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I am reading some papers on numerical algorithms for simulation of plasma in the context of nuclear fusion in a tokamak. I am getting a little lost as there is a huge number of references, and it is difficult to actually know what kind of algorithms are being used now for such simulations.

In a more specific sense, my question is: on which timescale is the numerical error from the current best algorithms acceptable? Can we accurately simulate a tokamak on timescales comparable to those of the actual experiments? If so, when do the current algorithms start to break down?

Any help would be much appreciated.

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    $\begingroup$ Perhaps you could link us some of the papers you've been looking at... $\endgroup$ – lemon Jun 17 '16 at 11:45
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    $\begingroup$ How ti simulate an entire tokamak is an extremely broad question. I doubt that there is a simple answer to it or that it's being done in one simulation. It is much more likely that there is a series of simulations on different scales that are being stitched together and verified and calibrated with actual experimental data. If one could simulate an entire tokamak from scratch, there would be no need to build one for experiments. $\endgroup$ – CuriousOne Jun 17 '16 at 21:47
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    $\begingroup$ @lemon: for instance, this is a good representative: www-irma.u-strasbg.fr/~helluy/Tonus/tonus2014.pdf, CuriousOne: good point, I should have thought about it. But do we even have an indication of how code has performed with current or past experiments? $\endgroup$ – snefs Jun 18 '16 at 13:58
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    $\begingroup$ I have not worked specifically with tokamak plasmas but in space plasmas one generally needs to compromise between the ion-to-electron mass and the cyclotron-to-plasma frequency ratios due to computational limitations. Though we have become semi-adept with creating "vacuums" on Earth, the best ones are still ~6-12 orders of magnitude more dense than the space around Earth (i.e., the magnetosphere). Thus, they probably have to worry about ion-, electron-, and neutral-neutral collisions, which pose an additional computational constraint. $\endgroup$ – honeste_vivere Jun 23 '16 at 13:55
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    $\begingroup$ @honeste_vivere, do you know approximately the timescale (in terms, for instance, of the cyclotron frequency) after which numerical errors start to be significant, with current methods? Sorry if this is exactly the same question I asked for tokamaks, but (given what you pointed out) at least we will have an upper bound. $\endgroup$ – snefs Jun 23 '16 at 14:07

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