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Fig.6_taue 6_Fig_taue: Energy confinement times form the ISS95 [24] scaling vs. experimental confinement times. The colored data indicate contributions to.

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Presentation on theme: "Fig.6_taue 6_Fig_taue: Energy confinement times form the ISS95 [24] scaling vs. experimental confinement times. The colored data indicate contributions to."— Presentation transcript:

1 Fig.6_taue 6_Fig_taue: Energy confinement times form the ISS95 [24] scaling vs. experimental confinement times. The colored data indicate contributions to the International Stellarator Confinement Data Base after von Dinklage: W7ASrev_Fig6.x_ScalingFig1 als.pdf

2 Fig.6_dose Fig. 6_dose: Left: Experimental results of a single variable density scan (full circles) compared to the predictions of the present semiempirical theory [Ref.Theory] (continuous line, shaded area represents the error, warum wird der so groß bei ganz kleinen und ganz großen Dichten ?) for B = 2.5 T, P = 0.45 MW, a = m. The input data (open circles) are shown regardless of additional variations in B, P, a, and are therefore spread all over. The histogram accounts for their distribution over the density axis. A least­squares fit of the input data would yield W ∝ n 0.39 (dashed line). Right: Single variable power scan with n = 2.4 × m − 3, B =2.5 T, a =0.176 m. The histogram is again with respect to the input data (Warum ergeben viele open circles so wenige schwarze Punkte ?). The result is represented by the solid line with the shaded area as the error. A least­squares fit of the input data would yield W ∝ P 0.5 and hence τ E ∝ P −0.5 (dashed line) [5]. -> warum liegt der fit ganz woanders als die Daten ? von Dinklage: W7ASrev_Fig6.x_dose als.pdf

3 Fig.6_stroth Fig. 6.3: Left: Evolution of the energy confinement time in a density scan in W7­AS. The discharges at B =2.5 T and ι a =1/3 were heated with 0.45 MW ECH. The dashed curve is a result from a regression analysis restricted to n<4.5 × m −3. Right: Discharges from density ramps with P =0.68 MW. The hatched areas indicate the predictions for the saturation density according to an empirical scaling as n sat ∝ V −0.45 P 0.55 M 0.6 Z −0.4 [21]. von Dinklage: W7ASrev_Fig6.x_Strothdensit als.pdf

4 Fig.6_chiHPchiPB Fig.: Ratio of heat pulse to power balance electron thermal diffusivity in W7-AS as a function of heating power (from (Hartfuss_1994_PPCF)). For a dependence chi_E prop gradTe one expects chiHP/chiPB=1 von Stroth: hier screenshot aus.pdf

5 Fig.6_Abschalt Fig.:Figure 2: Simulations of the dynamic phase after decreasing the ECH power at t = 0 by 0.45 MW. Three models are used: chi(r) changes instantaneously with P (solid line), chi(r) prop T(r) (dashed) and prop gradT(r) (dotted). The simulated changes in T are compared with ECE data at r/a = 0.22 for example. (Adapted from (Stroth_1996_PPCF)) von Stroth: hier screenshot aus.pdf

6 Fig.6_recentchHPchiPB Fig.: von Stroth: hier screenshot aus.pdf

7 Fig.6_iroot Fig. 6.3: Particle fluxes from particle balance analysis compared with ambipolar neoclassical predictions from the DKES code (dashed) for a discharge in the optimum confinement and with normal confinement at comparable conditions. The neoclassical transport coefficients were predicted to decrease in the outer radial region due to their temperature dependence. -> 1.35 MW NBI+750kW ECRH : #34313 n0=6 1020m-3 QiQe  neErTe,i aus: Referenz: Kick_1999_PPCF (SW), Kick_EPS Vortrag in Farbe, Baldzuhn_1998_PPCF exp. und neo Flüsse der Vergleichsentladung (links) mit in Fig. eintragen (Kick_1999_PPCF) Linien sind in den DKES Ausdrucken oft nicht leicht auseinander zu halten: Bild besser machen ? (Farbe ?))

8 Fig.6_ehmler Fig. Figure [Er_Li-beam]: Er(r) measured by the Li-CXS diagnostic (symbols; the data of C6+ have higher accuracy) compared with results from neoclassical calculations: Without Er-diffusion (b), with radial diffusion that determines the width of the i.e. a velocity shear layer (c) and the approximation proportional to the pressure gradient. (stimmt das - im paper nachlesen) b) the solution of the algebraic ambipolarity constraint; c) the solution of a diffusion equation for the radial electric field based on a thermodynamic approach. The diffusivity originates from the plasma viscosity. von Ehmler

9 Fig.6_eroot Fig. 6_eroot: radial electric fields were measured in the plasma center by active charge-exchange recombination spectroscopy of He impurity lines [baldzuhn_1998_ppcf]. Qi Qe  ne Er Te,i zunächst von Balddzuhn.pdf

