Validation of theory based transport models in tokamak plasmas Giovanni Tardini PhD thesis Supervisor: Hon. Prof. Dr. R. Wilhelm Special thanks to: Dr. A. G. Peeters (supervisor at IPP), Dr. G. V. Pereverzev, Dr. F. Ryter and the ASDEX Upgrade team G. Tardini, PhD defense, Garching, June 17th 2003

Outline Motivation:  Ultimately, achieve controlled nuclear fusion  Better understanding of energy confinement in tokamak plasmas Outline of the talk  State of the art in transport studies and frame of this thesis  Physics ingredients: fluid drifts, instabilities, critical gradient  Experimental evidence and profile stiffness  Simulation with 1D fluid models  Conclusions G. Tardini, PhD defense, Garching, 17th June 2003

Tokamak configuration Lost by the plasma: particles and energy flowing radially n toroidal windings r dq q = s = n poloidal windings q dr G. Tardini, PhD defense, Garching, 17th June 2003

“State of the art” of tokamak heat transport  Particles “stick” to magnetic surfaces, Coulomb collisions cause radial energy losses Fourier’s law: qj = - nj cj Tj High temperatures for good D-T fusion rate.  good confinement (low c) desired. Heat diffusivities: Predicted: i  0.1 m2/s e  0.001 m2/s Experimental: i  e  1 m2/s  Transport higher in reality + equal for ions and electrons! Not understood? ANOMALOUS. G. Tardini, PhD defense, Garching, 17th June 2003

Plasma turbulence and transport models Anomalous transport: due to small scale microinstabilities (  20 ri  2-5 cm) driving turbulence. Middle 90es: Simplified (1D) theory based models No ad hoc free parameters to fit the data. Affordable computing time compared to full simulations. Easy to check dependences and stimulate experiments. physics interpretation + reliable predictions for new experiments. Free room for extensive modelling! G. Tardini, PhD defense, Garching, 17th June 2003

Particle orbits and drifts Particles gyrate around B, the guide centers follow the field lines. Actually: Drifts due to forces Particle trapping in “magnetic mirror” configuration G. Tardini, PhD defense, Garching, 17th June 2003

Growth of the Ti (ITG) driven instability Cold plasma to cold region: unstable! A mechanism stabilises the mode until a critical Ti is reached G. Tardini, PhD defense, Garching, 17th June 2003

Trapped Electron Mode (TEM) Fast parallel e- motion: e- see also favourable curvature (high field side)  Only fast modes (short wavelengths) !  Small heat transport! γ > vth/qR But trapped e- lock parallel dynamics!! Long wavelengths, high heat transport G. Tardini, PhD defense, Garching, 17th June 2003

T driven modes and profile stiffness G. Tardini, PhD defense, Garching, 17th June 2003

Experimental database ITG dominates with strong ion heating, TEM with electron heating 70 discharges, pure NBI 7 discharges, NBI+ECH 14 discharges, pure ECH Standard: 4 < ne [1019 m-3] < 7 PNBI = 5 MW Ipl = 1 MA Not shown here: ECH power modulation  heat pulses  transient analysis! Ideal to measure stiffness. • moderate stiffness • heat pulses well predicted! • heat flux dependence too 0.8 < PECH [MW] < 1.6 0. < rdep < 0.33 Power scan: 1.8 < PNBI [MW] < 12.5 Current scan: 0.4 < Ipl [MA] < 1.2 Density scan: 3 < ne [1019 m-3] < 8 G. Tardini, PhD defense, Garching, 17th June 2003

Description of the models IFS/PPPL (Dorland, Kotschenreuther) 1995 ITG-TEM, ci and Lcr formulas by fitting gyrokinetic (GK) simulations. ce  ci . Limitations: s > 0.5, Ln > R/6, no electromagnetic (em) effects. Weiland (Weiland, Nordman) 1998 ITG-TEM, fluid equations closed by taking f maxwellian in the 3rd moment (diamagnetic heat flux). Quasi linear transport. Collisionless TEM. No em effects. Simplified q and s dependence. kri = 0.1 . GLF23 (Waltz, Kinsey) 1997 (v1.4) ITG-TEM, fluid closure: trial functions with free parameters fitted to GK theory. Landau damping and s-a stabilisation taken into account. Impurities: default=dilution. Em: default=off. Spectrum with 10 values of kri. CDBM (Itoh, Itoh) 1996 Self-sustained turbulence through current diffusion. Analytical formulas for c, ce = ci . G. Tardini, PhD defense, Garching, 17th June 2003

Experiment and modelling: Ti profile stiffness MODELS • Clear proportionality, Ti(.4)/Ti(.8)2 • Ratio: largely independent on scan and boundary Ti. • ECH lower ratio: due to Te/Ti ITG models reproduce linear relation; right factor. Non-ITG: no proportionality G. Tardini, PhD defense, Garching, 17th June 2003

Electron temperature: moderate stiffness EXPERIMENT MODELS Ratio>2, higher for power scan! Scattering + lower ratio for high Te. Weak stiffness! IFS/PPPL: wrong when electron heating increases (NBI+ECH) due to ce  ci Weiland: very good! Too optimistic for low current. Oversimplified q-dependence GLF23: good. High transport for high ne (occurs at low collisionality). CDBM: too flat profiles! Like ion transport. G. Tardini, PhD defense, Garching, 17th June 2003

