indicate a moderate deviation since the measured decrease of the transparency is steeper than the drop of both simulated curves. For the MCAT215 (see Fig. 10) and the MCAT305 structure (see Fig. 11) the comparison between the measurement and the simulation behaves quite similarly. The measured relative pulse height for Edrift;0 ¼ 300 V=cm ðZ0 ¼ 5:8  103 Þ is renormalised to 84.7% for the MCAT215 and 18.9% for the MCAT305 structure, respectively. There is no 100%-transparency plateau formation, neither for the MCAT215 nor for the MCAT305 structure; the maximum electron transparency amounts to about 85% and 24%, respectively. The discrepancy in the electron transparencies due to the differing geometry of the upper and the lower side of the MicroCAT structure is in the

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

electron transparency/pulse height [%]

100

the MC method approximates the upper limit, set by the RK method.

renormalised measured rel. pulse height simulation (RK method) simulation (MC method)

90 80

MCAT215

70

4. Ion feedback simulations and measurements

60 50 40 30

charge losses due to recombination at low drift fields

20 10 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

η

Fig. 10. Comparison between the renormalised measured pulse heights and the simulated electron transparency for the MCAT215 structure.

100

electron transparency/pulse height [%]

167

90

MCAT305

80 70

renormalised measured rel. pulse height simulation (RK method) simulation (MC method)

60 50 40 30 20 10 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

η

Fig. 11. Comparison between the renormalised measured pulse heights and the simulated electron transparency for the MCAT305 structure.

order of some percent. The usual construction of the detector, in which the larger opening is directed towards the drift region (see Fig. 1), provides the larger transparency. The influence of the hole geometry, itself, on the charge transfer behaviour will be further examined in Section 5.1. In addition, a simulation series is carried out, increasing the gas pressure. Due to the smaller electron diffusion in the used gas mixture at higher pressure the electron transparency calculated by

An advantage of micropattern devices like the MicroCAT structure is due to the small amount of ions, which drift back from the gas gain region towards the drift cathode. In case of a large ion feedback local field perturbations in the conversion region can originate spatial reconstruction distortions. A quantitative estimation of this effect is carried out in Section 5. 4.1. General considerations A simplified model is proposed for the ion feedback simulation, regarding just one hole of the MicroCAT structure: since the electrons are all approximately focused pointlike after their transition through the MicroCAT holes the avalanche process starts for each event at the same spatial x=y-position (see RK-drift lines in Fig. 5). Assuming that the gas gain process takes place only shortly above the readout structure instead along the whole way, where the electric field is high enough for multiplication, the lateral extension of the charge cloud is mainly determined by the transverse diffusion st of the electrons in the gas gain region. The effect of electrostatic repulsion of the charged particles can be neglected for usual avalanche sizes up to 106 [12]. Summarising all these approximations, the projection of the charge spreading onto the readout anode is assumed to be normally distributed in two dimensions with a pffiffiffi standard deviation of st ¼ st0 d ; where st0 denotes the transverse diffusion for 1 cm drift in the high electric field of the gas gain region and d the cathode distance. With the consideration of this simple model, the starting points of the ions for the ion feedback simulation are chosen normally distributed around the symmetry axis of a hole directly above the anode. The diffusion of the ions, themselves, up to very high electric fields of some 10 kV=cm is well described by the Einstein approximation, which is in good accordance to the measurement [13]. This

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

168

ion diffusion can be neglected due to its smallness of sion E10 mm=cm0:5 for an electric field of 40– 60 kV=cm: Therefore, only the RK method is applied for the ion drift simulation with Garfield. Fig. 12 shows the influence of the width of the lateral avalanche extension st on the expected ion feedback, demonstrated for an MCAT155 structure with a gas pressure of 1 bar Ar=CO2 ð90=10Þ: A decrease of the charge avalanche extension st leads to an enormous rise of the ion feedback. As a consequence all gases with low diffusion result in larger ion feedbacks. To increase the diagrams’ clarity the fit functions in Fig. 12 and all following ion feedback plots are chosen to yfit ¼ AxP — where A and P are fitted parameters—, although they have no direct physical background. The ion feedback model, described above, represents one extreme case concerning the size of the avalanche, that certainly depends on the spatial distribution of the electrons after their transition through the holes of the gas gain structure, which was assumed to be Delta-like in space. The resulting width of the spatial charge distribution shortly above the anode can more generally be described as a convolution of this spatial electron distribution function and the (Gaussian) spreading function due to, i.e. the electron diffusion in the gas gain region. In the

