Why is the Anode at the Center of a GM Tube?

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SUMMARY

The Geiger-Mueller (GM) tube is polarized to facilitate interactions between liberated electrons and gas atoms, resulting in a detectable avalanche discharge. The anode is positioned at the center of the tube to maximize electric field strength, which is approximately two orders of magnitude greater than at the outer electrode. This configuration minimizes damage to the cathode, which is located on the outside, and reduces quench time and detector noise. Reversing the polarity would disrupt these optimal conditions, leading to decreased performance.

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Why is the GM tube polarised?

What benefit comes from having the anode at the centre of the tube? What happens if you reverse the polarity?
 
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The Geiger-Mueller counter (and gas-filled proportional counters in general) is polarized in order to cause interactions of the electrons liberated by the radiation with atoms in the gas, which causes a detectable avalanche discharge, as well as collecting the charges (electrons).

The electric field density is proportional to 1/r, and so the electric field is stronger at the central electrode (typically ~ two orders of magnitude greater than that at the outer electrode). Since electrons (photoelectrons) are emitted from the cathode, it is preferred to have the cathode on the outside because the current density on a centrally located cathode would be quite high and thus the damage from discharge would be greater for a given voltage, and the quench time and detector noise would be greater because secondary events would more easily cause electons to be emitted from the cathode.
 
Many thanks. A clear answer.

I had suspected it was something to do with the increased field strength at the centre of the tube, but was unsure of the reason.
 

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