Sorry, Danny... Disagreement here. I believe the Cynan is right.
The battery supplies, even a 1Ah supply, will deliver 300A+ if short-circuited. That is, it has a latent current delivering capacity of much more than the 7A our amp will draw. So whether it's 1Ah, 2Ah, 3Ah, or more... it will deliver way more current than we can use until it's out of gas, which will result in lower voltage.
Which does make size relevant because you don't want it being drawn down beyond the point where the charger can't keep up. We think 5Ah (1 amp for 5 hours) is plenty.
The tube buffer is a bit of a hog. We go from idle drain of around 200mA to maybe 500mA. Heavy passages could draw 7A but average draw under normal listening conditions is much less.