35 considering bunching effect of holes 30

ion feedback [%]

25

σ t =20
m σ t =28
m σ t =36
m

MCAT155 geometry (hole diameter 116 µm)

20 15 10

case of a Delta-like starting distribution, the avalanche extension is identical with the spreading function. The other extreme case, where the electrons, coming from the conversion region, are not focused at all during their transition through the holes would lead to a spatial distribution at the anode, resulting in a convolution of the projection of the hole and the Gaussian spreading function. The output of the ion feedback simulation on basis of this second case (no bunching) is also shown in Fig. 12 for a transverse diffusion spreading of st ¼ 20 mm: It is reflected that the ion feedback gets very small compared to a Delta-like spatial distribution of the electrons assuming the same diffusion spreading. In fact, the real ion feedback is supposed to be in between the two extreme cases, because the electrons are not really bunched to one point but nevertheless a general focussing effect is existent (see MC-drift lines in Fig. 5). It is expected, that the quality of the ion feedback simulation gets better if the main part of the avalanche extension is due to the charge spreading, e.g. by diffusion processes. This especially holds true for tiny holes. Increasing the hole diameter entails a rising deviation of the simulation to the measured ion feedback. Another possible source of error can be ascribed to the not very well-known diffusion coefficient at these high electric fields and other physical effects that influence the charge cloud extension in the gas gain region (i.e. widening of the avalanche head by UV-photons). Like in Section 3, the dependence of the simulated ion feedback on the constant ratio Z ¼ jEdrift ðUMCAT =dÞ1 j ¼ 1=90 with varying cathode distance d and drift field Edrift and constant mesh voltage UMCAT ¼ 450 V is studied as an example for the MCAT215 structure for two different widths st of the lateral charge cloud extension (see Fig. 13). It turns out, that the simulated ion feedback is constant except for small deviations caused by limited statistics.

5

σ t =20
m (no bunching) 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

4.2. Examination of the three existing MCAT types 0.07

η

Fig. 12. Ion feedback simulation for the MCAT155 structure as a function of the ratio Z ¼ jEdrift =Egain j for different lateral extensions st of the charge cloud.

Measuring the currents at the drift cathode and the gas gain structure the ion feedback for all three existing MicroCAT types is determined with Eq. (5) using Ar=CO2 ð90=10Þ at a pressure of

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

7

1000

MCAT215 6

Edrift [V/cm]

ion feedback [%]

800 5 600

4 σ t =20µm 3

σ t =36µm

drift field

400

2 200 1 0 0

50

100

150

200

250

0 300

cathode distance [
m]

Fig. 13. Ion feedback simulation for the MCAT215 structure as a function of the cathode distance d for a constant ratio Z ¼ 1=90 for two different lateral extensions st of the charge cloud and a d-distribution of the electrons’ starting positions in the gas gain region. Additionally, the applied drift fields for the particular cathode distances are shown.

25

ion feedback [%]

20

simulation (σt =20µm) MCAT155 MCAT215 MCAT305

measurement MCAT155 MCAT215 MCAT305

15

10

5

0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

η

Fig. 14. Comparison of the ion feedback simulations to the measurements for all three MCAT structures.

1 bar; a cathode distance of 130 mm and gas gains in the range of 5000: For the illumination a slightly collimated 55 Fe source is used. The comparison of the measurement to the simulation with the Magboltz calculated transverse electron diffusion for Egain E30–40 kV=cm of st0 E100 mm=cm0:5 ðst ¼ 20 mmÞ is shown in Fig. 14. It turns out, that the simulated ion feedback for the MCAT155, which is proposed by the model using the Delta-like electron starting point distribution, is

169

too large especially for small drift fields. On the other hand, the disregard of the bunching effect of the holes in combination with the same electron diffusion in the gas gain region calculates an ion feedback which is too small mainly for high drift fields (compared to Fig. 12). Nevertheless, the deviations between measurement and simulation decrease for smaller hole diameters, as it becomes obvious for the MCAT215 and MCAT305 structures. In a good approximation, for hole diameters smaller than h0 E4st ¼ 80 mm (which nearly corresponds to the hole diameter of the MCAT215 structure), the ion feedback simulation becomes sufficient in spite of the coarse model and the poor knowledge of the charge cloud extension.

