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Recent years, we have seen the development of many fields of gas detectors. The MICROMEGAS (Micro-Mesh Gas Structure) appeared as the very promising detector. It is a major family of position detectors in High Energy Physics. This work is done in normal (NTP) based gas mixtures: neon are noble gas and isobutane and DME (dimethyl-ether) as moderators gas (quenchers), using 55Fe as a radiation source (X-ray 5.9 keV). To address the modeling of MICROMEGAS detector, a descriptive model of different physical and geometrical phenomena MICROMEGAS was established by developing a simulation program to spreading the detector response. After, an analytical calculation of the potential and the electric field distributions has been presented briefly, to better estimate electrical and geometric configuration. Finally, simulation results of electrical signals based on gas mixtures (Neon-isobutane, Neon-DME) produced by MICROMEGAS were presented and analyzed in order to improve the MICROMEGAS performance (spatial (12 μm) and temporal (0.7 ns) resolutions).

MICROMEGAS [^{8} mm^{2}∙s^{−1}, position-sensitive with spatial resolution better than 100 microns and good performance of radiation hardness [

The detector gain depends directly on the distance between the micromesh and anode; therefore, controlling the geometry of the amplification region is crucial in order to achieve good energy resolution and excellent timing properties [

Detailed descriptions of MICROMEGAS are given in [^{2} and of micro-mesh pitch (p_{g}) with a conversion gap of 3 mm, an amplification gap of 100 mm with a strip pitch of 317 mm, have been designed and fabricated. The parallelism between the micromesh grid and the anode is maintaining by spacers of 150 mm in diameter and placing every 2 mm. They are printedon a thin epoxy substrate by conventional lithography of a photo-resistive polyamide film. The thickness of the film defines the amplification gap. This cheap and simple process allows the construction of large detectors with excellent uniformity and energy resolution over the whole surface.

The geometry of MICROMEGAS detector is then, reproduced by form of cuboids

where p_{g} is the Micro-Mesh pitch p_{strip} is the strip pitch.

The knowledge of the shape of the electric field lines close to the micromesh is a key issue for an optimal operation of the detector and especially for an efficient transfer of electrons to the amplification gap. The electric field is homogeneous in both the conversion and the amplification gap. It exhibits a funnel like shape around the openings of the micro-grid: field lines are highly compressed towards the middle of the openings, into a small pathway equal to a few microns in diameter. The compression factor is directly proportional to the ratio of the electric fields between the two gaps.

The electrons liberated in the conversion gap by the ionizing radiation follow these lines and are focused into the multiplication gap where amplification process takes place. The ratio between the Electric Field in the amplification gap and that in the conversion gap must be set at large values (>5) to permit a full electron transmission, and to reduce a part of ion cloud, produced in the avalanche, to escape into the conversion gap.

The mathematic term of potential is often calculated analytically using conformal transformations or Schwartz- Chritoffel transformation [

After all calculus, considering all processes, we established the following form of Potential:

where _{D} is the Dirichlet Function (Green Function) the weighting potential is presented in

The weighing field is deduced from Equation (2)

Equations (2) and (3) have been implemented in a MATLAB program; we treat different cases related to the geometric shapes of a track to determine the optimal width and pitch of the tracks. The results of the 3D potential and field distributions are shown in

Note that the estimate of the potential distribution is insufficient to determine the optimal width of the tracks to get a good configuration MICROMEGAS detector. But it seems that the configurations (w1 = 280 microns, w2 = 317 microns and D) are satisfactory because the distributions are well presented. By against the corresponding distributions of the widths w = 100 µm tracks, have signal distortion (deformation) which causes instabilities and system disturbances.

The distributions of different configurations of weighting field are shown in the figure above. Note that the distributions of peaks increase with the growth of D. Moreover, the peaks of the first column of the field distribution (w = 100 microns) are very close, which produces overlaps (spark between the wire of the tracks). The remaining columns have peaks with a larger spacing. It is concluded that sufficient choice of track width minimizes system instability, as an example of the third column (w = 317 microns), which has only one peak band which further improves the stability; have good performance (better resolution) to MICROMEGAS.

The analytical study of our system leads us to extract some equations that lead us to model our detector described above. The simulation model of the physical processes occurring within MICROMEGAS is based on the MATLAB Program that is the tool of simulation, and more effective for our work. In the general case, there are three types of parameters affecting the detector: the parameters related to the chamber (geometry), the gas parameters (diffusion, gain, mixing coefficients), the parameters of the trace (angle, energy, signal, type of particles).

