Unfortunately while this holds true for ideal gas?s and while it is true for low density plasma's that behave similar to gases as you used in your example, it is not true for high pressure plasma's that behave more akin to a fluid (like the sun's core in my example). The answer in those extreme situations is best described as complicated
True, that there energy requirement is exceptionally high for the purposes of armour.
However allow me to hypothesize for a moment. Let us imagine a high powered laser used for point defence on a nuclear warship. Due to the nature of this laser being the last line of defence against incoming missiles its power out put is rather high. Due to this laser's power output it is physically rather large and the military has decided not to place any additional weight upon it due to the distorting effects this would have on the highly sensitive optics. This creates an interesting problem that the laser is now unarmoured and even small hail storm, could damage the weapon. A light plasma field is placed round portions of the laser allowing it to fire out and offering modest protection against small shrapnel, hail, salt water, etc? This example may prove unfeasible/unneeded but I?m merely pontificating.
Presumably the incoming projectiles charge distribution will be 0 with a rigid structure of electrons, in which case no EM force will be able to interact with it, for instance: A lump of granite.
Since this is a sci-fi forum if my memory serves me right, the Culture, in I M Banks novels, warships main armaments are EM fields which they can manipulate locally to the point of being able to separate individual electrons from atoms in combat.
The maximum speed that a plasma can expand at is limited by the average velocity of the particles in it, which is solely a function of temperature. The Joule-Thompson effects dictates that any expansion driven by pressure will cause the plasma to cool as it expands.
However allow me to hypothesize for a moment. Let us imagine a high powered laser used for point defense on a nuclear warship. Due to the nature of this laser being the last line of defense against incoming missiles its power out put is rather high. Due to this laser's power output it is physically rather large and the military has decided not to place any additional weight upon it due to the distorting effects this would have on the highly sensitive optics. This creates an interesting problem that the laser is now unarmored and even small hail storm, could damage the weapon. A light plasma field is placed round portions of the laser allowing it to fire out and offering modest protection against small shrapnel, hail, salt water, etc? This example may prove unfeasible/unneeded but I?m merely pontificating.
Quite so. Thankfully the plasma in this case if confined to a specific volume by an exceptionally strong EM force, so the talk of dissipation is largely a moot point.
It merely strikes me as an elegant solution to the compounding issue of increasing the weight of large optical devices causing distortions. As you say it is at the emissions point the plasma window?s unique properties will shine.
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