This is really quite delightful, and I feel like a terrible killjoy for pointing out that your magical nuclear fusion analysis has several problems....
The first is that you haven't really looked at how to heat the rock to T_C. You've calculated the required density needed to get your estimated Coulomb Pressure, assuming the temperature is (somehow) T_C. So how do we go from room-temperature rock to a 3 GK plasma? Rapidly forcing all that rock into a smaller volume *will* heat it up, of course, and maybe you could approximate that as an adiabatic process? (I think the problem might actually be that you pass T_C long before you reach your estimated critical density.)
The second is that silicon burning is *not* actually the fusion of two Si nuclei, so the Coulomb Pressure and critical density calculations are irrelevant. Silicon burning is a complex set of reactions based around the photodissociation of Si (and other) nuclei by gamma rays and subsequent reactions involving the interactions of the protons, neutrons, and alpha particles liberated by the Si (etc.) photodissociation.
(As it happens, the density of a stellar core undergoing silicon burning is more like 10^8 g/cm^3, so you've probably significantly overestimated the number of Enlarge spells needed.)
The third problem is that the plasma will rapidly cool down due to all the photons leaking out through the force wall (it's invisible, after all!), so I suspect that if you *do* get nuclear-burning reactions started, they won't last very long.
And in fact they really won't last very long, because the final problem is that the leakage of thermal photons from a gigakelvin plasma will definitely fry the surroundings, including the spellcasters. Since both spells last only as long as concentration is maintained, the result will be the almost instantaneous vaporization of the casters, followed immediately by the failure of the Wall of Force *and* the Enlarge spells and a (small-ish) blast due to the expanding and cooling hot plasma, which only has as much mass as the original pile of rocks -- though it is very, very hot.
So it's an amusing way of creating a (suicide) bomb, but not one with any meaningful amount of fusion.
Hey, you sound like someone who actually knows how nuclear physics works! Two questions:
1. Would a spell like Darkness save them from the Blackbody radiation they’re creating? It would be perfect shielding from gamma rays, and the wall of force would shield from any charged particle radiation.
2. Do you think the wizards are better off creating some sort of magical tokamak? Let’s stick with the idea of creating molten rock as fuel - Perhaps if you had a sufficient number of wizards with the ability to fabricate large iron magnets and cast lightning bolt, you could make a giant one-shot magnet strong enough to get the rock to fuse in one big theta-pinch? What sorts of critical densities/temperatures are required for tokamak-style fusion? Would the wizards need some tritium?
Well, since I'm an extragalactic astronomer, I tend to think of my nuclear-physics knowledge as kinda limited... ;-) though I know some of the basics, and know how/where to look things up.
1. Darkness -- that's pretty clever. I think the simplest interpretation would be that it just eats all the photons that travel or originate within it, so it *would* protect against blackbody emission from the plasma. And, sure, Wall of Force confines the plasma, so it confines all the charged particles. Although...
A. This wouldn't stop the plasma from cooling off, assuming that it still emits photons (which are immediately eaten by Darkness);
B. It would presumably eat all the photons *inside* the plasma, which would cool it off even faster *and* sabotage the silicon burning (if you get rid of the photons, you won't get any photodissociation of the Si nuclei);
C. There's also the problem of whether the Enlarge casters can do their work if they can't see the target.
(Sorry, I've got to work on a talk, so maybe I'll get to the tokomak part in a day or two...)
This is some great and important work. On the second hypothesis, there’s only one problem as I see it. The way I’ve always played Wall of Force is that spells can’t be cast across it. I.e. they block spell casting. So the stone is never enlarged.
That is very sensible, and as the DM I would almost definitely rule something similar to prevent my players from nuking the world.
However, the Wall of Force text says nothing PHYSICAL can pass through the barrier, and that the only requirement for Enlarge/Reduce is that you can see the object. I feel like that leaves some room to argue that you can magically affect things through the Wall of Force, and that it doesn’t work the same way as, for example, Antimagic Field.
