Proceedings of ITC/ISHW2007

ECCD scenarios for different configurationsof the W7-X Stellarator
N.B. MARUSHCHENKO, C.D. BEIDLER, V. ERCKMANN, H. MAASSBERG and Yu. TURKIN
Max-Plank-Institut für Plasmaphysik, IPP-EURATOM-Association, 17491 Greifswald, Germany
October 15, 2007
In order to avoid significant change of the edge value of the rotational transform in the W7-X stellarator,
electron cyclotron current drive (ECCD) will be used for compensating the bootstrap current (an ohmictransformer is absent). Since ECCD efficiency is quite sensitive not only to the plasma parameters, but also to themagnetic configuration, it is an important task to estimate properly the range of ECCD values taking into accountall features of the magnetic configuration, and to assess its ability to counteract the residual bootstrap current. In
this work we analyze the requisite ECCD for scenarios with the different magnetic configurations with help of
the ray-tracing code TRAVIS, coupled self-consistently with the 1D transport code. The neoclassical transportmodeling is based on the DKES database of mono-energetic transport coefficients.
Keywords: stellarator, bootstrap current, electron cyclotron heating, current drive
1. Introduction
The W7-X stellarator (under construction in Greifswald, Germany) is a large-scale device with average major radius R0 ' 5.5 m and plasma radius a ' 0.53 m,
equipped with superconducting coils, with a low-shear
configuration of the Helias (Helical Advanced Stellarator) type [1] with five field periods. The toroidal mirror
ratio Bmax /Bmin on axis can be varied significantly, from1.004 to 1.22 for the “low-mirror” and the “high-mirror”
configurations, respectively (for the “standard” configuration Bmax /Bmin = 1.09). The corresponding trappedparticle fractions on axis are varied due to ripples fromftr ' 0.02 for “low-mirror” up to ftr ' 0.45 for ‘highmirror”, while ftr ' 0.3 for the “standard” configuration.
Through its dependence on the toroidal mirror ratio value,mono-energetic bootstrap current coefficients are largest
for the “low-mirror” configuration. In particular, the bootstrap current is minimized for the “high-mirror” configuration, whereas the neoclassical confinement is optimum inthe “standard” configuration. The total plasma current affects the edge value of the rotational transform, which may
fall outside the required range for proper island divertor
operation without external field compensation. Due to theabsence of an ohmic transformer, electron cyclotron current drive (ECCD) will be used for compensating the bootstrap current. Since the ECCD efficiency is quite sensitive
not only to the plasma parameters, but also to the magnetic
configuration, it is an important task to estimate properly
the range of ECCD values taking into account all featuresof the magnetic configuration, and to check its ability tocounteract the residual bootstrap current. It is necessary totake special care for high densities where the ECCD efficiency is reduced. Additionally, the effects of finite plasma
author’s e-mail: nikolai.marushchenko@ipp.mpg.depressure (β > 0) may play a significant role, especiallyin the high-density scenarios, changing the deposition andcurrent drive profiles. Since the task of self-consistent simulation of this case is still too complex, the effects of finite
β will be only briefly discussed (when it is possible), justto indicate the tendency.
2. W7-X ECRH system and ECCD scenarios
The ECRH system in W7-X is designed for continuous operation with a total injected power up to 10 MW
at 140 GHz [2] (the resonance magnetic field is B0 = 2.5T). The ports for launching the RF power are situated symmetrically around two “bean-shaped” planes, i.e. near themaximums of B (the ports E10 and A51 near the crosssections φ = 0 and φ = 72◦ , respectively). In order to prevent an overheating of the chamber by the shine-throughpower and to control its reflection, mirrors are installed at
the inner wall and all beams planned for O2 operation must
be directed to these mirrors. Because of symmetrical location of the mirrors about the launch ports, only five beams
out of ten can be launched in the same direction, and operation with maximal counter-ECCD is possible with a total power up to only 5 MW. While the X2 (extra-ordinarymode at the 2nd harmonic) scenario is applicable in thedensity range ne < 1.2 × 1020 m−3 , for higher densities, up
to 2.2 × 1020 m−3 , the O2 (ordinary mode at the 2nd harmonic) scenario will be applied. Note, that for densities
near the O2 cut-off, ne ' 2.4 × 1020 m−3 , single-pass absorption of the O2-mode is strongly reduced together withincreasing refraction effects, the upper density limit for operation is about ne ' 2.2 × 1020 m−3 (or even less, depending on the specific case). Due to the high optical thicknessof the plasma for the X2-mode, there are no strict launch
conditions for this scenario, and this freedom can be usedfor tailoring a desired deposition and current drive profile