From Equation (4) [_{i}(t) (I = 1 to 5) in MICROMEGAS for different proportions of each gas mixture; using X-rays (5.9 keV) as a radiation source, the same program remains what we need to change the values of the coefficients A_{i} and B_{i} [

Input Parameters | Output Parameters | Gas Mixture | Radiation-Source | |
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Amplification Field E_{Amp} (kV/cm) | Drift Velocity (v_{d}) | |||

Magnetic Field B (T) | Longitudinal Diffusion (D_{L}) | ^{ } | ||

Gas Mixture | Transverse Diffusion (D_{T}) | Neon-Isobutane | ^{ } | |

Mixing Coefficients (A_{i}, B_{i}, I = 1 to 5) | Charge (Q(t)) | (Ne-iC_{4}H_{10}) | ^{55}Fe X-Rays (5.9 keV)^{ } | |

Temperature T_{N} (Normal Condition) | Electron Fraction Charge (f_{e}) | Neon-Dimethyl-Ether | ^{ } | |

Pressure p_{atm} (Atmospheric) | Ion Fraction Charge (f_{ion}) | (Ne-DME) | ^{ } | |

Drift Field E_{d} (V/cm) | Resolution | ^{ } | ||

Gas Mixture | Proportion (%) | A (cm^{−1}) | B (kV cm^{−1}) | |||
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Ne-Isobutane | 6 | 3400 | 48.90 | |||

11 | 3700 | 56.80 | ||||

20 | 4400 | 74.00 | ||||

30 | 5600 | 97.80 | ||||

37 | 6900 | 118.80 | ||||

Ne-DME | 6 | 3200 | 46.00 | |||

11 | 3300 | 50.70 | ||||

30 | 3800 | 65.30 | ||||

50 | 5800 | 99.80 | ||||

where T_{w} is the first Townsend Coefficient calculated in [_{0} is the electron number in Micro-Mesh.

The results are shown in

First, we note that the temporal evolution of the total charge for both gas mixtures keeps the same evolution qualitatively. On the other hand, the charge decreases with the increase in the proportion of the quencher, and increases with the increase the electric field, in addition, the variation for Ne-isobutane is greater than that of Ne-DME. It is interesting to note that the total charge is simply the gain multiplied by the primary charge, and that in fact the amplified electrons do not contribute much to the final detected charge. The main contribution is clearly due to ions [_{e} of the signal due to electrons is given by:

Similarly, we can calculate the proportion of charge induced by ions:

Q_{e} is the charge induced by electron.

From this figure, it is found that the fraction of charge induced by the electron for each gas mixing follows an exponential law; it decreases with increasing the amplification field and the proportion of the quencher. It tends to a minimum value (saturation) until the field is very intense. However, the proportion of charge induced by ions increases with increasing the field and the quencher, it tends to a limit value in higher field. The boundary value was:

Mixture | Quencher (%) | E_{a}_{1} =50 kV/cm | E_{a}_{2} =80 kV/cm | ||||
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T_{Wi} d | f_{e} (%) | f_{ion} (%) | T_{wj} d | f_{e} (%) | f_{ion} (%) | ||

Ne-isobutane | 6 | 12.86 | 7.78 | 92.22 | 18.45 | 5.42 | 94.58 |

11 | 11.88 | 8.42 | 91.58 | 18.19 | 5.50 | 94.50 | |

20 | 10.02 | 9.98 | 90.02 | 17.45 | 5.73 | 94.27 | |

30 | 7.92 | 12.62 | 87.38 | 16.49 | 6.06 | 93.94 | |

37 | 6.41 | 15.57 | 84.43 | 15.63 | 6.40 | 93.60 | |

Ne-DME | 6 | 12.75 | 7.84 | 92.16 | 18.01 | 5.55 | 94.45 |

11 | 11.97 | 8.35 | 91.65 | 17.51 | 5.71 | 94.29 | |

30 | 10.29 | 9.71 | 90.29 | 16.80 | 5.95 | 94.05 | |

50 | 7.88 | 12.68 | 87.32 | 16.66 | 6.00 | 94.00 |

The detector operating is the result of a detailed analysis of the physical phenomena. The calculus of the magnitudes characterizing this system (amplification, signal), depending on the thickness of the space, the gas mixture, geometrical configuration and the electrical distribution allowed amplification to determine the thickness of the space of the optimum gain, minimizing the effect of slight geometrical variations of the micro-grid. An amplification gap of 100 microns is optimal if it is desired to minimize the influence of the defects of planarity of the grid relative to the tracks. Simulations of μ-mega focused on the study of gas mixtures. To conduct this study, we used a ^{55}Fe source emitting photons of 5.9 keV. For a gap width of 100 microns and a micro-grid prototype 500 LPI 5 × 5 cm^{2}, based on Ne-isobutane and Ne-DME gas mixtures. In this study, we clarified the signal (Collected charge in MICROMEGAS). In MICROMEGAS, the avalanche starts much closer to the cathode due to the uniform electric field in the amplification gap. This property allows MICROMEGAS to obtain faster and more intense signals improving its performance (Spatial and temporal resolutions).

In conclusion, the good agreement between experimental measurements and simulation suggests that our simulation model is all the more satisfying. However, if there are disagreements. We are tempted to interpret these observed differences, as it is in any case of systematic uncertainties in the simulation, and physical phenomena occurring within the detector were not taken into account in our simulation program: as an example, the propagation of photons in the avalanche contributing to the extension of the lateral size of the avalanche, and the Pening effect, the discharge phenomenon, ..., these phenomena are taken into account as a perspective in the future work.

In brief, through the various comparisons between real data and simulated data, we achieved a better understanding of MICROMEGAS chambers by improving its performance.