EF2200 Plasma Physics: Fusion plasma physics

Transcription

1 EF2200 Plasma Physics: Fusion plasma physics Guest lecturer: Thomas Jonsson, Department for Fusion Plasma Physics School of Electrical Engineering 1

2 ITER (EU, China, India, Japan, Russia, South Korea, USA) ITER one of the largest scientific experiment ever Under construction in France Based on over 60 years of research First plasma miljoner o C Produce 500 MW by 2035 Price: ~13x10 9 Euro Photo by Thomas Jonsson, 12 Sept. 2016

3 Outline Fusion reactions and energy needs Fusion plasma physics Magnetic confinement Plasma transport Power balance and the Lawson s criteria The road to fusion energy - history and future plans Keys research topics at KTH 3

4 Fusion reactions (Deuterium) (Tritium) (Helium) (Neutron) 2 H + 3 H 4 He +n + 4 He + + n +

5 Fusion energy A single fusion reaction releases 17.6 MeV Where does this energy go?

6 What s needed for fusion? Deuterium can be extracted from sea water Tritium is radioactive the half life is 12 years Tritium from lithium Fusion: D + T = n + He4 Li6 + n = T + He4 Fuel breeding: Li7 + n = T + He4 + n We have practically limitless resources of water and lithium! But, requires 200 million oc

7 What does 17.6 MeV mean? 0.7 gram of D-T mixture can provide 60 MWh Corresponding to: annual per capita energy consumption Sweden 8 ton coal 27 ton biomass ( m 2 farm land) 1% of annual production large wind power plant (3 MW max power, 90 m high, 60 m diameter wings)

8 How to make use of the fusion energy The fusion reaction produces An alpha particles with a velocity of 13x10 6 m/s A neutron with velocity 52x10 6 m/s (the circumference of earth is 40x10 6 m) How do these particles move and where do they go? 8

9 Destiny of fusion products Alpha particle is magnetised; confined inside the plasma The energy of the neutron heats the blanket; the heat is turned into electricity in a generator The reaction Li 6 +n produces tritium, which is feed back into the plasma Li 6 He 4 T Lithium blanket When colliding with D, T and electrons the alpha transfers its kinetic energy, thus heating the plasma alpha heating 9

10 Conditions for fusion reactions Nuclear reaction requires that particles are sufficiently close Fusion reaction are more tricky than e.g. fission reaction since both particles have positive charge they repel! For particles to get close enough requires high energy This is why we need extreme temperatures - why fusion is hard to achieve! 10

11 Cross sections To predict the reaction rate in a plasma we need the concept of cross sections Cross sections measure the probability for a reaction to occur between two particles with a relative velocity v-v. Example: consider a deuterium distribution, f D (r,v), and a tritium distribution, f T (r,v ). The number of reactions is given by R = - d 3 r - d 3 v - d 3 v 2 f D (r, v)f T (r, v ) v v 2 σ(r, v v 2 ) v v Integrating over velocity space we have a more useful expression: R = - d 3 r n D r n T r < vσ r > 11

12 Cross sections Approximate expression for reactivity: < σv > ~K A T B 12

13 Outline Fusion reactions and energy needs Fusion plasma physics Magnetic confinement Plasma transport Power balance and the Lawson s criteria The road to fusion energy history and future plans Keys research topics at KTH 13

14 Fusion plasma physics At 200 million o C (17 kev) all matter is in a plasma state (unless under extreme pressure) For carbon all 6 electrons are stripped, while heavier elements tend to have some electrons in bounded states Confinement: Let particles gyrate around magnetic field lines How large B-fields are needed to confine a deuterium ion? B 14

15 Fusion plasma physics Fusion reactor requires super conducting coils (Ohmic losses in copper coils would be too large) Limits B-field to ~6 T Ion Larmor radius: 4mm Electron Larmor radius: 0.1 mm Larmor orbits are tiny compared to machine size This is a requirement for magnetised fusion! Key parameter: minor radius / Larmor radius 15

16 The pinch effect How to confine a hot plasma fluid how to keep the pressure from expanding? Driving a current in wire the current generates a B-field As a current is a flow of charge, there is a j B force on the flowing charged particle. Which is the direction of the force? B j 16

