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ELECTROSTATIC SIMULATION

Extensive electrostatic simulations have been performed before the construction of a MGWC prototype in order to optimize its parameters. Two electrostatic programs have been used in a complementary way. ELECTRO and COULOMB were used for a 2-D and 3-D simulation respectively, allowing for the dielectric material simulation, which could not be achieved with the GARFIELD program [7]. The latter was used for gas studies (diffusion, drift velocity, ion mobility etc ... ) and signal simulation.

Fig. 3 shows the equipotential lines around a grounded anode wire, the cathode plane being at a voltage of -575 V. The electric field at the wire surface is higher than 400 kV/cm. Fig. 4 presents the variation of the electric field on the surface around an anode wire, while fig. 5 presents the dielectric polarization. The polarization reduces the electric field near the anode wires at the cathode plane side, thus reducing the electric field variation between this side and the opposite side (drift volume side) where the majority of the avalanches are produced. In this way, the dielectric polarization does not reduce the gain as it does in MSGC's and MGC's, where the polarization is produced at the place where the avalanches are developing.

Figure 3 : Equipotential lines around an anode wire (10  µm diameter).

Figure 4: Electric field on the surface of an anode wire.

Figure 5: Dielectric polarization.

Using the gas mixture 75% CH₄ + 25% C₂ H₆ , already used for the Barrel RICH MWPC's of DELPHI [3] to detect single photoelectrons, and having the drift electrode at 3 mm of the cathode plane, the whole electron collection created in the drift volume lasts about 40 ns (for a cathode-drift electrode voltage difference of 600 V). Fig. 6 displays the electron trajectories for electrons created near the drift electrode (maximum drift path) along one chamber cell whilst fig. 7 shows the drift velocity variation as a function of the electron distance to the anode wire (these two figures were produced with GARFIELD, without dielectric strips).

The positive ion velocity and trajectories are two very important parameters determining the signal rise-time and duration. Fig. 8 shows the ion trajectories for ions created at the surface of the anode wire. More than 95% of the ions are collected by the cathode in a time less than 1.5  µ s for the gas mixture mentioned before.

Figure 6 : Trajectories of electrons created near the drift electrode. The distance between two dotted lines corresponds to a drift time of 10 ns ( 75% CH₄ + 25% C₂ H₆ ).

Figure 7 : Drift velocity as a function of the electron position with respect to the anode wire (for electrons of figure 6).

Figure 8 : Positive ions trajectories. The distance between two dotted lines corresponds to a drift time of 500 ns ( 75% CH₄ + 25% C₂ H₆ ).

  ...COULOMB      Integrated Engineering Software, 46-1313 Border Place, Winnipeg, Manitoba, Canada R3H OX4.

Marcos Dracos Sat Apr 4 18:31:19 METDST 1998

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