1 Low-collisionality density-peaking in GYRO simulations of C-Mod plasmas D. R. Mikkelsen, M. Bitter, K. Hill, PPPL M. Greenwald, J.W. Hughes, J. Rice, MIT J. Candy, R. Waltz, General Atomics APS Division of Plasma Physics Annual Meeting Atlanta, 2-6 November 29
2 Overview of density peaking simulations Angioni, et al., Phys. Plasmas 1 (23) GLF23 simulations apparently explain observations. Higher collisionality reduces the anomalous pinch due to trapped electrons. Angioni, et al., Phys. Plasmas 12 (25) GS2 quasilinear gyrokinetic estimates of particle flux. raising collisionality turns off the pinch, but the transition is much too early. poor mode choice: low k θ ρ i ~.2 (motivated by TEM heat transport study) Mikkelsen, et al., APS-DPP 27; nonlinear GYRO, C-Mod H-mode pinch is driven by modes with k θ ρ i >.5 - missing from quasilinear work! Maslov, et al., Nucl. Fusion 49 (29) 7537, QL peaking in JET H-modes. different mode choice: modes at max. growth rate do generate a pinch. raising T e /T i increases the pinch (if ITG is still the dominant instability). Angioni, et al., Phys. Plasmas 16 (29) 672. nonlinear GYRO for AUG: k-spectrum of particle flux similar to C-Mod. collisionality and energy dependence in analytic quasilinear expression.
3 Is Peaking Factor the Same for D & H? Different peaking factors for D & T in ITER could be important: stronger tritium peaking would make tritium fueling easier (and vice versa). Phase-contrast-imaging system on C-Mod enables core n H /n e measurement. Data indicates that core n H /n e is lower than edge n H /(n D +n H ) (from D α light); and plausible Z eff can't explain the diffference. A dedicated experiment with controlled H puffing is planned with n H ~n D. GYRO simulations can be used to derive the density profile shape that is 'predicted' to produce null particle flux, when the pinch balances diffusion; this applies to steady-state C-Mod plasmas with no core fuelling. Quasilinear estimates of particle flux are unreliable, so nonlinear 'global' simulations are used here.
4 C-Mod peaked-density regime Discovered with JFT-2M shape: produced low-density H-mode plasmas. low κ, high δ lower >.75, lower target density. Pedestal density is especially low, and T ped is high,.8-.9 kev Pedestal is wider, infer larger D causes lower n e, higher T e ELMs. Higher density ohmic EDA H-modes with same profile shape are not unusual. Density peaking also seen in standard shape, with lower I p. Surprise result: Density profile is peaked; in RF-heated H-mode plasmas peaking is never seen at higher densities. ITBs have central density peaking, but flat periphery; this regime has flat central region and a density gradient for >.5
5 Lower Density H-Modes Have Peaked Profiles Greenwald, et al., Nuclear Fusion 47 (27) L26 Lower L-H threshold density ELMs seem to reduce rate of density rise in H-mode Whatever the cause: Standard H-mode n e /<n e > = L n >> a, R/L n ~, R/L Te ~ 6-7 Low-Density H-mode n e /<n e > = 1.5 R/L n ~ 3-4, R/L Te ~ 6-7
6 Difference In Profile Shape Is Notable Peaking is seen over outer 6% of plasma radius H-mode profiles evolve quickly; τ << a/v WARE Transport in center of plasma may be affected by sawteeth These are of large amplitude; δt e /T e ~ 25% Radii chosen to characterize peaking in ASDEX-U are =.4 Sawtooth Inversion Radius =.8 appropriate for C-Mod profiles
7 Increased Density Peaking At Low Collisionality Observed For ICRF Heated H-Modes In C-Mod New Shape Standard Shape
8 C-Mod Data Helps Break Covariance Between ν eff and n/n G ITER ITER ICRF Only ICRF Only ν EFF = ν ei /ω D.1RZ EFF <n e >/<T e > 2
9 T i Differs from T e at Low Density Low collisionality is linked to other important changes in C-Mod plasmas. T i profile is less peaked than T e in low-density H-mode plasmas. T e -T i can be large, but Q ie is < 1 MW. central T i is apparently not consistent with the neutron rate, but is the deuterium distribution Maxwellian at 2 nd harmonic of ICRH? Measured L Ti is longer than L Te for ~.6 relaxed T i profile at low density reduces the ITG drive, but Higher T e /T i increases ITG drive. Kinetic electron drive depends strongly on collisionality at these densities. The relative importance of different microinstability drives changes as collisionality is reduced, so the details may differ from JET and AUG.
