Standard and Advanced Tokamak Operation Scenarios for ITER Hartmut Zohm Max-Planck-Institut für Plasmaphysik, Garching, Germany EURATOM Association Lecture

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)


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


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’


Stiffness can be overcome locally by sheared rotation

• edge transport barrier (H-mode)

• internal transport barrier (ITB)






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

[%]



‘Resistive’ MHD limit (on local current redistribution time scale ~ 100 ms)

ASDEX Upgrade

Optimisation of nT: resistive pressure limit



‘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






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

ASDEX Upgrade

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

ASDEX Upgrade

Current drive (PECRH / Ptotal = 10-20 %) results in removal

method has the potential for reactor applications

Suppression of (2,1) NTM by ECCD

ASDEX Upgrade






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)

ASDEX Upgrade

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

)






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

Documents

Standard and Advanced Tokamak Operation Scenarios for ITER Hartmut Zohm Max-Planck-Institut für Plasmaphysik, Garching, Germany EURATOM Association Lecture