When heat transport flips: simulations explain the formation of the H-mode

For more than 40 years, the H-mode has been considered the desired operating scenario for tokamak-type fusion facilities. But why it suddenly develops remains a mystery. Now, with the help of simulations, physicists have found an explanation for the first time that is based solely on fundamental physical principles. The work is published in the journal Physical Review Letters.

On 4 February 1982, researchers at the Max Planck Institute for Plasma Physics (IPP) in Garching made a discovery that continues to shape nuclear fusion research worldwide. During experiments with the ASDEX tokamak facility, the hot plasma transitioned within milliseconds to a state in which thermal insulation improved. Physicists call this measured variable “energy confinement time.” Only when the values are sufficiently high can the construction and operation of a fusion power plant even be considered, because if the heat losses are too great, the plasma cannot heat itself and extinguishes. This new state – which scientists called High Confinement Mode, or H-mode for short – is now used in all tokamaks and is also to be used in future experiments such as the large-scale international ITER experiment in southern France. It differs dramatically from the previously known state, L-mode (Low Confinement Mode).

Despite countless experiments and theoretical attempts at explanation, the occurrence of H-mode remained a mystery. Scientists were able to work with it, but they did not understand why H-mode occurred at a certain plasma heating power. "Experience showed at what power level confinement improved. And this knowledge was extrapolated for the design of new, larger machines. However, if you don't understand the physics, such extrapolations can be fraught with uncertainty," explains Dr Wladimir Zholobenko, physicist in the IPP's Tokamak Theory Division in Garching, where he heads a group working on the development of predictive models for boundary layer turbulence in tokamaks and stellarators.

Improved GRILLIX code as the key to the breakthrough

In their search for a sound explanation, Dr Zholobenko and his fellow researchers have now achieved a breakthrough: for the first time, the scientists were able to qualitatively simulate the formation of the H-mode using supercomputers based solely on fundamental physical principles. In other words, they did not “parameterise” the transition to H-mode, but allowed it to arise in a complex simulation of the plasma edge itself. In their model, the heating power is increased step by step – and the plasma is allowed to react freely, form profiles, build up flows and develop turbulence. It is precisely this type of “flux-driven” edge simulation that is considered particularly challenging. To do this, the researchers used and improved the software code GRILLIX developed at the IPP, which is particularly good at simulating turbulence in plasma edge layers.

In earlier work, they had already demonstrated that the code can simulate the stationary L and H modes very well. Such calculations take one to two weeks on supercomputers and are now routine. However, calculating the development of turbulence in the plasma at the transition from L-mode to H-mode over a period of 50 milliseconds represented a new level of complexity. It kept a supercomputer busy for a whole year.

After 32 milliseconds, heat transport reverses

The result: after a prolonged phase of slow turbulence development, an abrupt reversal of heat transport in the plasma occurs at around 32 milliseconds of simulation time. Within just 100 microseconds, a so-called pedestal builds up at the edge – the steep pressure and temperature edge that is typical of H-mode. At the decisive moment, a certain type of microinstability disappears abruptly and another emerges: the simulation reveals a sudden change from drift wave turbulence to kinetic ballooning modes. Such a transition had already been partially suspected. “But the simulation also reveals a surprise: not only is heat transport to the outside reduced, it even reverses temporarily and moves inwards,” says Dr Zholobenko.

“This is actually a violation of thermodynamic laws, but because these only apply statistically, it is physically possible for a tiny fraction of a second – until the transport direction reverses again.” Physicists call this transition to H-mode a phase transition in turbulence because there is also an abrupt change in the phase shift between fluctuations at the microscopic level. This means that the turbulence changes its internal organisation. The fluctuations suddenly lose their previous rhythm, and this is precisely what causes the heat transport to tip over.

Next goal: quantitative replication of the transition to H-mode

The simulation was based on the conditions of the IPP tokamak ASDEX Upgrade, so that the numerical calculations could be compared with experimental results. The simulation shows that it reproduces exactly those effects that can also be observed in the experiment. However, the researchers have not yet been able to achieve satisfactory quantitative agreement – in other words, the actual measurements from ASDEX Upgrade are either above or below the simulated results. “We haven't reached our goal yet, but the simulations provide insight into what is still missing,” says Dr Zholobenko. ‘That's why we will continue to improve the GRILLIX code.’ The aim is to end up with a simulation model that can predict the experimental parameters at which H-mode occurs in fusion facilities that have not yet been built. 

This would then be a digital twin that existed long before its real-life counterpart.

Frank Fleschner

Link to the original publication: https://doi.org/10.1103/b2s6-b5c1