5. Optimised MicroCAT parameters The essential idea of the MicroCAT detector is the combination of the MicroCAT gas gain structure with a 2D interpolating readout structure [14–16]. The detector’s recent applications can be found in the scope of crystallography using hard X-ray synchrotron radiation [17] or in the field of time-resolved X-ray imaging [18]. Requirements for such a detector system are a spatial resolution in the range of typically 100–500 mm; large active areas of some 10  10 cm2 and a good time resolution at least in the ms-range. In the following, the demands on the gas gain structure are discussed. The effective gain, which is defined as the product of the gas gain G and the electron transparency e; should be at least in the order of 2000 to reach a spatial resolution of about 200 mm for 8 keV photons in argon [17]. Therefore, the transparency should be as large as possible (e.g. > 80%) over a wide range up to drift fields of Edrift ¼ 1000 V=cm; in particular if high-Z gases like xenon are used or high photon rates are needed, where a gas gain of larger than a few thousand is no longer possible [19]. In order to avoid field distortions in the conversion region, the amount of backdrifting ions from the gas gain region towards the drift cathode should be kept as small as possible, again at least for high-rate applications [20]. To estimate

170

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

the maximum acceptable ion feedback, the following ion tube model is applied describing space charge effects in the drift region: a continuous pointlike photon beam produces after a short period an equilibrium state where the positive charged ions move within an ion tube from the anode to the drift cathode (see Fig. 15). Since the distance between the anode and the gas gain structure is negligibly small compared to the drift length of usually several millimetres only the conversion region between the upper side of the MicroCAT structure and the drift cathode is further considered. Averaged over a larger period of time the total charge of Qion ¼ ðNprim tdrift þ Nprim deGtdriftmax ÞRe is drifting towards the drift cathode. Nprim denotes the number of primary electron/ion-pairs per photon produced in the conversion region, tdrift is the mean drift time of these ions (depending on the absorption coefficient of the gas, the photon energy and the maximum drift length), tdriftmax is

the ion drift time for the way from the MicroCAT structure to the drift cathode, R is the incoming photon rate and e the elementary charge. The second term becomes dominant for a large electron transparency, an ion feedback in the range of some percent and a gas gain larger than about 1000: Qion ENprim deGtdriftmax Re: The ion drift time tdriftmax can be calculated as the quotient of the total drift length l and the ion drift velocity vion ¼ mion Edrift =p lp tdriftmax ¼ mion Edrift where mion denotes the ion mobility, Edrift the applied drift field and p the gas pressure. Using Gauss’ law, the electric field E produced by the ion charge cloud can be calculated I Qion dA  E ¼ ð8Þ E0 ðV Þ where ðV Þ is the surface of the ion tube and E0 the vacuum permittivity. The length of the tube l is given by the distance between the upper side of the MCAT and the drift cathode; the radius r0 is in a first approximation determined by the transverse diffusion of the primary electrons in the conversion region. Already for drift lengths of some millimetres one obtains, that r0 5l: Therefore, the area of the ion tube’s front sides (pr20 Þ are small compared to the surface of the cylinder ðpr0 lÞ; hence the electric field has only a radial component Er : Solving the integral in Eq. (8) and dividing it by Edrift the ratio between the radial electric field component Er and the drift field Edrift is determined by Er Qion Nprim edeGRp ¼ ¼ for rXr0 : 2 r Edrift 2pE0 lEdrift r 2pE0 mion Edrift The expected spatial distortion rd due to this field perturbation can then be calculated as Er ðrÞ rd ðrÞ ¼ l ð9Þ Edrift

Fig. 15. Schematic of the ion tube model. The back drifting ions with charge Qion ; coming from the gas gain region through the holes of the MicroCAT structure, move with the velocity vion towards the drift cathode within a tube with radius r0 : To calculate the effect of this space charge, a weak spot is placed close to the hot spot with a distance of rS :

and increases with low ion mobilities, high pressure and gas gain, rate, photon energy and drift length, whereas it is getting small for huge drift fields and large distances r to the centre of the ion tube.

