Stochastic diffusion of energetic ions in Wendelstein-line stellarators: Numerical validation of theory predictions and new findings

Abstract

Stochastic motion of 3.5-MeV alpha particles with orbits that vary between locally trapped and locally passing states (transitioning particles) in a Helias reactor is observed numerically for the first time. This validates theory prediction that the collisionless stochastic diffusion of these particles represents a mechanism of considerable delayed loss of fast ions in quasi-isodynamic stellarators [Beidler et al., Phys. Plasmas 8, 2731 (2001)]. The numerical calculation has also demonstrated a possibility to prevent the escape of particles to the wall by making the separatrix between the locally trapped and passing states closed, as was proposed in Tykhyy et al. [Plasma Phys. Control. Fusion 49, 703 (2007)]. It is found that stochastic regions can vary from very narrow to very wide that occupy almost the whole plasma cross section. It is shown that the fraction of alpha particles with closed separatrix in the population of transition alphas can be considerable. Potentially, this fraction can be increased, and the number of transitioning particles can be reduced by a special optimization of the magnetic configuration, which decreases delayed losses of alphas by means of reducing the separatrix maximum radius.

Alpha particle confinement metrics based on orbit classification in stellarators

“…in Kolesnichenko et al. 2022), but also regular. At the same time, ideal orbits are never transient.…”

“…The backward transition ('detrapping') is the inverse process where the domain of bounce motion abruptly increases. In both transitions of the second kind, the guiding-centre orbit crosses the separatrix of one-dimensional bounce motion (Kolesnichenko, Lutsenko & Tykhyy 2022) which results in the abrupt change of the parallel adiabatic invariant. Thus, 'transient' orbits are defined as those which undergo these class transitions of the second kind.…”

“…In the full guiding-centre model, where the bounce phase is retained, transient orbits cannot only be chaotic (as for the ones studied, e.g. in Kolesnichenko et al 2022), but also regular. At the same time, ideal orbits are never transient.…”

Confinement of transitioning particles in bi-helical Wendelstein-type configurations

“…Nevertheless, numerical modelling shows that a significant fraction of trapped energetic particles suffer delayed losses (Lotz et al 1992;Drevlak et al 2014). These delayed losses, which occur on timescales much larger than the drift timescale, have been theorised to occur due to stochastic diffusion Tykhyy 2018), as particles drifting between magnetic field lines repeatedly become trapped in or escape from local magnetic wells associated with the mirror harmonic of the magnetic field; this hypothesis has recently been corroborated by numerical simulations following orbits of individual particles over an extended period (Kolesnichenko, Lutsenko & Tykhyy 2022). Note that stellarator-based reactor designs assume high alpha heating efficiencies: 90 % or even 95 % (see, e.g., Sagara, Igitkhanov & Najmabadi 2010).…”

“…This approximation is rather good in the plasma core of Wendelstein-type configurations: with suitable values of k i , deviations of harmonics from (2.9a-e) do not exceed 5 % when r/a < 0.5, which is of the same order as the minor harmonics not included in the model magnetic field (2.1), and its simplicity allows us to obtain analytical expressions characterising the separatrix. With the harmonics given by (2.9a-e), (2.5) at ϑ = {0, π} reduces to a quadratic equation in x with the roots (Kolesnichenko et al 2022)…”