Chapter 12

Magnetic Fusion Toroidal Machines:

Principles, results, perspective

S. AtzeniMay 10, 2010; rev.: May 16, 2012English version: May 17, 2017

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Magnetic confinement fusion plasmas

•  low density (1020-1021 m-3) plasma, ���

•  In nearly steady-state conditions, ���

•  confined by appropriately shaped magnetic fields

2

Open and closed magnetic configurations

•  Open configurations: magnetic mirrors (see lectures on charged particle motion in external fields, Ch. 2 of this course)

•  Closed configurations (in practice toroidal configurations):

-  Tokamak

-  Stellarator

-  Reversed Field Pinch

These notes mainly concern the tokamak device, because so far this is the most studied and best performing device. We shall say a few words about stellarators, too.

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Toroidal device

Magnetic field

Toroidal + Poloidal+ Vertical

Main concepts:

- Tokamak

-  Stellarator

source: Chen, Introduction to Plasma Physics, 19744

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Rotational transform (i.e. poloidal field + toroidal field) required for stability

Tokamak configuration

• The tokamak is a toroidally stabilized (see Lectures on “equilibrium”), in which •  toroidal field is generated by external magnets•  poloidal field is generated by the electrical current

flowing in the plasma (plasma = secondary loop of a transformer) => the (conventional) tokamaks is a pulsed machine

• A vertical field Bv is also required to generate a force (j x Bv) balancing the radial expansion force due to the gradient of magnetic pressure (since toroidal field decreases with distance from major axis as1/r)

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Tokamak

source: Pease, in Dendy 19937

Tokamak

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Textor Tokamak(Julich, Germany)

courtesy of M. Mangels, Forschungszentrum Jülich GmbH

dal sito ENEA

FTU, Frascati Torus Upgrade (ENEA, Frascati0

Stellarator

•  both toroidal and poloidal fields created by external magnets(with elicoidal coils in the simplest case)

source: Pease, in Dendy 199311

Tokamak vs stellarator

Tokamak:

-  simpler (axisymmetric)-  better confinement

(at least so far)

-  instrinsically pulsed(induced current)

Stellarator:

-  steady-state

but a modular structure can be built (see next)

but a non-inductive current can be generated, by auxiliary power sources (micro-waves, fast particle beams)

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Modular stellarator

Conceptual scheme of Weldenstein 7 AX, operating at Greinswald (Germany) since 2016 (see http://www.ipp.mpg.de/w7x)

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Modular Stellarator

Weldenstein 7 X [Greinswald, Germania]

Diagnostics (I)

plasma conditions:

n ≈ 1020 m-3

T = 0.1 - 20 keVT = 5 - 15 TL = 0.5 - 5 m

required resolution•  Δx = cm•  Δt = µs - ms

•  detailed knowledge of plasma composition essential

electrical & magnetic measurements, measure of electron and ion densities, electron and ion temperatures, radiation emission, fluctuations, ...

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Diagnostics (II)

•  probes for electrical and magnetic measurements

•  interferometry, polarimetry, reflectometry to measure electron density

•  (multi-channel) Thomson scattering (multicanale), ���electron cyclotron radiation spectra to infer electron temperature and features of the electron distribution function

•  neutral ion emission and neutron spectra to measure ion temperature

•  bolometry, X-ray spectroscopy

•  e..m. probes, refelctometry, heavy ion scattering to diagnose fluctuations

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Physics: issues and achievements (I)

•  equilibrium: well understood (MHD + control)•  macroscopic stability: OK (MHD + control + enforcement of opeational

limits )•  microscopic stability: a number of different processes; some of them not yet

fully understood, not fully predictable and controllable; kinetic theories with detailed account of magnetic topology required

•  Confinament: not fully understood (turbulence, field errors, microinstabilities, ...) ==> experimental scaling laws, e.g.

==> enlarge the machine to improve confinement17€

tE∝ I2

nTfgeom = (3 fgeom )1/ 2 I

(Pinput )1/ 2

€

tE∝ I0.85R1.2

(Pinput )1/ 2 (a0.3B0.2R0.2n0.1)

Source: European Fusion Development Agency (EFDA)18

•  note:

Major simulation effort

The problem is a real Grand challenge: (3+3)-dimensional kinetic problem, with complex field topology, multiple space- and-time scales

So far, a lot of physics insight, not yet fully predictive transport simulations

Promising results for fast fusion particle – plasma interactions

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Confinement time scaling and extrapolation to ITER

Reactor

courtesy of G. Mazzitelli, ENEA

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Physics: issues and achievements (II)

•  Ohmic heating (ηj2): insufficient beacuse η ∝T-3/2

==> auxiliary heating:•  fast neutral particle (100 - 1000 keV) injection• microwaves (100 MHz - 150 GHz), at ion cyclotron

frequency, electron cyclotron frequency, lower-hybrid frequency, etc

•  Fusion alpha-particles:• Coulomb slowing down •  particle-wave interactions? (vα ≈ valfven)

[major physics unknown for thermonuclear high-Q device ==> simulation; scaled down experiments?

