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

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What is a ‚tokamak scenario‘? p = 1 I p = 800 kA f NI = 37% p = 1 I p = 800 kA f NI = 14% A tokamak (operational) scenario is a recipe to run a tokamak discharge Plasma discharge characterised by external control parameters: B t, R 0, a, , , P heat, D … integral plasma parameters: = 2 0 /B 2, I p = 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) current density (a.u.) total j(r) noninductive j(r) total j(r) noninductive j(r)

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Control of the profiles j(r)and p(r) is limited ohmic current coupled to temperature profile via ~ T 3/2 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: j bs ~ (r/R) 1/2 p/B pol safety factor: ITER simulation (CEA Cadarache)

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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 ~T 3/2 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

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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’

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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)

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

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Aim is to generate power, so P fusion /P heat (power needed to sustain plasma) should be high P heat determined by thermal insulation: E = W plasma /P heat (energy confinement time) In present day experiments, P heat comes from external heating systems Q = P fus /P ext P fus /P heat ~ nT E In a reactor, P heat mainly by -(self)heating: Q = P fus /P ext (ignited plasma) The aim is to generate and sustain a plasma of T ~ several 10 keV, E ~ several seconds and n ~ particles / m 3 Figure of merit for fusion performance nT

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Optimising nT means high pressure and, for given magnetic field, high = 2 0 / B 2 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 ~ I p /(aB), leads to definition of N = /(I p /(aB)) at fixed aB, shaping of plasma cross- section allows higher I p (low q limit, see later) higher additionally, also N,max improves with shaping of poloidal cross-section Optimisation of nT : ideal pressure limit N = /(I/aB)=3.5 [%]

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Optimising nT means high pressure and, for given magnetic field, high = 2 0 / B 2 This quantity is limited by magneto-hydrodynamic (MHD) instabilities ‘Resistive’ MHD limit (on local current redistribution time scale ~ 100 ms) ASDEX Upgrade Optimisation of nT : resistive pressure limit

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Optimising nT means high pressure and, for given magnetic field, high = 2 0 / B 2 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

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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, n Gr ~ I p /( a 2 ) high I p helps to obtain high n q edge = 2 1/q edge (normalised current) Optimisation of nT : density limit

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BUT: for given B t, I p is limited by current gradient driven MHD instabilities Limit to safety factor q ~ (r/R) (B tor /B pol ) for q < 1, tokamak unconditionally unstable central ‘sawtooth’ instability for q edge 2, plasma tends to disrupt (external kink) – limits value of I p Hugill diagram for TEXTOR JET q edge = 2 normalised density 1/q edge (normalised current) Optimisation of nT : current limit

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Empirical confinement scalings show linear increase of with I p note the power degradation ( E decreases with P heat !) ‘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 I p 0.93 P heat B t 0.15 …

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N.B: for steady state tokamak operation, high I p 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 j bs ~ (r/R) 1/2 p/B pol f NI ~I bs /I p ~p/B pol 2 ~ pol ‘Advanced’ scenarios, which aim at steady state, need high , low I p, have to make up for loss in E 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 Tokamak optimisation: steady state operation

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

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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, I p > 30 MA) pulsed reactor The (low confinement) L-mode scenario

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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, I p ~ 20 MA) pulsed reactor

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‘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’)

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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 ~ r 2 / decor ) xB

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

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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 lifetime for 1 st ITER divertor

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-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)

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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 limit (Greenwald) Access to edge transport barrier Pressure driven MHD instabilities

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…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

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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

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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

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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

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Suppression of (2,1) NTM by ECCD ASDEX Upgrade

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Current drive (P ECRH / P total = %) results in removal method has the potential for reactor applications Suppression of (2,1) NTM by ECCD ASDEX Upgrade

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

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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 j bs ~ (r/R) 1/2 p/B pol f NI ~I bs /I p ~p/B pol 2 ~ pol Recipe to obtain high bootstrap fraction: low B pol, i.e. high q – elevate or reverse q-profile (q=(r/R)(B tor /B pol )) eliminates NTMs (reversed shear, no low resonant q-surfaces) high pressure where B pol is low, i.e. peaked p(r) Both recipes tend to make discharge ideal MHD (kink) unstable! In addition, j bs profile should be consistent with q-profile Advanced tokamak – the problem of steady state

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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) j bs (r) p(r) ASDEX Upgrade

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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

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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)

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Good performance can only be kept for several confinement times, not stationary on the current diffusion time (10 – 50 E in these devices) Advanced Tokamak Stability is a tough Problem duration/ E H 89 N /q duration/ E Hybrid scenarios: Reversed shear scenarios ITER reference (Q=10) ITER advanced (Q=5) QDB scenarios JET, JT-60U DIII-D AUG DIII-D JT-60U JET Tore Supra Fusion Performance (~ nT E )

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

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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) A compromise: the ‚hybrid‘ scenario

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A ‘hybrid scenario’: the improved H-mode H 89 N /q (a/R) p q-range ~ Bootstrap fraction ITER (shape corrected) 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 Fusion Performance (~ nT E )

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duration/ E H 89 N /q duration/ E H 89 N /q 95 2 Hybrid scenarios: Reversed shear scenarios ITER reference (Q=10) ITER advanced (Q=5) QDB scenarios JET, JT-60U DIII-D AUG DIII-D JT-60U JET Tore Supra Presently, hybrid scenarios perform better in fusion power and pulse length A ‘hybrid scenario’: the improved H-mode Fusion Performance (~ nT E )

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

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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 L-mode H-mode Advanced operation Safety factor q Hybrid

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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)

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