Why does increasing the expansion amount accelerate the growth rate of the main cooling liquid?

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When it is necessary to increase the production of liquid oxygen, the degree of expansion of the expander is usually increased. As we know, the temperature of the expanded air entering the upper tower at this time is not low, and it seems that this does not contribute much to an increase in the level of liquid oxygen. Why is that? My views mainly consist of two points: First, the increase in muscle mass leads to an increase in pressure in the upper tower. To maintain a certain pressure in that tower, it is necessary to open the vent valve for the backflow gas, which increases the amount of cold air entering the heat exchanger. This helps ensure that the main heat exchanger has sufficient cold capacity, thereby facilitating the production of liquid oxygen. II. Increasing the amount of expanded air will inevitably reduce the amount of air entering the tower, which in turn lowers the load on the condensation evaporator and reduces the amount of oxygen that evaporates, thereby facilitating an increase in the production of liquid oxygen. These are just my humble opinions; I welcome feedback from my colleagues.