Warning

[Vort]

Perhaps the concept is to use the energy of the planet to destroy itself.  It is a common concept of self defense - to use the power of one's opponent against them.

 

This link suggests that the energy needed to destroy an Earth-sized solid planet in the way the Deathstar destroyed Alderaan is about 2 x 10^27 joules. (Basically, it says, how much energy is required to provide all matter in a planet iwth escape velocity, which of course shrinks as the planet gets smaller.)

 

Let's assume that the Deathstar destroys planets by injecting them with antimatter (so its "primary laser" is actually a huge antimatter injection gun) and letting the subsequent matter/antimatter annihilation superduperheat the rock of the planet so that it blows itself apart. I can't think of a more efficient delivery system for such vast quantities of energy. Using the above figure and solving E=mc² for mass gives m = E/c² = (2 x 10^27 joules) / (299792458 m/s)² ≈ 9 x 10^16 kg of matter turned completely into energy. So roughly 10^17 kg, or 100 quadrillion kg (100 trillion metric tons).

 

In such a case, the Deathstar would have to inject about half this amount, or around fifty trillion metric tons, of antimatter into the planet (presumably its core) so that it could annihilate an equal mass of matter and provide the requisite energy. That's 50 trillion cubic meters of antiwater, assuming it uses antiwater. If it uses some form of matter ten times denser than water, that's still 5 trillion cubic meters of matter delivered in a few seconds. Perhaps it uses something 100 times denser than water (!!), which reduces the needed volume to a mere 500 billion cubic meters.

 

In a few seconds.

 

Remember, light travels less than 300 million meters per second, so a one-square-meter-cross-sectional beam would take over fifteen minutes just to exit the gun, plus travel time to the planet, assuming the antimatter beam were traveling just under the speed of light (which would up the power requirements). I suppose if the beam is 1000 square meters in cross-section, or about 120 feet across, it could inject the antimatter within a couple of seconds. But we have not yet even touched on the creation of such vast quantities of antimatter.

 

At this point, we no longer have science fiction, but just pure fantasy. Which is fine; fiction that confined itself to known reality would not be very fictive. But the point is, from a physics view, it's nonsense.

[NeuroTypical]

The death star doesn't operate with conventional energy weapons.  It fires a ray which converts the planet into a grammar nazi planet, then beams over the text of an urban slang dictionary in binary.  The planet explodes.