•  plasma-wall interactions (sputtering, heating, etc.)•  impurity poisoning (Prad ∝ne <Z2>)

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Fisica: problemi e risultati (III)

• “record” performance (JET device):

•  n τ T = 1021 m-3 s keV •  Q = 0.3 (per 1 s)•  Pfus = 22 MW

[Phys Rev Lett 80, 5548 (1998)]

•  other devices, with superconducting coils, operate with pulses of several minutes

•  tokamak physics is studied on a number of devices; such devices have contributed to sstudies on confinement, plasma-wall interaction, magnetic configuration optimization, stability control, auxiliary heating, divertor physics, ...

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JET (Joint European Torus; see www.euro-fusion.org/jet/ )Major radius = 3 minor radius = 1 m; B = 3.8 T, I = 7 MA,

auxiliary heating (rario-frequency + neutral injection) up to 50 MW

(courtesy of EFTA-JET)

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Next step: ITER (see www.iter.org)

Main parameters

•  dimensions: JET x 2major radius: 6.2 m minor “radius”: 2 melongation: 1.8

•  plasma current: 15 MA•  magnetic field: 5.3 T on axis

12 T maximum, on conductors•  superconducting magnets•  auxiliary heating: 73 - 110 MW

plasma volume = 800 m3

Goal:•  Fusion power: 500 MW•  Q ≥ 5•  Pulse duration ≥ 400 s

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•  international collaboration (EU, Russia, Japan, USA, India, Cina, S. Corea)

•  cost: 30 G€ (?)

• under construction

• first plasma in 2024

•  integrated expts in 2028

• Deuterium-tritium expts in 2036

(source D.J. Campbell, Iter organization at the American Physical Society Plasma Physics Division Conf., Nov. 2016)

www.iter.org

www.iter.org

Iter experiments / The unknowns

•  confinement

•  α-particle – plasma interactions

•  macroscopic disruptions

•  divertor

•  localized heat loads on the first wall

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Reactor dimensioning

•  Temperature is more or less fixed (20 keV, see Lawson criterion)•  3.5 MeV alpha-particle containement => current•  stability: once current and aspect-ratio fixed => toroidal field•  toroidal field (& cross section shape) ==> pressure ==> plasma density•  density and temperature ==> power density•  heating and confinement => dimensions, auxiliary heating power

•  Additional constraints to dimensions set both by allowable thermal and neutron wall loads, and by confinement

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From Iter to the reactor

•  Fusion power x 6

•  pulse duration: from tens of minutes to hours (or even steady-state)

•  tritium breeding (ITER does not include a full blanket)

•  costs must be reduced

•  to be proved: reliability, duration, mantainance (e.g. wall replacement via remote handling, access to magnets, ...)

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A. Pizzuto (a cura di), ENEA (2015), ISBN 978-88-8286-318-0http://fsn-fusphy.frascati.enea.it/DTT/downloads/Report/DTT_ProjectProposal_July2015.pdf

DTT: una proposta italiana tokamak di supporto ad ITER per lo studio di sistemi di rimozione del calore e di riduzione dei carichi termici sulla prima parete

A Fusion Power Plant

D + T → 4He + n + Energy

n + 6Li → 4He + T

A Lithium Blanket produces Tritium

A heat exchanger in this blanket produces steam that drives turbines

!

Electricity 33

Any alternative to ITER?

•  In principle, high-Q operation could be demontrated with devices employing higher magnetic field, and with substantially smaller size.

•  Such devices could allow studying the peculiar physics of thermonuclear plasmas (low collisionality plasmas, with fusion reactions, α-particle – plasma interactions, etc.) at lower cost and on a shorter time scale.

•  A long-standing proposal: Ignitor (B. Coppi)

•  However, it seems difficult to conceive a high-magnetic field power-producing reactor. 34

•  dimensions:major radius: 1.32 m minor “radius”: 0.47 m

•  plasma current: 11 MA

•  on-axis magnetic field: 13 T

•  Copper magnets

•  auxiliary heating power: 15 MW

•  Fusion power: 100 MW

source: Detragiache, ENEA

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Bibliography

•  Elementary discussion of tokamak configuration: ���G.Pucella e S.E. Segre, Fisica dei Plasmi, Zanichelli (2010), par. 2.4 (in Italian).

•  Elementary presentation of tokamak configuration and tokamak reactor: J. Wesson, Tokamaks, 3rd Ed., Oxford University Press (2004), Sec. 1.6 e Secr. 1.7.

•  A treatise on tokamaks: J. Wesson, op. cit. (749 pp.).

•  Intermediate level lectures: ���Chapters 8, 17 and 18 of R. Dendy (Ed.): Plasma Physics, Cambridge University Press (1993).

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Bibliography – status of research [Nature Physics 12 (May 2016)]