Post on 15-Jan-2016
Standard and Advanced TokamakOperation Scenarios for ITER
Hartmut Zohm
Max-Planck-Institut für Plasmaphysik, Garching, Germany
EURATOM Association
Lecture given at PhD Network Advanced Course, Garching, 06.10.2010
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
What is a ‚tokamak scenario‘?
p = 1Ip = 800 kAfNI = 37%
p = 1Ip = 800 kAfNI = 14%
A tokamak (operational) scenario is a recipe to run a tokamak discharge
Plasma discharge characterised by
• external control parameters: Bt, R0, a, , , Pheat, D…
• integral plasma parameters: = 20<p>/B2, Ip = 2 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)
curr
en
t d
en
sity
(a
.u.)
curr
en
t d
en
sity
(a
.u.)
total j(r)noninductive j(r)
total j(r)noninductive j(r)
Control of the profiles j(r)and p(r) is limited
• ohmic current coupled to temperature profile via ~ 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
safety factor:
p
tor
pol
tor
IB
Rr
BB
Rr
q2
ITER simulation(CEA Cadarache)
Control of the profiles j(r)and p(r) is limited
Pressure profile determined by combination of heating / fuellingprofile and radial transport coefficients
• ohmic heating coupled to temperature profile via ~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 -heating ~ (nT)2
Control of the profiles j(r)and p(r) is limited
Pressure profile determined by combination of heating / fuellingprofile 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
Aim is to generate power, so
• Pfusion/Pheat (power needed to sustain plasma) should be high
• Pheat determined by thermal insulation:
E = Wplasma/Pheat (energy confinement time)
In present day experiments, Pheat comesfrom external heating systems
• Q = Pfus/Pext Pfus/Pheat ~ nTE
In a reactor, Pheat mainly by -(self)heating:
• Q = Pfus/Pext (ignited plasma)
The aim is to generate and sustain a plasma of T ~ several 10 keV, E ~ several seconds and n ~ 1020 particles / m3
Figure of merit for fusion performance nT
Optimising nT means high pressure and, for given magnetic field,high = 20 <p> / B2
This quantity is limited by magneto-hydrodynamic (MHD) instabilities
‘Ideal’ MHD limit (ultimate limit, plasma unstable on Alfvén time scale ~ 10 s,only limited by inertia)
• ‘Troyon’ limit max ~ Ip/(aB), leads to definition of N = /(Ip/(aB))
• at fixed aB, shaping of plasma cross- section allows higher Ip (low q limit, see later) higher
• additionally, alsoN,max improves with shaping of poloidal cross-section
Optimisation of nT: ideal pressure limit
N=/(I/aB)=3.5
[%]
Optimising nT means high pressure and, for given magnetic field,high = 20 <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 nT: resistive pressure limit
Optimising nT means high pressure and, for given magnetic field,high = 20 <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
Optimisation of nT: resistive pressure limit
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/(a2) high Ip helps to obtain high n
qedge = 2
1/q
edge
(no
rma
lise
d c
urr
en
t)
Optimisation of nT: density 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
Hugill diagramfor TEXTOR JET
qedge = 2
normalised density
1/q
edge
(no
rma
lise
d c
urr
en
t)
Optimisation of nT: current limit
Empirical confinement scalings show linear increase of with Ip
• note the power degradation (E decreases with Pheat!)
