Amanda:
My home has a simple PVC 4-6 in. diameter vent pipe about 25 feet high extending from below the basement slab in the gravel layer to a foot or two above roof line. The warm air in the pipe creates a convection flow upward since the pipe is kept warm within the envelope of the house. Make up air is drawn in through an horizontal pipe that begins on the opposite side of the basement from the vertical vent pipe. It is buried down below grade as it leaves the house and then exits to open air about 20 feet from the basement wall. (The grade slopes away from the house at this point.) I would guess that in the summer with A/C on in the house, the air flow in the system may reverse and flow down the vent pipe and out through the buried make-up air pipe. In either case, the radon is vented out of the house. You would need to include the root cellar area and slab it over also to make this passive system work.
This was approved by my local county inspectors in Montgomery County, MD. Of course a scheme like this depends on a reasonable amount of gravel below the basement slab, preferably covered with plastic sheeting before the slab is poured. If you have such a basement this could work quite well.
If you can't do this, consider a creating a constant low flow of fresh air through the basement and use a small solar panel and several batteries to power the vent fan which would exhaust the air..

We are in the process of buying a house, and it's an ideal house in nearly all respects, but the inspection found unacceptably high levels of radon in the basement. The only radon pump I've ever seen was electrically driven. We intend to ask the local radon mitigation folks about off-grid solutions, but wondered if anyone here had successfully mitigated radon without using grid electric, oil, or propane on an otherwise grid-linked property...all resources and ideas welcome.
Also, I'm wondering if the radon situation (once mitigated) would preclude building a root cellaring area in the basement. The floor is mostly poured concrete except for about a 5x8' area that is dirt, and I had intended to put the root cellar over the dirt. Thanks in advance for any insights.