Proceedings of ITC/ISHW2007[3]. For the O2-mode, the plasma is optically “gray”, andthis scenario is more limited for the expected range of parameters. Since the optical depth for the O2-mode scalesas τO2 ∝ T e2 , the most attractive path to the O2 scenario
is to preheat the plasma by the X2-mode, then change thepolarization from X- to O-mode by means of rotation of
the corrugated mirrors, and finally to increase the density
to the requested value [4, 5].
Below we consider in detail both ECCD scenarios,with the X2-mode for the moderate density range, ne <1020 m−3 , and with the O2-mode for the higher densities.
To simplify comparison of the X2 and O2 scenarios, thelaunch conditions for the X2-mode are taken identical tothose required for the O2-mode.
3. Numerical tools
The numerical models for calculating the ECCD efficiency developed to date (both the Fokker-Planck [6] calculations and the adjoint approach [7] in ray-tracing calculations) do not cover completely the range of collisional
regimes for the electrons involved in the current drive, especially in stellarators. Only two opposite limits are in use,with and without taking into account the trapped particles.
The first one, called the collisional limit, is formulated under the condition νe  τ−1b , where νe and τb are the electron collision frequency and the bounce-time, respectively.
This limit, being, in fact, the straight magnetic field line
approach, overestimates the ECCD efficiency. The secondlimit, called the collisionless one, is based on the opposite
assumption, νe  τ−1b , i.e. takes into account the trappedparticles. This limit may lead to underestimating of theECCD efficiency. Nevertheless, the collisionless limit ismore reasonable for the W7-X conditions, especially forthe regimes with moderate densities and high temperatures. In this work we analyze the requisite ECCD scenarios for operating with the different magnetic configurations
with help of the ray-tracing code TRAVIS [8, 9]. The (adjoint) Green’s function applied for the ECCD calculations
is formulated with momentum conservation taken into account [4]; this is especially important and even critical for
those scenarios, where the number of trapped particles isquite small, ftr  1, and/or mainly bulk electrons are responsible for absorption of the RF power (e.g. when theobliqueness of launch is not high and Nk  1).
The plasma profiles and bootstrap current were calculated by the 1D transport code [5] (for details, see also[10]) coupled self-consistently with the ray-tracing code
TRAVIS [8, 9]. The transport modeling is based on theDKES database of mono-energetic transport coefficients,and thermal transport coefficients are obtained by energy
convolution with a local Maxwellian. The DKES code [11]uses as collision operator the Lorentz pitch-angle scattering term without momentum conservation, leading to an
overestimate of the bootstrap current depending on Zeff (inpresent the calculations, Zeff = 1.5 is assumed).