• ‘H-factor’ H measures the quality of confinement relative to the scaling
Optimisation of nT: confinement scaling
Empirical ITER 98(p,y) scaling:
E ~ H Ip0.93 Pheat
-0.63 Bt
0.15…
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 ~ pol
‘Advanced’ scenarios, which aim at steady state, need high , low Ip,have to make up for loss in E by increasing H
Without the ‘steady state’ boundary condition, a tokamak scenariois called ‘conventional’
N.B.2: ‘Long Pulse’ = stationary on all intrinsic time scales
‘Steady State’ = can be run forever
Tokamak optimisation: steady state operation
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
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 (low confinement) L-mode scenario
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 E 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
• 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 ~ r2/decor)
xB
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
But: ELMs may pose a serious threat to the ITER divertor
• large ‘type I ELMs’ may lead to too high divertor erosion
acceptable lifetimefor 1st ITER divertor
-limit in H-modes usually set by NTMs
Present day tokamaks limited by (3,2) or (2,1) NTMs (latter disruptive)
• while onset N is acceptable in present day devices, it may be quite low in ITER due to unfavourable p
* scaling (rather than machine size)
H-mode is ITER standard scenario for Q=10…
The design point allows for…
• …achieving Q=10 with conservative assumptions
• …incorporation of ‚moderate surprises‘
• …achieving ignition (Q ) if surprises are positive
H = E,ITER/E,predicted
Density lim
it
(Greenwald)
Access to edge transport barrier
Pressure drivenMHD instabilities
…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
Injection of pellets triggers ELMs – allows to increase ELM frequency
• at the same time, ELM size decreases and peak power loads are mitigated
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ELM control by Resonant Magnetic Perturbations
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
DIII-D
Active control is possible by generating a localised helical current in the island to replace the missing bootstrap current
NTM control by Electron Cyclotron Current Drive
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
Suppression of (2,1) NTM by ECCD
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• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
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 ~ pol
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
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
Advanced tokamak – the problem of steady state
conventional
j(r)
q(r)
jbs(r)
p(r)
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Broad current profile leads to low kink stability (low -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)
Problems of the Advanced tokamak scenario
RWM control by Resonant Magnetic Perturbations
Feedback control using RMPs shows possibility to exceed no-wall limit
• rotation plays a strong role in this process and has to be understood better (ITER is predicted to have very low rotation)
Good performance can only be kept for several confinement times, notstationary on the current diffusion time (10 – 50 E in these devices)
Advanced Tokamak Stability is a tough Problem
duration/E
0.0
0.2
0.4
0.6
0.8
duration/E
Hybrid scenarios: Reversed shear scenarios
ITER reference (Q=10)
ITER advanced (Q=5)
QDB scenarios
40 60 80 0 20 40 60 800 20 40 60 80
JET, JT-60U
DIII-D
AUGDIII-DJT-60UJETTore Supra
Fus
ion
Per
form
ance
(~
nT E
)
Control of ITB dynamics is nontrivial
Example: modelling of steady-state scenario in ITER – delicate internaldynamics that may be difficult to control with present actuator set
CRONOS Code (CEA)
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…
Reversed shear, ITB discharges
+ very large bootstrap fraction
+ steady state should be possible
- low -limit (kink, infernal, RWM)
- delicate to operate
Zero shear, ‘hybrid’ discharges
+ higher -limit (NTMs)
+ ‘easy’ to operate
- smaller bootstrap fraction
- have to elevate q(0) (also avoids sawteeth, NTMs)
0
1
2
3
4
5
0 0.5 1r/a
strong
weak
q-profiles
StandardH-mode
~ zero shear
Reversedshear
0
1
2
3
4
5
0 0.5 1r/a
strong
weak
q-profiles
StandardH-mode
~ zero shear
Reversedshear
A compromise: the ‚hybrid‘ scenario
A ‘hybrid scenario’: the improved H-mode
0.1
0.3
0.5
0.7H89N/q95
2
0.1 0.3 0.5 0.7 0.9 1.1
(a/R)p
3-44-55-66-7
q-range
~ Bootstrap fraction
ITER
(sha
pe co
rrecte
d)
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
Fus
ion
Per
form
ance
(~
nT E
)
0.0
0.2
0.4
0.6
0.8
duration/E
H89 N
/q95
2
0.0
0.2
0.4
0.6
0.8
duration/E
H89 N
/q95
2
Hybrid scenarios: Reversed shear scenarios
ITER reference (Q=10)
ITER advanced (Q=5)
QDB scenarios
0 20 40 60 80 0 20 40 60 800 20 40 60 80
JET, JT-60U
DIII-D
AUGDIII-DJT-60UJETTore Supra
Presently, hybrid scenarios perform better in fusion power and pulse length
A ‘hybrid scenario’: the improved H-modeF
usio
n P
erfo
rman
ce (
~ n
T E
)
• What is a ‘tokamak (operational) scenario’?
• Short recap of fusion and tokamak physics
• Conventional scenarios
• Advanced scenarios
• Summary and conclusions
Summary and Conclusions
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
0
1
2
3
4
5
0 0.5 1r/a
strong
weak
q-profiles
StandardH-mode
~ zero shear
Reversedshear
0
1
2
3
4
5
0 0.5 1r/a
strong
weak
q-profiles
StandardH-mode
~ zero shear
Reversedshear
L-modeH-mode
Advancedoperation
Saf
ety
fact
or
q
Hybrid
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 andverify 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)
Scenario: Standard Low q Hybrid Advanced
Ip [MA] 15 17 13.8 9Bt [T] 5.3 5.3 5.3 5.18N 1.8 2.2 1.9 3Pfus [MW] 400 700 400 356Q 10 20 5.4 6tpulse [s] 400 100 1000 3000