10 Standard H-mode Flat density profile n e ()~3.3x1 2 m -3
11 n e ()~2.1x1 2 m -3 Peaked density H-mode
12 n e (1 2 /m 3 ) T i profile relaxes as density drops As density is lowered the density peakedness rises, and T i () drops (T i is less tightly coupled to T e at all radii). Consequently, the L Ti is longer than L Te for ~.6 The relaxed T i profile at low density reduces the ITG drive, very close to the ITG threshold for the lowest density cases. 3 2 T i (kev)
13 Simulation Procedure Electrostatic turbulence, with kinetic ions and electrons. Measured T e (r) and n e (r) are used in GYRO simulations presented here. The measured T i (r) has been used but these have stable regions, so oscillations in R/L Ti are removed to smooth the profiles. Simulations have only deuterium and electrons, but the 'resistive' Z eff value is used in the collisionality. Shaped geometry is used. ExB shear is ignored (but expected to have a small effect). As the density gradient is varied, the particle flux changes; this is used to estimate the R/Ln that would produce null particle flux at each radius. The extrapolated R/Ln is integrated to find the 'predicted' density profile.
14 3 2 T i (kev) 1 T i modifications are small T i (kev) flattened R/L Ti profles Measured T i (r) is matched near center and edge, R/L Ti is smoother in between. 1 R/L Ti R/L Ti
15 Stronger density peaking at low e ! e -.5 sec flat R/L Ti -.1 Exptl. ne R/Ln raised 3% Inward pinch is much stronger with lower collisionality below..2.1 sec flat R/L Ti (exptl. " e )/3 n e (1 2 /m 3 ) sec flat R/L Ti Exptl. ne Extrapolated! e = sec flat R/L Ti! e Exptl. ne R/Ln raised 1% n e (1 2 /m 3 ) 2 Exptl. ne Extrap. exptl.! e Extrap. (exptl.! e )/
16 D e (k! " s ) (arb. units) Higher k modes are responsible for the pinch exp. # e # e / k! " s More modes contribute to the pinch at lower collisionality. Raising the density gradient reduces the pinch at all k θ ρ s. D e (k! " s ) (arb. units) Need to do some simulations with higher maximum k θ ρ s k! " s Missing inward flux at low collisionality is probably larger than missing outward flux at high collisionality, so the present simulations probably underestimate the density peaking at the null flux condition exp. R/L n R/L n *2.4 R/L n *2
17 a/l n, a/l Ti and Mix of Ions is Varied Results from six pairs of simulations are shown next. Use particle fluxes, Γ x, for the standard a/l n & lower a/l n of each pair to estimate the a/l n that would give Γ x =. Two sets of a/l Ti are used for each combination of ions. Need assessment of power dependence of peaking factor, simulations with more ITG drive may show less peaking. Only D, with standard a/l Ti and 1% boost. 5:5 D:H at all radii, with standard a/l Ti and 1% boost. 42:42:3 D:H:B at all radii, with 2% & 3% boost of a/l Ti. (dilution of hydrogenic isotopes reduces turbulence)
18 Extrapolation Exhibits Density Peaking! e.2.1 (a.u.) a/l ne 1.5 Std a/l n low a/l n DH_gT Std. al n low a/l n! e = root polynomial fit DH_gT a/l ne for Γ e = diverges where simulated fluxes cross: ~.41, but the extrapolation integrates to make only a small n e (r) jump. The smoother polynomial fit to the Γ e = root is not needed here. n e (r) (1 2 /m 3 ) Std. a/l n low a/l n!= root polynomial fit DH_gT
19 Electron Density Peaking is Robust 2.4 Electron density peaking is insensitive to variations in the ion species mix and to a wide range of transport powers. n e (r) (1 2 /m 3 ) GYRO Q tot (MW) 3 D_gT1 DH_gT1 DHB_gT2 DHB_gT
20 ! D.2.1 (a.u.) a/l nd.5 Ion Fluxes Require Smoothing Std. a/l n low a/l n Std. smoothed low smoothed Std. a/l n low a/l n! D = root polynomial fit D_gT1 D_gT Low-order (n=2,3) polynomial smooths the ion fluxes. Extrapolated root and n D (r) are similar to companion run's n e (r). Expect this for ambipolar ExB transport with one ion species. n D (r) (1 2 /m 3 ) Std. a/l n low a/l n! D = polynomial fit D_gT
