Multi-phase simulation of fast ion profile flattening due to Alfvén eigenmodes in a DIII-D experiment

A multi-phase simulation that is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid is developed to simulate the nonlinear dynamics on the slowing down time scale of the energetic particles. The hybrid simulation code is extended with realistic beam deposition profile, collisions and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111, the stored beam ion energy is saturated due to Alfven eigenmodes (AE modes) at a level lower than in the classical simulation. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. It is demonstrated that the fast ion spatial profile is significantly flattened due to the interaction with the multiple AE modes with amplitude v/vA ~ δB/B ~ O(10−4). The dominant AE modes are toroidal Alfven eigenmodes (TAE modes), which is consistent with the experimental observation at the simulated moment. The amplitude of the temperature fluctuations brought about by the TAE modes is of the order of 1% of the equilibrium temperature. This is also comparable with electron cyclotron emission measurements in the experiment.

[1]  L. L. Lao,et al.  Separation of β̄p and ℓi in tokamaks of non-circular cross-section , 1985 .

[2]  R. Nazikian,et al.  Fast ion induced shearing of 2D Alfvén eigenmodes measured by electron cyclotron emission imaging. , 2011, Physical review letters.

[3]  Christopher Portier,et al.  Risk factors for childhood leukaemia. Discussion and summary. , 2008, Radiation protection dosimetry.

[4]  J. Park,et al.  Alfvén eigenmode stability and fast ion loss in DIII-D and ITER reversed magnetic shear plasmas , 2012 .

[5]  S. Mahajan,et al.  Kinetic theory of toroidicity-induced alfvén eigenmodes , 1992 .

[6]  R. Budny,et al.  A STANDARD DT SUPERSHOT SIMULATION , 1994 .

[7]  M. Pekker,et al.  Simulation of Alfven wave-resonant particle interaction , 1995 .

[8]  Robert G. Littlejohn,et al.  Variational principles of guiding centre motion , 1983, Journal of Plasma Physics.

[9]  A. Napartovich,et al.  Non-thermal plasma instabilities induced by deformation of the electron energy distribution function , 2014 .

[10]  Donald A. Spong,et al.  Linearized gyrofluid model of the alpha‐destabilized toroidal Alfvén eigenmode with continuum damping effects , 1992 .

[11]  W. Heidbrink,et al.  Particle distribution modification by low amplitude modes , 2010 .

[12]  K. Shinohara,et al.  Role of convective amplification of n = 1 energetic particle modes for N-NB ion dynamics in JT-60U , 2013 .

[13]  W. Heidbrink,et al.  Particle simulation of energetic particle driven Alfvén modes in NBI heated DIII-D experiments , 2009 .

[14]  R. White,et al.  Beam Distribution Modification By Alfven Modes , 2010 .

[15]  Zhihong Lin,et al.  Verification and validation of linear gyrokinetic simulation of Alfvén eigenmodes in the DIII-D tokamak , 2012 .

[16]  H. Berk,et al.  Simulation of Alfvén eigenmode bursts using a hybrid code for nonlinear magnetohydrodynamics and energetic particles , 2012 .

[17]  R. White,et al.  Anomalous flattening of the fast-ion profile during Alfvén-Eigenmode activity. , 2007, Physical review letters.

[18]  L. Chen,et al.  Theory and simulation of discrete kinetic beta induced Alfvén eigenmode in tokamak plasmas , 2010 .

[19]  K. Watanabe,et al.  Magnetohydrodynamic Vlasov simulation of the toroidal Alfven eigenmode , 1995 .

[20]  Neville C. Luhmann,et al.  Measurements and modeling of Alfvén eigenmode induced fast ion transport and loss in DIII-D and ASDEX Upgrade , 2011 .

[21]  Scott E. Parker,et al.  Three-dimensional hybrid gyrokinetic-magnetohydrodynamics simulation , 1992 .

[22]  H. Berk,et al.  Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands , 2012 .

[23]  Tetsuya Sato,et al.  Linear and nonlinear particle-magnetohydrodynamic simulations of the toroidal Alfvén eigenmode , 1998 .

[24]  Herbert L Berk,et al.  Simulation of intermittent beam ion loss in a Tokamak Fusion Test Reactor experiment , 2003 .

[25]  G. Vlad,et al.  Hybrid magnetohydrodynamic‐gyrokinetic simulation of toroidal Alfvén modes , 1995 .

[26]  C. Domier,et al.  Gyrokinetic simulations of reverse shear Alfvén eigenmodes in DIII-D plasmas , 2012 .

[27]  V. Bobkov,et al.  Convective and diffusive energetic particle losses induced by shear Alfvén waves in the ASDEX upgrade tokamak. , 2010, Physical review letters.

[28]  W. Heidbrink,et al.  CORRIGENDUM: The behaviour of fast ions in tokamak experiments , 1994 .

[29]  Allen H. Boozer,et al.  Monte Carlo evaluation of transport coefficients , 1981 .

[30]  C. Holcomb,et al.  Measurements, modelling and electron cyclotron heating modification of Alfvén eigenmode activity in DIII-D , 2009 .