Tokamak physics and thermonuclear perspectives

Alexei DnestrovskijKurchatov Institute, Moscow Russia

This lecture was prepared during the visit to the Culham Science Centre, UK

Outline

•Requirements for fusion energy release, Lawson criterion •Tokamak device•Tokamak basic physics•Examples of Tokamak experiment•The next step – ITER

The combined mass of the The combined mass of the two small nuclei is greater two small nuclei is greater than the mass of the nucleus than the mass of the nucleus they producethey produce

The extra mass is changed The extra mass is changed into energyinto energy

We can calculate the energy We can calculate the energy released using Einstein’s released using Einstein’s famous equation:famous equation:

D+T=He + nD+T=He + n

3.5MeV 3.5MeV 14.1MeV14.1MeV

E = mcE = mc22

It occurs when two light nuclei are forced together, It occurs when two light nuclei are forced together, producing a larger nucleusproducing a larger nucleus

To overcome strong repulsive To overcome strong repulsive forces, fusion nuclei require forces, fusion nuclei require very high energies - matter very high energies - matter becomes a …becomes a …

Fusion requires high plasma

pressure and confinement

(p=n*T and E)

High temperatures (Te and Ti) are required

for fusion events < v >

High density (n ) is required for reaction rate

Fusion power n2 < v >E characterises energy loss time =

Requirement for ignition (Lawson criterion):

nE > 1.5x1020m-3s

At T~30keV ~300MoC

stored energyloss rate

1 10 100

Cross section:

Ion Temperature /keV

D-D

D-He3

D-T

<v

>

10 1001

Fusion factor:

Q= Fusion power External power

… on some history• Anomalous Bohm confinement

During 50s- late 60s it correlated with wide variety of data on radial diffusion in different devices.

eB

cTD eB 16

1

• Tokamak experiments in 1965Artsimovich and colleagues reported an excess of Bohm confinement

by a factor approximately 3

• So it was the beginning of TOKAMAK ERA in fusion

– Toroidal Field coils to provide atoroidal magnetic field

What is the TOKAMAK ?• Tokamak, from the Russian words: toroidalnaya kamera and magnitnaya katushka

meaning “toroidal chamber” and “magnetic coil”

A tokamak is a toroidal plasma confinement device with:

– Transformer with a primary winding to produce a

– The current generates a poloidal magnetic field

– Other coils shape the plasma

toroidal current in the plasma

and therefore twisted field lines which creates a perfect “trap”

Major Progress Towards Fusion Power

Fusion factor:

Q= Fusion power External power

Q=0.65 achieved in JETQ~1 in Neutron SourceQ~10 in ITER

Q>50 in Power Plant

Magnetic fusion activities

Future steps• ITER (International Thermonuclear Experimental

Reactor), project is ready• 3 medium size tokamaks under construction: KSTAR

(S.Korea), HT-7U (China), SST-1 (India). Main aims: steady-state long pulse operations

• CTF (Component Test Facility), preliminary studies

In operation• 3 large fusion devices operational (JET, JT-60U, LHD),

a big stellarator under construction (W7-X)• 11 medium size tokamaks are operational• … plus ~ 50 small size devices

Progress on JET

(Joint European Torus)JET parameters:

Major radius 3mMinor radius 1mPlasma height 3.5mPlasma current 3MAToroidal B = 2.7T

Example: B drift

• Magnitude of B varies with position• Larmor radius varies as 1/B

ions

Tokamak Basics

• What happens in tokamak plasma due to the drift?

•Charge separation•Vertical electric field•ExB plasma losses

Drifts in nonuniform plasma

B

B

•Outwards ExB drift

B

+ + + + +

- - - - - - -

E

+ + + + +

- - - - - - -

EB ExB

B

electrons

B

Toroidal current in tokamak produces poloidal magnetic field

• Field lines become helical• Particles can move to short out any E field produced

by gradient/curvature drifts

Plasma current

Toroidal magnetic field

Poloidal magnetic field q=toroidal turnspoloidal turns

Important parameter for stability analysissafety factor q

Edge q >2 for stability

Tokamak Basics

Strong parallel transport : V||/V┴ ≈ 106

gives the formation of magnetic surfaces

MAST in UK

ASDEX-Upgrade in Germany

Fast processes (10-8 – 10-7 s)•Plasma pressure becomes a function of magnetic surfaces p=p(ψ) where ψ – poloidal magnetic flux•Equilibrium installed p = jxB

Quasineutrality of plasma Σnjej=0

provides to use fluid MHD equations

Tokamak Basics

Plasma forms magnetic surfaces

Magnetically confined Fusion plasmas suffer from:

Magnetic confinement problems

1) Instability - difficult to confine a high density and temperature plasma with low magnetic fields.

