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Optimizing the current ramp-up phase for the hybrid ITER scenario

Optimizing the current ramp-up phase for the hybrid ITER scenario G.M.D. Hogeweij 1 , J.-F. Artaud 2 , T.A. Casper 3 , J. Citrin 1 , F. Imbeaux 2 , F. Köchl 4 , X. Litaudon 2 , I. Voitsekhovitch 5 , and ITM-TF ITER Scenario Modelling group

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Optimizing the current ramp-up phase for the hybrid ITER scenario

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  1. Optimizing the current ramp-up phase for the hybrid ITER scenario G.M.D. Hogeweij1, J.-F. Artaud2, T.A. Casper3, J. Citrin1, F. Imbeaux2, F. Köchl4, X. Litaudon2, I. Voitsekhovitch5, and ITM-TF ITER Scenario Modelling group 1FOM Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM, Trilateral Euregio Cluster, Nieuwegein, The Netherlands, www.rijnh.nl 2CEA, IRFM, F-13108 St-Paul-Lez-Durance, France 3ITER Organization, F-13115 Saint Paul lez Durance, France 4Association EURATOM-ÖAW / ATI, Atominstitut, TU Wien, 020 Vienna, Austria 5 EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB UK Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  2. Research Questions to be addressed: • Find ”best scenario” for current ramp-up phase of hybrid ITER discharges: • arrive at hybrid q profile (q0~1, large low shear region) at L-H transition • while minimizing flux consumption • Knobs: settings of heating systems , density, Ip ramp rate • Assess sensitivity of result with regard to choices like • - transport model used • - density profile shape • - density • - Zeff • - boundary conditions (Te, Ti) • - choice of geometry Note: Optimization of Current Ramp-up for baseline 15 MA ITER scenario well documented and well validated (e.g. Hogeweij EPS2010; Imbeaux Nuc.Fus.2011) However this phase not well established for hybrid scenario (~12 MA) Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  3. Overview 1. Choice of transport model – validation 2. Assumptions made 3. What is a “good” q profile 4. Choice of heating and current drive scheme 5. Reference scenario with and without LHCD 6. Sensitivity analysis 7. Current ramp rate and current overshoot 8. Operational limits and Flux consumption 9. Extrapolation to burn phase 10. Conclusions and Discussion Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  4. Choice of transport model – validation • Various transport models have been validated to current ramp-up phase of JET, AUG, • TS, and (recently) also to DIII-D: • Empirical scaling-based model with a prescribed radial shape of ce = ci (parabola plus high power of r to have high edge diffusivity), renormalised to H-mode scaling of global energy content H98 = 0.4; [or, equivalently, L-mode, L97=0.6] • Semi-empirical Bohm-gyroBohm model (L-mode version, ITB shear function off) • Semi-empiricalCoppi-Tang model – will not be used here • First-principle based GLF23 – will not be used here Generally both scaling-based model with H98 = 0.4 and Bohm-gyroBohm (L-mode version) do a good job on existing experiments Next sheet: some examples from DIII-D and JET Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  5. Choice of transport model – validation (ctd) Left: JET, LHCD-assisted ramp-up case Black: data Cyan: Bohm-gyroBohm Red: scaling-based Right: DIII-D, NBI-heated ramp-up case Black: data Blue: Bohm-gyroBohm (ASTRA: solid, CRONOS: dashed) Red: scaling-based Green: Coppi-Tang [Voitsekhovitch, ITPA pres., Oct 2011] Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  6. 2. Assumptions made • Expanding ITER shape, starting on LFS of torus (geometry taken from ITER team) • X-point formation takes place after 15s, when Ip = 3.5 MA. • (ii) Zeff profile flat, decreasing in time with increasing ne, with final value of 1.7 • (iii) A rather low density of ne = 0.25 ne,GW is taken. • (iv) ne profile parabolic with moderate peaking factor ne(0)/<ne> = 1.3 • Compromise between the (unrealistic) flat ne profile used by the ITER team and the peaking factor of ~1.5 predicted by scaling studies • Total input power below the L-H threshold during whole ramp-up phase; • come back to issue of L-H transition during ramp-up later • Ip ramp rate is chosen such that Ip = 12 MA is reached after 80 s • faster current ramp and current overshoot dealt with later on • Other assumptions (Te,i(edge), initial Te,i , initial li) based on experimental evidence The simulations start 1.5 s after breakdown, when Ip = 0.5 MA Simulations are done with CRONOS suite of transport codes Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  7. 