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, 06.10.2010
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…
bp = 1
bp = 1
Ip = 800 kA
fNI = 14%
Ip = 800 kA
fNI = 37%
total j(r)
noninductive j(r)
current density (a.u.)
current density (a.u.)
• plasma profiles: pressure p(r) = n(r)*T(r), current density j(r)
total j(r)
noninductive j(r)
 operational scenario best characterised by shape of p(r), j(r)
Control of the profiles j(r)and p(r) is limited
safety factor:
r Btor r 2 Btor
q

R B pol R I p
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
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
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’
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)
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
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
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 crosssection allows higher Ip (low q limit,
see later) higher b
• additionally, also bN,max improves with
shaping of poloidal cross-section
bN=b/(I/aB)=3.5
b
[%]
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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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
1/qedge (normalised current)
Optimisation of nTtE: density limit
qedge = 2
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
Optimisation of nTtE: current limit
BUT: for given Bt, Ip is limited by current gradient driven MHD instabilities
1/qedge (normalised current)
qedge = 2
Hugill diagram
for TEXTOR
JET
normalised density
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
Optimisation of nTtE: confinement scaling
Empirical ITER 98(p,y) scaling:
tE ~ H Ip0.93 Pheat-0.63 Bt0.15…
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
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
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
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
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
‘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’)
Mechanism for edge transport barrier formation
xB
• 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)
Stationary H-modes usually accompanied by ELMs
Edge Localised Modes (ELMs) regulate edge plasma pressure
• without ELMs, particle confinement ‚too good‘ – impurity accumulation
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
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)
H-mode is ITER standard scenario for Q=10…
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
…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
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
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
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
Suppression of (2,1) NTM by ECCD
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Suppression of (2,1) NTM by ECCD
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Current drive (PECRH / Ptotal = 10-20 %) results in removal
method has the potential for reactor applications
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
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
Advanced tokamak – the problem of steady state
conventional
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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
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)
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)
Advanced Tokamak Stability is a tough Problem
AUG
DIII-D
JT-60U
JET
Tore Supra
Reversed shear scenarios
QDB scenarios 0.8
Fusion Performance (~ nTtE)
rid scenarios:
0.6
ITER reference (Q=10)
0.4
ITER advanced (Q=5)
DIII-D
0.2
 JET, JT -60U
0.0
40
duration/tE
60
80
0
20
40
duration/tE
60
80
Good performance can only be kept for several confinement times, not
stationary on the current diffusion time (10 – 50 tE in these devices)
Control of ITB dynamics is nontrivial
CRONOS Code (CEA)
Example: modelling of steady-state scenario in ITER – delicate internal
dynamics that may be difficult to control with present actuator set
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…
A ‘hybrid scenario’: the improved H-mode
Fusion Performance (~ nTtE)
0.7
q-range
H89bN/q952
3-4
4-5
5-6
6-7
0.5
0.3
0.1
(a/R)bp
0.1
0.3
0.5
0.7
0.9
~ Bootstrap fraction
1.1
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
A ‘hybrid scenario’: the improved H-mode
Hybrid scenarios:
Reversed shear scenarios
QDB scenarios 0.8
0.6
2
0.6
ITER reference (Q=10)
0.4
0.4
ITER advanced (Q=5)
DIII-D
0.2
0.2
 JET, JT -60U
0.0
0.0
0
20
40
duration/tE
60
80
0
20
40
duration/tE
60
80
Presently, hybrid scenarios perform better in fusion power and pulse length
b
Fusion Performance
H89bN/q952 (~ nTtE)
0.8
AUG
DIII-D
JT-60U
JET
Tore Supra
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
Summary and Conclusions
Safety factor q
Advanced
operation
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
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
Scenario: Standard Low q Hybrid Advanced
Ip [MA]
Bt [T]
bN
Pfus [MW]
Q
tpulse [s]
15
5.3
1.8
400
10
400
17
5.3
2.2
700
20
100
13.8
5.3
1.9
400
5.4
1000
9
5.18
3
356
6
3000
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)