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

The electrons, produced in another photon spot, which is placed close to this hot spot at a distance rS ; are attracted by the ion tube generated by the strongly illuminated point (see Fig. 15). Supposing a moderate gas gain of G ¼ 2000; a high spot rate of R ¼ 106 Hz of 8 keV-photons in 1 bar Ar=CO2 ð90=10Þ; respectively Nprim ¼ 300 and mion ¼ 1:67  104 m2 bar=V=s; a drift field of Edrift ¼ 1000 V=cm and an electron transparency of e ¼ 0:8 leads to a field ratio Er ðrÞ=Edrift ¼ 8:3  104 m d=r: Assuming a two spot configuration with a distance of r ¼ rS ¼ 2 mm; a total drift length of l ¼ 10 mm and a maximum spatial distortion limit of rd ¼ 200 mm due to space charge effects the ion feedback should not exceed dmax ¼ 5% as can be calculated from Eq. (9). For higher gas pressures or heavy noble gases with slow ion mobilities like xenon the maximum ion feedback should be far below 5%. Another criterion for an optimised MicroCAT structure is the mechanical stability combined with the handling properties. For those reasons, the thickness of the MicroCAT should not be less than about 20 mm: Likewise, the optical transparency must not exceed a value of approximately 50% to grant a mechanically stable gas gain structure. Finally, all the requirements are again summarised, ordered by priority: (1) high electron transparency of e\80% up to ZE1–2  102 to provide a high effective gas gain. (2) ion feedback of dt5% which leads to a quotient e=d\15; to suppress distortions due to space charge effects. (3) mesh thickness of t\20 mm and an optical transparency of t50% to guarantee an easy handling and a mechanically stable mesh.

171

One should keep in mind that the simulated ion feedback is only reliable for hole diameters ht80 mm and is getting too large for big holes. 5.1. Hole geometry An essential parameter which influences the charge transfer behaviour of the MicroCAT structure is the hole geometry itself. For the quantitative study, seven types of hole geometries are examined, differing in hole shape and open area, but keeping the hole volume as well as the number of holes=in: ¼ 215 constant as a criterion for the mechanical stability of the MicroCAT (see Fig. 16). The first and easiest geometry is a cylindrical hole with a radius of r ¼ 79 mm (open area ¼ 40:6%). The second and third tested shapes are single conical with r1 ¼ 94:8 mm and r2 ¼ 62:1 mm ðopen area ¼ 25:1%) with the large hole diameter on top (2) and on bottom (3), respectively. Double conical hole shapes, also with r1 ¼ 94:8 mm and r2 ¼ 62:1 mm; form the fourth and fifth geometry (open area ¼ 25:1%). For the sixth simulation a square hole with l ¼ 70 mm (open area ¼ 40:5%) is assumed and finally the hole shape is chosen hexagonally (7) with an edge length of l ¼ 43:5 mm (open area ¼ 40:6%). The charge transfer simulations (see Fig. 17) reveal that the cylindrical hole (1) offers the largest electron transparency whereas all conical hole shapes are inferior. However, the cylindrical hole also suffers from a very high ion feedback. Both the square (6) and the hexagonal (7) geometry behave relatively similarly to the cylindrical one, because the total open area is almost identical. Small hole openings orientated towards the drift region (shapes 3 and 5) feature disadvantages with respect to electron transparency, whereas the reversed

Fig. 16. Presentation of twice the basic simulation cell of all seven simulated hole geometries. The hole shapes are cylindrical (1), conical with large opening on top (2), conical with small opening on top (3), double conical with small opening in the middle (4), double conical with small opening on top and on bottom (5), square (6) and hexagonal (7).

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

172 100

70 60

100

8 17 6

7

90 4

6 2 3 5

5

electron transparency [%]

electron transparency [%]

80

(1) cylindrical (2) conical (3) conical (4) double conical (5) double conical (6) square (7) hexagonal

ion feedback [%]

90

4 3 2

50

1

40

0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

η

30 20 10 0.00

80 70 60 50 40

η = 0.89⋅10

-2 -2

30

η = 1.78⋅10 η = 2.89⋅10

-2

20

η = 4.44⋅10

-2

10

η = 6.67⋅10

-2

0

0.01

0.02

0.03

0.04

0.05

0.06

0

0.07

5

10

15

20

η

Fig. 17. Simulated electron transparency and ion feedback as a function of Z ¼ jEdrift ðUMCAT =dÞ1 j for different hole geometries with a constant hole volume and a constant number of holes/in. of 215.

