Hybrid finite-volume/Monte Carlo methods in nuclear fusion

Together with Tine Baelmans from the Thermal and Fluids Engineering group, we are working on new numerical methods for the simulation of the plasma edge in next-step nuclear fusion devices.

Two types of particles are modeled in plasma edge codes: the plasma, consisting of charged particles (ions and electrons), and the neutral particles. The plasma can usually be described with a Navier-Stokes-like fluid model, discretized in space with a suitable finite volume (FV) method. For the neutrals, however, a more microscopic, kinetic description is necessary, in which the particle distribution is modeled in a position-velocity phase space. This is because the neutral gas is so rarefied that the fluid approach does not hold for this component. Further, the velocity distribution of the neutral particles is typically so far from equilibrium that a fluid description, based on density, momentum and energy, is not sufficiently accurate. Due to the additional dimensions in velocity space, the kinetic neutral model is solved via Monte Carlo (MC) simulation.

Since the plasma and neutral particles interact with each other, the corresponding models need to be coupled, leading to serious computational bottlenecks. Using present-day stopping criteria, simulations for DEMO last approximately 1 year.  We are developing and analyzing new computational methods that alleviate the following main problems:

  1. The statistical noise introduced by the Monte Carlo simulation on the computed neutral density, and – via the coupling – also on the computed plasma solution.
  2. The increasing importance of simulating in a so-called ‘detached
    regime’, in which there is increased interaction of the neutrals with the ions, leading to excessive computation times if each individual interaction needs to be resolved.
  3. High variance on the simulations because neutral particles that are launched from the target into the interior of the fusion reactor don’t penetrate very far into the plasma. This leads to a high variability of the computed source terms  in the interior of the reactor.

Recent publications

  1. M. Baeten, K. Ghoos, M. Baelmans, G. Samaey, Analytical study of statistical error in coupled finite-volume/Monte-Carlo simulations of the plasma edge, Contributions to Plasma Physics, 2018. In press.
  2. W. Dekeyser,  M. Blommaert, K. Ghoos, N. Horsten, P. Boerner, G. Samaey, M. Baelmans, Divertor design through adjoint approaches and efficient code simulation strategies, Contributions to Plasma Physics, 2018. In press.
  3. N. Horsten, G. Samaey, and M. Baelmans, Development and assessment of 2D fluid neutral models that include atomic databases and a microscopic reflection model, Nuclear Fusion 57:116043, 2017.
  4. M. Baelmans, K. Ghoos, P. Börner and G. Samaey, Efficient code simulation strategies for B2-EIRENE, Nuclear Materials and Energy 12:858-863, 2017.
  5. N. Horsten, W. Dekeyser, G. Samaey and M. Baelmans, Assessment of fluid neutral models for a detached ITER case, Nuclear Materials and Energy 12: 869-875, 2017.
  6. K. Ghoos, W. Dekeyser, G. Samaey and M. Baelmans, Accuracy and convergence of coupled finite-volume/Monte-Carlo codes for plasma edge simulations of nuclear fusion reactors, Journal of Computational Physics 322:162–182, 2016.
  7. N. Horsten, W. Dekeyser, G. Samaey, P. Börner and M. Baelmans, Fluid neutral model for use in hybrid simulations of a detached case, Contributions to Plasma Physics 56:610-615, 2016.
  8. N. Horsten, W. Dekeyser, G. Samaey and M. Baelmans, Comparison of fluid neutral models for 1D plasma edge modelling with a finite volume solution of the Boltzmann equation, Physics of Plasmas 23:012510, 2016.
  9. K. Ghoos, W. Dekeyser, G. Samaey, P. Börner, D. Reiter and M. Baelmans, Accuracy and convergence of coupled finite-volume/Monte-Carlo codes for plasma edge simulations, Contributions to Plasma Physics, 2016. In press.