Nuclear Fusion in Stars 7.1 Introductions 3

Home , Lawson criterion, Plasma stability

TOPICS IN MAGNETIC CONFINEMENT FUSION

Nuno Loureiro IPFN, IST Outline

1. Introduction 7. Plasma Heating 2. Nuclear Fusion in Stars 7.1 Introductions 3. Nuclear Fusion on Earth 7.2 Ohmic Heating 4. Nuclear Fusion reactions 7.3 Compressions 7.4 Neutral beams 5. Plasma Confinement 7.5 Radio-frequency waves 5.1 Gravitational Confinement 7.6 Self-heating 5.2 Electrostatic Confinement 8. Lawson Criterion 5.3 Inertial Confinement 5.4 Magnetic Confinement 9. Progress in magnetic confinement 6. Magnetic configurations fusion 6.1 Plasma Stability in toroidal 9.1 Introduction confinement devices 9.2 Tokamaks 6.2 Tokamak 9.3 Other magnetic configurations 10. DEMO/PROTO 1. Introduction 1. Introduction

Nuclear Fusion - advantages

1) No greenhouse gas emission

2) No long-lived radioactive waste

3) Intrinsically safe

4) Effectively infinite fuels 2. Nuclear Fusion in Stars

“That some form of the meteoric theory is certainly the true and complete explanation of solar heat can scarcely be doubted, when the following reasons are considered: (1) No other natural explanation, except by chemical action, can be conceived. (2) The chemical theory is quite insufﬁcient, because the most energetic chemical action we know, taking place between substances amounting to the whole sun's mass, would only generate about 3,000 years' heat. (3) There is no difﬁculty in accounting for 20,000,000 years' heat by the meteoric theory.” Lord Kelvin, 1862 2. Nuclear Fusion in Stars

The proton temperature (i.e., kinetic energy) has to be high enough to overcome electrostatic repulsion. In the core of the Sun the temperature is ~ 107K (~1KeV) 3. Nuclear Fusion on Earth

Ivy Mike: the only man-made fusion reactor to achieve ignition Nuclear Fusion Reactions

1) Light elements required 2) Can’t use neutrons --- there are no natural neutron sources on Earth

D2 + T 3 H4 + n1 1 1 → 2 e 0

3.5MeV 14.1MeV

Note that any of these reactions is a lot more difficult to get started than fission reactions Plot of the collisional cross-section vs. (e.g., Uranium 92) Deuterium energy for three different reactions. 5. Plasma Confinement

At the very high temperatures required for fusion, the gas ionizes and becomes a plasma --- a mixture of positively charged ions (Deuterium and Tritium, for example), and free electrons. How to confine these particles long enough for sufficient fusion reactions to occur? 5. Plasma Confinement

Philo Farnsworth 5.2 Electrostatic Conﬁnement

Farnsworth-Hirsch fusor 5.3 Inertial conﬁnement

1. Laser beams (or laser-produced radiation) strike a solid target and ionize its surface, forming a plasma.

2. Reaction forces to the surfaces blow-off compress the target

3. The fuel core reaches the density and temperature required for fusion

4. The rest of the target is ignited by the fusion energy released at the core. 5.3 Inertial Conﬁnement

National Ignition Facility (NIF) 5.4 Magnetic Conﬁnement 6. Magnetic conﬁgurations

Magnetic mirror mv2 Conservation of the magnetic moment allows µ = ⊥ some conﬁnement, but losses are too high. 2B 6.1 Plasma stability in toroidal conﬁgurations

A. Sakharov

I. Tamm 6.2 Tokamak 6.2 Tokamak

L. Artsimovich

The first tokamak: T1, Kurchatov Institute (Soviet Union, ~1960) 6.2 Tokamak

Typical parameters of a modern reactor (e.g., JET) B 3.5T T ≈ I 3 4MA ≈ − R 3m ≈ a 1m ≈ 20 3 n 10 m− ≈ T 10 20keV ≈ − 6.2 Tokamak

Basic outline of electricity production cycle:

Blanket

Heat Electric Turbine Generator exchanger Power Coolant Steam

Plasma 7. Plasma Heating

• The goal is to reach ignition temperature, T~10-20 KeV. Two distinct stages: 1) Ohmic heating and auxiliary heating raise temperature to ~5-7 KeV 2) At that stage, there are enough fusion reactions that alpha particles can be relied upon to raise the temperature to the required level

• Auxiliary heating: 1. Neutral beam injection 2. Radio-frequency waves 7. Plasma heating - methods

Ohmic Heating

Plasma heats itself up because of toroidal current and electron-ion collisions

2 PΩ = ηj Heating per unit volume 7. Plasma heating - methods

Ohmic Heating

Plasma heats itself up because of toroidal current and electron-ion collisions

2 PΩ = ηj Heating per unit volume

Problem: 3/2 η T − ∝ e 7. Plasma heating - methods

Neutral beam injection

1) Inject a high energy (much higher than10KeV) beam of neutral ions (e.g., Deuterium) 7. Plasma heating - methods

Neutral beam injection

1) Inject a high energy (much higher than10KeV) beam of neutral ions (e.g., Deuterium) 2) Neutral particles are not affected by the magnetic field and so can penetrate to the core of the tokamak (in a straight line) 3) The neutral particles collide with the plasma and get ionized. 4) The injected particles are now confined by the magnetic field; they give out their remaining energy by collisions with the background plasma 7. Plasma heating - methods

Neutral beam injection 7. Plasma heating - methods

Neutral beam injection

Problems:

1) Very energetic beams are required for the typical densities and dimensions of a fusion reactor (~1 MeV for ITER) Very challenging technical problem --- conversion efﬁciency for positive ions decreases with beam energy. Negative ions may be the solutions