25

30

35

40

45

50

55

60

mesh thickness [
m]

Fig. 18. Simulated electron transparency e as a function of the mesh thickness for an MCAT215 structure with a cylindrical hole shape for different ratios of Z:

60

5.2. Mesh thickness The thickness of the gas gain structure represents another crucial parameter which is of basic interest with respect to the optimisation of the charge transfer behaviour. Thin foils feature a sharp transition from the low drift field to the high gas gain field (see Fig. 4). Therefore, both the electrons and the ions are heavily pushed into the gas gain region and the drift region, respectively. For thicker meshes this effect is less pronounced. To study this effect quantitatively a simulation series is carried out for the MCAT215 structure with a cylindrical hole shape, varying the mesh thickness from 55 mm down to 5 mm in 10 mmsteps. The electron transparency e; plotted for several ratios of Z in Fig. 18, rises nearly linearly with decreasing mesh thickness and finally converges to 100%. Roughly speaking, for large Z the electron transparency doubles when the mesh thickness is halved. On the other hand, the ion feedback d (see Fig. 19) rises in a non-linear manner while

-2

16

-2

14

-2

12

55

η = 0.89⋅10

50

η = 1.78⋅10 η = 2.89⋅10

45

-2

η = 4.44⋅10

-2

η = 6.67⋅10

40

ε/δ

ion feedback [%]

conical geometries (2 and 4) offer larger electron transparencies. The double conical hole shape (4) represents a good compromise between a high electron transparency and a small ion feedback.

10 8

35

6

30

4

25

2 5

10 15 20 25 30 35 40 45 50 55

20

mesh thickness [µm]

15 10 5 0 0

5

10

15

20

25

30

35

40

45

50

55

60

mesh thickness [
m]

Fig. 19. Simulated ion feedback d and ratio e=d as a function of the mesh thickness for an MCAT215 structure with a cylindrical hole shape for different ratios of Z:

decreasing the mesh thickness. As a consequence the ratio e=d is getting slightly unfavourable for thinner meshes and small values of Z (see also Fig. 19), because the electron transparency cannot exceed 100%, whereas the ion feedback is still growing. Associated with a large quotient Z; the ratio e=d approaches a nearly constant plateau. Obviously, larger values of Z lead to a smaller ratio e=d:

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

5.3. Influence of the hole diameter, the number of holes/in. and the optical transparency Eq. (1) represents the relationship between the hole diameter, the number of holes/in. and the optical transparency. In order to realise a systematic simulation series in the following three subsections, one of these parameters is fixed while the others are varied. These simulations are carried out with a constant mesh thickness of 55 mm and a cylindrical hole shape (the deviation to holes with smoothed edges was already shown in Section 3.2). The charge transfer behaviour is investigated in the range of 4:4  103 oZo3:6  102 : In the following it is only mentioned, in which way the parameters are varied, and just the most conspicuous results are discussed, before an optimised MicroCAT structure is designed in Section 5.4. 5.3.1. Constant optical transparency At first, the optical transparency is fixed to 40.6%. The hole diameter is varied from 34 mm up to 109 mm in 15 mm-steps and hence the number of holes/in. is changed from 500 to 156. Both the electron transparency as well as the ion feedback increase for larger hole diameters. 5.3.2. Constant number of holes/in. In the next part of this simulation series the number of holes/in. is fixed to 215, thereby the hole diameter is increased from 34 mm up to 109 mm and the optical transparency from 7.5% up to 77.2%, respectively. Once again it turns out, that larger holes increase the charge transfer. 5.3.3. Constant hole diameter At last, the hole diameter is kept constant to h ¼ 79 mm: The simulations are carried out for 125 up to 305 holes/in., corresponding to an optical transparency of 13.7% up to 81.6%. The electron transparency rises nearly linearly with the number of holes/in. and with the optical transparency, respectively. Conspicuous, however, is, that the fraction of back drifting ions is only weakly affected by the increase of the number of holes/in. This can be explained by the model used for the ion feedback determination. There it was

173

assumed, that the ions of one avalanche start normally distributed around the symmetry axis of a hole. Then, the ion feedback per avalanche only depends on the hole shape, the hole diameter or the mesh thickness, but not on the number of holes/in.

