T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 T. Hellsten 1, T. Bergkvist 1, T.Johnson 1, M. Laxåback 1 and L.-G. Eriksson 2 1 Euratom-VR association, Alfvén Laboratory, Royal Institute of Technology, SE Stockholm, Sweden 2 Association Euratom-CEA, F St. Paul lez Durance, France Self-consistent calculations of the distribution function and wave field during ICRF heating and global Alfven wave excitation

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Alfvén eigenmodes in JET during ICRH with +90° and -90° phasing of the antennae +90°-90° L.-G. Eriksson, et al Phys Rev. Lett 81 (1998) 1231 M. Mantsinen et al Phys. Rev. Lett. 84(2002).

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Evolution of drift orbits during ICRH, the effect of that  P  =n  /   E Interactions with waves propagating parallel to plasma current anti-parallel to plasma current 0.5MeV 1.0MeV 2.0MeV 0.5MeV 1.0MeV 2.0MeV T. Hellsten et al Phys. Rev. Lett. 1995

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego o ICRH phasing: trapped 3 He ions displaced outwards.  emission from turning points of trapped ions at cyclotron resonance +90 o ICRH phasing: trapped 3 He orbits pinched, then detrapped to co-current wide passing orbits at the low field side of the center Tomographic reconstruction of the  - emission profiles from JET Tomographic reconstruction by C. Ingesson V. G. Kiptily et al Nucl. Fusion 42(2001)999

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Simulation of Alfvén wave excitation by thermonuclear  -particles with ICRH. Energy distribution of ICRH and alpha particles similar. Details of the distribution function different not only damping. Heating with +90 o and -90 o in JET result in different excitations. ICRH de-correlate interactions with Alfvén waves Modelling of Alfvén wave excitation requires detailed calculation of the distribution function including ICRH and interactions with Alfvén modes.

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Wave particle interaction Resonance condition ICRH contribution

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 MHD and ICRH represent a one dimensional diffusion processes in the invariant space (E, P ,  ) MHD ICRH

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Wave-particle interactions at guiding centre drift frequencies will displace the orbit invariants along the curve and for cyclotron interactions along the curve

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Characteristics for ICRH

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Monte Carlo code FIDO for calculating the distribution function J. Carlson et al, “Theory of Fusion Plasmas” Varenna 1996, L.-G. Eriksson and P. Helander Phys. Plasmas (1994), T. Bergkvist et al 15th Topical Conf. On RF-power in Plasmas, Wyoming 2003.

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Trajectories of MHD modes and ICRH E PP  ICRH MHD Resonance

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Different behaviour of wave- particle interactions: Low amplitude slow diffusion High amplitude fast diffusion High amplitude non-linear bouncing

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Low amplitude slow diffusion MHD increments for n interactions during one decorrelation time  decorr, n  b =  decorr

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 High amplitude non-linear bouncing Bouncing frequency Excursions along the trajectory in phase space Assume the orbit to be randomly displaced along the MHD trajectory in the phase space in the interval |E-E res |<  E after an decorrelation time

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Amplitude of Alfvén eigenmode

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 SELFO -code Define equilibrium, antenna spectrum, power, type of MHD mode etc. Calculate wave field for ICRH (LION code 1 ) and amplitude of Alfvén eigenmode Calculate changes in orbit invariants by collisions, ICRH and MHD with the FIDO code Calculate dielectric tensors from distribution functions Output 1 LION code L. Villard et al, Computer Physics Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 SELFO -code 1 LION code L. Villard et al, Computer Physics Reports 4(1986)95 and Nucl. Fusion, 35(1995)1173 Define equilibrium, antenna spectrum, power, type of MHD mode etc. Calculate wave field for ICRH (LION code 1 ) and amplitude of Alfvén eigenmode Calculate changes in orbit invariants by collisions, ICRH and MHD with the FIDO code Define equilibrium, antenna spectrum, power, type of MHD mode etc. Output

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Simulation of distributionn function for different antenna phasing +90°-90° For +90° high energy de-trapped ions with non-standard orbits are formed. For -90° the high energy ions have lower energy and are trapped with the turning point close to the magnetic axis

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Comparison of the gamma emissitivity in the mid-plane z=0 between tomographic reconstructions (full line) dashed region (confidence interval) and the density of high-energy 3 He ions calculated with the SELFO code (boxes ) +90-phasing location of the excited TAE modes indicated -90-phasing SELFO code modelling by T. Johnson

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Initial energy given to the mode versus mode frequency

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Evolution of the mode amplitude

T. Hellsten IAEA TM Meeting on Energetic Particles, San Diego 2003 Conclusion The details of the the distribution function is important for the stability and growth of Alfvén eigenmodes. The decorrelation by RF-heating important for the non-linear growth of the Alfvén eigenmodes. SELFO code has been extended to self-consistent include the MHD and ICRH interactions.