Measurement and simulation of two-phase CO₂ cooling for the AFTER electronics of the Micromegas modules for a Large Prototype of a Time Projection Chamber

The readout electronics of a Micromegas (MM) module consume nearly 26 W of electric power, which causes the temperature of electronic board to increase upto $70\,^{\circ}{\rm C}$. Increase in temperature results in damage of electronics. Development of temperature gradient in the Time Projection Chamber (TPC) may affect precise measurement as well. Two-phase CO$_2$ cooling has been applied to remove heat from the MM modules during two test beam experiments at DESY, Hamburg. Following the experimental procedure, a comprehensive study of the cooling technique has been accomplished for a single MM module by means of numerical simulation. This paper is focused to discuss the application of two-phase CO$_2$ cooling to keep the temperature below $30\,^{\circ}{\rm C}$ and stabilized within $0.2\,^{\circ}{\rm C}$.