1. Tokamak physics and thermonuclear perspectives
Alexei Dnestrovskij
Kurchatov Institute, Moscow Russia
This lecture was prepared during the visit to the Culham Science Centre, UK

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

3. E = mc2 D+T=He + n 3.5MeV 14.1MeV What is FUSION?
It occurs when two light nuclei are forced together, producing a larger nucleus
The combined mass of the two small nuclei is greater than the mass of the nucleus they produce
The extra mass is changed into energy
We can calculate the energy released using Einstein’s famous equation:
E = mc2
D+T=He + n
3.5MeV 14.1MeV

4. Fusion in the 21st Century
Great Balls of Fire!
Fusion in the 21st Century
Fusion is the Process
Powering the Sun
To overcome strong repulsive forces, fusion nuclei require very high energies - matter becomes a …
PLASMA

5. E characterises energy loss time = nE > 1.5x1020m-3s
Cross section:
Ion Temperature /keV
D-D
D-He3
D-T
<v>
Fusion requires high plasma
pressure and confinement
(p=n*T and E) 1 10
100
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):
nE > 1.5x1020m-3s
At T~30keV ~300MoC
Fusion factor: Q=
Fusion power
External power
stored energy
loss rate

6. … on some history So it was the beginning of TOKAMAK ERA in fusion
Anomalous Bohm confinement
During 50s- late 60s it correlated with wide variety of data on radial diffusion in different devices.
Tokamak experiments in 1965
Artsimovich and colleagues reported an excess of Bohm confinement by a factor approximately 3
So it was the beginning of TOKAMAK ERA in fusion

7. meaning “toroidal chamber” and “magnetic coil”
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:
Toroidal Field coils
to provide a toroidal magnetic field
Transformer with a
primary winding to produce a
toroidal current in the plasma
The current generates a poloidal magnetic field
and therefore twisted
field lines which creates a perfect “trap”
Other coils shape the plasma

8. Major Progress Towards Fusion Power
Fusion factor: Q=
Fusion power
External power
Q=0.65 achieved in JET
Q~1 in Neutron Source
Q~10 in ITER
Q>50 in Power Plant

9. 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

10. (Joint European Torus)
Progress on JET
(Joint European Torus)
JET parameters:
Major radius 3m
Minor radius 1m
Plasma height 3.5m
Plasma current 3MA
Toroidal B = 2.7T

11. Tokamak Basics Drifts in nonuniform plasma electrons Example: B drift
Magnitude of B varies with position
Larmor radius varies as 1/B
ions
What happens in tokamak plasma due to the drift?
Outwards ExB drift B E B B B
Charge separation
Vertical electric field
ExB plasma losses
ExB

12. toroidal turns poloidal turns
Tokamak Basics
Toroidal current in tokamak produces poloidal magnetic field q=
toroidal turns poloidal turns
Important parameter for stability analysis
safety factor q
Edge q >2 for stability
Plasma current
Poloidal magnetic field
Toroidal magnetic field
Field lines become helical
Particles can move to short out any E field produced by gradient/curvature drifts

13. ASDEX-Upgrade in Germany
Tokamak Basics
ASDEX-Upgrade in Germany
Plasma forms magnetic surfaces
Quasineutrality of plasma
Σnjej=0
provides to use fluid MHD equations
Strong parallel transport :
V||/V┴ ≈ 106
gives the formation of magnetic surfaces
MAST in UK
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

14. Magnetic confinement problems
Magnetically confined Fusion plasmas suffer from:
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

15. Examples of plasma behaviour: sawteeth
Oscillations of plasma parameters
Name from SXR trace
Shown by most tokamaks
appear when q<1
2 very different time scales (crash ~ µs, ramp ~ 10’s ms) TS
What is the sawtooth?
Kadomtsev model

16. Examples of plasma behaviour: Plasma heat and particle losses
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.

17. Examples of plasma behaviour: H-mode
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)

18. 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
Dα line intensity

19. H-mode and ELMs: movie from MAST shot
plasma current
Dα - signal

20. Examples of plasma behaviour: Modes with Internal Transport Barrier (ITB)
The role of q-profile JT 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 Ti Te q

21. The Future for Fusion Power
Pulse duration
When? Q
JET
MW ~1 second <1
MW <30 minutes >10
~ ~ ~1 day ~50
4000MW
ITER
Power
Plant

22. 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

23. $$$$$$ 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 gigawatt
power plant
Oil fuel $100 billion in last year spent
exploration and development by 30 top oil firms
(not for production)

24. To summarize the reviewed problems …
The tokamak device picks up many physical problems together:
Plasma confinement:
Different kinds of instabilities
Plasma transport across the magnetic surfaces
Disruptions
Diagnostics
External Heating
Tokamak-reactor problems (challenge for ITER):
Power exhaust
Neutrons