Proceedings of ITC/ISHW2007

Electron cyclotron heating of plasma with density above 1020m-3
in W7-X
Yuriy TURKIN, Craig D. BEIDLER, Volker ERCKMANN, Joachim GEIGER, Heinrich P. LAQUA,Henning MAAßBERG, Nikolai B. MARUSHCHENKO, and W7-X Team
Max-Planck-Institut für Plasmaphysik, EURATOM-Association, Greifswald, Germany
12 October 2007
Electron cyclotron resonance heating (ECRH) of plasma in the Wendelstein 7-X (W7-X) stellarator at highdensities is investigated by means of predictive simulations using coupled 1-D transport and ray-tracing codes. Theheating efficiency and level of non-absorbed radiation are examined for various heating and plasma parameters. The
transport modeling with the assumption of neoclassical core confinement has shown that high-β plasmas up to 5.5%
are achievable at a magnetic field of 2.5T for the multi-pass O2-mode heating with overall absorption efficiencyof 95%. The finite β-effects that can deteriorate power absorption efficiency are discussed.
Keywords: ECRH, W7-X, stellarator, plasma heating, O2-heating, steady-state operation, neoclassical transport
DOI: 10.1585

The W7-X stellarator being built at IPP-Greifswald
will be equipped with a flexible ECRH system designed
for 30 minutes operation with total power 10 MW
generated by 10 gyrotrons [1]. The ECRH system will be
the main heating source during the initial stage of W7-X
operation. At low to moderate densities, heating is with the2nd harmonic of the extraordinary mode (X2 at 140GHzand B=2.5T) with low-field-side launch in a bean-shaped
plane. High-density and high-β regimes above theX2-cut-off density, i.e. from 1.2×1020m-3 to 2-2.1×1020m-3,
are accessible using the 2nd harmonic of the ordinarymode (O2).
In the present work the high performance O2-heating
scenarios for W7-X are investigated by means of predictive
simulations using a new 1-D transport code [2].
Neoclassical core confinement with empirical anomaloustransport at the plasma edge is assumed [3]. The
anomalous diffusivity scales inversely with plasma density
in the region of high density gradient and exponentiallydecays towards the plasma axis. The radial electric field,electron and ion temperatures
are advanced
self-consistently with a calculation of the power depositionprofiles by the ray-tracing code TRAVIS [4]. The shape ofthe density profile with a gradient region of about 10cm isfixed. The modeling is performed for the standard
magnetic configuration, which is optimized for maximum
confinement. More details about approaches used insimulations presented here can be found in reference [5].
Geometry of the ECRH heating system used insimulations is shown in Fig. 1. To prevent overheating ofauthor’s e-mail: yuriy.turkin@ipp.mpg.dethe vessel and in-vessel components by the shine-throughradiation a reflecting mirror is foreseen opposite to theECRH launchers, thus allowing the second pass absorptionof the microwave beam and thereby significantly reducing
the focused non-absorbed ECRH power.

plasmamirrorvessel
beams ofport AFig. 1 Geometry of the ECRH beams; only six beams from 12(10 plus 2 spare) [1] are shown: three beams (right)
launched through port A and three beams (left) launchedthrough port E; the other six beams are locatedsymmetrically in the next module; the reflecting
stainless-steel liners between ports are not shown. Thebeam in red is the spare beam.

Preliminary calculations [1] have shown thatsingle-pass absorption of the power decreases from 80% to
50% when the density increases from 1020m-3 to
2.1×1020m-3 due to unfavorable temperature dependence
and even after two passes of the microwave beam thenon-absorbed ECRH power can be high. To increase
absorption, the third pass of beams is provided by thereflecting stainless-steel liner installed on the outer side of
the vessel between the ECRH ports.

Proceedings of ITC/ISHW2007(a)(b) X2 at <β>=0%(c) O2 at <β>=2%(d) O2 at <β>=4%Fig. 2 Effect of high-β on the W7-X standard magnetic configuration: (a) magnetic field along major radius in bean-shape plane fordifferent volume averaged β and the same coil currents; the magnetic axis positions are shown by markers; (b, c, d) ECRH
deposition zones (red ellipses) projected onto bean-shape plane for X2/O2 heating scenarios and different magnetic configurations.
The dashed line in (a) and magenta lines in (b, c, d) are the cold resonance positions (B=2.5T).