17 Force balance Thus the jxb force pinches the wire! This force can be used to confine a plasma with a pressure p force balance ρ dv dt = j B p In equilibrium (steady state) ρ and v are static j B = p 17

18 Interpretation of the jxb force 1(2) Note that any current parallel to B generates zero jxb force Only perpendicular current contribute to jxb But in magnetised plasma, the perpendicular motion is constrained by Lorentz (vxb) force. How can a plasma conduct a perpendicular current? What type of particle motion forms the current? j B = p Pressure gradients are balanced by the vxb force, the force that drive the gyro motion ; this is a diamagnetic current 18

19 Confinement with toroidal field All we need is some magnetic field to confine our plasma sounds simple! NOTE: particles are lost where field lines meet material surfaces Let us bend the field lines into a torus Current, I B What is the drift motion of ions and electrons in this field? 19

20 Drift motion in a toroidal field Magnetic field (integral form of Ampere s law): Radius of curvature: C = Rφ\ B(R) = μ XI 2πR φ \ Current, I v i, B +v i,curv B B E v e, B +v i,curv v ExB Drift motion: v B = μ B B qb 2 v curv = mv B C B qb 2 v U V = E B qb 2 The plasma drift outwards it is not confined! 20

21 The trick to confine a toroidal plasma! Use both toroidal and poloidal field The sum of the poloidal and toroidal fields is a helical field Current, I B tor J tor B-poloidal B pol J-axial (in B-helical plasma) What is the drift motion in this configuration? (outside the scope of this course, but good exercise!) 21

22 Nested flux surface The helical field lines form so called nested flux surfaces Lorentz force prevents motion perpendicular to field lines Particle motion along field lines cause rapid equilibration on each flux surface Pressure/density/temperature is constant on each flux surface! What is the direction of the plasma current? B p 22

23 Outline Fusion reactions and energy needs Fusion plasma physics Magnetic confinement Plasma transport Power balance and the Lawson s criteria The road to fusion energy history and future plans Keys research topics at KTH 23

24 But toroidal plasmas leak energy Unfortunately, plasmas are not quite as ideal they leak! Particles can move from one flux surface to the next via collisions or turbulence Turbulence: Like boiling water the plasma uses eddies to transport heat out of the plasma 24

25 Modelling plasma transport The transport of particles and heat across the flux surfaces is similar to diffusive mixing Diffusion equation for the plasma pressure p where D p = diffusion coefficient and P`abc = power density Order of magnitude estimate Assume: plasma leaks on a time scale τ Gradients are determined by the machine size and P`abc = 0 p t = f D g p P`abc t 1 τ 1 a τ~ ab D p Larger plasmas leak more slowly! p B a R Heating with 1 MW and a confinement time of 2 second, what is the plasma energy? 25

26 Diffusion and random walks Diffusion can be the result of a random walk Assume that the motion of a particle is coherent (deterministic) on time scales t. During this time it moves a distance x i.e. it has a speed v = x/ t This results in a diffusion with a diffusion coefficient D = ( x)b 2 t = v x 2 Question: Derive the Bohm diffusion coefficient, assuming: Particles E B drift in an electro-static turbulent field The amplitude of the electrostatic potential fluctuations is eφ = ct, where T is the temperature and c = 1/8 26

27 Plasma heating To reach fusion relevant temperature requires intense heating The three main techniques are Ohmic heating: the plasma current is dissipated by plasma resistivity (like a light bold) Radio frequency heating (like a microwave own) Neutral beam injection: Neutrals do not experience the Lorenzo force. Inside the plasma they get ionised and consequently magnetised. Once at fusion temperatures the energy from the fusion reactions will help heat the plasma, so called alpha heating. 27

28 Energy balance Fusions plasma get their energy from Auxiliary heating, P aux Alpha heating, P a They loose energy due to: Turbulent and collisional losses, P transp =W/τ Radiation losses, P rad Energy content Confinement time P b~ + n n < σv > V = W τ + P b Assume: n n a = 2n = 2n T T a = T = T W = 3 2 n at a + n T + n T V ntτ = 4TB < σv > 3 + τ P b P b~ ntv 28

