Disclaimer: A friend of mine who has a PhD in Physics from UIUC tried to solve this and gave up stumped.

Schematic: http://imgur.com/Yb5fZ2x

Challenge: - What is the efficiency of the capacitor? - Will there be issues with overheating? (PV=NRT) - What are the equations that describe the energy storage capacity of this capacitor? Please keep the equations as general as possible, allowing for different density gases, voltages, capacitor sizes etc..

Design Description: A solid conducting sphere is placed within a larger hollow conducting sphere. It is suspended in the center of the larger sphere by a thin conducting rod. Both spheres and the rod are coated with a very good insulator. A charged gas is used to fill the space between the two spheres (for example H+ gas molecules). Since the gas is charged and like charges repel the gas will tend to stay towards the outer edge of the sphere.

Charging consists of connecting the capacitors terminals to a voltage source. Electrons will flow into the smaller, inner sphere and out of the larger outer sphere. As a negative charge builds on the inner sphere the H+ ions become attracted towards the center and compressed. The more charge that builds on the inner sphere the more the gas becomes compressed and the more energy is stored in the electric fields.

Alternative designs There are countless alternative designs. I imagine, depending on the application, there are advantages and disadvantages to each. Here is one such example: Dual Chamber Piezoelectric/Pump: http://imgur.com/UZbJjKB (this design can be implemented with either a piston, or a stationary charge plate.)

Bonus Questions: - How does the choice of different gases affect the properties of the capacitor? - What are the equations describing the piezoelectric and stationary rectangular capacitor?