4. Simulation results
The calculations were done for five different beams
launched from the ports E10 and A51 with 1 MW power
for each beam. Both X2 and O2 scenarios are modeled forthe same fixed launch conditions for three different magnetic configurations. While the RF-beams in O2 scenarios must be directed onto the corresponding mirrors at theinner wall, the chosen direction is not optimal for ECCD
efficiency in X2-mode. Since the single-pass absorption of
the O2-mode is less than 100%, four passes are taken into
account in the calculations. If after two passes through theplasma less than 90% of the power was absorbed, this scenario was excluded from consideration.
Keeping in mind the general scenario which requires
switching from the X2 to the O2 scenario, let us consider
first the moderate density range, ne . 1020 m−3 , where
both scenarios can work. For the present conditions, thechoice B = 2.562 T seems as optimum for both X2 andO2 scenarios. For the X2 scenario, an off-axis absorption
does not lead to the “electron-root” feature and collisional
decoupling of electrons and ions. For the O2 scenario, due
to the shift of the resonance in the low-field-side direction,
absorption appears in the region of increasing (along theray) T e , prolonging the area of effective cyclotron interaction and, consequently, increasing the single-pass absorption.
In Fig.1 (top), the X2 ECCD profiles, jcd (ρ), whichsummarize the contributions from all beams, are shown(the corresponding deposition profiles have a very similarshape). Negative ECCD is chosen since the bootstrap current is positive for these simulations. Due to very high optical thickness, the location of the deposition profile (ECCDas well) for the X2-mode is almost completely definedby the resonance location, and the Doppler broadening is
mainly responsible for the width of jcd (ρ) profile. For eachconfiguration, the temperature dependence during the density scan is not strongly pronounced due to an absence of
its strong variation: for the “standard” configuration withne increased from 0.4×1020 m−3 to 1.1×1020 m−3 , T e is varied from 5.7 keV to 4.4 keV, respectively. Since the “standard” configuration is optimized for neoclassical confinement, the steady-state temperature obtained by transport
simulation is highest in comparison with the “low-” and“high-mirror” configurations. On the other hand, due to thereduced trapped particle fraction, the longitudinal conductivity is higher in the “low-mirror” configuration, whichleads to an increase of ECCD. Nevertheless, due to the
reduced confinement the temperature in the “low-mirror”
configuration is for the same heating conditions also lower,
and the decrease of ftr is masked by a decrease of T e . In
the case of the “high-mirror” configuration, an increaseof ftr and a decrease of T e have the same effect, and theECCD efficiency is significantly reduced. For comparison,
the case of the “standard” configuration with hβi = 0.02 isshown (see Fig.1, dashed red). One can see, that the finite
pressure effects may lead to a very strong effect. Due to theProceedings of ITC/ISHW2007
0-1x1055-3x105-4x10j

cd, A / m2-2x105-5x10X2, standard
X2, standard, < >=2%

5-6x100.25 * j

X2, low-mirror

Single-pass absorption, %

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O2, high-mirr. conf.

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X2, high-mirror

cdO2, standard conf.

1.00/ a00.40.8

1.2ne20/ 10

1.6, m2.0-3Fig. 2 Single-pass absorption of the O2-mode summarized forall beams: the same as in Fig.1.

05-1x10

5jcd, A / m

2-2x105-3x105-4x105-5x10O2, standard conf.
O2, standard conf., < >=2%

5-6x10O2, low-mirror conf.
O2, high-mirror conf.

5-7x10

0.00

0.25

0.50

reff

0.75

1.00

/ aFig. 1 Summarized ECCD profiles (5 beams 1 MW each) for thedifferent configurations: “standard” (red), “low-mirrors”(blue), and “high-mirrors” (green). Additionally, the caseof hβi = 0.02 for the “standard” configuration is shown(pink dashed). Top - X2 scenario, bottom - O2 scenario.
For all cases, the density is the same, ne = 0.8 × 1020 m−3 .

Shafranov shift combined with the diamagnetic effect, thedeposition profile (ECCD as well) moves into the axial region, making an appearance of the “electron-root” almost
unavoidable.
The O2 scenario is more sophisticated. First of all, theplasma is optically “gray” and a significant part (up to 20%
or even more) of the power is absorbed during the second
pass (third and fourth passes are of minor importance). Direct consequence of it is involving in cyclotron interaction
the electrons with kk vk < 0 (“anomalous” Doppler effect),which create the current contribution of opposite sign, reducing jcd (ρ) in this point [7]. Interesting, that for the“standard” configuration with hβi = 0.02 this effect is mostpronounced, and even negative values of jcd (ρ) appear (seeFig.1, bottom, red dashed). Important to mention also, that
despite of launching the RF beams near the maximum of B(“bean-shaped” plane) the trapped particles are quite wellinvolved in the cyclotron interaction, absorbing up to 10%of the power and significantly reducing the ECCD. The absorption of the O2-mode, being proportional to T e2 , is very
sensitive to the shape of T e profile (ne profile is almost
flat in the present simulations). On the other hand, the T eprofile is defined mainly by the deposition profile. Dueto this feedback, the resulting deposition profiles (as wellas ECCD) for the scenarios with the resonance shifted to
the low-field-side are rather independent of density, and its
shape is quite similar to those shown in Fig.1 (bottom) for
quite broad range of densities (with only change of jcd (ρ)
magnitude, which scales roughly as 1/ne ).
In the Fig.2, the single-pass absorption for the O2 scenario as a function of density is shown. The values obtained (summation over five beams) are quite high for all
tested magnetic configurations, i.e. are about 80 - 90% forne < 1.8 × 1020 m−3 . Important to mention here, that thesingle-pass absorption in the “standard” magnetic configuration with hβi = 0.02 is significantly reduced in comparison with the vacuum configuration (compare the red solidand pink dashed lines). As was mentioned above, this effect is due to a combination of the Shafranov shift and of
the diamagnetic effect, which leads, in fact, to shifting of
the deposition profile into the high-field-side direction, reducing the optical depth.
In Fig.3, the results of the density scan for the threemagnetic configurations are shown. Following the standard theoretical predictions, the current drive for both X2and O2-mode scales roughly as 1/ne . As expected, the current driven by X2-mode is larger than that of the O2-mode
for all tested configurations. There are three main factors
which lead to this jump of ECCD efficiency (from red circles to red triangles). First, the single-pass absorption of
the O2-mode is less than 90%, and the rest of the power isabsorbed in the plasma periphery, where the temperature
is low. Second, since the deposition profile is quite broad,both the “anomalous” Doppler effect and the participationof the trapped particles in the cyclotron interaction reducethe ECCD efficiency.
The bootstrap current can be compensated by X2ECCD for the “high-mirror” and “low-mirror” configurations (in the last case, the uncompensated residual current appears acceptable). For the “standard” configuration(apart from the lower densities), this compensation can beProceedings of ITC/ISHW2007
80
CD, X2

