From: daellis94@gmail.com   
      
   On Saturday, July 28, 2018 at 3:55:04 PM UTC-4, els.d...@gmail.com wrote:   
   > On Thursday, July 26, 2018 at 12:26:02 PM UTC-5, David Ellis wrote:   
   > > So, I've been exposed more to the idea of 'Q' when talking about nuclear   
   fusion reactions during my time on this forum, and it has gotten me wondering   
   something.     
   > >    
   > > Talking about a reactor that can achieve a Q of 10 or 100 or 500 is fine.    
   It's not hard to imagine why a Q of 500 is much more impressive than a Q of   
   10, and how it might be much harder to accomplish.     
   > >    
   > > Are there known theoretical maximum values for Q for the fusion reactions   
   usually considered by folks like us?  That is, for deuterium-tritium,   
   deuterium-deuterium, helium-3-deuterium, boron-hydrogen, etc.     
   > >    
   > > As far as I can tell, any fusion reaction, be it a deuterium nucleus   
   slamming into a tritium nucleus, will be giving off a certain amount of   
   energy.  We know this.  It will form a helium nucleus and eject a neutron, and   
   we know the energy each    
   product will represent.  I would imagine, as well, that, for any given pair of   
   fusion reactants, the nuclei must slam together with at least a given amount   
   of energy, otherwise the reaction will not take place, and the nuclei will   
   simply bounce off of    
   one another.     
   > >    
   > > Surely, the energy released by the reaction divided by the minimum energy   
   required would give the maximum value for Q that it is physically possible to   
   achieve for any given fusion reaction.     
   > >    
   > > Am I right in thinking this?  Does anyone know what such Q values are for   
   the reactions that are normally of most interest to us for science-fiction   
   purposes?  Would the theoretical maximum Q of He3/H2 fusion, for example,   
   leave a lot of room for    
   technological growth, say, with a theoretical maximum of Q=10 000 or something   
   like that, or is it much lower, maybe in the less impressive realm of a few   
   hundred?   
   >    
   > The Q factor is a measure of how much energy that you are getting out of a   
   reactor versus the amount that you are putting into the reactor to keep it   
   going.    
   >    
   > If you have a self-sustained fusion reaction, then the energy from one set   
   of reactions can supply the energy for the next. So if the first generation of   
   reactions produces 200 times the power that you need to catalyze a reaction   
   then it can allow 200    
   times as many reactions to happen, which then release 40,000 times the initial   
   power input. The trick is the ability to keep the produced power inside of the   
   plasma long enough to allow for additional reactions to be catalyzed.    
   >    
   > Energy leaves a plasma based on its surface area, but power produced would   
   seem to be based on its volume. So if the radius increased by a factor of 10   
   then the surface area increased by a factor of 100, but the volume by a factor   
   of 1000. This means    
   that energy will stay in the plasma longer and the temperature of the plasma   
   will rise, which will further increase the reaction rate. Confinement time   
   will also increase. These are reasons why the power output of tokamaks   
   actually scale with the    
   increase of the radius to the 4th power, not the 3rd. The power density and   
   the Q factor are therefore increased by simply building a bigger reactor.   
      
   So, I spent a while trying to wrap my head around this idea.  I can understand   
   the notion of energy leaving the surface of what we can approximate as a   
   sphere, where the energy of the fusion plasma is manifested in the whole   
   volume, and, of course,    
   volume of that sphere will increase with radius faster than surface area   
   will.  Of course, I imagine this isn't an ideal description since I think some   
   X-rays would be radiating from inside the plasma sphere without being absorbed   
   by outer layers of the    
   plasma, which would mean power is leaving the plasma from the surface, as well   
   as from "surfaces" some depth inside the plasma, where depth decreases power   
   radiated, but I digress.  It's obviously good enough.     
      
   However, I just couldn't shake the notion that it shouldn't work that way.  I   
   mean, if you are looking to constantly harvest energy from the plasma, using   
   as little as you possibly can to keep the fusion going, a self-sustaining   
   fusion reaction would,    
   for any number of individual fusion reactions, take X amount of energy from   
   its surroundings (subtracting X from the energy you are able to harvest from   
   the rest of the fusion plasma) and produce Y amount of energy as a result.    
   So, I figured that, even    
   if you don't harvest energy from the plasma initially and let the first round   
   of plasma reactions ignite another round, those still only release Q times as   
   much energy as was taken from the plasma.  So, even a self-sustaining fusion   
   plasma would not be    
   able to give you as much power as it is able to produce because you are   
   constantly sapping off 1/Q of its total power to keep the fusion going.     
      
   It just dawned on me, though, that I think your point is that the surface area   
   vs volume question is the key.  Is that correct?  That the larger your reactor   
   is (and thus, the larger your ball of plasma is) the more energy you have   
   "trapped" in the    
   plasma to increase total fusion power, so, even if you can't harvest it faster   
   than the surface area grows, the total power available makes up for it?     
      
   I imagine this isn't entirely true in the case of direct energy conversion,   
   where the reactor isn't relying solely on radiated power, and is instead using   
   magnetic fields to tap off the kinetic energy of charged particles zipping   
   around the torus.   
      
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