Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Introduction to the Diagnosis of Magnetically Confined Thermonuclear Plasma Introduction J. Arturo Alonso Laboratorio Nacional de Fusión EURATOM-CIEMAT E6 P2.10 arturo.alonso@ciemat.es version 0.1 (February 12, 2013) Introduction, A. Alonso, copyleft 2010 1 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Outline Relevant physical parameters for thermonuclear fusion 1 Relevant physical parameters for Magnetic Confinement 2 Fusion 3 Plasma regions and typical parameters Introduction, A. Alonso, copyleft 2010 2 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Outline Relevant physical parameters for thermonuclear fusion 1 Relevant physical parameters for Magnetic Confinement 2 Fusion 3 Plasma regions and typical parameters Introduction, A. Alonso, copyleft 2010 3 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary To fuse hydrogenic atoms Nuclear fusion aims at the production of energy through the fusion of light atoms to yield products that carry the mass defect in the form of kinetic energy. For the D - T case the reaction rate peaks at ∼ 800 keV = 10 9 K. Fusion reactants are in a Plasma State The energetics of this reaction is D + T → He 4 ( 3 . 52MeV ) + n ( 14 . 06MeV ) . Tritium supply is addressed by a Lithium "breeding blanket" Li 6 + n → He 4 + T + 4 . 8MeV . Introduction, A. Alonso, copyleft 2010 4 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Fusion Power Balance The power balance of a fusion reactor involves different energy sources and sinks that balance in steady state S α + S h = S B + S κ . Where S α fusion-produced α -particle heating power S h input heating power (generaly ohmic and auxiliary as microwave or radio frequency injection) S B Bremstralung radiation (EM radiation emited in ion-electron Coulomb collisions) S κ diffusive heat flux through the plasma boundary Introduction, A. Alonso, copyleft 2010 5 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Fusion Power Balance The power balance of a fusion reactor involves different energy sources and sinks that balance in steady state S α + S h = S B + S κ . Expressions for the sources and sinks can be obtained under certain approximations [Freidberg(2008)] p 2 � σ v � p T 2 p 2 , S α = K α S B = K B T 3 / 2 , S κ = K κ , τ E where the K factors are known constants and T and p = nT are the plasma temperature and pressure respectively a . a The last of the above equation is a definition of the energy confinement time τ E , that can be obtained experimentally, rather than a physics-based expression for the heat flux through the plasma boundary. Introduction, A. Alonso, copyleft 2010 5 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Ignition Condition The ignition condition is reached when the α -heating by itself is sufficient to counterbalance the losses, i.e., S α ≥ S B + S κ . Using the above expressions this leads to K κ T 2 p τ E ≥ K α � σ v � − K B T 1 / 2 where p τ E is known as a the Lawson parameter. minimum T to ignite the plasma, T ≥ 4 . 4 keV . for lager T minimum p τ E ( p τ E ) min = 8 . 3 atm s @ T min = 15 keV Introduction, A. Alonso, copyleft 2010 6 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Sumarising. . . The above discussion is meant to illustrate the importance of several plasma parameters, Temperature T Density n = n e = n i (plasma neutrality) Pressure p = p i + p e = 2 nT (for isothermal plasma) In the next section, we will see how the Magnetic Confinement approach to fusion addresses the problem of confining a thermonuclear plasma : how MC attempts to make τ E sufficiently long. This will bring other plasma physics parameters that are fundamental to ensure that the plasma can approach (an eventually, probably in ITER, reach) ignition. Introduction, A. Alonso, copyleft 2010 7 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Outline Relevant physical parameters for thermonuclear fusion 1 Relevant physical parameters for Magnetic Confinement 2 Fusion 3 Plasma regions and typical parameters Introduction, A. Alonso, copyleft 2010 8 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Embeding the plasma in a strong B -field (Remember the Lorentz force is F = q v × B ). Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Embeding the plasma in a strong B -field (Remember the Lorentz force is F = q v × B ). Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Embeding the plasma in a strong B -field (Remember the Lorentz force is F = q v × B ). Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Not any field structure works! → needs nested magnetic surfaces. 0.2 0 −0.2 1.5 1 1.5 0.5 1 0 0.5 −0.5 0 −0.5 −1 −1 −1.5 −1.5 Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Not any field structure works! → needs nested magnetic surfaces. Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary The Magnetic Confinement approach to Fusion Fast, nearly unrestricted particle movement along the field lines, the thermodynamic fields flux functions, f ( ψ ) . T , T n , n i e i e Flux Label Flux Label Introduction, A. Alonso, copyleft 2010 9 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Equilibrium and Stability The pressure gradient thus formed is counterbalanced by the Lorentz force, i.e, to first order j × B = ∇ p , (1) where j is the electric current density present in the plasma and B is the magnetic field → design requirement for MCF devices to be able to maintain a stable equilibrium of this form (Grad-Shafranov equation). Important to have spatialy resolved measurements. To ensure stability well time resolved measurements are necesary. Real-time control to make a soft landing if things get hairy. Introduction, A. Alonso, copyleft 2010 10 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Transport Provided a stable plasma equilibrium exists, the next problem is to control the radial transport of particles and energy 1 Neoclassical transport generally depends on the magnetic field topology and the plasma profiles, for instace [Helander and Sigmar(2002), page 170] � 1 � dT i 0 · ∇ ψ = − ( IB κ i ∧ ) 2 1 q PS B 2 − dr . i κ i � B 2 � � Turbulent transport is generally attributed to the advection of heat and density by the fluctuating E × B velocity, i.e., the turbulent particle flux is given by v r � = 1 n ˜ Γ turb = � n ˜ B � ˜ E θ � . 1 The mesured radial transport is generally substantially greater than the NC transport estimations. This discrepancy is attributed to the presence of micro-instabilities. Introduction, A. Alonso, copyleft 2010 11 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Outline Relevant physical parameters for thermonuclear fusion 1 Relevant physical parameters for Magnetic Confinement 2 Fusion 3 Plasma regions and typical parameters Introduction, A. Alonso, copyleft 2010 12 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Plasma Regions Core innermost region of the plasma column where the CORE Edge conditions for fusion are to be met. SOL Edge transition region between the central plasma and the walls with strong gradients. SOL (Scrape-Off Layer) outermost plasma region, where field lines terminate in a material surface. Introduction, A. Alonso, copyleft 2010 13 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Limited and Diverted Plasmas (I): definition There are two ways to limit the plasma column extent A limiter is a solid body that concentrate the interaction with the plasma by intersecting the field lines. By modifying the magnetic topology at the edge of to divert field lines to a distant wall region (divertor). Introduction, A. Alonso, copyleft 2010 14 / 23
Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary Limited and Diverted Plasmas (I): definition Introduction, A. Alonso, copyleft 2010 15 / 23
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