Introduction to the Diagnosis of Magnetically Confined Thermonuclear - - PowerPoint PPT Presentation

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

1

Relevant physical parameters for thermonuclear fusion

2

Relevant physical parameters for Magnetic Confinement 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

1

Relevant physical parameters for thermonuclear fusion

2

Relevant physical parameters for Magnetic Confinement 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 = 109 K. Fusion reactants are in a Plasma State The energetics of this reaction is D + T → He4(3.52MeV) + n(14.06MeV) . Tritium supply is addressed by a Lithium "breeding blanket" Li6 + n → He4 + 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 Sα + Sh = SB + Sκ . Where Sα fusion-produced α-particle heating power Sh input heating power (generaly ohmic and auxiliary as microwave or radio frequency injection) SB Bremstralung radiation (EM radiation emited in ion-electron Coulomb collisions) Sκ 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 Sα + Sh = SB + Sκ . Expressions for the sources and sinks can be obtained under certain approximations [Freidberg(2008)] Sα = Kα σv T2 p2 , SB = KB p2 T3/2 , Sκ = Kκ p τE , where the K factors are known constants and T and p = nT are the plasma temperature and pressure respectively a.

aThe last of the above equation is a definition of the energy confinement

time τE, 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., Sα ≥ SB + Sκ. Using the above expressions this leads to pτE ≥ KκT2 Kασv − KBT1/2 where pτE is known as a the Lawson parameter. minimum T to ignite the plasma, T ≥ 4.4 keV . for lager T minimum pτE (pτE)min = 8.3 atm s @Tmin = 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 = ne = ni (plasma neutrality) Pressure p = pi + pe = 2nT (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 τE 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

1

Relevant physical parameters for thermonuclear fusion

2

Relevant physical parameters for Magnetic Confinement 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 = qv × 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 = qv × 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 = qv × 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.

−1.5 −1 −0.5 0.5 1 1.5 −1.5 −1 −0.5 0.5 1 1.5 −0.2 0.2

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

i e

n , n

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 energy1 Neoclassical transport generally depends on the magnetic field topology and the plasma profiles, for instace [Helander and Sigmar(2002), page 170] qPS

i

· ∇ψ = −(IBκi

∧)2

κi

• 1

B2 − 1 B2 dTi0 dr . 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 Γturb = n˜ vr = 1 B˜ n˜ Eθ .

1The 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

1

Relevant physical parameters for thermonuclear fusion

2

Relevant physical parameters for Magnetic Confinement 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 conditions for fusion are to be met. Edge transition region between the central plasma and the walls with strong gradients. SOL (Scrape-Off Layer)

• utermost plasma region,

where field lines terminate in a material surface.

CORE Edge SOL

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

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

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Limited and Diverted Plasmas (II): pros and cons

The main advantages of a diverted plasma are Plasma-wall interaction is kept away from the plasma core → much better main species and impurtity density control. Diverted SOLs tend to have larger connection lengths → allow to have substantially different plasma parameters in the divertor region and in the upstream SOL in ‘contact’ with the plasma EDGE. the main advantage of limiters is they are much simpler

Introduction, A. Alonso, copyleft 2010 16 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Plasma in the open field lines: the SOL

The radial extent of the SOL is determined by the competition of the particle parallel streaming to the material surfaces at sound speedand the particle’s diffusion perpendicular to the field line2.

2this and previous figure taken from [Pitts(2008)] Introduction, A. Alonso, copyleft 2010 17 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Plasma in the open field lines: the SOL

The lifetime of a particle in the SOL is τ = L/cs , where L is the connection length and cs = (2T/mi)1/2 is the sound speed. During this time, collisions difusse particles across the B-field. Dimensionaly, the diffusivity D⊥ is D⊥ = λ2

SOL

τ . An estimate for the SOL width resutls from the substitution τ = τ λSOL =

• D⊥L

cs . using typical values for D⊥, L and cs one obtains λSOL ≈ 1 cm.

Introduction, A. Alonso, copyleft 2010 18 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Typical parameters: few (probably known) definitions

Thermal velocity is a tyical measure of the velocity of a Maxwellian population of particles with temperature T and is given by vT =

• 2T

m . (2) Denoting ·f =

• ·f(x, v, t)dv, where f(x, v, t) is the

single particle probability density function, the thermal speed is given by vT =

• v2f .

Larmor radius is the gyro-radius, around a straight line of force,

• f the orbit of a particle with v⊥ = vT,

ρ = vt Ω (3) where Ω is the particle’s gyrofrequency Ω = eB

m .

Introduction, A. Alonso, copyleft 2010 19 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Typical parameters: few (probably known) definitions

Magnetisation parameter given by the ration of the thermal Larmor radius ρ and the characteristic length scale

• f the system L.

δ = ρ L = vT/L Ω . L is sometimes approximated by the typical plasma profile variation L ∼ Lp = − d ln p

dr

∼ a, the plasma minor radius. For strongly magnetised plasmas (δ ≪ 1), a gyrating particle sees a homogeneous plasma in its excursion around the gyro-centre. General neoclassical theory is constructed around a expansion in this assumed small parameter δ.

Introduction, A. Alonso, copyleft 2010 20 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Typical parameters: few (probably known) definitions

Collisionality the quotient of the mean free path and the characteristic scale of variation of the B-field along the field line. This generaly given by the connection length approximated by qπR for a Tokamak configuration ν∗ = qπR λmfp = qπR vTτ ; τ ∝ T3/2 n where τ is a collision time. Collisions tend to restore an isotropic Maxwellian velocity

• distribution. The quantity qπR

vT is the transit time

that is roughly the time it takes for a typical particle to explore the field structure it lives in. Transport regimes (Pfirsch-Schlüter, plateau, banana) depend mainly on collisionality.

Introduction, A. Alonso, copyleft 2010 21 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Typical parameters

magnitude units @core @edge @SOL Tempertarure T keV 10 0.5 10−2 Density n 1019m−3 10 1 0.1 Larmor radius ρi mm 6.7 1.5 0.21 Magnetization δ d-less ∼ 10−3 2 × 10−4 3 × 10−5 Collision time τii ms 17 2.3 0.21 Thermal velocity vTi m s−1 1.3 × 106 3.0 × 105 4.2 × 104 Collisionality ν∗ d-less 1.3 × 10−3 4.3 × 10−2 3.7

Introduction, A. Alonso, copyleft 2010 22 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

After this lecture you must. . .

know what are the general requirements to achieve nuclear fusion undestrand the steady state power balance and the ignition condition understand magnetic confinement approach to nuclear fusion know the core/edge/SOL regions in a MCF plasma and have a rough idea of their typical parameters know how limiters and divertors limit the plasma column extent and understand how to estimate the SOL radial extent

Introduction, A. Alonso, copyleft 2010 23 / 23

Relevant Parameters for Fusion Relevan Parameters for MCF Plasma Regions and Parameters Summary

Jeffrey P Freidberg. Plasma physics and fusion energy. Cambridge Univ. Press, Cambridge, 2008. P . Helander and D. J. Sigmar. Collisional transport in magnetized plasmas. Cambridge monographs on plasma physics, 4. Cambridge University Press, Cambridge, 2002. Richard Pitts. Tokamak edge physics and plasma-surface interactions. volume 988. AIP , 2008.

Introduction, A. Alonso, copyleft 2010 23 / 23