You need to solve a 5-dimensional (+ time) nonlinear integro-differential equation. Not only that, but you need to keep it going for a long enough time for turbulent fluctuations to average out, and cover both ion and electron scales (that last bit is the big new contribution here).
And once you're done with that, you need to repeat it at even higher resolution as evidence that what you're seeing is physical.
Bravo!
Not all differential equations are nicely behaved. Many do not have analytic solutions at all, meaning that we can't even write down a function that satisfies the equation. However, such equations can still be solved approximately using computational techniques. This can be incredibly difficult and computationally expensive (note the huge resources required to achieve this breakthrough) but can produce very useful results.
Explain like I have a high school physics education.
I had the same curriculum but was utterly bewildered by derivatives being the first topic. For the simple reason that until that point I had habitually looked at "wholes" in the external world, only then to wonder "what kinds of things progressively make it up?"
I feel like to derive something, you start with the assumption that you know what you're talking about fist. Yet the thing is actually the sum of its parts. Therefore integration seems more natural at first, and only then can things similar to it be derived with confidence.
So the teaching order seemed backwards. I wonder if anyone has felt the same way.
I have an online series that starts with the historic order which you might like:
They start with the calculating slope on a curve f(x) being lim h->0 f(x+h)-f(x)/h - spend a few weeks deriving various derivatives, show how you can find tops/bottoms of curves (derivate=0), talk about limit theory a bit, take a bunch more complicated equations derivatives.
Then, once that's figured out - take the inverse, and look at area's under curves, volumes, etc... My brain lost it at integration by parts (so many parts) - too much memorization, and so came an end to my mathematics education in that space.
I'm happy they were taught in that order, mostly on being exasperated with having to memorize all the integration by parts formulas.
And even with that background, our foreign lecturers were regularly disappointed at our lack of mathematics competency in University ("Now I have to waste the next 4 weeks teaching you things we learnt in highschool in my home country before I can move on to what this subject is actually about").
These were Asian/Indian and a Ukrainian lecturer, that I recall.
I know Russia values math highly and does push their students, but there's a limit to believability.
True in general, but it would be nice to meet the five-year-olds for whom it's the right forum.
It turns out that one of the simplifying assumptions that physicists have been making over the years does change the result. Giving up the "spare change" does make you "go bankrupt." In this case, ignoring small-scale turbulence makes you lose a significant amount of heat. But figuring that out required some really hairy math and a butt-load of computing power.
Is that simple enough for you?
Scientists often assume that you can accurately approximate stuff by neglecting irrelevant parts of the physics (basketballs vs ping pong balls; protons vs electrons). Turns out that ping pong balls greatly affect the outcome and amount of heat/energy dissipation in the basketballs.
This doesn't surprise me too much, since critical behavior often happens in regimes where two separate aggregate effects become relevant. But the details are all still just a big mystery :)
P.S. someone posted a much better description than the OP. I'll reiterate: http://news.mit.edu/2016/heat-loss-fusion-reactors-0121
What MIT did was make it easier to open all these poke balls in a sustained way. This is important because once fusion is sorted out, our political leaders like Ted Cruz could use all that energy to do really interesting things.
One side effect is that a lot of poke monsters will be released as well, which could cause problems...and so we as a society need to think about the long term ramifications.
Now there are two main parts to the stuff inside the reactor, ions & electrons. Think of them as mac & cheese. When the reactor gets really hot, these bits start jostling around. (It's in the nature of hot things to want to move more, and really "hot" means that the little atomic components of everything are wiggling and moving faster and more excitedly.) Think of boiling the mac and cheese. For a long time scientists thought that the wiggles of the ions would diminish the wiggles of the electrons, because 1) the ions & electrons want to be near each other so they form a clump (like how the noodles absorb the cheese but waaaay stronger) and 2) because each ion/noodle is way bigger than each piece of cheese powder/electron, so its wiggles should be way stronger.
Now to figure these things out, scientists have to use computers to predict how it all might work. But the formulas they use don't have a single answer they can just solve by hand. Instead the computer can take a guess and then spend a lot of time seeing how good the guess was, and trying to make it better. A computer can do things fast, but it's hard because when it does math, it's only figuring out how a single piece of cheese dust moves at a time! There are so many little pieces and knowing how a few cheese dusts move won't give us a good idea what a big pot of mac n' cheese is like. (Could you learn how sand feels by holding one grain?) So they have to keep the computer running until it can tell them what a lot of cheese moves like. Even harder is that they need to watch the cheese move for a long time to make sure it's "stable". (For example, if you put mac and cheese back on a hot stove it might be quiet for a bit before suddenly a big cheese bubble burst and splattered everywhere. We need to know if there are bursting bubbles or not, so just looking for a second won't be enough to tell us.) So the computer also has to do this guessing for many little tiny moments, until they add up to a longer amount of time. Then they can figure out how the sauce behaves when you leave it on the stove for a while.
Ultimately these scientists found that the ions & electrons don't act exactly like we thought. The heat actually causes the electrons/cheese to stretch out into long strands that pull away from the main blob! Also when the cheese starts swirling around, instead of bumping into the noodles and stopping, they can bump strong enough that the noodles and cheese all start swirling together crazily. These two things give us big clues on why our reactors won't stay as hot as we want them to, because they explain why the mac and cheese gets so wiggly and wild, and with the discovery we can now try to find new ways to build better reactors that work better.
All the guessing by the computers was so much work it would've taken a single computer 15 million hours (over 1700 years!), but they got 17000 computers to all work as a team and give them answers in about a month. Then the scientists could get a couple answers in a year, which made them feel more confident that they probably did things right.
NOTE: Totally not a physicist or anything, and I probably started with a bad analogy, but wanted to try this as a writing challenge. Also I know you probably didn't want it this simpified, but I tried to take "ELI5" at face value for once.