ER15-CEA-09

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Kinetic modelling of runaway electron dynamics

Principal Investigator:

Yves Peysson (CEA)

Project Participants:

Girogos Anastassiou (NTUA), Jean-François Artaud (CEA), Adám Budai (BME), Joan Decker (CRPP), Ola Embréus (CU), Tünde Fülöp (CU), Eero Hirvijoki (CU), Kyriakos Hizanidis (NTUA), Yannis Kominis (NTUA), Taina Kurki-Suonio (AU), Philipp Lauber (IPP-Garching), Roland Lohner (BME), Jan Mlynár (IPP-Prag), Sarah Newton (CCFE), Emelie Nilsson (CEA), Gergely Papp (IPP-Garching), Gergo Pokol (BME), François Saint-Laurent (CEA), Cristian Sommariva (CEA), Adam Stahl (CU), Panagiotis Zestanakis (NTUA),

Participating Research Institutions:

Aalto University, Finland, BME – NTI, Budapest, Hungary, Chalmers University, Göteborg, Sweden, Culham Centre for Fusion Energy, UK, Institute for Plasma Physic, Prag, Czech Republic, IRFM-CEA, Cadarache, France, Max-Planck Institute for Plasma Physics, Garching, Germany, National Technical University of Athens, Greece, CRPP, Swiss Federal Institute of Technology, Switzerland

External Participants:

Eric Nardon (CEA), Cédric Reux (CEA),

Meeting:

The 3rd Runaway Electron Meeting (REM 2015) will takes place the 17-19th of June 2015 at Pertuis, France

All details (registration, accommodation, program,... ) will be soon available here .

EURO-fusion support:

For participants to the meeting who are also parts of the EURO-fusion Enabling Research project ER15-CEA-09, some travel expenses may be funded by the project ER15-CEA-09. Please fill the standard Mission Application form which is available here .

Objectives:

One of the most remarkable characteristics setting fusion plasmas aside from neutral gases is that the collisional friction force acting on suprathermal electrons decreases with the electron velocity. Therefore, in the presence of a parallel electric field larger than some critical value, electrons with sufficient initial velocity will be continually accelerated. The so-called runaway electrons may reach energies in the 10 MeV range [1,2].

As the critical field is proportional to the electron density, runaway electrons are generated in plasma regions of low density and/or large electric field. In particular, they can be produced in great numbers during plasma disruptions, when the rapid cooling associated with a thermal quench gives rise to a large parallel electric field. These runaways are sometimes rapidly lost during the subsequent current quench, and sometimes form a runaway beam [3]. This beam, which can carry a significant fraction of the initial current, can become unstable and hit the wall over a relatively small area, thereby creating great damage [4].

Understanding the runaway dynamics has been identified as a critical issue for ITER [5]. In present-day tokamaks also, the danger of runaway-induced damage often limits the range of operation parameters. The following questions can be formulated regarding runaway electron dynamics during disruptions: Under which conditions do disruptions give rise to a runaway beam? Can this process be prevented or mitigated ? Is it possible to transport runaway electrons as soon as they are generated ? If a runaway beam nonetheless forms, what are its characteristics, i.e. what is the electron energy distribution ? Is it possible to slow it down progressively ? What are the effects of mitigation techniques such as massive material injection ?

Answering all these questions ultimately requires a complete disruption simulator solving both a kinetic equation for the runaway dynamics, and a fluid-MHD evolution including massive gas or pellet injection, ionization physics, impurity transport, etc. This is a long term objective for the community. In the near future, it is necessary to improve separately both the kinetic description of runaways, which is the subject of the present project.

During disruptions, the generation of runaway electrons can be dominated by the so-called “avalanche process”, in which a head-on collision between an existing runaway electron and a slow electron can kick the latter into the runaway region [6]. Because the primary runaway electron is ultra relativistic, it can transfer a significant fraction of its initial energy to the secondary electron while keeping a velocity near the speed of light, thereby remaining in the runaway region.

Runaway electrons can therefore “multiply” through this avalanche process with an exponential growth. The secondary runaway generation being proportional to the density of existing runaway, the runaway dynamics can be highly non-linear. Consequently, small variations in the balance between runaway generation and runaway transport can lead to large differences in the resulting density of runaways, and determine whether a significant runaway beam is formed or not [3].

