SOLAR STEAM PUMP
Solar heat and biomass, both abundant in Bihar , will generate steam to push water out of borewell

Solution

This idea makes the borewell casing behave like a cylinder and the water inside like a piston.Since there are no mechanical or electrical  losses,  this may be the most efficient method to pump water. It might be even twice as efficient as solar PV pumps.



A parabolic trough reflector with telescopic sections for portability heats water to pressure of 1.5 kgs. This steam is piped into the borewell  whose mouth is sealed. The steam pushes the water column down and water comes out from a 2 inch outlet pipe.A floating seperator prevents the steam from  the water.
The steam is also  generated by a burning the abundant biomass in a  burner on cloudy days or at night.
Pressure guage and safety valve will have to be installed to control the flow.
My guess is that we will need about 6 square meters of solar reflector to generate the steam required for pumping 3 litres of water per sec. 
Working on detailed calculations.
29Sept update
We will need a 10 sq m parabolic trough to heat a black iron pipe placed at its focal point.  Water passing through this pipe is converted to  steam  and piped into the sealed top of the borewell.  
I am looking out for a steam engine expert to check this idea and comment.
I am also looking at Fresnel reflectors to heat the pipe. They will be easier to fold and make the system portable.

We will have to try and see whether water comes out of the outlet or is pushed into the ground when steam is released into the borewell top.

As suggested by Conradius we will put a footvalve at a depth of approx 15 m so it prevents water from escaping down when steam pressure is applied. When all water is pushed out the steam shuts off to allow water to come up through the footvalve and recharge the well. Cycle is repeated .