low-mirror config.

CD, O2
BC, X2
BC, O240

20I

cd, Ibc, kA

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0-20
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1.6, m2.0-3Fig. 3 Density scan for different magnetic configurations. BothIcd (red color, circles for X2 and triangles for O2 scenarios) and Ibc (blue color, stars for X2 and rectangles for O2scenarios, respectively) are shown.

done by further optimization of the launch conditions (inthe present study, all beams are directed onto the mirrors,
although this is not necessary). Full current control at highdensity (in operation with O2-mode) is only obtained forthe “high-mirror” configuration. Note, that for the “standard” configuration with hβi = 0.02, the bootstrap current
is significantly increased, while the ECCD is almost unchanged. This problem requires additional study.
5. Discussion
In the present paper, the results of numerical simulations of different ECCD scenarios for W7-X are presented,
the X2 scenario, which is applicable for the low and moderate density range, ne < 1.2 × 1020 m−3 , and the O2 scenario for higher densities up to ne < 2.2 × 1020 m−3 . Threedifferent magnetic configurations have been tested, withthe trapped particle fraction varied from 1.004 to 1.22. The
aim of this study was to estimate the ability of the ECRH
system of W7-X for compensating the residual bootstrap
current and to control the edge value of the rotational transform.
In high-density operation at low ECRH power, thebootstrap current might exceed the maximum ECCD bothfor the X2- and the O2-scenarios. Only the “high-mirror”
configuration was shown to have rather small bootstrap
currents thus confirming the corresponding W7-X optimization criterion. For the ”standard” configuration withimproved neoclassical confinement, however, ECCD control of the bootstrap current is only possible in X2-mode atlower density. With full current control by ECCD, only afew skin-times (i.e. less than 10 sec) are necessary to obtain stationary conditions for optimum divertor operation.
High density scenarios are also important for the W7X island divertor operation since fairly high separatrix densities (about 0.4 × 1020 m−3 ) are required. Consequently,
the O2-scenarios are expected to be very important for
longer discharges. For these conditions, however, only the“high mirror” configuration allows for bootstrap current
control by ECCD. In particular for the “standard” configuration, another discharge scenario must be chosen to obtainstationary conditions. Here, the edge value of the rotationaltransform in the vacuum configuration must be reduced by
the amount which is generated by the bootstrap current in
the final steady state. The discharge is operated at low density and rather low heating power with strong co-ECCD (inX2-mode) up to roughly stationary plasma current, i.e. thedesired island divertor configuration is reached. In this scenario, however, the evolution of the plasma current scales
on the L/R-time (i.e. several 10 sec). Then, the density
as well as the heating power can be ramped up and the coECCD is reduced with the increasing bootstrap current, i.e.
the total current is controlled. The internal current densities and the ι-profile
become stationary again on the skin¯
time. Such a discharge scenario, however, is much more
complex compared to the case of full ECCD control of thebootstrap current.
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