In the simulations described below all beams areaimed to the reflecting mirrors and the ray tracing code
simulates three-pass absorption. The creation andsustaining of hot dense plasma by ECRH strongly depends
on the magnetic field. And at the same time the high-β
plasma changes the magnetic configuration. In Fig. 2a themagnetic field strength dependence on volume averaged
plasma β is shown. With increasing <β> the magnetic fieldat the axis is reduced from 2.56T to 2.35T due to theShafranov shift and plasma diamagnetism. Fig. 2bcd show
schematically the power deposition zones which are
painted by mapping of deposition profiles to thecorresponding flux surfaces for the beam arrangement
shown in Fig. 1. It is seen that the ECRH resonance region
moves to the high field side. In this case the O2 absorption
can degrade due to the decrease of the electron temperaturein the resonance zone.
The ECRH power scans for the standard magnetic
configuration have been performed for densities of
0.8-2.1×1020m-3 and O2-mode (140GHz at B=2.5T)
heating from 1MW to 10MW taking into account theβ-effects mentioned above. The value of magnetic field has
been chosen to have the central O2-mode ECRH
deposition for the <β>=2% configuration, see Fig. 2c. The
simulations have been started from low density at given
power using off-axis X2-heating (100% single-passabsorption) and vacuum magnetic configuration (Fig. 2b)with simultaneous ramp-up of the density. Then below theX2-cut-off density at 0.8×1020m-3, the magnetic
configuration has been changed to the <β>=2%
configuration and the polarization has been switched toO2-mode. The calculations have been continued withincreasing density till O2-cut-off. To model the moving of
the absorption zone from central deposition to off-axis
deposition and thus absorption degradation due to theβ-effects, the <β>=4% configuration (Fig. 2d) has beenused for higher densities and powers; see gray areas inFig. 3. The results of scans are depicted in Fig. 3. It is seenthat nearly full absorption is achieved for a wide range ofdensity and input power; see region below 95% curve(cyan) in Fig. 3a; the single-pass absorption for theseconditions is about 70%; see Fig. 3b. The discontinuities inFig. 3 are related to the absorption degradation for far
off-axis power deposition and to the modeling procedure inwhich precalculated equilibriums are used instead ofself-consistent recalculation of them. However the main
results remain valid. In order to prevent confinement
degradation, the coil currents must be raised within therange of 5% along with the β increase to compensate
magnetic field decrease at the axis. The heating efficiencyof the O2-mode depends on plasma parameters, especiallyon electron temperature, because the optical thickness is
proportional to Te2 . The electron temperature in turndecreases with density increase as predicted by scalinglaws [3] leading to absorption degradation and finally tothermal collapse; see solid red lines in Fig. 3.
(a)

(b)

Fig. 3 Percentage of absorbed power for the three-pass scheme of
O2-mode heating as a function of input power and plasma
density: (a) after three passes; (b) after the first pass.
Calculations in grayed area have been performed with
<β>=4% equilibrium for standard magnetic configuration,
for the other (ne, P) the 2% equilibrium has been used.

Proceedings of ITC/ISHW2007

(a)

(b)

(d)

(c)

X2-mode(e)

O2-modeFig. 4 (a) initial temperature and (b) low-field-side power deposition profiles at ne=0.6×1020m-3; (c) time evolution of the main plasma
parameters: central Te, Ti, triple product niTiτE in 1020m-3 keV·s, central ne, energy confinement time τE; (d,e) final temperatures andECRH profile at ne=2×1020m-3 and high-field-side deposition.