29 The Lawson criteria The two largest terms in the energy balance are the alpha power and the turbulent transport ntτ = 12TB < σv > Here ntτ is called the tripple product. The RHS has a minimum at T=25keV, thus nτ > BX s/m 3 This is the Lawson criteria 29

30 Outline Fusion reactions and energy needs Fusion plasma physics Magnetic confinement Plasma transport Power balance and the Lawson s criteria The road to fusion energy history and future plans Keys research topics at KTH 30

31 Early experimentalist were optimistic! Reverserad Pinch, Oxford, Stellarator, US early 1950 s Tokamaken T-3, Moskva, 1968

32 1968 Collaboration England/Soviet! Fusion, Oct 1968

33 R=25cm a=3cm Plasma instabilities but the plasma was unstable and instabilities enhance the leakage

34 From experiment to a reactor T3 6 m 3 ~0 MW JET 80 m 3 ~16 MW th ITER 800 m 3 ~ 500 MW th DEMO ~ m 3 ~ MW th

35 JET the world s largest fusion experiment In Oxford, England European project 1983-present

36 Success of JET

37 What have we learnt so far? ITER If the scaling is applicable, then ITER will work and we can also build a power plant! τ E = IP B P R n M ε κ 0.78

38 ITER (EU, China, Japan, Russia, South Korea, India, USA) ITER the largest scientific experiment ever Under construction in France First plasma miljoner oc Produce 500MW Q=10 (2035) (Q=fusion/input energy) Present record: JET, Q=0.6 Test physics/technology Price: ~13x109 Euro A good investment? ITER is an experiment and not a power plant; no power to the grid

39 Size of ITER

40 ITER partners The ITER partners includes more than half the world population ITER is the worlds largest energy research project. 40

41 Animation of ITER

42 Inirtial fusion Alternative to magnetic fusion Like a tiny bomb! Lasers shine into a capsule X-ray radiation is emitted inside the capsule The X-rays hit s a frozen D-T pellet The pellet implodes, get heated and the fusion starts causing an explosion

43 Inertial fusion Largest experiment is NIF in the USA A combined fusionenery and military research facility Energy production requires exploding >10 pellet/s Similar problems with wall loads as in magnetised fusion

44 Outline Fusion reactions and energy needs Fusion plasma physics Magnetic confinement Plasma transport Power balance and the Lawson s criteria Extrapolations towards a reactor The road to fusion energy history and future plans Keys research topics at KTH 44

45 EXTRAP T2R, Alfvénlaboratoriet, KTH The only fusion experiment in Scandinavia

46 PLASMA INSTABILITIES Plasma instabilities can reduce the plasma temperature cause damage to the walls perturb the magnetic field (which hold up the plasma) such that the confinement is lost and the discharge is terminated Example of instability: Resistive wall-mode Experimental data from EXTRAP T2R

47 EXTRAP T2R: Feedback system At KTH a feedback system has been developed to control plasma instabilities ACTIVE COILS SENSORS

48 EXTRAP T2R CONTRIBUTION The feedback system includes: - sensors - aktive coils - software implementation of feedback algorithms Thus resistive wall-modes can be controlled!

49 Plasma-Wall Interaction Extreme environment! Heat fluxes of MW/m 2 From fast particles, radiation and dust Neutrons activate the wall Research areas Erosion of wall materials Material migration Tritium retention and pretty much anything wall related Toroidal view inside the TEXTOR tokamak during upgrade in Jülich, Germany (

50 Plasma-modified wall materials 5 µm 5 µm 10 µm Electron microscopy images of eroded surfaces of tokamak wall

51 KTH: Fusion theory Interface Physics Graphics

52 Summary Fusion power is large scale, long term, without producing long lived radioactive isotopes Fusion fuel: D (from water) + T (from lithium) Due to Coulomb barrier reactions require ~20 kev plasmas (200 million degree) Confine hot fusion plasmas using magnetic fields Strong magnetisation, ρ a Energy leakage is approximatively diffusive Plasma turbulence approximately Bohm diffusion D~T/B Ultimate goal burning plasma Lawson criteria, nτ > BX s/m 3 ITER is under construction fusion power 10 times input power!