# Computational plasma physics HT

## Mission

- develop the theory for the burning plasma core of a fusion reactor, including the effects of fast particles, MHD stability and the heating and current drive for plasma start-up and burn control,
- develop the tools for integrated Tokamak modeling for ITER coordinated by EFDA
- exploit commonalty in modelling and numerical tools with the Computational Low-Temperature Plasma Physics Group
- provide theoretical and modeling support to the FOM Tokamak Physics and Plasma Diagnostics Groups

## Programme

The programme is aimed at developing the theory for controlled burn of the ITER core plasma, including ITER scenario development. In collaboration with the EFDA Task Force on Integrated Tokamak Modeling, modeling tools are developed to describe the MHD behavior of the burning plasma and its control by localized electron cyclotron resonance heating (ECRH) and current drive (ECCD) at different levels of complexity.

The group collaborates closely with the DIFFER CPP-LT group exploiting common modeling and numerical tools.

The programme is funded by the FOM programme “Physics of burn control”. The work also forms part of the NWO-RFBR Centre of Excellence for Fusion Physics and Technology which coordinates the collaboration with the Russian Federation Institutes IAP, Ioffe and Kurchatov.

See Annual Report 2011 section Fusion Research - Computational Plasma Physics-High Temperature

#### Electron Cyclotron Wave Physics

In collaboration with the plasma turbulence group of Risø and the Institute of Applied Physics Nizhny Novgorod, the effects of plasma edge turbulence on electron cyclotron wave propagation are investigated. A benchmark experiment has been defined and the importance of edge turbulence for the ECCD power deposition and current drive profile in ITER is being quantified.

Fokker-Planck studies are performed of ECRH and ECCD inside magnetic islands. The main questions concern the power threshold for a nonlinear plasma response and the effects of time dependence introduced by plasma rotation. The ray-, beam-tracing and Fokker-Planck codes are being made available to the EFDA Integrated Tokamak Modelling platform.

#### Tearing mode physics and control

Theoretical modelling of tearing mode control based on the generalized Rutherford equation is continued. In particular, the consequences of the time dependence of the heating and current drive sources in rotating plasma are being investigated. Tearing mode control and EC Fokker-Planck codes are being merged (PhD Bircan Ayten).

To benchmark the generalized Rutherford equation against a more complete physics model, the 3D nonlinear reduced MHD code JOREK is implemented. Particular attention is paid to the stabilizing effects of (EC) heating and current drive inside the magnetic islands (PhD Diego De Lazzari).

The 3D nonlinear MHD modelling will be integrated step-wise with the ray- and beam-tracing codes and with the Fokker-Planck modelling. Integration of the MHD and ray-tracing codes will face new research challenges such as the effect of MHD instabilities (sawteeth, NTM, ELMs, …) on the EC wave propagation. This work will be performed in close collaboration with the IMP12 and IMP5 projects of the EFDA ITM taskforce. The long term aim of this work is the development of an integrated Fokker-Planck – MHD modelling capacity for tearing mode control by ECRH and ECCD.

#### Magneto-hydrodynamics of plasmas with equilibrium flow and sawteeth

Equilibrium flows have a large impact on the stable and unstable magneto-hydrodynamic spectrum. The MHD spectrum in the presence of flow is investigated with particular emphasis on the low frequency part (PhD Willem Haverkort). The consequences of flow for energetic particle modes is studied by the integrated suite of codes of FINESSE (equilibrium), PHOENIX (linear wave spectrum), and HAGIS (nonlinear energetic particle dynamics and quasi-linear wave) by EFDA Fusion Research Fellow Jan-Willem Blokland. This work will be extended towards the interaction of energetic particles with saw-teeth modes. Highly simplified models for the sawtooth cycle, based on Porcelli and Kadomtsev models, are being developed for the modelling of sawtooth control (PhDs Gert Witvoet en Menno Lauret, Tokamak Physics Group).

#### ELM modelling and the Low-High confinement mode transition

The general 0-D mathematical bi-furcation model that has been developed as a generic model for the L- to H-mode transition in Tokamaks will be applied to existing physical models of the L-H transition (PhD Wolf Weymiens). This includes the set up of a 1D transport model of the L-H transition. In addition, the inclusion of ELMs in the mathematical model is investigated. The use of both the full 3D MHD version of JOREK as well as of AMRVAC to the study of ELM control is investigated (PhDs Willem Haverkort and Bram van Es). For this purpose, AMRVAC is being adapted to the toroidal geometry of a tokamak. A particular problem that must be addressed in this context is the fact that the AMRVAC grid is not aligned with flux surfaces. This might impede the application of the code to the strongly anisotropic plasma behaviour of the high temperature plasma in a tokamak.

