When buying a portable battery, is it okay to use a lower amp source if the voltage and polarity are the same?
For example, I'm looking for something that will charge my laptop that draws 19V 6amp. Is it okay to use an intocircuit power castle, which can provide 19V at 3amps? Regardless of theoretical speed (as higher amps typically allow for faster charge), will it charge at all? And more importantly, will it bad for the laptop's battery life?
Is there a bottom limit for trickle charging or will it work as long as there is current?
It will work as long as there is a voltage differential. Initially it will work at the full rated amps on a low battery. As the battery acquires a charge the internal resistance builds up and reduces the charging amps. This will go on until the battery is fully charged.
This applies to automotive batteries too. Fast charging on these will tend to buckle the plates and damage the battery (shorting plates).