1. Standard and Advanced Tokamak Operation Scenarios for ITER
Hartmut Zohm
Max-Planck-Institut für Plasmaphysik, Garching, Germany
EURATOM Association
What is a ‘tokamak (operational) scenario’?
Short recap of fusion and tokamak physics
Conventional scenarios
Advanced scenarios
Summary and conclusions
Lecture given at PhD Network Advanced Course, Garching,

2. What is a ‚tokamak scenario‘?
A tokamak (operational) scenario is a recipe to run a tokamak discharge
Plasma discharge characterised by
external control parameters: Bt, R0, a, k, d, Pheat, FD…
integral plasma parameters: b = 2m0<p>/B2, Ip = 2p  j(r) r dr…
plasma profiles: pressure p(r) = n(r)*T(r), current density j(r)
 operational scenario best characterised by shape of p(r), j(r)
bp = 1
Ip = 800 kA
fNI = 37%
bp = 1
Ip = 800 kA
fNI = 14%
current density (a.u.)
current density (a.u.)
total j(r)
noninductive j(r)
total j(r)
noninductive j(r)

3. Control of the profiles j(r)and p(r) is limited
safety factor:
ITER simulation
(CEA Cadarache)
ohmic current coupled to temperature profile via s ~ T3/2
 inductive current profiles always peaked, q-profiles monotonic
external heating systems drive current, but with limited efficiency
(typically less than 0.1 A per 1 W under relevant conditions)…
pressure gradient drives toroidal ‘bootstrap’ current: jbs ~ (r/R)1/2 p/Bpol

4. Control of the profiles j(r)and p(r) is limited
Pressure profile determined by combination of heating / fuelling
profile and radial transport coefficients
ohmic heating coupled to temperature profile via s ~T3/2
external heating methods allow for some variation – ICRH/ECRH
deposition determined by B-field, NBI has usually broad profile
gas puff is peripheral source of particles, pellets further inside
but: under reactor-like conditions, dominant a-heating ~ (nT)2

5. Control of the profiles j(r)and p(r) is limited
Pressure profile determined by combination of heating / fuelling
profile and radial transport coefficients
anomalous (turbulent) heat transport leads to ‘stiff’ temperature
profiles (critical gradient length T/T) – except at the edge
density profiles not stiff due to existence of ‘pinch’

6. Control of the profiles j(r)and p(r) is limited
Stiffness can be overcome locally by sheared rotation
edge transport barrier (H-mode)
internal transport barrier (ITB)

7. What is a ‘tokamak (operational) scenario’?
Short recap of fusion and tokamak physics
Conventional scenarios
Advanced scenarios
Summary and conclusions

8. Figure of merit for fusion performance nTtE
Aim is to generate power, so
Pfusion/Pheat (power needed to sustain
plasma) should be high
Pheat determined by thermal insulation:
tE = Wplasma/Pheat (energy confinement time)
In present day experiments, Pheat comes
from external heating systems
Q = Pfus/Pext  Pfus/Pheat ~ nTtE
In a reactor, Pheat mainly by a-(self)heating:
Q = Pfus/Pext   (ignited plasma)
The aim is to generate and sustain a plasma of T ~ several 10 keV,
tE ~ several seconds and n ~ 1020 particles / m3

9. Optimisation of nTtE: ideal pressure limit
Optimising nT means high pressure and, for given magnetic field,
high b = 2m0 <p> / B2
This quantity is limited by magneto-hydrodynamic (MHD) instabilities
‘Ideal’ MHD limit (ultimate limit, plasma
unstable on Alfvén time scale ~ 10 ms,
only limited by inertia)
‘Troyon’ limit bmax ~ Ip/(aB), leads to
definition of bN = b/(Ip/(aB))
at fixed aB, shaping of plasma cross-
section allows higher Ip (low q limit,
see later) higher b
additionally, also bN,max improves with
shaping of poloidal cross-section
N=/(I/aB)=3.5 
[%]

10. Optimisation of nTtE: resistive pressure limit
Optimising nT means high pressure and, for given magnetic field,
high b = 2m0 <p> / B2
This quantity is limited by magneto-hydrodynamic (MHD) instabilities
‘Resistive’ MHD limit (on local current
redistribution time scale ~ 100 ms)
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11. Optimisation of nTtE: resistive pressure limit
Optimising nT means high pressure and, for given magnetic field,
high b = 2m0 <p> / B2
This quantity is limited by magneto-hydrodynamic (MHD) instabilities
‘Resistive’ MHD limit (on local current
redistribution time scale ~ 100 ms)
‘Neoclassical Tearing Mode’ (NTM)
driven by loss of bootstrap current
within magnetic island

12. Optimisation of nTtE: density limit
qedge = 2
1/qedge (normalised current)
Since T has an optimum value at ~ 20 keV, n should be as high as possible
density is limited by disruptions due to excessive edge cooling
empirical ‘Greenwald’ limit, nGr ~ Ip/(pa2)  high Ip helps to obtain high n

