In the film we can see him making a miniature simplified Arc Reactor with palladium and so on.
I know it is like a mini nuclear reactor, but what exactly are its inner workings or principles?
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The ARC reactor is definitely fusion. The industrial size one on the Stark campus is obviously modeled after a tokamak-type fusion reactor, and Vanko's schematics at the start of Iron Man 2 reinforce this. The one used in the base of Stark Tower in Avengers similarly matches a tokamak reactor.
Him making a tiny one that fits in his chest is basically magic. That Stark's had one running for decades on the campus is super-science (in real life we currently don't have fusion reactors that generate more energy than they take in).
Although of dubious canonicity, during San Diego Comic Con 2014, Marvel had a science-focused MCU presentation. They state:
Although never permitted to investigate it directly, Dyches suspects that the reactor uses a tokamak design paired with low-temperature fusion.
It runs on Applied Phlebotinum (TV Tropes link). But the use of palladium seems to imply some kind of cold fusion, or at least inspiration therefrom. Another candidate would be triggered isomer release, but both of these are maybe a half level up from snake oil, unfortunately, at least in regards to actually breaking even in energy production.
The ARC reactors shown are low-radiation source fusion reactors. This implies strongly LENR (low energy nuclear reactor), as does the use of palladium.
The lack of high powered magnetic fields rules out traditional tokomak reactors.
That said, the brilliant glow in operation is counter to LENR, so it's some form of mid-energy nuclear reactor.
According to the Marvel Wikia, it's a repulsor based fusion system.
That said, it's comic book physics. It works because the story needs it to.
Note, however, that while repulsor fields are as yet fantasy, the use of repulsors to cause fusion should work; magnetic tokomaks work by magnetic compression of hydrogen plasma. (At present, sustained fusion is an energy losing phenomenon - it takes more energy to generate the containment/compression than can be extracted from the resulting reaction.)
Before I answer this, let me make one important point clear:
It is already commonly assumed that IronMan's reactor uses (fission and/or) fusion. With that in mind, it is further assumed that the latter is the primary reaction, and that the former is a secondary reaction if mentioned at all.
The arc reactor depicted onScreen may use a bit of 'comic book' physics, but it does still have underlying principles that relate to actual science. As such, the arc reactor can be theorized about in five main ways:
The reactor depicted does the following throughout IronMan I, II, and III:
With this delineated, certain things can be assumed. One, the reactor is able to produce and/or store energy for prolonged periods. Two, the reactor is emitting a harmful bi-product of some sort during its operation. Three, the reactor has to be able to produce (electrical) energy directly - there's no room for secondary energy-conversion processes here. Fourthly, the reactor (is covered in coils that look like magnets and) appears to be controlling a glowing substance of some sort - could this be plasma? Fifth, if it is plasma, and does resemble a Tokamak, this could be a reaction that relies off of energized collisions. That would also explain the poisoning partially (radiation and trace elemental bi-products). Also, why else would it glow like that?
But the question then becomes, what type of fuel/energy source is it using? The answer is, Palladium isotopes. The reactor ionizes and accelerates palladium isotope 103, and uses other Pd isotopes to facilitate electron release and/or capture. The resulting radiation that is released is usually used to aid in catalyzing the reaction further, producing more energy. This process changes somewhat, however, when he does his famous "Unibeam". Instead, the resulting energies from the reactor (mainly gamma and electricity) are sent outward in a focused beam. The verdict: Tony Stark used (comic book) physics to create a Pd Decay Plasma Nuclear Reactor.
But wait - there's more! Tony then created his own element to stave off the harmful effects of the old Pd reactor. This synthesis of a new element is not as fictional as it may seem - many elements and isotopes have been created in colliders before:
And that is the simplistic version of how the Arc Reactor (theoretically would) work. Please see this article for more details:
There are good answers been provided already, but maybe you are interested in a youtube video of a phsicisist talking about Iron Man and also about the Arc Reactor (starting at about 2:00 min)
Check this site, it explains every thing you want:
It kind of works out of palladium (a specified one to be exact ). It has a beta decay property that will convert the high energy electrons into gamma rays. But sadly it is not the latest arc reactor which is powered by unobtanium.