3. What is a “good” q profile ITG theory predicts critical gradient like (this one from Romanelli, but many similar formulas) So it makes sense to maximize the volume integrated s/q under the constraint q(r) >~ 1 to avoid sawteeth, thus to avoid NTM triggering • Therefore hybrid regime: q profile characterized by • q(r) >~ 1 everywhere: avoid sawteeth, thus avoid triggering NTMs • large region of flat q(r), in order maximize magnetic shear in outer region, • and thus to maximize “figure of merit” ℱ = <s/q> • no regions with strong negative shear should exist • [to avoid the creation of ITB, which would make control of the plasma much more complicated, and to avoid deleterious MHD, e.g. double tearing modes] Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  8. 4. Choice of heating and current drive scheme • To avoid too fast drop of q profile we need off-axis heating & current drive • When we look at the systems available on ITER: • ICRH: heats on- or off-axis (by choosing freq.), but does not drive strong off-axis current • ECCD from Equatorial Launcher: heats very centrally (for ramp-up parameters) • Useful systems are • NBI (off-axis mode) – wide power deposition, typical rdep ~0.3 • ECCD from Upper Port Launcher – narrow power deposition, • typical rdep >~ 0.4 / 0.6 for 4th / 5th antenna • LHCD – narrow power deposition, typical rdep ~0.3-0.6 depending on plasma params • Furthermore: • LH does not belong to ITER base line design, so we will optimize both with and without LHCD, to see what one wins with LHCD • We want to stay in L-mode, so total input power <~ threshold power for L-H transition Example of driven current density profiles: 8 [+5] MW of ECCD from UPL 3 MW of LHCD 16.5 MW of NBI (green). Plus bootstrap current And total non-inductive current Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  9. 5. Reference scenario with and without LHCD (ctd) a. Best scenario with LHCD using scaling model Left: Time traces for the reference case, assuming scaling model – additional heating is switched on at 55 s to avoid q(0) from dropping below 1 Lower frames: also time traces without additional heating (dotted) Right: Te,i and q profiles @ 80 s for the same cases Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  10. 5. Reference scenario with and without LHCD (ctd) b. scenario without LHCD (still using scaling model) What happens if we do not use LH (power was 3 MW)? Compare profiles at end of ramp-up (80 s), using scale model: So LHCD has only marginal effect both on q and on Te at end of ramp-up • However, LHCD is most efficient current driver, in particular in early phase of ramp-up  • early switch-on of strong LHCD can reduce flux consumption significantly (~10-15%), • thus enabling extension of burn phase by several 100s of seconds • Early LHCD can create strongly reversed magnetic shear, • important for ITB/Steady State scenario (not elaborated here) Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  11. 6. Sensitivity analysis a. choice of transport model Bohm-gyroBohm model is more pessimistic than scaling model Predicted faster current penetration compensated by 20 s earlier switch-on of LH + ECH Left: Time traces for the optimized scenario, assuming scaling model (full lines) or Bohm-gyroBohm model (dashed lines) Right: Te,i and q profiles @ 80 s for the same cases Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  12. 6. Sensitivity analysis b. effect of Zeff and of density profile shape Current density evolution affected by ne shape: more/less peaked ne flatter/more peaked Te  slower / faster current penetration Similar effect of Zeff : lower/higher Zeff slower / faster current diffusion Effect can be counteracted by 5-10 s later / earlier heating Effect can be counteracted by 10-15 s later / earlier heating Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  13. 6. Sensitivity analysis (ctd) c. effect of lower/higher density, of lower/higher Te,i(edge) • Lower / higher density • (modelled 0.15 / 0.35 neGW in stead of 0.25 neGW): • Can be accounted for in similar way. • Higher density may be profitable: • Higher L-H threshold power; • NBI can be switched on earlier (less risk of shine-through) Lower/higher edge temperature: only small effect on current penetration, can be easily accounted for (not shown here) Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  14. 6. Sensitivity analysis (ctd) d. effect of initial geometry Recently the ITER team is considering breakdown at HFS instead of at LFS  different geometry in very early phase of the discharge. q profiles @ 50 s Effect of this on the current density evolution turns out to be negligible after ~50s Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  15. 