Electromagnetic Waves

Introduction to Nuclear Fusion. Prof. Dr. Yong-Su Na. How to heat up a plasma?. 2. Plasma Heating. http://iter.rma.ac.be/en/img/Heating.jpg. 3. Wave heating by resonance. 4. Electromagnetic Waves Tuning fork. Resonance KBS. 스펀지:목소리로 와인 잔 깨기. 2006.3.11 http://www.kbs.co.kr/end_progra m/2tv/enter/sponge/view/vod/13 86311_1027.html 5. Electromagnetic Waves. Tacoma Narrows Bridge (1940. 11. 4) 6. Electromagnetic Waves. Broughton Suspension Bridge. http://www.joysf.com/?mid=forum_sf&document_srl=4265290&page=5. 7. Electromagnetic Waves. Microwave oven (2.45 GHz) http://blog.naver.com/rlhyuny27?Redirect=Log&logNo=30029307561 http://cafe.naver.com/nadobaker.cafe?iframe_url=/ArticleRead.nhn%3Farticleid=82. 8. Electromagnetic Waves • Electron Cyclotron Resonance Heating (ECRH). Linear / Circular polarisation 9. Electromagnetic Waves Excitation of plasma wave (frequency ω) near plasma edge ⇓ wave transports power into the plasma center Antenna ω. 10 http://www.asc-csa.gc.ca/images/radarsat2_figure2_l_h.jpg. Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001. Resonance zone. Electromagnetic Waves Excitation of plasma wave (frequency ω) near plasma edge ⇓ wave transports power into the plasma center Antenna ω ⇓ absorption near resonance, e.g. ω ≈ ωc , i.e. conversion of wave energy into kinetic energy of resonant particles ⇓ Resonant particles thermalise. B. ω = ωc. qB ωc = m R. 11. Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001. Resonance zone. Electromagnetic Waves. Antenna ω. B KSTAR first plasma. ω = ωc. qB ωc = m R. 12. Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001. Waves in a plasma. 13. Plasma Waves • Considering externally driven perturbations in the magnetic and electric fields and in the current, relative to an equilibrium condition for a cold plasma w/o external magnetic fields.    1 ∂E ∇ × B = µ0 j + 2 c ∂t  Maxwell equation  ∂B ∇× E = − ∂t    2      ∂B  ∂j 1 ∂ E ∂ 2   ∇ × (∇ × E ) = ∇(∇ ⋅ E ) − ∇ E = −∇ ×   = − ∇ × B = − µ 0 − 2 2 ∂t c ∂t ∂t  ∂t  j ≡ ∑ ni qi ui. (. ). i.       ∂ u  i + (ui ⋅ ∇)ui  = ni qi ( E + ui × B) − ∇pi mi ni   ∂t      ∂ui ni qi2  ∂j ∂ui qi = ∑ ni qi =∑ E ⇒ = E ∂t ∂t mi ∂t mi i i. Equations of motion: isotropic pressure assumed. 14. Plasma Waves  2 2     ni qi  1 ∂ E 2  E − 2 2 ∇(∇ ⋅ E ) − ∇ E = − µ 0  ∑ c ∂t  i mi .   2   ∂j 1 ∂ E ∇(∇ ⋅ E ) − ∇ 2 E = − µ 0 − 2 2 ∂t c ∂t   ∂ui ni qi2  ∂j = ∑ ni qi =∑ E ∂t ∂t mi i i. 15. Plasma Waves  2 2     ni qi  1 ∂ E 2  E − 2 2 ∇(∇ ⋅ E ) − ∇ E = − µ 0  ∑ c ∂t  i mi       ni qi2   ω 2  2 E + 2 E − k (k ⋅ E ) + k E = − µ 0  ∑  c  i mi . Plane waves with space and time dependences. [. ].   exp i (k ⋅ r − ωt )  k : wave vector.  ∂ ∇ = ik , = −iω ∂t. ω : frequency k k||. k⊥ B0 External magnetic field 16. Plasma Waves  2 2     ni qi  1 ∂ E 2  E − 2 2 ∇(∇ ⋅ E ) − ∇ E = − µ 0  ∑ c ∂t  i mi       ni qi2   ω 2  2  E + 2 E − k (k ⋅ E ) + k E = − µ 0  ∑ c  i mi       ni qi2   ω 2  2  E − 2 E = 0 − k (k ⋅ E ) + k E + µ 0  ∑ c  i mi   → ()E = 0. Plane waves with space and time dependences. [. ].   exp i (k ⋅ r − ωt )  k : wave vector. ω : frequency. Determinant (...)= 0 → Disperison relation D(w, k) = 0 17. Plasma Waves  2 2     ni qi  1 ∂ E 2  E − 2 2 ∇(∇ ⋅ E ) − ∇ E = − µ 0  ∑ c ∂t  i mi       ni qi2   ω 2  2  E + 2 E − k (k ⋅ E ) + k E = − µ 0  ∑ c  i mi . •.   k || E. [. ].   