During a disruption in a tokamak, a beam of very energetic electrons, known as ‘runaways’, can form and potentially damage the inner wall. ITER is paying particular attention to this issue. Simulations carried out by the IRFM have highlighted an effect that has been ignored until now: the reduction in the generation of runaways due to the vertical instability of the plasma.
During a disruption in a tokamak, a beam of very energetic electrons, known as ‘runaways’, can form and potentially damage the inner wall. ITER is paying particular attention to this issue. Simulations carried out by the IRFM have highlighted a hitherto ignored effect: the reduction in the generation of runaways due to the vertical instability of the plasma. A disruption is an abrupt termination of the plasma in a tokamak, which can occur when operating too close to the stability limits or following an event such as the penetration of dust into the plasma. It results in the total loss of plasma confinement in less than a millisecond (stochastisation of the field lines). During a disruption, the sudden drop in the current circulating in the plasma induces a strong electric field in the plasma, which can lead to the formation of a beam of electrons at relativistic energies (several MeV), known as ‘runaways’, carrying a substantial fraction of the initial plasma current. This beam can then impact the inner wall of the tokamak, causing severe damage.
ITER is looking closely at this problem because the high plasma current (15 MA) makes it very difficult to avoid generating such a beam in the event of a disruption. A major reason for this is the so-called “avalanche” mechanism, which results from the fact that a runaway can convert a thermal electron into a new runaway (while remaining itself a runaway) by a sufficiently close collision. The simplest theory predicts that the gain in the population of runaways due to the avalanche (Gay) increases as the power of ten of the plasma current expressed in mega-amperes (Gav ≈ 10Ip[MA]). This expression shows the much greater importance of the avalanche in ITER (Gav~ 1015) compared with current machines (Gav ~ 103 or less). Understanding these phenomena, characterising them and studying processes that can lessen the consequences of disruptions (by massive injection of gas or rapid injection of fragmented ice cubes, for example) are very important areas of study for ITER and, more generally, for tokamaks.
However, this simple theory does not take into account the rapid vertical movement of the plasma during disruption, which the plasma position control system cannot handle. This movement results naturally from the vertically unstable magnetic configuration (due to plasma elongation) and the decay of the plasma current. The effect on runaway generation was recently investigated by IRFM researchers using the magnetohydrodynamics code JOREK [1]. As shown in the figure, the plasma moves vertically during disruption, leading initially closed magnetic surfaces (thin black contours) to gradually intersect the wall. The runaways present on these surfaces are then almost instantaneously lost in the wall (which happens without damage if the population of runaways is small enough at this stage).
Figure : Current density (colours) and magnetic surfaces (thin black contours) at two successive instants of a disruption in ITER simulated by the JOREK code.
This effect leads to a reduction in Gav of about 7 orders of magnitude compared with simulations carried out with another code, DREAM, which have been the reference until now [Vallhagen 2024]. The avoidance of runaway beams in ITER using the disruption mitigation system (based on the injection of fragmented ice cubes) could therefore be less difficult than expected, but the problem remains difficult because the Gav predicted by JOREK remains very large (~1010). New DREAM simulations that take this effect into account are currently underway and could provide new answers. Preliminary results show that in certain scenarios, the generation of a runaway beam is avoided whereas it was not previously the case, which is encouraging [Vallhagen 2025].
[1] The effect of vertical displacements on the runaway electron avalanche in ITER mitigated disruptions, DOI 10.1088/1741-4326/ad8d66