5.4. Choice of the optimum mesh parameters Since the determination of the optimum mesh parameters represents a complicated interplay of the varied parameters, one has to consider carefully the particular requirements. As a first step the hole geometry is examined. In principle, the cylindrical hole shape is well suited, offering the largest electron transparency but unfortunately the largest ion feedback, too. In case of the conical (2) or double conical (4) hole shape the ratio e=d is more favourable. In combination with smooth edges one can additionally gain a factor of up to 1.5 in the electron transparency—depending on Z—in comparison to a cylindrical hole shape. In fact, the actual hole geometry of the existing slightly double conical MicroCAT structures (see Fig. 1) is very close to this proposed hole shape, also because the surface is smooth and no sharp edges can be found, which is important for an stable electrical operation. Therefore, this shape should be further used, if possible. Concerning the mesh thickness, it is recommendable to reduce the thickness from 55 to 25 mm; gaining (losing) a factor of about 2 in electron transparency (ion feedback) for larger values of Z; thus keeping the ratio e=d nearly constant (see Fig. 19). As all simulations concerning the optimisation with respect to the parameters hole diameter, optical transparency and number of holes/in. are carried out for a mesh thickness of 55 mm: The influence of the new aspired mesh thickness of 25 mm has to be considered for the further optimum mesh design: a reduction of the mesh thickness in such a way increases the electron transparency from about ð40710Þ% to ð80710Þ%, which is the desired value for a ratio ZE2  102 (compared to Fig. 18). Therefore, the objective for the next reflections is to reach an

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

electron transparency of 30–50% and a ratio e=d\15: The parameter set composed of hole diameter, optical transparency and number of holes/in. is of enormous importance. The electron transparencies as a function of the hole diameter (see Fig. 20), of the number of holes/in. (see Fig. 21) and of the optical transparency (see Fig. 22) are plotted for different values of Z; each keeping one parameter fixed (compare to Section 5.3). Furthermore, Figs. 23–25 show the ratio e=d between the electron transparencies e and the ion feedbacks d: In the following, the optimised parameters with respect to the hole diameter, the number of holes/ in. and the optical transparency are derived for a value of Z ¼ 1:33  102 : At first it has to be investigated, where the ratio e=d becomes larger than 10 and how it changes when the above-mentioned parameters are varied. It turns out that one curve is of special interest: the constant optical transparency of 40.6% as a function of the hole diameter (see Figs. 23 or 24). The ratio e=d gets larger than 10 for hole diameters smaller than 80 mm down to 35 mm: However, the electron transparency for hole diameters t65 mm falls below the given limit of about 30% (see Fig. 20). As a consequence, the hole diameter should not be chosen smaller than 65 mm; and it

should not exceed 80 mm: To achieve an optical transparency of 40.6%, which was assumed for this simulation, the number of holes/in. has to be adapted to about 230–260, depending on the chosen hole diameter. Figs. 21 and 24, for example, clarify that the electron transparency and the ratio e=d; respectively, can still be increased by enlarging the

100

70 60

-2

η = 1.33⋅10

-2

η = 3.56⋅10

-2

50 40 30 20

60 50

150

-2

200

250

300

350

400

450

500

number of holes/inch

Fig. 21. Simulated electron transparency as a function of the number of holes/in. for a constant hole diameter of 79 mm and for a constant optical transparency of 40.6%, respectively, for three different ratios of Z:

100 90 80

η = 0.44⋅10

-2

η = 1.33⋅10

-2

η = 3.56⋅10

-2

70 60 50 40 30 20 10 0

Fig. 20. Simulated electron transparency as a function of the hole diameter for a constant number of holes/in. of 215 and for a constant optical transparency of 40.6%, respectively, for three different ratios of Z:

-2

η = 3.56⋅10

30

0

hole diameter [
m]

-2

η = 1.33⋅10

40

10

30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

η = 0.44⋅10

0

number of holes/inch=215=const. optical transparency=40.6%=const. η = 0.44⋅10

70

10

electron transparency [%]

electron transparency [%]

80

80

20

100 90

optical transparency =40.6%=const. hole diameter =79
m=const.

90

electron transparency [%]

174

hole diameter=79
m=const. number of holes/inch=215=const. 0

10

20

30

40

50

60

70

80

90

optical transparency [%]

Fig. 22. Simulated electron transparency as a function of the optical transparency for a constant hole diameter of 79 mm and for a constant number of holes/in. of 215, respectively, for three different ratios of Z:

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177 65

65 60 55

number of holes/inch=215=const. optical transparency=40.6%=const.