The time traces of the plasma parameters for the10MW O2-mode scenario are shown in Fig. 4. Initially the
0.6×1020m-3 plasma is heated by 5MW X2-mode with
low-field-side deposition as in Fig. 2b. Then the heating isswitched to O2-mode with the same input power, but withthe central deposition and <β>=2% magnetic configuration(Fig. 2c). The central power deposition increases theelectron temperatures leading to temperature decoupling in
the center. The simulation is continued by ramping-up thedensity (magenta curve in Fig. 4c) towards the target
density 2×1020m-3. At the density 1020m-3 the heating isincreased to 10MW and the <β>=4% configuration with
5%-increase of the coil currents (that corresponds to themagnetic field increment of 0.12Tesla) to retain central
power deposition is loaded. More heating increases theelectron temperature; the ion temperature also goes up dueto the strong collisional coupling at high densities. The
final temperatures are shown in Fig. 4d, for the density
profile see Fig. 6a. The following plasma parameters arereached: niTiτE=5.5×1020m-3 keV·s, τE=0.67s, and volume
averaged <β>=5.5% with power absorption efficiency of95%.
In Fig. 5 the projections of the beams to the poloidal
and equatorial planes are shown. The intensity of red spots
on the rays are proportional to the absorption rate, most of
the ECRH power (>70%) is absorbed at the first pass. Thebeams propagate at angles optimized with respect to theabsorption efficiency for O2 or X3-mode operations andrefraction effects are quite small even at high density.
Finally, for comparison with O2 ECRH plasmas, wehave simulated the plasma heated by “positive” NBI(p-NBI, 60 keV H+); see Fig.6. In the p-NBI case, the main
power is absorbed at outer radii, especially the low energy
components of the beam. This leads to confinement
degradation, whereas for the O2 case the more central

(a)

C1

reflecting liner(b)A1reflectingmirrors

D1Fig. 5 Trajectories of ECRH beams: (a) poloidal plane with only
one beam shown, (b) equatorial plane with the twobeams going from mirror A1 of port E and mirror D1 ofport A; magenta lines are the cold resonance positions;color lines in figures are the lines of constant magneticfield.

Proceedings of ITC/ISHW2007
deposition allows for higher temperatures and improved
confinement times. Indeed for these heating parameters,
τE=0.46s at <β>=4.2% and τE=0.67s at <β>=5.5% are
obtained for p-NBI and O2 ECRH, respectively.

SummaryThe O2-ECR heating efficiency is analyzed forvarious plasma parameters and heating conditions using
ray tracing modeling coupled with a 1D-transport code.
The transport modeling with the assumption ofneoclassical core confinement has shown that high-β
plasmas up to 5.5% are achievable at a magnetic field of
2.5T for the multi-pass O2-mode heating with overall
absorption efficiency of 95%. The O2-mode heating
scenarios look promising for high-density-operation
regimes of W7-X with high separatrix density that is themost favorable condition for operation of the divertor. It is
worth noting that the neoclassical predictions give an upper
limit of plasma performance in W7-X. Further predictive
transport simulations will be considered for high-β plasmas
for which the moving of the resonance zone due to theShafranov shift and the diamagnetic current can decrease
absorption efficiency.
[1]

[2]
[3]

[4]
[5]

V. Erckmann, P. Brand et al. Electron cyclotron heating for
W7-X: Physics and Technology. Fusion science andtechnology, 52, 291(2007)
Yu. Turkin, H. Maaßberg et al. Fusion Science andTechnology, 50, 387(2006)
Yu. Turkin, C. D. Beidler et al. Transport Simulations for
W7-X. 33rd EPS Conference on Plasma Phys. Rome, 19 23 June 2006 ECA Vol.30I, P-2.113 (2006)
N. B. Marushchenko et al. in Proc. of the 16th Toki Conf.,
Japan, December 2006, http://itc.nifs.ac.jp/index.html
C. D. Beidler, J. Geiger et al. Transport Modeling for
W7-X on the Basis of W7-AS Experimental Results. Paper
I-21 in Proc. of the 17th Toki Conf., Japan, October 2007

Fig. 6 (a) and (b): Plasma profiles for a 10MW heating
simulation of W7-X. The solid line in figure (b) refers toO2 ECRH power depositions in plot (d). The dotted linein (b) refers to NBI power depositions shown in plot (c).
The dotted line in (c) corresponds to the power depositedto ions.