The construction of shower maximising sensitive MCP detector

Abstract

The set-up described here involves a large-area microchannel plate (MCP) detector, equipped with a 90-degree bender used to reflect the lightweight charged particles. To measure the energy of ions, ions have to be passed through the detector. The assembled MCP detector provides the signature of the detection of high-energy particles by producing a shower of secondary electrons. The MCP detector is designed and developed using a reflecting mirror, supporting screws, conversion foil, a teflon base and a collimator. The passage of ions through the collimator and then from the conversion foil generates secondary electrons which are bent down by the reflector before the detection. Also, the working of the MCP detector developed at BARC is tested with strontium-90 (primary electron source) and Th$^{\mathrm {232}}$ (alpha emitter). Lower cost and low value of fall time constant (less than 2 ns) are the attractive features of the MCP. Additionally, the MCP has been used in the detection of a low-energy electron where a timing resolution of a few hundreds of picosecond to nanoseconds is desired.

Appendix

The potential P(x,y) inside the mesh of the electrostatic mirror is given by

$$\begin{aligned} P\left( x,y \right)= & {} \frac{4\pi q\mathrm {'}(d_{1}+y)}{C}+4q\mathrm {'}\sum \limits _{i=0}^\infty {\frac{1}{i}\left[ \mathrm {cos}\left( \frac{2i\pi x}{c} \right) \right] } \\&\times \left[ \mathrm {sinh}\left( \frac{2i\pi \left( d_{1}+y \right) }{C} \right) \right] . \end{aligned}$$

Proof

The electrons drift inside the drift chamber due to the electrostatic field. Figure 22 shows a drift chamber in which a single wire from the grid is held at the central position (0,0).

Fig. 22

Drift chamber to find potential field due to single wire with grounded conductors.

The boundaries along the y-direction of this drift chamber are dielectric whereas boundaries along the x-direction of this drift chamber are grounded electrodes; parallel to the dielectric surfaces are the field lines. Here $q\mathrm {'}$ is the charge of the wire per unit length and $d=d_{\mathrm {1}}+d_{\mathrm {2}}$. From another set of simulation studies with computer simulation technology software (CST), it is found that electric field lines are parallel to surfaces $x= \pm c$ $/$2 [12]. On the right side of the wire is the region ${y}> 0$ and on the left side of the wire is the region $y < 0$. The boundary conditions are stated as

$$\begin{aligned}&P\!\left( x,d_{1} \right) =P\left( x,d_{2} \right) =0\,\nonumber \\&\text {and }\nonumber \\&\frac{\partial (-c/2,y)}{\partial x}=\frac{\partial (c/2,y)}{\partial x}=0. \end{aligned}$$

(25)

According to Gauss’s law,

$$\begin{aligned} - \frac{\partial p\left( x,0^{+} \right) }{\partial y}+\frac{\partial p\left( x,0^{-} \right) }{\partial y}=4\pi q^{\prime }\delta \left( x \right) . \end{aligned}$$

(26)

Then, the potential satisfying the boundary conditions can be expressed in terms of the Fourier series as given below:

$$\begin{aligned} P\!\left( x,y>0 \right)= & {} A_{0}d_{1}\left( d_{2}-y \right) \nonumber \\&+ \sum \limits _{i=1}^\infty {A_{n}\cos \frac{2i\pi x}{c}} \nonumber \\&\times \sinh \frac{2i\pi (d_{2}-y)}{c} \sinh {\frac{2i\pi d_{1}}{c}} \end{aligned}$$

(27)

$$\begin{aligned} P\!\left( x,y<0 \right)= & {} A_{0}d_{2}\left( d_{1}+y \right) \nonumber \\&+ \sum \limits _{i=1}^\infty {A_{n}\cos \frac{2i\pi x}{c}}\nonumber \\&\times \sinh \frac{2i\pi (d_{1}+y)}{c} \sinh \frac{2i\pi d_{2}}{c}. \end{aligned}$$

(28)

Using condition (26), the coefficient $A_{0}$ and $A_{{n}}$ can be obtained as

$$\begin{aligned}&A_{0}=\frac{4\pi q'}{cd}\quad \text { and } \quad A_{n}=\frac{2q'}{i\mathrm {sinh}\left( \frac{2i\pi d}{c} \right) }\nonumber \\&P\!\left( x,y>0 \right) =\frac{4\pi q'd_{1}\left( d_{2}-y \right) }{cd}\nonumber \\&\qquad \qquad \qquad \qquad +\, 4q'\sum \limits _{i=1}^\infty {\cos \frac{2i\pi x}{c}} \nonumber \\&\qquad \qquad \qquad \qquad \times \sinh \frac{2i\pi (d_{2}-y)}{c} \frac{\sinh \frac{2i\pi d_{1}}{c}}{i \sinh \frac{2i\pi d}{c}}\nonumber \\ \end{aligned}$$

(29)

$$\begin{aligned}&P\left( x,y<0 \right) =\frac{4\pi q'd_{2}\left( d_{1}+y \right) }{cd}\nonumber \\&\qquad \qquad \qquad \qquad + 4q'\sum \limits _{i=1}^\infty {\cos \frac{2i\pi x}{c}} \nonumber \\&\qquad \qquad \qquad \qquad \times \sinh \frac{2i\pi (d_{1}+y)}{c} \frac{{\sinh }\frac{2i\pi d_{2}}{c}}{i{\sinh }\frac{2i\pi d}{c}} \end{aligned}$$

(30)

$$\begin{aligned}&P\left( x,y \right) = \lim _{d_{2}\rightarrow \infty }{P\left( x,y<0 \right) }\nonumber \\&\qquad \qquad \,\,\,=\frac{4\pi q'\left( d_{1}+y \right) }{c}\nonumber \\&\qquad \qquad \quad \quad +\, 4q\mathrm {'}\sum \limits _{i=1}^\infty {\frac{1}{i}\left[ \cos \frac{2i\pi x}{c} \right] }\nonumber \\&\qquad \qquad \quad \quad \times \sinh \frac{2i\pi \left( d_{1}\!+\!y \right) }{c}. \end{aligned}$$

(31)

From this expression, it is very clear that electric potential in the electrostatic mirror depends on the constant pitch (c) and distance between the grounding plane and grid wire ($d_{\mathrm {1}})$. The horizontal component of the electric field decelerates the incoming electron whereas the vertical component bends down the incoming electron toward the sensor of the MCP.