What is the concept behind the "Miniature Arc Reactor" built by Tony Stark?

The Stark Arc Reactor is most likely a Multi-Isotope 

Radio-Decay Cell.

As this a fictitious device and there is no official explanation of this technology behind the Stark arc reactor. So I'am going to make something up, something real science and fake science. 

Let's take a look on the Arc reactor on Iron Man 1 & 2 :-

The full sized arc reactor looks like a Toroidal plasma containment system for standard 'Hot Fusion' :

Real world equivalent: ITER  fusion reactor :

The reactor pictured here is under construction and is expected to produce a net gain of energy. Basically it mashes two isotopes of Hydrogen deuterium and tritium at very high energy into one atom.One Helium atom and one neutron is produce in this collision. Together the mass of Helium+Neutron is less than the Deuterium+tritium, so the extra mass is converted into large amount of energy. This energy can be captured to run a steam driven turbine (like any other power plant).

So what does the Torus (Donut) shape of this reactor tell us? It means that the charged particles are moving in the circular path by magnetic field. Generally the high energy charged particles have high energy because they are moving very fast.The magnetic field is applied to move them in circular field. This increases the space to them to collide at high kinetic energy.

You may notice that current fusion reactor designs have a lot of magnet coils on the outside of the torus, whereas the Stark Industries arc reactor has a viewing window. Plasma containment is the single biggest challenge for hot fusion, but the arc reactor makes it look effortless. From this we can conclude that a key technology in the full-scale arc reactor is a way to contain the reaction in a self-sustaining ring.

There is also remarkable lack of cooling loops, steam turbines, or anything a traditional thermal reactor would require. So we need a technology which produces electric energy directly rather into the heat energy. Back to the drawing board!

What else do we know about the miniature arc reactor?

• Contains a palladium core
• The palladium is damaged by neutrons, so the specific isotope is important
• Has electromagnetic coils in a torus
• Emits blue-white light
• Can be built in a cave with tools of moderate complexity
• Requires no exotic materials outside what you could scavenge from dismantled conventional weapons systems
• Runs low on power at inconvenient times, meaning it must have some sort of fuel or consumed charge

Palladium has a property that it can be used as a substrate in 'cold' fusion that does not require the hot plasma and containment toroids. Palladium does, however, have some interesting capture and decay properties. Wikipedia: Isotopes of palladium

The palladium core of the device would most likely be Pd-107, which emits high-energy electrons as it decays into silver. This is a pretty stable isotope that we would expect to be present in the normal (non-separated) palladium that Tony might salvage from a conventional weapon. 

So to summarize: Electrons projected outward from the inner core and the gamma rays projected from the outer ring. This electron/photon counterflow create a deficit of electrons in the core, a massive potential is developed and the Palladium core attracts the lower-energy electrons from the suit's wiring.The ejection of electrons from the core towards the rim of the device produces an electrical cell capable of generating enormous voltage and current. 

Here's the full proposed reactor start-up process:

• Using external power, Pd-103 is ionized by an electric arc, and accelerated to high velocity in the outer ring. There may also be some externally-powered gamma ray production to jump-start the inner core.
• Pd-107 in the inner core starts to emit high-energy electrons as it decays to Ag-107. The electrons escape the core and are directed by magnetic fields into the outer ring. Lack of electrons creates a net positive charge in the core, which slows further emission (preventing run-away decay) until the electrons can be externally replenished.
• In the outer ring, the high-energy free electrons collide with high-energy Pd-103+ ions. This causes instantaneous electron capture and gamma ray emission. The gamma rays are deflected inward towards the core, thus catalyzing further electron emission and producing a self-sustaining reaction. Note that the reaction is self-sustaining, but very slow while the reactor is idle.
• The electron flow from the inner core to the outer core creates an electric potential difference. When a circuit is created through the suit's electrical loads, the outer ring has an excess of electrons and the inner core has a shortage of electrons. This creates current.
• The electrical current through an external load relieves the electrostatic charge accumulations that initially slowed the reactions. So the less power the suit draws, the slower the reactor produces radioactive decay, and the more power the suit draws, the faster the reactions are catalyzed. That way, the power output automatically throttles according to demand.
• The palladium slowly converts to Rh-103 and Ag-107, and the reactor runs out of power when the palladium is fully consumed.

Miniature Arc Reactor Concept: