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This is not a bad question (turbulent transport is very important for magnetic confinement fusion), but the answer is unfortunately "very little". This work con

This is not a bad question (turbulent transport is very important for magnetic confinement fusion), but the answer is unfortunately "very little". This work considered only hydrodynamics, which does not describe the inclusion of magnetic fields. Turbulence in magnetohydrodynamics is much more complicated and it is not clear how the present result would be generalized to cover that case as well. Also we do have results for neo-classical transport in MHD turbulence, even we don't have mathematically rigorous proofs.

pge 7y ago
Also, there are almost no implications to real-world applications from this proof because the result has been assumed to be true for a long time. I don't mean to diminish the value of the proof, which is an impressive bit of work; it's just that the value here is more academic and in the theory realm than in the practical or experimental where the theorem has been treated as true without a formal proof.
willis936 7y ago
Oh hey I’m sitting in an office down the hall from a neoclassically optimized stellarator. :) I’m not a scientist, but from my layman view there seems to be a lot of empirical work being done to characterize turbulence beyond what MHD models tell us. Afaict, hydrodynamics is a set of empirically derived equations that describe fluid macro scale behavior. Neoclassical MHD models apply Maxwell’s equations to these, but that isn’t sufficient for most plasma regimes. Gyrokinetic approximations of particle simulations are the lead that most people are following, but they aren’t able to agree with real world measurements very well yet. I have the impression that particle level simulation works but we are several orders of magnitude away from that in terms of computational capacity.
- petschge 7y ago
  You can derive hydrodynamical (and magnetohydrodynamical) equations in a rigorous (as opposed to empirical) way. BUT that gets you an infinite hierarchy of equations where the equation for the density contains the flows, the equations for the flows contains the pressure, the equations for the pressure contains the heat flux and so on. So in praxis we end this hierarchy at some point and "close" the system of equations by imposing e.g. a empirical description of the pressure based on density, flow and temperature (this would be an equation of state. you could also set the heatflux based on lower order equations and close there). That said, yes there is deviation from what even MHD turbulence predicts for a stellerator. Gyrokinetic simulations are more complicated (you keep lot and lot of the individual particles that make up the fluid, but ignore at what angle along their gyro orbit they are, basically describing them as charged little rings), consequently much more computationally costly, but closer to real life. A full particle simulation (retaining pointlike particles with a correct gyro phase) with something like a PiC code would be even better but is indeed order of magnitude out of reach at the moment. tl;dr: you have acquired a good high-level view via diffusion from the people around you.

pge 7y ago

Also, there are almost no implications to real-world applications from this proof because the result has been assumed to be true for a long time. I don't mean to diminish the value of the proof, which is an impressive bit of work; it's just that the value here is more academic and in the theory realm than in the practical or experimental where the theorem has been treated as true without a formal proof.

willis936 7y ago

Oh hey I’m sitting in an office down the hall from a neoclassically optimized stellarator. :) I’m not a scientist, but from my layman view there seems to be a lot of empirical work being done to characterize turbulence beyond what MHD models tell us. Afaict, hydrodynamics is a set of empirically derived equations that describe fluid macro scale behavior. Neoclassical MHD models apply Maxwell’s equations to these, but that isn’t sufficient for most plasma regimes. Gyrokinetic approximations of particle simulations are the lead that most people are following, but they aren’t able to agree with real world measurements very well yet. I have the impression that particle level simulation works but we are several orders of magnitude away from that in terms of computational capacity.

petschge 7y ago
You can derive hydrodynamical (and magnetohydrodynamical) equations in a rigorous (as opposed to empirical) way. BUT that gets you an infinite hierarchy of equations where the equation for the density contains the flows, the equations for the flows contains the pressure, the equations for the pressure contains the heat flux and so on. So in praxis we end this hierarchy at some point and "close" the system of equations by imposing e.g. a empirical description of the pressure based on density, flow and temperature (this would be an equation of state. you could also set the heatflux based on lower order equations and close there). That said, yes there is deviation from what even MHD turbulence predicts for a stellerator. Gyrokinetic simulations are more complicated (you keep lot and lot of the individual particles that make up the fluid, but ignore at what angle along their gyro orbit they are, basically describing them as charged little rings), consequently much more computationally costly, but closer to real life. A full particle simulation (retaining pointlike particles with a correct gyro phase) with something like a PiC code would be even better but is indeed order of magnitude out of reach at the moment. tl;dr: you have acquired a good high-level view via diffusion from the people around you.