10 Fig.6_RADI Fig. 6_RADI: zunächst von Balddzuhn.pdf

11 Fig.6_Wdiaiota Fig.6_Wdiaiota: Variation of the plasma energy with the boundary value  a of the rotational transform in net current free discharges. Symbols represent the measured diamagnetic energy. In addition, the electron kinetic energy content is shown as calculated from the transport model (see 6.4.2) with the small shear in the vacuum field taken into account (full line) or not (dashed line). (PECRH = 340 kW, ne about m-3) SHOT NUMBERS von Brakel: f02.cm4c1.ioscan&17028.gif

12 Fig.6_WdiaItorr [W7ASrev_6_Fig_WdiaItorr]: Plasma energy (experiment, derived from diamagnetic loop data, for details see ref. PPCF97 or NF02) and calculated electron kinetic energy content (model) versus  a for various net plasma currents I p. For three discharges with 5 kA density control has been lost and the measured energy (crossed squares) has been scaled to the reference density by n e 1/2. (P ECRH = 450 kW, n e  4.0  m -3 ) von Brakel: f03.iota-ip-scan.gif, rechte Seite nicht unbedingt notwendig (braucht aber keinen zusätzlichen Platz

13 Fig.6_profileiotascan [W7ASrev_6_Fig_profileiotascan]: Electron density and temperature profiles for selected discharges of Fig. 3 at degraded and optimum confinement. von Brakel: f ff.thoms_prof.gif

14 Fig.6_RTPW7AS [W7ASrev_6_Fig_RTPW7AS]: The enhancement  nm of the anomalous electron heat conductivity at rational surfaces according to Eq.6.2 of the transport model for  = 0. The position of the low order rational values is indicated. The heat conductivity from the RTP model is shown for comparison [23]. von Brakel: f08.chinm.gif

15 Fig.6_transpanalysis [W7ASrev_6_Fig_transpanalysis]: Electron temperature profiles and profiles of the electron heat conductivity derived from power balance and from neoclassical calculations for selected discharges of Fig.6_profileiotascan at different plasma currents and iota_a = von Brakel: f ff.te_und_chi.gif

16 Fig.6_lohi-exptheo [Fig.6_lohi-exptheo]: Experimental (data points and full lines, from Thomson scattering) and calculated (dotted lines, from the model) radial profiles of n e, T e, and  e and  for discharges with low (I p = 0) and high (I p = 5 kA) confinement at  a = For comparison the  - profiles calculated by the NEMEC and DKES codes are also given (dashed-dotted lines). von Brakel: f09.cm2c1_vs_exp.io480.gif

17 Fig.6_Itfree [W7ASrev_6_Fig_Itfree]: Evolution of plasma current (left) and diamagnetic energy (right) for discharges with initial current control at levels I p,0 and free running current after the external loop voltage is switched off (vertical bar). The right frame shows the full evolution to high confinement of W dia, I p and central T e (from ECE). Because the stationary high confinement regime with a bootstrap current of 8.1 kA cannot be reached within a discharge time at W7-AS, the full evolution is constructed by shifting the time scale of the Ip,0 = 2, 5, 7.3 kA discharges such that their traces continuously match. (P = 400 kW, n e  4.0  m -3,  ex,a = 0.45). von Brakel: f12.bif.48107ff.w_and_ip.gif, zugeschnitten: nur oberer und unterer frame

18 Fig.6_kspect Fig. Poloidal wavenumber spectrum from a SOL signal of 20 Langmuir probe tips. The in fluence of spatial aliasing and spectral leakage on the shape of the spectrum is discussed in [Bleuel et al 2002]. von Endler

19 Fig.6_halpha Fig. Raw data from the H-alpha fluctuation diagnostic at W7-AS: The intensity is coded in grey scale (light: high intensity, dark: low intensity). The data of the 16 channels are plotted above each other and are interpolated poloidally. Individual fluctuation events" propagating in poloidal direction (ion diamagnetic drift direction) with fairly uniform velocity can easily be identified as inclined structures (from [Bleuel et al 2002]). von Endler

20 Fig.6_bleuel Fig. Radial-poloidal correlation function (time lag = 0). The fluctuation structures are inclined in the radial-poloidal plane due to local magnetic shear. A calculation of this function for dierent values of shows that the fluctuation structures propagate predominantly in poloidal direction (from [Bleuel et al 2002]). von Endler


22 Fig.6_Itfreeprof [Fig.6_Itfreeprof]: Experimental (from Thomson scattering) and calculated (from the model) radial profiles for the states of low and high confinement which are observed at iota_ext,a=0.45 in discharges without current control. The Thomson profiles are taken at iota=1.0s from the discharges with I p,0 =0 and 7.3 kA in Fig.6_Itfree. The assumed ECRH power density profile is indicated. von Brakel: f13.gif.cm2c1_vs_exp.ipfree.gif

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