Being a hard-core crystal set builder, I was delighted to read about a battery-less audio amplifier. It used a second crystal set peaked on a local station to charge up a 0.3 FARAD cap. It took most of the day to charge it up to some 1.5 volts , but that was sufficient to run a micropower op amp drawing a microamp for 3 hours.
For details see article 25 on
www.bentongue.com/xtalset/xtalset.html
John.