exp i (k ⋅ r − ωt )  k : wave vector. ω : frequency ni qi2 ω = ∑ ≡ ω p2 ε 0 i mi. Plasma frequency. ω 2 = c 2 k 2 + ω p2. Plasma wave. 2. •. Plane waves with space and time dependences. 1.   k ⊥E. 18. Dispersion Relation • Plasma waves are solutions of disperison relation D(ω, k)=0. Generally: ω given by generator k|| given by antenna where k||>k||,Vacuum. Special cases: 1. k⊥→ 0 „cutoff“. solution: k⊥ = k⊥ (ω, k||). Perpendicular to magnetic field reflection tunnelling. 2. k⊥→ ∞ „resonance“ 19 http://www.srh.noaa.gov/srh/jetstream/atmos/ionosphere_max.htm. Dispersion Relation • Plasma waves are solutions of disperison relation D(ω, k)=0. Generally: ω given by generator k|| given by antenna where k||>k||,Vacuum. Special cases: 1. k⊥→ 0 „cutoff“. solution: k⊥ = k⊥ (ω, k||). Perpendicular to magnetic field reflection tunnelling http://www.srh.noaa.gov/srh/jetstream/atmos/ionosphere_max.htm. 2. k⊥→ ∞ „resonance“ 20 http://star.mk.co.kr/new/view.php?sc=40500009&year=2010&no=391063&mc=PT&mc=PT. Wave heating in a tokamak. 21. Electromagnetic Wave •. Ion Cyclotron Resonance Heating (ICRH): occurring only when two or more ion species are present ω ~ ωci, 30 MHz – 120 MHz (λ ~ 10 m). ωc1ωc 2 (1 + n2 m2 / n1m1 ). zi eB ω = , ωci = (m2 Z1 / m1Z 2 + n2 Z 2 / n1Z1 ) mi 2 ii. : Ion-ion resonance frequency. • Lower Hybrid (LH) Resonance Heating: ωci < ω < ωce, 1 GHz – 8 GHz (λ ~ 10 cm) 2 ≈ ω pi2 /(1 + ω pi2 / ωce2 ), ω pi2 >> ωci2 ω LH. •. Electron Cyclotron Resonance Heating (ECRH): ω ~ ωce, 100 GHz – 200 GHz (λ ~ mm) 2 2 ωUH ≈ ω pe + ωce2 22. ICRH – Wave Propagation ASDEX Upgrade. Alcator C-Mod. Re(Ey). Multiple current straps 23. ICRH – Wave Propagation. 24. https://www.burningplasma.org/newsandevents/?article=enews&issue=081507. Ion Cyclotron Resonance Heating • JET ICRH System. λ ~ 10 m. 25. Lower Hybrid Heating • JET LH System λ ~ 10 cm. 26. Electron Cyclotron Heating • KSTAR ECH System λ ~ mm. 27 Y. S. Bae et al, Fusion Science and Technology 52 321 (2007), 65 88 (2014). Alpha particle heating. 28. α-Particle Heating • Intrinsic self-heating by Coulomb collision of fusion α particles with plasma particles in D-T reactions. D + T → n (14.1 MeV ) + He 4 (3.5 MeV ) leaves plasma. • Heating power density: N D N T where. σv ∝ Ti. σv. heats plasma if sufficiently long confined. QDT 5. ⇒ peaked heating profile • α-particle loss mechanisms: field ripples MHD events e.g. Alfvèn Eigenmode (AE) A.V. Melnikov et al, NF 53 093019 (2013). 29. α-Particle Heating • DT-Experiments only in - JET - TFTR • with world records in JET: - Pfusion = 16 MW - Q = 0.64. 30. Current drive. 31. Non-inductive Current Drive • Asymmetric velocity distribution can be a side effect of plasma heating. ions electrons. j = ∑ qs ns ∫ v|| f (v|| ) dv s. • Needed for: Steady-state tokamak current profile control in tokamaks bootstrap current compensation in stellarators. 32. Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001. Neutral Beam Current Drive Tangential injection B. JT-60U high βp ELMy H-mode 33. Dirk Hartmann, “Plasma Heating”, IPP Summer School, IPP Garching, September 20, 2001. Heating and Current Drive Heating Scheme. Advantages. Disadvantages. OH. Efficient. Cannot reach ignition. NBI. Reliable. Close to torus, Negative ion source necessary. LH. Efficient current drive (CD). Antenna close to plasma, off-axis CD. ECRH. Reliable, Flexible Localised CD. Electron heating. ICRH. Ion heating Central heating. Antenna close to plasma, Antenna coupling 34.