2) High price per Watt. 7. Plasma heating - methods

Radio-frequency waves

- Inject in the plasma RF waves at frequencies resonant with the plasma (ion and electron cyclotron frequencies, for example)

- Similar to a microwave (e.m. waves resonant with the water molecule) 7. Plasma heating - methods

Radio-frequency heating: problems

1) Plasma density and magnetic ﬁeld spatially dependent 2) Toroidal geometry 3) Anisotropy generated by the magnetic ﬁeld

From the physics point of view, the challenge is to calculate the propagation of an e.m. wave in a (very) complex medium. 7. Plasma heating - methods 8. Lawson criterion

W Plasma energy τE = Ploss Power lost (losses to the walls, radiation) Energy confinement time 8. Lawson criterion

W Plasma energy τE = Ploss 3 W = k n T dV 2 B s s species 8. Lawson criterion

W Plasma energy τE = Ploss 3 W = k n T dV 2 B s s species Assume: 1) ideal mixture: nD = nT

2) thermal equilibrium: TD = TT = Te

Quasi-neutral plasma ni = nD + nT = ne 8. Lawson criterion

W Plasma energy τE = Ploss 3 W = k n T dV 2 B s s species W 3n k TV P 3n k TV/τ ≈ e B ⇒ loss ≈ e B E 8. Lawson criterion

Energy gain due to fusion reactions:

• number of reactions per unit time per unit volume: 2 f = nDnT < σv>= ne < σv>/4

• each reaction contributes the energy E ch to heat the plasma, i.e., fE ch is the heating rate per unit volume 8. Lawson criterion

“The gains must exceed the losses.”

fEch >Ploss

12 k T (J. D. Lawson) n τ L B e E ≥ ≡ E σv ch For DT reactions we have: n τ 1.5 1020s/m3 e E ≥ × 8. Lawson criterion

“The gains must exceed the losses.”

fEch >Ploss

(J. D. Lawson) 12 kBT neτE L ≥ ≡ Ech σv 2 Fusion triple product: 12kB T neT τE ≥ Ech σv For DT reactions we have: n T τ 1021keV s/m3 e E ≥ 8. Lawson criterion 9. Progress in magnetic conﬁnement fusion 9.1 Introduction

Plasma conﬁnement suffers for numerous macro and micro instabilities. In general, instabilities prevent the build up of pressure to the desired levels.

Kink mode Solar flare 9.2 Tokamaks: progress 9.2 Tokamak progress – Lawson criterion 9.2 Tokamaks: the future

State of the art: ITER

The purpose of ITER is to demonstrate the possibility of fusion energy (gain factor Q~10) 9.2 Tokamaks

JET vs. ITER:

B 3.5T BT 5.3T T ≈ ≈ I 3 4MA I 15MA ≈ − ≈ R 3m R 6.2m ≈ ≈ a 1m a 2.0m ≈ ≈ 20 3 20 3 n 10 m− n 10 m− ≈ ≈ T 10 20keV T 10 20keV ≈ − ≈ − 9.2 Tokamaks: open problems

Some problems that must be solved if ITER is to be successful:

1) Anomalous transport – physics problem: tokamak plasmas are often in a turbulent state. This gives rise to fast diffusion of heat, and particle loss, from the core to the edge. A key research topics is how to control / limit turbulence levels. 9.2 Tokamaks: open problems

Some problems that must be solved if ITER is to be successful:

2) Heating – technological problem: existing heating methods need to be improved to be efﬁcient in a tokamak the size of ITER. 9.2 Tokamaks: open problems

Some problems that must be solved if ITER is to be successful:

2) Heating – technological problem: existing heating methods need to be improved to be efﬁcient in a tokamak the size of ITER.

3) Alpha particle physics: a large number of fusion reactions will introduce a new species into the plasma: the alpha particles. These have their own instabilities, but since we’ve never operated in that regime, we don’t know what we’ll ﬁnd! 9.2 Tokamaks: open problems

4) Neutral ﬂux to the wall: must withstand 14MeV neutrons - International Fusion Materials Irradiation Facility (IFMIF)

5) Superconducting coils to generate the magnetic ﬁeld (unprecedented size and intensity)

6) Blanket: absorbs the neutrons and generates Tritium – never tested

7) etc. 9.3 Other magnetic conﬁgurations

L. Spitzer

Stellarator (e.g. Wendelstein 7-X): no equilibrium current, so intrinsically stable to some instabilities and disruptions However, large complexity makes them hard to build. 9.3 Other magnetic conﬁgurations

Spherical Tokamaks

MAST 10. DEMO/PROTO

DEMO will be a demonstration power plant, the last step before commercialization of fusion energy

Goals: 1) Produce 2-4 GW of energy in continuous mode of operation (compared with ITER’s 500MW during~500s) 2) Generate electricity!

Expect to operate in the 2030’s (uncertain)

PROTO will be a prototype of a magnetic fusion power plant (probably not before 2050) “Fusion is thirty years away, and always will be…” “Fusion is thirty years away, and always will be…” Bibliography

Introductory: • Nuclear Fusion – Half a century of magnetic conﬁnement fusion research, C.M. Braams & P.E. Stott, Taylor&Francis (2002) • Fusion as an Energy Source: Challenges and Opportunities, W.J. Nutall, IoP Report (2008) ( http://www.iop.org/publications/iop/2008/page_38223.html) • Wikipedia ( www.wikipedia.org )

Advanced • Tok am ak s, J. Wesson, Oxford University Press (2000) • Plasma Physics and Fusion Energy, J. Freidberg, Cambridge University Press (2007) •The Theory of Toroidall y Conﬁned Plasmas, R. White, Imperial College Press (2001)