6. Sensitivity analysis (ctd) e. real-time adaptive determination of auxiliary power switch-on time Current diffusion sensitive on parameters that are not easily controlled  development of real time control important to reach target q profile First step: real-time adaptive determination of auxiliary power switch-on time Sensitivity analysis showed: for many parameters deviation of expected value accounted for by shift of heating wave form Denote a set of observables (Zeff, <ne>, etc.) as: Let the values of the reference case be: and let t0 be the starting time of the external heating in the reference case. Then start time of the heating would depend on the measured values of the observables in the early phase of the current ramp-up as follows: where the ai have been determined by the sensitivity analyses as shown before Example: combination of flat density and high Zeff q profiles @ 80 s Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  16. 7. Current ramp rate and current overshoot • So far, all simulations were done with a moderate current ramp rate, reaching • the flat top of 12 MA at 80 s. • However, the ITER hardware would allow for a faster current rise • Current overshoot: • Improved confinement shown in recent JET experiments • Favourable effect also shown in control oriented approach [Felici PPCF 2012] • solve non-linear, constrained, finite-time optimal control problem to find the • tokamak actuator time evolution required to optimally reach a given point • in the tokamak operating space while satisfying a set of constraints • Therefore simulations have been done • with a higher current ramp rate, reaching the flat top of 12 MA at 60 s • and with, additionally, a current overshoot up to 14 MA at 70 s, lasting for 10 s Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  17. 7. Current ramp rate and current overshoot (ctd) • Time traces for 3 cases: • the reference case (blue) • fast current ramp case (green) • case with fast current ramp and current overshoot (red) • For the latter two cases the heating scheme was re-optimized Conclusion: Current overshoot gives by far the most favourable q profile Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  18. 8a. Operational limits Post process simulation results with free boundary equilibrium code FREEBIE [run in Poynting mode] to check that simulations are within boundaries put by the design values of CS and PF coils Most critical coils turn out to be the central solenoid coil CS1ULU+CS1ULL and the first poloidal field coil PF1 • Currents in the most critical coils for 3 cases: • the reference case without additional heating (blue) • reference case with additional heating (green) • case with fast current rise and current overshoot (red) • Maximum and minimum allowed currents are plotted in black • Conclusion: • Scenario, also with faster current rise and overshoot, well within operational limits • However, extrapolating: current rise cannot be much faster Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  19. 8b. Flux consumption Long flat-top phase  reduce flux consumption during current rise as much as possible Distinguish between resistive and inductive flux Follow method first described by Ejima, applying Poynting's theorem to the poloidal field: Total poloidal flux change at plasma surface: with ∆YI at end of current ramp-up determined by poloidal field, e.g. the q profile, attained; since this should always be close to the same, ideal shape, ∆YI will always be more or less the same at the end of the ramp-up Hence, if flux consumption is to be saved, it should be in the resistive part; therefore, we restrict the analysis to ∆YR. Note: at end of ramp-up phase both parts are of the same order of magnitude. • Two ways to reduce ∆YR: - by (very) early heating • - by early transition to the H-mode • For both a representative example will be shown … Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  20. 8b. Flux consumption (ctd) • Early heating: • @ 30s add 10 MW LHCD + 6 MW ECH (EQL) •  considerable core heating & current drive • 2. Early transition to the H-mode: • @50 s full (33 MW) NBI power + 37 MW ECRH • L-H transition @55 s • after transition: 4 keV pedestal, ne = 0.9*ne,Gw • H-mode phase simulated both with the empirical scaling model (now assuming H = 0.8) and with the GLF23 transport model, with quite similar results. • Result: Significant reduction of flux consumption (most with early heating) • However, there is a price to be paid ….. Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  21. 