-2

60

-2

55

-2

50

η = 0.44⋅10 η = 1.33⋅10 η = 3.56⋅10

50

limit of reliability of ion feedback simulation

35 30

-2

η = 1.33⋅10

-2

η = 3.56⋅10

35

limit of reliability of ion feedback simulation

30

25

25

20

20

15

15

10

10

5

5 0

0

0

30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

Fig. 23. Simulated ratio e=d as a function of the hole diameter for a constant number of holes/in. of 215 and for a constant optical transparency of 40.6%, respectively, for three different ratios of Z: The accuracy of the ion feedback simulation becomes worse for larger holes as already shown in Section 4.2. Since the reliability of the ratio e=d is also affected the curves for h > 79 mm are represented by grey lines.

optical transparency=40.6%=const. hole diameter=79µm=const. -2

η = 0.44⋅10

45

η = 1.33⋅10

40

η = 3.56⋅10

-2 -2

35 limit of reliability of ion feedback simulation

30 25

20

30

40

50

60

70

80

90

Fig. 25. Simulated ratio e=d as a function of the optical transparency for a constant hole diameter of 79 mm and for a constant number of holes/in. of 215, respectively, for three different ratios of Z: Again, the grey lines indicate the limit of the reliability of the ion feedback simulation.

tion of the curves for a constant hole diameter of 79 mm: For 260–280 holes/in. the optical transparency reaches the demanded limit of about 50% (compared to Section 5) for a hole diameter of 70 mm: The combination of this new set of parameters leads to an estimated electron transparency of e\45% (for a mesh thickness of 55 mm) with a ratio e=d\18: For an MCAT structure with a thickness of only 25 mm the electron transparency will thus expected to be \90%. Summarising all optimised parameters one obtains for the new mesh:

65

50

10

optical transparency [%]

hole diameter [
m]

ε/δ

-2

η = 0.44⋅10

40

ε/δ

ε/δ

40

55

hole diameter=79
m=const. number of holes/inch=215=const.

45

45

60

175

20 15 10 5 0 150

200

250

300

350

400

450

500

*

number of holes/inch

Fig. 24. Simulated ratio e=d as a function of the number of holes/in. for a constant hole diameter of 79 mm and for a constant optical transparency of 40.6%, respectively, for three different ratios of Z: Again, the grey lines indicate the limit of the reliability of the ion feedback simulation.

number of holes/in. and the optical transparency, respectively, for a constant hole diameter. The curves for a fixed hole diameter of about 70 mm have not been simulated but most likely the shape of the curves behaves very similar to the simula-

* * *

cylindrical holes or even better the (smooth, slightly double conical) geometry of the existing MCAT types, mesh thickness: ð2575Þ mm; hole diameter: ð7075Þ mm; number of holes/in.: 270710:

In order to confirm these considerations concerning the optimised mesh parameters another simulation is carried out realising a MicroCAT structure with the above-mentioned parameters. The results of the electron transparency and the ion feedback simulation as well as the ratio e=d are shown for cylindrical sharp edged holes in Fig. 26.

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177

176 100

35

90

electron transparency ion feedback

70

30 25

60 20

50

ε/δ

40

optimised MCAT sharp edges

30

ε/δ

charge transfer [%]

80

15 10

20 5

10 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0 0.07

η

Fig. 26. Simulated electron transparency e; ion feedback d and ratio e=d for the optimised MicroCAT structure with sharpedged cylindrical holes.

The predictions are very well confirmed by this additional simulation: indeed, the electron transparency amounts to about 90% and the ion feedback is close to 5%, which corresponds to a ratio e=d\17 for Z ¼ 1:33  102 : The ratio e=d is a little bit smaller than expected because the assumption, that the size e=d does not depend on the thickness is not exactly fulfilled for Zt2  102 (see Section 5.2 and Fig. 19). The combination of the smooth and slightly double conical geometry of the existing MCAT types with the optimised mesh parameters results in a nearly full electron transparency up to Zt2  102 ; whereas still a ratio e=d > 10 can be realised. These results are even better than those for the cylindrical hole shape.