21 ! H.2.1 (a.u.) a/l nh.5 Hydrogen Density is Less Peaked Std. a/l n low a/l n Std. smoothed low smoothed DH_gT Std. a/l n low a/l n! H = root polynomial fit DH_gT Extrapolated Γ H = root has much lower values of a/l nh, so n H (r) peaking is lower than for the electron density, and n D (r) peaking is higher n H (r) (1 2 /m 3 ) Std. a/l n low a/l n! H = polynomial fit DH_gT
22 Deuterium is More Peaked than Hydrogen D & H density peaking is insensitive to the variation in the transport power. 1.2 n(r) (1 2 /m 3 ) 1 D DH_gT1 D DH H DH H DH_gT
23 Improved Simulation Methodology A significant separation of a/l nx at all is needed. varying the overall a/l ne is undesirable, that changes Q tot. GYRO can handle multiple ions, so use 2-3 ion species with identical A,Z for each isotope. Make offsetting changes to a/l n so total density is unaffected. Same turbulent eddies affect both high- and low-a/l n 'species', so the dependence on a/l n is accurately captured in one run. Two 'species' define D and V pinch, three confirm linearity. This method works very well for trace impurities (see N.Howard poster) New run with extrapolated density profiles needed to confirm the prediction: the turbulent drive is affected by the new a/l n.
24 Summary of Isotope Peaking GYRO simulations exhibit collisionality-dependent peaking. Nonlinear work supports analytic quasi-linear estimates that may provide a detailed framework for understanding. See E. Fable, et al., PPCF 5 (28) 1155, and C. Angioni, et al., Phys. Plasmas 16 (29) 672 and PPCF 51 (29) D & H have different peaking factors in GYRO simulations. A C-Mod experiment to measure D&H peaking is planned. ITER simulations are needed to study D&T peaking. A more robust simulation methodology will be used in future.
25 'Predicting' Intrinsic Rotation C-Mod has long exhibited 'intrinsic' rotation with no (intended) momentum source (RF deposition may be preferential?). GYRO can calculate radial transport of toroidal momentum. [Waltz, et al., Phys. Plasmas 14 (27) 12257] Use it to assess the rotation generated by turbulence. Assume there is no external torque in the simulation domain. Look for the rotation profile that is consistent with null radial flux of toroidal momentum - i.e., consistent with steady rotation. The controlling GYRO input variable is actually E r ; NEO will be used to 'back out' the implied rotation speeds. The E r profile is modified iteratively to achieve null flux; for this problem, the radial gradient of E r is varied to find the root.
26 Null-flux Root has Smaller E r Gradient.4! mom (a.u.) a*(de r /dr) (kv/m) Std. E r E4.3*grad-E r Std. E r.3*grad-e r! mom = root E4-15 polynomial fit de r /dr for Γ mom = diverges where simulated fluxes cross: ~.7, so smooth out the ragged root with a polynomial fit. Integrate the polynomial fit to find the profile of E r : E r (kv/m) Std. E r.3*grad-e r fit to root E
27 4 Qualitative 'Agreement' with Expt. 4 E4 E29 E r (kv/m) 2 E r (kv/m) 2 E r (kv/m) Std. E r.3*grad-e r fit to root Std. E r grad-e r =-2 fit to root E Std. E r.3*grad-e r fit to root Higher rotation cases, '4 & '29 are 'predicted' to have higher rotation (implicit in E r profiles). The implied rotation profiles are expected to lie well outside the uncertainties of the v φ data. The prediction uncertainties are not yet estimated.
28 Improved Simulation Methodology-2 A significant separation of de r /dr at all is needed. integrate (Std. de r /dr - Constant) to create the secondary E r. This will change the ExB shear, so move de r /dr toward zero to avoid strengthening the ExB-shear turbulence quenching. New runs are in progress, but no results are available yet. At this point the turbulently generated intrinsic rotation is not sufficient to explain the observed rotation speeds - but there are other proposed mechanisms that may shoulder the burden. On the other hand, it appears that turbulently driven rotation is not small enough to ignore when building a complete picture.