13. Optimisation of nTtE: current limit
BUT: for given Bt, Ip is limited by current gradient driven MHD instabilities
Limit to safety factor q ~ (r/R) (Btor/Bpol)
for q < 1, tokamak unconditionally unstable  central ‘sawtooth’ instability
for qedge  2, plasma tends to disrupt (external kink) – limits value of Ip
qedge = 2
1/qedge (normalised current)
Hugill diagram
for TEXTOR
JET
normalised density

14. Optimisation of nTtE: confinement scaling
Empirical confinement scalings show linear increase of tE with Ip
note the power degradation (tE decreases with Pheat!)
‘H-factor’ H measures the quality of confinement relative to the scaling
Empirical ITER 98(p,y) scaling:
tE ~ H Ip0.93 Pheat-0.63 Bt0.15…

15. Tokamak optimisation: steady state operation
N.B: for steady state tokamak operation, high Ip is not desirable:
Tokamak operation without transformer: current 100% noninductive
external CD has low efficiency (remember less than 0.1 A per W)
internal bootstrap current high for high jbs ~ (r/R)1/2 p/Bpol
 fNI ~Ibs/Ip ~p/Bpol2 ~ bpol
‘Advanced’ scenarios, which aim at steady state, need high b, low Ip,
have to make up for loss in tE by increasing H
Without the ‘steady state’ boundary condition, a tokamak scenario
is called ‘conventional’
N.B.2: ‘Long Pulse’ = stationary on all intrinsic time scales
‘Steady State’ = can be run forever

16. What is a ‘tokamak (operational) scenario’?
Short recap of fusion and tokamak physics
Conventional scenarios
Advanced scenarios
Summary and conclusions

17. The (low confinement) L-mode scenario
Standard scenario without special tailoring of geometry or profiles
central current density usually limited by sawteeth
temperature gradient sits at critical value over most of profile
extrapolates to very large (R > 10 m, Ip > 30 MA) pulsed reactor

18. The (high confinement) H-mode scenario
With hot (low collisionality) conditions, edge transport barrier develops
gives higher boundary condition for ‘stiff’ temperature profiles
global confinement tE roughly factor 2 better than L-mode
extrapolates to more attractive (R ~ 8 m, Ip ~ 20 MA) pulsed reactor

19. ‘Hot’ (low collisionality) edge by divertor operation
plasma wall interaction in well defined zone further away from core plasma
possibility to decrease T, increase n along field lines (p=const.)
high edge temperature gives access to edge transport barrier, if
enough heating power is supplied (‘power threshold for H-mode’)

20. Mechanism for edge transport barrier formationxB
in a very narrow (~1 cm) layer at the edge very high plasma
rotation develops (E = v x B several 10s of kV/m)
sheared edge rotation tears turbulent eddies apart
smaller eddy size leads to lower radial transport (D ~ dr2/tdecor)

21. Stationary H-modes usually accompanied by ELMs
Edge Localised Modes (ELMs) regulate edge plasma pressure
without ELMs, particle confinement ‚too good‘ – impurity accumulation

22. Stationary H-modes usually accompanied by ELMs
acceptable lifetime
for 1st ITER divertor
But: ELMs may pose a serious threat to the ITER divertor
large ‘type I ELMs’ may lead to too high divertor erosion

23. b-limit in H-modes usually set by NTMs
Present day tokamaks limited by (3,2) or (2,1) NTMs (latter disruptive)
while onset bN is acceptable in present day devices, it may be quite
low in ITER due to unfavourable rp* scaling (rather than machine size)

24. H-mode is ITER standard scenario for Q=10…
Pressure driven
MHD instabilities
Density limit
(Greenwald)
Access to edge transport barrier
H = tE,ITER/tE,predicted
The design point allows for…
…achieving Q=10 with conservative assumptions
…incorporation of ‚moderate surprises‘
…achieving ignition (Q  ) if surprises are positive

25. …but some open issues remain…
Need to minimise ELM impact on divertor
reduce power flow to divertor by radiative edge cooling
special variants of the scenario (Quiescent H-mode, type II ELMs)
ELM mitigation – pellet pacing or Resonant Magnetic Perturbations
Need to tackle NTM problem
NTM suppression by Electron Cyclotron Current Drive demonstrated,
but have to demonstrate that this can be used as reliable tool

26. ELM control by pellet pacing
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Injection of pellets triggers ELMs – allows to increase ELM frequency
at the same time, ELM size decreases and peak power loads are mitigated

27. ELM control by Resonant Magnetic Perturbations
DIII-D
Static error field resonant in plasma edge can suppress ELMs
removes ELM peaks but keeps discharge stationary with good confinement
very promising, but physics needs to be understood to extrapolate to ITER

28. NTM control by Electron Cyclotron Current Drive
Active control is possible by generating a localised helical current in the island to replace the missing bootstrap current

29. Suppression of (2,1) NTM by ECCD
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30. Suppression of (2,1) NTM by ECCD
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Current drive (PECRH / Ptotal = %) results in removal
method has the potential for reactor applications

31. What is a ‘tokamak (operational) scenario’?
Short recap of fusion and tokamak physics
Conventional scenarios
Advanced scenarios
Summary and conclusions