6. Conclusion The electron transparency behaviour of all three existing MicroCAT structures has been simulated. In the 3D-field simulations, which have been used as a basis for a subsequent drift simulation, the MicroCATs’ geometry has thoroughly been taken into account. Except some inaccuracies which are most likely due to geometry variations between the simulated and the real meshes every simulated electron transparency behaviour is close to the experimental results. Obviously, a simple ion

feedback model is well suited to describe the charge transfer of the ions for hole diameters of ht80 mm: For larger holes it serves as an estimation of the upper limit of what can be expected experimentally. The influence of the hole shape, the mesh thickness and the parameters hole diameter, number of holes/in. and optical transparency was systematically investigated. The optimisation of these parameters led to a new MicroCAT design, whose charge transfer behaviour is theoretically predicted and has to be confirmed experimentally, provided the optimised MicroCAT structure can be produced with respect to the properties demanded.

Acknowledgements The authors are especially indebted to Rob Veenhof (CERN) for both his support and many helpful hints concerning the Garfield simulation software. We want to thank A. Sarvestani for the data on the relative pulse height measurements.

References [1] F. Sauli, Nucl. Instr. and Meth. A 386 (1997) 531. [2] Y. Giomataris, Ph. Rebourgeard, J.P. Robert, G. Charpak, Nucl. Instr. and Meth. A 376 (1996) 29. [3] F. Bartol, M. Bordessoule, G. Chaplier, M. Lemonnier, S. Megtert, J. Phys. III (France) 6 (1996) 337. [4] A. Sarvestani, H.J. Besch, M. Junk, W. Meissner, N. Sauer, R. Stiehler, A.H. Walenta, R.H. Menk, Nucl. Instr. and Meth. A 410 (1998) 238. [5] A. Sharma, Nucl. Instr. and Meth. A 454 (2000) 267. [6] O. Bouianov, M. Bouianov, R. Orava, P. Semenov, V. Tikhonov, Nucl. Instr. and Meth. A 450 (2000) 277. [7] P. Cwetanski, Progress in Simulations of Micropattern Gas Avalanche Detectors, 2000 IEEE Nuclear Science Symposium Conference Record, Lyon, 2001, pp. 5–39. [8] Maxwell 3D Field Simulator Version 5.0.04, Ansoft Corporation, Pittsburgh, PA, USA. [9] Garfield, CERN Wire Chamber Field and Transport Computation Program written by R. Veenhof, Version 7.05, 2001. [10] S.F. Biagi, Nucl. Instr. and Meth. A 421 (1999) 234. [11] Magboltz, CERN transport of electrons in gas mixtures computation program written by S.F. Biagi, Version 2.

A. Orthen et al. / Nuclear Instruments and Methods in Physics Research A 492 (2002) 160–177 [12] H. Hess, Der elektrische Durchschlag in Gasen, Berlin, 1976. [13] R.N. Varney, et al., J. Phys. B 14 (1981) 1695. [14] H.J. Besch, M. Junk, W. Meissner, A. Sarvestani, R. Stiehler, A.H. Walenta, Nucl. Instr. and Meth. A 392 (1997) 244. [15] A. Sarvestani, H.J. Besch, M. Junk, W. Meissner, N. Pavel, N. Sauer, R. Stiehler, A.H. Walenta, R.H. Menk, Nucl. Instr. and Meth. A 419 (1998) 444. [16] H. Wagner, H.J. Besch, R.H. Menk, A. Orthen, A. Sarvestani, A.H. Walenta, H. Walliser, Nucl. Instr. and Meth. A 482 (2002) 341.

177

[17] A. Sarvestani, H. Amenitsch, S. Bernstorff, H.J. Besch, R.H. Menk, A. Orthen, N. Pavel, M. Rappolt, N. Sauer, A.H. Walenta, J. Synchrotron Rad. 6 (1999) 985. [18] A. Sarvestani, N. Sauer, C. Strietzel, H.J. Besch, A. Orthen, N. Pavel, A.H. Walenta, R.H. Menk, Nucl. Instr. and Meth. A 465 (2001) 354. [19] A. Sarvestani, H.J. Besch, R.H. Menk, N. Pavel, N. Sauer, C. Strietzel, A.H. Walenta, Nucl. Phys. B (Proc. Suppl.) 78 (1999) 431. [20] D. Friedrich, G. Melchart, B. Sadoulet, F. Sauli, Nucl. Instr. and Meth. 158 (1979) 81.