Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Global particle-in-cell imulation of Alfvénic mode Alexey Mihchenko, Axel Könie, Roman Hatzky Keyword: gyrokinetic, global particle-in-cell, Alfvén Eigenmode, fat-particle detabilization, Energetic Particle Mode Acknowledgment: J. Nührenberg, P. Helander Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Role of the fat particle Fuion born fat particle (3.5 MeV), NBI (.1 MeV), ICRH (1 MeV): characteritic time cale (e.g. tranit frequency ω t ) ω TAE effective reonant interaction/detabilization Bad new: outward tranport of fat particle non-even heat load on the wall + poible quenching of the fuion reaction Good new: weak detabilization MHD pectrocopy, alpha particle channeling (direct tranfer the energy of fuion alpha into ion without intermediate tep of lowing down on thermal electron) ALFVÉN MODE DYNAMICS IS IMPORTANT FOR FUSION Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Gyrokinetic Vlaov-Maxwell equation Linearized gyrokinetic Vlaov equation: δf t + R () δf R + δf v() = R (1) F v R F v(1) v Gyrocenter equation of motion (p -formulation): ( Ṙ = v q ) m A b + 1 b [ µ B + q ( φ v qb A )] v = 1 m [ µ B + q ( φ v A )] b The gyro-averaged potential are defined a uual: dθ dθ φ = 2π φ( R + ρ), A = 2π A ( R + ρ) Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Gyrokinetic Vlaov-Maxwell equation Gyrokinetic quaineutrality equation and parallel Ampére law (p -formulation): q 2n ρ 2 φ = q δn T =i,f =i,e,f ˆβ 2 A = µ δj =i,e,f ρ 2 =i,e,f The gyrocenter perturbed denity and current: δn = d 6 Z δf δ( R + ρ x), δj = q d 6 Z δf v δ( R + ρ x) The background denitie atify the quaineutrality equation q n = =i,e,f Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Numerical approach linear δf- particle-in-cell (PIC) method field dicretization uing B-pline phae factor tranform Fourier tranform in the direction of ymmetry mot eriou numerical problem to olve for electromagnetic calculation: cancellation problem iterative olution of Ampere law to cancel unphyical adiabatic current detailed decription: R. Hatzky, A. Könie, and A. Mihchenko, J. Comp. Phy. 255, 568 (27) Similar to Y. Chen and S. Parker approach Performance optimization: parallel efficiency 97%, 496 core, Blue Gene/P (weak caling) Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Tokamak configuration.8 q 1.85 1.8 Here, the gap i formed ω, x 1 6 rad/.7.6.5.4 PIC TAE MHD TAE 1.75.3 1.7.1.2.3.4.5.6.7.8.9 1 r / r a.2.2.4.6.8 1 Large-apect-ratio, circular cro-ection Major radiu R = 1 m, minor radiu r a = 1 m Magnetic field on the axi B = 3. T, Flat bulk-plama temperature and denity (β bulk.18%) Toroidal mode number n = 6 Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Time ignal 4e-13 2e-13 2e-2 1e-2 Re (φ) Re (A ) -2e-13-1e-2-4e-13.2.3.4.5.6 time, -2e-2.2.3.4.5.6 time, Time ignal reulting from the PIC imulation. Dominant harmonic in φ have the ame phae. Dominant harmonic in A have the oppoite phae. Thi correpond to the property E. Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Radial tructure 1.5e-13 2.5e-2 2e-2 φ 1e-13 A 1.5e-2 5e-14 1e-2 m = 9 m = 12 5e-21 m = 9 m = 12.2.4.6.8 1.2.4.6.8 1 Radial pattern reulting from the PIC imulation (in ome particular point of time) It reemble a typical TAE tructure. Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation The fat-particle profile 2 1.75 4 3 - dn f /dr - (dn f /dr) / n f n f / n f 1.5 1.25 1.75 2 1.5.2.4.6.8 1.2.4.6.8 1 Nonuniform fat-particle denity i ued to drive the mode Poition of max. d ln n f /dr coincide with the poition of the gap The fat-particle temperature i flat Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Fat-particle denity weep ω, x 1 6 rad/.9.8.7.6.5.4.3 table TAE β fat < β bulk EPM (I) β fat > β bulk untable TAE continuum gap continuum 1e+16 1e+17 1e+18 n f [m -3 ], T f =.4 MeV γ, x 1 3 rad/ 4 3 2 1 PIC hybrid-mhd table TAE β fat < β bulk EPM (I) β fat > β bulk untable TAE continuum gap 1e+16 1e+17 1e+18 n f [m -3 ], T f =.4 MeV TAE detabilized by fat particle. It i continuouly modified into EPM a the drive increae. Hybrid-MHD calculation (CAS3D-K) overetimate the growth rate (FLR and FOW are neglected in CAS3D-K) Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Energetic Particle Mode (Type I) φ 1e-7 5e-8 m = 9 m = 12 A 4e-15 3e-15 2e-15 1e-15 m = 9 m = 12 EPM (Type I) β f 1.8% n f = 1 18 m 3 T f =.4 MeV.2.4.6.8 1.2.4.6.8 1 φ 1.5e-13 1e-13 5e-14 m = 9 m = 12 A 2.5e-2 2e-2 1.5e-2 1e-2 5e-21 m = 9 m = 12 table TAE (no fat particle) β f =.2.4.6.8 1.2.4.6.8 1 Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Fat-particle temperature weep (I).46 reonance (v thf = v A / 3).44 3 ω (MHz).42.4.38.36 EPM (II) untable TAE gap continuum γ (khz) 2 1 continuum gap FOW tabilization k perp ρ E ~ 1.34 2e+5 4e+5 6e+5 8e+5 1e+6 1.2e+6 T f [ev] (β f kept cont) 2e+5 4e+5 6e+5 8e+5 1e+6 1.2e+6 T f [ev] (β f kept cont) Dependency on the fat-particle temperature (β f =.134% kept contant) Detabilization i mot effective near the reonance v thf v A /3 At large T f, finite-orbit-width (FOW) tabilization i een At maller T f (larger n f to keep β f contant), an EPM appear Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Untable Toroidal Alfvén Eigenmode φ 2e-11 1.5e-11 1e-11 5e-12 m = 9 m = 12.2.4.6.8 1 A 1e-18 5e-19 m = 9 m = 12.2.4.6.8 1 untable TAE β f.134% n f =.5 1 17 m 3 T f =.6 MeV φ 1.5e-13 1e-13 5e-14 m = 9 m = 12 A 2.5e-2 2e-2 1.5e-2 1e-2 5e-21 m = 9 m = 12 table TAE (no fat particle) β f =.2.4.6.8 1.2.4.6.8 1 Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Energetic Particle Mode (Type II) φ 6e-13 4e-13 2e-13 m = 9 m = 12.2.4.6.8 1 A 4e-2 3e-2 2e-2 1e-2 m = 9 m = 12.2.4.6.8 1 EPM (Type II) β f.134% n f = 6 1 17 m 3 T f =.5 MeV φ 1.5e-13 1e-13 5e-14 m = 9 m = 12 A 2.5e-2 2e-2 1.5e-2 1e-2 5e-21 m = 9 m = 12 table TAE (no fat particle) β f =.2.4.6.8 1.2.4.6.8 1 Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Energetic Particle Mode (Type II) ω, x 1 6 rad/.8.7.6.5.4 PIC TAE MHD TAE n=-6.3 EPM (II).2.2.4.6.8 1 Location and frequency of the EPM mode are determined by continuum Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation Fat-particle temperature weep (II).48 5 ω, x 1 6 rad/.46.44.42.4 continuum gap γ, x 1 3 rad/ 4 3 2 1 PIC, with FLR PIC, w/o FLR hybrid-mhd.38 continuum 2e+5 4e+5 6e+5 8e+5 T f [ev], (n f fixed) 1e+5 2e+5 3e+5 4e+5 5e+5 6e+5 7e+5 8e+5 T f [ev], (n f fixed) The fat-particle denity n f =.75 1 17 m 3 i kept contant The mode frequency remain in the gap (no modification into the EPM) At larger temperature, FOW tabilization can be een Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Fat particle. Untable Alfvén mode. Summary. Fat-particle detabilization of the TAE mode ha been modelled with PIC code A tranformation of the TAE mode into the EPM intability if the drive i large enough ha been oberved Next tep Benchmarking: ORB5, LIGKA, GENE (global), GTC (?) Numerical equilibria, maller apect ratio (more reactor-like) Alexey Mihchenko IPP Greifwald, Stellaratortheorie
Max-Planck-Intitut für Plamaphyik, EURATOM Aociation WENDELSTEIN 7-X Global particle-in-cell imulation of Alfvénic mode Alfvén-ound coupling (BAE...), Alfvén cacade Kink mode, microtearing mode Nonlinear effect nonlinear TAE/EPM phae-pace dynamic (avalanche, pontaneou hole-clump pair creation, etc) nonlinear TAE-EPM aturation Alfvén Eigenmode + fat particle in tellarator (MAE, GAE, HAE etc) Alexey Mihchenko IPP Greifwald, Stellaratortheorie