2) Turbulence - limits the confinement time for a given sized machine.

3) Power loading - high volume to surface area ratio means power loading on surfaces is high.

4) Neutron activation - materials must withstand high neutron fluxes

Examples of plasma behaviour: sawteeth

TSTS

•Oscillations of plasma Oscillations of plasma

parametersparameters

•Name from SXR traceName from SXR trace

• Shown by most tokamaksShown by most tokamaks

• appear when q<1appear when q<1

• 2 very different time scales 2 very different time scales

(crash ~ µs, ramp ~ 10’s ms)(crash ~ µs, ramp ~ 10’s ms)

What is the sawtooth?What is the sawtooth?

Kadomtsev modelKadomtsev model

•Collisional transport•Fluctuations driven transport

δn/n ~ δT/T ~ eδ/T < 50%δBr/B ~ 10-4

It is commonly accepted: the enhanced transport is the result of fluctuations

Flux due to the electrostatic fluctuations :Γ=< δn δv >~< n c δE/B> ~< n c δ/L /B> ~< n/L cT/(eB)>Flux due to the electromagnetic fluctuations:Γ=n/B < δv|| δBr >

Can the fluctuations be suppressed ?

Bohm’s like scaling law.

Examples of plasma behaviour: Plasma heat and particle losses

• Upon exceeding a critical heating power (PL-H) transition from L-mode to H-mode occurs

• Transition occurs with spontaneous formation of an Edge Transport Barrier (ETB)– thin, situated at edge of plasma,

just inside of the scrape off layer (region II on picture)

Examples of plasma behaviour: H-mode

• Drop in D radiation indicating decrease in particle flux with formation of transport barrier

• Many evidences of fluctuation suppressing overall the plasma volume

• No commonly accepted complete physical model

Examples of plasma behaviour: H-mode

Dα line intensity

H-mode and ELMs:movie from MAST shot

50 ms H-mode

plasma current

Dα - signal

JT-60 1994

q

Ti

Te

Ne• An ITB is in essence similar to the

H-mode ETB, however it is not restricted to the edge– ITBs can be formed at almost

any point in the plasma• ITBs can dramatically increase

plasma performance• ITBs are obtained by manipulating

plasma’s q-profile– produce regions of weak or

reversed magnetic shear q’=rdq/dr

• ITBs form at min q or on a rational q close to the minimum

Examples of plasma behaviour: Modes with Internal Transport Barrier (ITB)The role of q-profile

When? Fusion Power

Pulse duration

Q

1997 16MW ~1 second <1

2015-2020 500-700MW <30 minutes >10

~2050 ~3000- ~1 day ~50

4000MW

The next step - ITER• To demonstrate integrated

physics and engineering at ~GW level at min. cost

• Superconducting coils, power-plant-level heat fluxes, “nuclear” safety

• Its design is realistic, detailed and reviewed like no other fusion device

• Negotiations in final phase for ITER

• Unofficially Europe now made a decision to built ITER in South France

Fusion economics

ITER cost 6 billion $(1989) per 500-700MW thermal energy

(over $1billion was spent for project design)

Usual fission $0.7billion per thermal gigawattpower plant

Oil fuel $100 billion in last year spentexploration and development by 30 top oil firms(not for production)

Plasma confinement:•Different kinds of instabilities•Plasma transport across the magnetic surfaces•Disruptions

DiagnosticsExternal HeatingTokamak-reactor problems (challenge for ITER):

•Power exhaust •Neutrons

To summarize the reviewed problems …

The tokamak device picks up many physical problems together: