Drift Time Pedestal (t$_0$)

When charged particles ionize the drift chamber gas, the resulting drift electrons travel to the anode wire (sense wire). The drift distance ($\ell$) the electron in the ionized gas must travel within the drift chamber to reach the sense wire is given by (26),

$$\ell = dv(t - t_0)$$ (5.1)

where $dv$ is velocity of the drift electron, $t$ is the time as measured in the TDC's, and $t_0$ is the time corresponding to $\ell=0$, i.e. the time in the absence of any drift, referred to as the time pedestal. The time pedestal for each wire was defined as the time corresponding to the half maxima at the leading edge of the TDC drift time spectra (Figure 5.1).

Figure 5.1: The drift time spectra for a sense wire in Super layer 1. As seen above, time pedestal $t_0$ is 50.63 FBTDC channels = 101.26 ns.

The mean fit residual for particles passing on the right side of the sense wire ($x_R$) and for particles passing on the left ($x_L$) is calculated using the set of time pedestal values ($t_0$). A correction for the time pedestal $t_0$ is obtained from,

$$\delta t = (x_R - x_L)/2dv \quad$$ (5.2)

Applying these corrections to the 1632 time pedestals, a new set of 1632 pedestals are obtained, and the process is repeated until the correction $\delta$t is found to be negligibly small. After ten iterations, $\delta$t was found to be vanishingly small, indicating convergence of the iteration procedure. A similar procedure was applied to the position of the sense wires, the wire position corrections however, were found to be negligible.