This is really quite delightful, and I feel like a terrible killjoy for pointing out that your magical nuclear fusion analysis has several problems....
The first is that you haven't really looked at how to heat the rock to T_C. You've calculated the required density needed to get your estimated Coulomb Pressure, assuming the temperature is (somehow) T_C. So how do we go from room-temperature rock to a 3 GK plasma? Rapidly forcing all that rock into a smaller volume *will* heat it up, of course, and maybe you could approximate that as an adiabatic process? (I think the problem might actually be that you pass T_C long before you reach your estimated critical density.)
The second is that silicon burning is *not* actually the fusion of two Si nuclei, so the Coulomb Pressure and critical density calculations are irrelevant. Silicon burning is a complex set of reactions based around the photodissociation of Si (and other) nuclei by gamma rays and subsequent reactions involving the interactions of the protons, neutrons, and alpha particles liberated by the Si (etc.) photodissociation.
(As it happens, the density of a stellar core undergoing silicon burning is more like 10^8 g/cm^3, so you've probably significantly overestimated the number of Enlarge spells needed.)
The third problem is that the plasma will rapidly cool down due to all the photons leaking out through the force wall (it's invisible, after all!), so I suspect that if you *do* get nuclear-burning reactions started, they won't last very long.
And in fact they really won't last very long, because the final problem is that the leakage of thermal photons from a gigakelvin plasma will definitely fry the surroundings, including the spellcasters. Since both spells last only as long as concentration is maintained, the result will be the almost instantaneous vaporization of the casters, followed immediately by the failure of the Wall of Force *and* the Enlarge spells and a (small-ish) blast due to the expanding and cooling hot plasma, which only has as much mass as the original pile of rocks -- though it is very, very hot.
So it's an amusing way of creating a (suicide) bomb, but not one with any meaningful amount of fusion.
Hey, you sound like someone who actually knows how nuclear physics works! Two questions:
1. Would a spell like Darkness save them from the Blackbody radiation they’re creating? It would be perfect shielding from gamma rays, and the wall of force would shield from any charged particle radiation.
2. Do you think the wizards are better off creating some sort of magical tokamak? Let’s stick with the idea of creating molten rock as fuel - Perhaps if you had a sufficient number of wizards with the ability to fabricate large iron magnets and cast lightning bolt, you could make a giant one-shot magnet strong enough to get the rock to fuse in one big theta-pinch? What sorts of critical densities/temperatures are required for tokamak-style fusion? Would the wizards need some tritium?
Well, since I'm an extragalactic astronomer, I tend to think of my nuclear-physics knowledge as kinda limited... ;-) though I know some of the basics, and know how/where to look things up.
1. Darkness -- that's pretty clever. I think the simplest interpretation would be that it just eats all the photons that travel or originate within it, so it *would* protect against blackbody emission from the plasma. And, sure, Wall of Force confines the plasma, so it confines all the charged particles. Although...
A. This wouldn't stop the plasma from cooling off, assuming that it still emits photons (which are immediately eaten by Darkness);
B. It would presumably eat all the photons *inside* the plasma, which would cool it off even faster *and* sabotage the silicon burning (if you get rid of the photons, you won't get any photodissociation of the Si nuclei);
C. There's also the problem of whether the Enlarge casters can do their work if they can't see the target.
(Sorry, I've got to work on a talk, so maybe I'll get to the tokomak part in a day or two...)
This is some great and important work. On the second hypothesis, there’s only one problem as I see it. The way I’ve always played Wall of Force is that spells can’t be cast across it. I.e. they block spell casting. So the stone is never enlarged.
That is very sensible, and as the DM I would almost definitely rule something similar to prevent my players from nuking the world.
However, the Wall of Force text says nothing PHYSICAL can pass through the barrier, and that the only requirement for Enlarge/Reduce is that you can see the object. I feel like that leaves some room to argue that you can magically affect things through the Wall of Force, and that it doesn’t work the same way as, for example, Antimagic Field.