8b. Flux consumption (ctd) • Good q profile is lost for both cases • Early heating case also shows strong reversed shear region (which was to be avoided) • Let’s look bit more systematic into trade-off • minimizing flux consumption  optimizing q profile • Useful figure of merit for the resistive flux consumption during the current ramp-up • is the so-called Ejima coefficient: • calculated at the end of the current ramp-up • Look at figures of merit, CE and ℱ, together Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  22. 8b. Flux consumption (ctd) • CEandℱ for • the reference case (square) • early heating case (diamond) • early H-mode transition case (circle) • fast current ramp case (pentagram) • current overshoot case (hexagram) • Horizontal axis: total input energy during ramp-up • To put into perspective: reduction of CE by 0.1 corresponds to a saving of ~9 Vs • This would correspond to an extension of flat top duration by 200-300 s, i.e. ~10% • So flat-top can be extended by ~10% by early heating or early H-mode, however at cost of a strong reversed shear region or less well-developed q profile, respectively • On the other hand, fast current rise combined with current overshoot leads to a superior q profile, but at the cost of a reduced flat-top length by ~10% • Two remarks to the latter case: • This reduction may be much smaller, since an optimized q profile leads to better plasma performance and thus lower Vloop during the flat-top • Since roughly Pfus ~ ℱ, it may well be that the neutron fluence [which maximization is one of the goals of the hybrid scenario] is higher for the case with current overshoot Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  23. 9. Extrapolation to burn phase Final goal is to sustain optimized q profile during the ~3000 s flat top, in order to maximize the neutron fluence two more questions important: how does the q profile react to the L-H transition can q be held stationary during the long flat top • a) Assess the evolution of the q profile during the L-H transition: • simulations based on the reference case, where in 20 s after end of the ramp-up: • power was raised to 70 MW (33/37 MW NBI/ECRH, clearly above L-H threshold) • L-H transition was forced by imposing 4 keV pedestal • At same time ne was raised to <ne>= 9 1019 m-3 i.e. hybrid scenario target density • a particle heating was taken into account in the modelling. • It turned out that during this transition the core q profile was preserved very well • b) Was addressed in earlier work, which showed that, under reasonable assumptions for the pedestal, indeed q can be held stationary during flat top [Citrin NF 2010] Note: non-optimized q profile at start of burn phase can be “cured” during burn phase However, due to the very low resistivity in this phase, this may take up to ~1000 s In such case one may expect a significantly reduced fusion power during the first ~1000 s of the total burn phase of ~3000 s Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  24. 10. Conclusions and Discussion The heating systems available at ITER allow the attainment of a hybrid q profile at the end of the current ramp-up, using NBI, ECCD (UPL) & LHCD A heating scheme with only NBI and ECCD is almost effective for attainment of hybrid q profile However, LHCD most effective when it comes to save flux consumption or to create strongly reversed shear for ITB/Steady State scenario FREEBIE post-processing shows scenario well within operational limits • Moreover, it was shown that the “good” q profile can be maintained • through the L-H transition • during ~3000 s flat top Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

  25. 10. Conclusions and Discussion (ctd) • Regarding sensitivity analysis: • Optimum heating scheme depends on chosen transport model • Modified assumptions on ne peaking, edge Tei and Zeff can be easily accounted for by • a shift in time of the heating scheme • Higher density during the ramp-up phase can be accounted for equally well, and might • even be profitable because it gives more freedom in the application of the CD sources • First result shown of real-timeadaptive determination of auxiliary power switch-on time • Regarding trade-off between flux consumption and optimized q profile: • early heating or early H-mode  longer flat-top, however at cost of a strong reversed shear region or less well-developed q profile, respectively • fast current rise combined with current overshoot  superior q profile, but at the cost of a reduced flat-top length • Due to superior fusion performance, neutron fluence [total number of neutrons per discharge] may be higher for the case with current overshoot Further study needed with regard to discrepancy between Bohm-gyroBohm and scaling model (which is in contrast with results on existing experiments) Dick Hogeweij, ISM Working Session, Vienna, 21 May 2012

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