Particle-in-cell Monte Carlo collision simulations of ICRF discharge initiation in tokamaks and stellerators

May 18, 2016, 2:45 PM
8h 15m



Mr Matej TRIPSKY (Laboratory for Plasma Physics-ERM/KMS, 1000 Brussels, Belgium)


M. Tripsky1,2, T. Wauters1, A. Lyssoivan1

1Laboratory for Plasma Physics-ERM/KMS, 1000 Brussels, Belgium

2Ghent University, Department of Applied Physics, 9000 Ghent, Belgium

The RFdinity1d3v particle-in-cell Monte Carlo collision (PIC-MCC) model is used to study discharges produced and sustained by ion cyclotron range of frequency (ICRF) waves in absence of plasma current for applications for wall conditioning (ICWC, Te=3−5eV, ne<1012cm−3) in superconducting fusion machines, for RF-assisted start-up in tokamaks and for target plasma production (ne=1013cm−3) in stellarators [1]. The model examines the breakdown phase of ICRF discharges, and its dependency on the RF discharge parameters (i) antenna input power Pi, (ii) RF frequency, (iii)~shape of the electric field and (iv) the neutral gas pressure (pH2).

The RFdinity1d3v PIC-MCC model (1D in displacements and 3D in velocity space) follows the motion of both electrons and ions in a narrow bundle of magnetic field lines close to the antenna straps, by the numeric Leapfrog schema. The charged particles are accelerated in the parallel direction with respect to the magnetic field BT by the Lorentz force resulting from the sum of two electric fields: (i) the vacuum RF electric field in front of the ICRF antenna ERFzERFz and (ii)~the electrostatic field EPzEPz determined by the solution of Poisson's equation. The toroidal profile of ERFz for each strap is in the present study approximated by the sum of two Gaussians with opposite sign centered around the two gaps between the strap and the antenna box. Earlier reported work employed ERFz profiles obtained by 3D CST Microwave Studio simulations with the actual design of the ICRF antenna [2]. The Poisson equation is solved for the toroidal charge density ϱ using the Fast Fourier Transform method respecting periodic boundary conditions. The charge density ϱ is obtained by a PIC approach, weighting the charges of each simulated particle on a toroidal cell-grid by b-spline functions of first order. For practical MC simulations of relevant electron densities, each of the simulated super-particles represents a number of real particles (both electrons or ions). In this stage of development, the model applies the Monte Carlo collision schema (MCCS) only on collisions between electrons and neutral hydrogen molecules (e−H2). The model includes 12 collisions grouped into 6 collision types (\textit{ionization, vibrational excitation, excitation, dissociation, dissociative ionization and elastic scattering}) [2]. The collision cross-sections are taken from [3]. We used the standard "null-collision" method applied in the PIC-MCC models with a constant collision frequency $\nu' = max(n_{H_2} \sigma^{e-H_2}T \upsilon)[5],toestimateafractionoftheelectronsthatundergocollisionswithinatimestep\Delta tas P{null}~=~1~-~\exp(- \nu' \Delta t)$ [5].

The most important improvement of the present model compared to our earlier work [2,4] concerns the acceleration of charged particles in the plasma-produced electric potential. The effect of EPz becomes important upon reaching intermediate densities ne≈1011m−3 that are still much lower than threshold densities for wave excitations (nSWe∼1013m−3). In contrast to the antenna vacuum RF field, ERFz which locates in the antenna area (LANT≈0.8m for one strap antenna) and oscillates with fixed shape and amplitude (E0≈0−100kV/m), EPz has a varying shape (resulting from the collective motions of the charged particles) and a varying amplitude (effect of the increasing density of the charged particles in time). Consequently, in the very early stage of discharge production when EPz is small, only a fraction of the electrons can access the area in front of the antenna to be accelerated by ERFz, most of the electrons (low energetic electrons) are reflected by the ponderomotive force at the edge of the antenna box. The amplitude of the EPz is below 1V/m for electron densities up to 1010m−3, and locates in the vicinity of the antenna area. As the magnitude of this potential increases in time, more electrons enter the antenna area for further acceleration by the ERFz. This effect is both visible by a dramatic increase in the electron multiplication rate and by a strong shift in the electron velocity distribution towards Maxwell distribution.

[1] A. Lyssoivan et al., Plasma Phys. Control. Fusion 54, 074014 (2012).

[2] M. Tripsky et al., Proceedings of the 21st Topical Conference 1689, California, USA (2015).

[3] D. Reiter, HYDHEL, Atomic and Molecular Data for EIRENE, Tech. rep., Fz-Juelich GmbH (2002).

[4] M. Tripsky et al., in European Conference Abstracts (ECA), 2014, vol. 38F, Berlin, Germany.

[5] V. Vahedi, M. Surendra, Computer Physics Communications 87 (1995).

Primary author

Mr Matej TRIPSKY (Laboratory for Plasma Physics-ERM/KMS, 1000 Brussels, Belgium)


Anatoli LYSSOIVAN (Laboratory for Plasma Physics, Ecole Royale Militaire-Koninklijke Militaire School, 1000 Brussels, Belgium, TEC Partner) J.-M. NOTERDAEME (Department of Applied Physics, Ghent University, Belgium) Michael VAN SCHOOR (Laboratory for Plasma Physics, Ecole Royale Militaire-Koninklijke Militaire School, 1000 Brussels, Belgium, TEC Partner) Tom WAUTERS (aboratory for Plasma Physics - Royal Military Academy)

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