32. Advanced tokamak – the problem of steady state
Advanced scenarios aim at stationary (transformerless) operation
external CD has low efficiency (remember less than 0.1 A per W)
internal bootstrap current high for high jbs ~ (r/R)1/2 p/Bpol
 fNI ~Ibs/Ip ~p/Bpol2 ~ bpol
Recipe to obtain high bootstrap fraction:
low Bpol, i.e. high q – elevate or reverse q-profile (q=(r/R)(Btor/Bpol))
eliminates NTMs (reversed shear, no low resonant q-surfaces)
high pressure where Bpol is low, i.e. peaked p(r)
Both recipes tend to make discharge ideal MHD (kink) unstable!
In addition, jbs profile should be consistent with q-profile

33. Advanced tokamak – the problem of steady state
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conventional
j(r)
q(r)
p(r)
jbs(r)
A self-consistent solution is theoretically possible
reversing q-profile suppresses turbulence – internal transport barrier (ITB)
large bootstrap current at mid-radius supports reversed q-profile

34. Problems of the Advanced tokamak scenario
Broad current profile leads to low kink stability (low b-limit):
can partly be cured by close conducting shell, but kink instability
then grows on resistive time scale of wall (Resistive Wall Mode RWM)
can be counteracted by helical coils, but this needs sophisticated feedback
Position of ITB and minimum of q-profile must be well aligned
needs active control of both p(r) and j(r) profiles – difficult with limited
actuator set (and cross-coupling between the profiles)

35. RWM control by Resonant Magnetic Perturbations
Feedback control using RMPs shows possibility to exceed no-wall b-limit
rotation plays a strong role in this process and has to be understood
better (ITER is predicted to have very low rotation)

36. Advanced Tokamak Stability is a tough Problem20 40 60 80
JET, JT -
60U
DIII D
AUG JT
JET
Tore Supra
Hybrid scenarios:
Reversed shear scenarios . 8
QDB scenarios . 8
Fusion Performance (~ nTtE) . 6 . 6 2 95 /q N b
ITER reference (Q=10) . 4 . 4 89 H
ITER advanced (Q=5) . 2 . 2 . . 20 40 60 80 t t d ur
ation / d ur
ation / E E
Good performance can only be kept for several confinement times, not
stationary on the current diffusion time (10 – 50 tE in these devices)

37. dynamics that may be difficult to control with present actuator set
Control of ITB dynamics is nontrivial
CRONOS Code (CEA) b
Example: modelling of steady-state scenario in ITER – delicate internal
dynamics that may be difficult to control with present actuator set

38. A compromise: the ‚hybrid‘ scenario
Reversed shear, ITB discharges
very large bootstrap fraction
steady state should be possible
low b-limit (kink, infernal, RWM)
delicate to operate
Zero shear, ‘hybrid’ discharges
higher b-limit (NTMs)
‘easy’ to operate
smaller bootstrap fraction
have to elevate q(0)
(also avoids sawteeth, NTMs)
Hybrid operation aims at flat, elevated q-profile discharges with high q(0)
Not clear if this projects to steady state, but it will be very long pulse…

39. A ‘hybrid scenario’: the improved H-mode
0.7
q-range
H89bN/q952
3-4
Fusion Performance (~ nTtE)
4-5
5-6
6-7
0.5
ITER
(shape corrected)
0.3
0.1
(a/R)bp
0.1
0.3
0.5
0.7
0.9
1.1
~ Bootstrap fraction
Improved H-mode (discovered on AUG) is best candidate for ‘hybrid’ operation
projects to either longer pulses and/or higher fusion power in ITER
flat central q-profile, avoid sawteeth – need some current profile control

40. A ‘hybrid scenario’: the improved H-mode. 2 4 6 8 d ur
ation / t E H 89 b N /q 95
Hybrid scenarios:
Reversed shear scenarios
ITER reference (Q=10)
ITER advanced (Q=5)
QDB scenarios 20 40 60 80
JET, JT -
60U
DIII D
AUG JT
JET
Tore Supra
Fusion Performance (~ nTtE)
Presently, hybrid scenarios perform better in fusion power and pulse length

41. What is a ‘tokamak (operational) scenario’?
Short recap of fusion and tokamak physics
Conventional scenarios
Advanced scenarios
Summary and conclusions

42. Summary and Conclusions
Advanced
operation
Safety factor q
Hybrid
L-mode
H-mode
A variety of tokamak operational scenarios exists
L-mode: low performance, pulsed operation, no need for profile control
H-mode: higher performance, pulsed operation, MHD control needed
Advanced modes: higher performance, steady state, needs profile control

43. Summary and Conclusions
ITER aims at operation in conventional and advanced scenarios
demonstrating Q=10 in conventional (conservative) operation scenarios
demonstrating long pulse (steady state) operation in ‚advanced‘ scenarios
One mission of ITER and the accompanying programme is to develop and
verify an operational scenario for DEMO
DEMO scenario must be a point design (no longer an experiment)
actuators even more limited (e.g. maximum of 2 H&CD methods)