Conclusions and outlook • Database: 91 ASDEX Upgrade discharges. Power, density, current scans, wide T-range, ions/electrons heating  suited for transport studies! • Core Ti  pedestal Ti, Ti (0.4)/Ti (0.8)  2 (all scans; also in JET): stiffness. • Electrons: Te (0.4)/Te (0.8) > 2 at low Te, bends for higher Te, higher with strong electron heating: moderate stiffness. • “New language”: data ordered by critical gradient length rather than . Pedestal pressure determines global confinement. • ITG: good for ion transport! Non-ITG: no stiffness. ITG + TEM: well predicted Te. • ce  ci  wrong for strong electron heating. Both ion and electron turbulence required! s and q play an important role, need accurate treating. Open issues: Particle transport (Dr. Angioni); momentum transport. Simulation of Internal Transport Barriers G. Tardini, PhD defense, Garching, 17th June 2003

Controlled fusion Tokamak Stellarator G. Tardini, PhD defense, Garching, 17th June 2003

Stiffness or constant c Reference profile Constant c Stiffness a) Fixed boundary T, increasing heating power b) Constant heating power, changing boundary T G. Tardini, PhD defense, Garching, 17th June 2003

Towards a burning plasma ITG and TEM are not dangerous for a reactor. However: • limit energy confinement  performance • prevent: steep T  bootstrap current  steady state operation Margins of confinement improvement: • high pedestal temperature, e. g. by strong plasma shaping • peaked density profile (problematic; achievable?) • suppressing or reducing turbulence: s < 0 stabilises ITG and TEM sheared plasma rotation. Too little torque in ITER’s plasma core. G. Tardini, PhD defense, Garching, 17th June 2003

Energy: quantitative evaluation G. Tardini, PhD defense, Garching, 17th June 2003

Electron energy: quantitative evaluation G. Tardini, PhD defense, Garching, 17th June 2003

Experimental data G. Tardini, Task Force T Meeting, Culham, May 9th 2003

The ASTRA code and the setup G. Tardini, Task Force T Meeting, Culham, May 9th 2003

“Modern” modelling results G. Tardini, Task Force T Meeting, Culham, May 9th 2003

Experiment and modelling: Ti profile stiffness MODELS • Clear proportionality, Ti(.4)/Ti(.8)2 • Ratio: largely independent on scan and boundary Ti. • ECH lower ratio: due to Te/Ti ITG models reproduce linear relation; right factor. G. Tardini, PhD defense, Garching, 17th June 2003

Experiment and modelling: Ti profile stiffness MODELS • Clear proportionality, Ti(.4)/Ti(.8)2 • Ratio: largely independent on scan and boundary Ti. • ECH lower ratio: due to Te/Ti ITG models reproduce linear relation; right factor. G. Tardini, PhD defense, Garching, 17th June 2003

Experiment and modelling: Ti profile stiffness MODELS • Clear proportionality, Ti(.4)/Ti(.8)2 • Ratio: largely independent on scan and boundary Ti. • ECH lower ratio: due to Te/Ti ITG models reproduce linear relation; right factor. G. Tardini, PhD defense, Garching, 17th June 2003

Electron temperature: moderate stiffness EXPERIMENT MODELS Ratio>2, higher for power scan! Scattering + lower ratio for high Te. Weak stiffness! IFS/PPPL: wrong when electron heating increases (NBI+ECH) due to ce  ci G. Tardini, PhD defense, Garching, 17th June 2003

Electron temperature: moderate stiffness EXPERIMENT MODELS Ratio>2, higher for power scan! Scattering + lower ratio for high Te. Weak stiffness! GLF23: good. High transport for high ne (occurs at low collisionality). G. Tardini, PhD defense, Garching, 17th June 2003

Electron temperature: moderate stiffness EXPERIMENT MODELS Ratio>2, higher for power scan! Scattering + lower ratio for high Te. Weak stiffness! Weiland: very good! Too optimistic for low current. Oversimplified q-dependence. G. Tardini, PhD defense, Garching, 17th June 2003

Tokamak configuration Lost by the plasma: particles and energy flowing radially n toroidal windings r dq q = s = n poloidal windings q dr G. Tardini, PhD defense, Garching, 17th June 2003

Conclusions and outlook • Database: 91 ASDEX Upgrade discharges. Power, density, current scans, wide T-range, ions/electrons heating  suited for transport studies! • Core Ti  pedestal Ti, Ti (0.4)/Ti (0.8)  2 (all scans; also in JET): stiffness. • Electrons: Te (0.4)/Te (0.8) > 2 at low Te, bends for higher Te, higher with strong electron heating: moderate stiffness. • “New language”: data ordered by critical gradient length rather than . Pedestal pressure determines global confinement. • ITG: good for ion transport! Non-ITG: no stiffness. ITG + TEM: well predicted Te. • ce  ci  wrong for strong electron heating. Both ion and electron turbulence required! s and q play an important role, need accurate treating. Open issues: Particle transport (Dr. Angioni); momentum transport. Simulation of Internal Transport Barriers G. Tardini, PhD defense, Garching, 17th June 2003