Yet, in most existing runaway models [7], the various processes governing the electron response to a parallel electric field – Spitzer (ohmic ) heating [8], Dreicer (primary) runaway generation [1,2], Rosenbluth avalanche (secondary) runaway generation [6], hot-tail formation [9] – are calculated separately, even though these mechanisms are all described by the same electron distribution function and are thus interdependent. In addition, runaway transport due to turbulence [10], resonant magnetic perturbation [11,12,13], kinetic instabilities [14, 15], etc, is often calculated based on a given electron distribution without any self-consistent interaction with the runaway generation.

The framework required to calculate runaway electron generation and transport self consistently is the electron kinetic equation. The linearized 3D relativistic finite-difference Fokker-Planck electron guiding-center code LUKE was primarily developed to calculate current-drive by RF waves [16,17]. Yet, with non-uniform grids and arbitrary time steps, it is particularly suited to the calculation of runaway dynamics. This project intends to make use of the code LUKE, GO [7] and CODE [21] and other tools to develop a new framework for realistic and quantitative runaway simulations.

References :
[1] H. Dreicer, Electron and Ion Runaway in a Fully Ionized Gas, I. Phys. Rev. 115, 238 (1959).</ref>
[2] H. Dreicer. Electron and Ion Runaway in a Fully Ionized Gas, II. Phys. Rev. 117, 329 (1960).
[3] T. Fülöp, H.M. Smith, G.I. Pokol. Magnetic field threshold for runaway generation in tokamak disruption. Phys. Plasmas 16, 022502 (2009).
[4] R. Nygren, et al. Runaway electron damage to the Tore Supra phase III outboard pump limiter. J. Nucl. Materials 241, 522 (1997).
[5] T.C. Hender, et al. Progress in the ITER physics basis. Nucl. Fusion 47, S128 (2007).
[6] M.N. Rosenbluth and S.V. Putvinski. Theory for avalanche of runaway electrons in tokamaks. Nucl. Fusion 37, 1355 (1997).
[7] T. Fehér, H. M. Smith, T. Fülöp, K. Gal. Simulation of runaway electron generation during plasma shutdown by impurity injection in ITER. Plasma Phys. Control. Fusion 53, 035014 (2011).
[8] R.S. Cohen, L. Spitzer and P. Routly. The electrical conductivity of an ionized gas. Phys. Rev. 80, 230 (1950).
[9] H. Smith, P. Helander, L.-G. Eriksson, and T. Fülöp. Runaway electron generation in a cooling plasma. Phys. Plasmas 12, 122505 (2005).
[10] R. Yoshino and S. Tokuda. Runaway electrons in magnetic turbulence and runaway current termination in tokamak discharges. Nucl. Fusion 40, 1293 (2000).
[11] G. Papp, M. Drevlak, T. Fülöp, P. Helander. Runaway electron drift orbits in magnetostatic perturbed fields. Nucl. Fusion 51, 043004 (2011).
[12] G. Papp, M. Drevlak, T. Fülöp and G. I. Pokol. The effect of resonant magnetic perturbations on runaway electron transport in ITER. Plasma Phys. Control. Fusion 54, 125008 (2012).
[13] L. Laurent and J. M. Rax Stochastic Instability of Runaway Electrons in Tokamaks, Europhys. Lett., 11 (3), pp. 219-224 (1990)
[14] A. Komar, G. I. Pokol and T. Fülöp. Electromagnetic waves destabilized by runaway electrons in near-critical electric fields. Phys. Plasmas 20, 012117 (2013).
[15] J.-M. Rax, L. Laurent and D. Moreau, Stochastic Instability of Relativistic Runaway Electrons Due to Lower Hybrid Waves, Europhys. Lett., 15 (5), pp. 497-502 (1991)
[16] J. Decker and Y. Peysson. DKE: A fast numerical solver for the 3D drift kinetic equation. Euratom-CEA Report EUR-CEA-FC-1736 (2004).
[17] Y. Peysson and J. Decker. Simulations of the rf-driven toroidal current in tokamaks. Fus. Sci.& Tech. 2014, 65, pp. 22-42.
[18] J. Decker and Y. Peysson and A. J. Brizard and F.-X. Duthoit, Orbit-averaged guiding-center Fokker-Planck operator for numerical applications, Phys. Plasmas, 2010, 17, 11, pp. 112513
[19] P. Lauber et al., J. Comput. Phys. 226/1, 447 (2007)
[20] S. D. Pinches et al., Comput. Phys. Commun. 111, 131 (1998)
[21] M. Landerman, A. Stahl and T. Fülöp, Numerical calculation of the runaway electron distribution function and associated synchrotron emission, Comp. Phys. Communications, 2014, 185, pp 847-855