Particle Distribution Modification by TAE mode and Resonant Particle Orbits POSTECH 1, NFRI 1,2 M.H.Woo 1, C.M.Ryu 1, T.N.Rhee 1,,2

Outlines -Hybrid scheme:ideal MHD background and energetic particles -Tokamak Equilibrium and TAE -Distribution function modification by TAE -Resonance particle interactions with the TAE wave Bouncing, circulating and potato orbits -Conclusions

Hybrid Code Structure Equilibrium (EFIT data) Re-normalization of Equilibrium(Chease) TOKAMAK Experiment Ideal MHD Solution (KINX) Non-inductive heating & Alpha particle TRANSP Data etc. Hot Particle Distribution Mode Frequency & Growth rate Test Particle code (ORBIT) Monte-Carlo Distribution

Calculation of Mode Frequency Modification Dispersion Relation for TAE Calculation of Mode Growth Rate Mode Growth-rate All the values shown here can be estimated from Simulation Kinetic & Fluid Contributions

Why Hybrid Code ? Full Particle simulation is not available Saving computation time Individual particle trajectory Immediate validation & examination of analytical theory Essential issues about energetic particle Alpha particle heating Turbulence Limitations Only perturbative treatment Not fully self-consistent Scale larger than Gyro-radius Slow time scale behaviors ( Drift scale, Not gyration scale)

Ideal MHD mode

Relation between displacement and Magnetic perturbation Total PerturbationDominant m=1 Perturbation

Particle Distribution Modification by TAE mode

Electron distribution for ECRH Ion distribution for NBI Electron & Ion distribution for ICRH Fusion Born Alpha particle distribution b=0.1 Example: Initial Maxwellian distribution (2000 particles) in simulation b=8

Interpolation of test particle distribution Smooth radial and energy profile These equations are used for analytical calculation of mode frequency and growth rate

Initial Distribution First orbit loss of the particles Final Distribution Pitch Distribution Energy Distribution Energy is conserved Particles with pitch around 0 are dominantly lost Large bounce orbit is the main reason for loss

Radial Distribution Theta Distribution Radially flattened due to finite bounce orbit Barely trapped or circulating particles are mainly lost

For the perturbation Energy distribution Resonance line More particles near the resonance line. Some particles gain very high energy High energetic particles (>150 keV) are lost Radial distribution Particles near the edge are lost Flattened compared to the no B perturbation case

Particle loss due to perturbation Dominant particle loss begins around First orbit loss is about 40% In average, particle gains energy Energy gain process shows a jump

Circulating-Passing particles: High energy No perturbation Clear precession outward-shift of orbit parameters

Non-Circulating, passing particles Same parameters with low energy This is the orbit of the particle that interact most strongly with TAE mode

Particle trajectory with B perturbation Non-Resonant case, large perturbation Orbit modification is not much.

Resonant case with small perturbation Particle has a little bit smaller velocity Particles are lost due to resonant interaction Wave phase velocity is about Here is alpha particle velocity

Resonant case with small perturbation -jumping orbit A sudden jump to other smaller orbit

Resonant case with small perturbation- jumping orbit For a very small perturbation, resonant particles change the direction of the movement, jumping to other stable orbit with pitch reversed.

Detailed Motion of Resonant Particles Phase trajectories of particles with different pitches Bouncing Potato Circulating

Conclusions Modification of particle distribution by the TAE mode is under investigation. A hybrid scheme of ideal MHD and energetic particle motion is used. Particles tend to jump from one orbit to other stable orbit Resonant particles interacting with TAE strongly mainly come from the potato orbit. Some particles with low pitch gain large energy and move in the reverse direction.

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