#### 1D Transport Code Modelling

The 1D transport code modelling focuses on the preparation of ITER discharge scenarios and the validation of the relevant physics models on current experiments like JET, AUG, DIII-D, and TS. Most of this work is carried out as contribution to the ITER Scenario Modelling activity of the EFDA ITM taskforce. Emphasis is on two main topics: the hybrid scenario and the current ramp.

In relation to the hybrid scenario, a validation of the q-profile dependence in the GLF23 transport model is performed on existing experiments (JET and ASDEX). In collaboration with CEA Cadarache, the quasi-linear gyrokinetic transport model QuaLiKiz is extended to regions of low magnetic shear. QuaLiKiz and GLF23 will be compared in modelling of JET, ASDEX, and ITER hybrids. Further opportunities for predictive modelling of ITER and/or JT- 60SA, as well as participation in q-profile shaping experiments in European tokamaks, will be exploited (PhD Jonathan Citrin).

The current ramp phase in JET, AUG, TS, and DIII-D has been modelled. Special attention is paid to the modelling and optimization of the JET current ramp-up to access the hybrid scenario and the subsequent current diffusion during the hybrid phase itself. The results are applied to the modelling of the current ramp up towards both the ITER 15 MA baseline scenario as well as towards an ITER hybrid scenario. The contribution to the JET experimental campaigns for 2011/12 is focused on the current rise phase, looking at access to current profiles as required for different discharge scenarios, and modelling q-profile control and the role of the q-profile for enhanced confinement (Dick Hogeweij).

A simple ‘Tokamak Flight Simulator’ solving the 1D energy transport and current diffusion equations on the basis of global scaling laws is being developed. The model obtained is mainly intended for educational purposes (VWO teacher Axel Westra).

## Scientific output 2010

#### Electron cyclotron wave physics

N. Bertelli, A.A. Balakin, E. Westerhof and M.N. Buyanova, ECCD calculations in ITER by means of the quasi-optical code, Nuclear Fusion 50 115008.

N. Bertelli, A. A. Balakin, E. Westerhof, O. E. Garcia, A. H. Nielsen and V. Naulin, The influence of the edge density fluctuations on electron cyclotron wave beam propagation in tokamaks, Journal of Physics Conference Series accepted for publication.

#### Tearing mode control

B.A. Hennen, E. Westerhof, P.W.J.M. Nuij, J.W. Oosterbeek, M.R. de Baar, W.A. Bongers, A. Bürger, D.J. Thoen, M. Steinbuch and the TEXTOR team, Real-time control of tearing modes using a line-of-sight Electron Cyclotron Emission diagnostic, Plasma Physics and Controlled Fusion 52 (2010) 104006. Remark: joint publication TPG.

B. Ayten, D. De Lazzari, M.R. De Baar, B. Hennen, E. Westerhof, and the TEXTOR Team, Simulation of tearing mode suppression experiments in TEXTOR based on the generalized Rutherford equation, submitted to Nuclear Fusion.

D. De Lazzari, and E. Westerhof, The role of asymmetries in the growth and suppression of neoclassical tearing modes by localized heating and current drive, submitted to Plasma Physics and controlled Fusion.

#### Energetic particles and magneto-hydrodynamics

S K Nielsen, H Bindslev, M Salewski, A Bürger, E Delabie, V Furtula, M Kantor, S B Korsholm, F Leipold, F Meo, P K Michelsen, D Moseev, J W Oosterbeek, M Stejner, E Westerhof, P Woskov and the TEXTOR team, Fast-ion redistribution due to sawtooth crash in the TEXTOR tokamak measured by collective Thomson Scattering, Plasma Phys. Control. Fusion 52 (2010) 092001.

J.W. Haverkort, H.J. de Blank and B. Koren, Low-frequency Alfvén gap modes in rotating Tokamak plasmas, submitted to Plasma Physics and Controlled Fusion.

#### Transport code modelling

J. Citrin, J.-F. Artaud, J. Garcia, G.M.D. Hogeweij and F. Imbeaux, Impact of heating and current drive mix on the ITER hybrid scenario, Nuclear Fusion 50 115007

## Personnel

Egbert Westerhof, Group leader

Hugo De Blank, Senior scientist

Dick Hogeweij, Senior scientist (80%)

Vacancy (FP120), integration with ray-tracing and FP code

Bircan Ayten OiO, NTM modeling

Jonathan Citrin OiO, 1D transport code modeling and anomalous transport

Willem Haverkort OiO, ELM modelling

Bram van Es OiO, ELM modelling

Wolf Weymiens OiO, Nonlinear modelling of ELMs and the edge transport barrier

Delyan Zhelyazov OiO, Nonlinear modelling of ELMs and the edge transport barrier

Fabien Jaulmes OiO, MHD simulations