TJ-II:Evaluation of Neoclassical transport correction terms in TJ-II

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Experimental campaign

2018 Spring

Proposal title

Evaluation of Neoclassical transport correction terms in TJ-II

Name and affiliation of proponent

D. Carralero, J.L. Velasco, T. Estrada and the TJ-II team

Details of contact person at LNF (if applicable)


Description of the activity, including motivation/objectives and experience of the proponent (typically one-two pages)


Neoclassical transport is widely considered to determine radial energy transport in high-temperature plasmas of stellarators up to a certain radial position [1]. In particular, for low-density ECH-heated stellarator plasmas, the levels of electron energy transport predicted by neoclassical simulations [2] are comparable to those estimated in the experiment, e.g. [3], and the measured density and power dependence of the energy confinement time [4] is in reasonable agreement with neoclassical predictions (assuming that the electrons are in the 1/nu transport regime). In this experiment, we would like to take a closer look to the parameter dependence of the energy flux and, in particular to the Er dependence.

Going beyond the plain comparison, for selected discharges, between the neoclassical predictions of radial fluxes and the experimental measurements is relevant for two reasons. For starters, it allows to identify and characterize possible systematic deviations. More interestingly, in a real plasma, the particles are not in a pure regime (e.g. the 1/nu, as mentioned above, sqrt(nu), plateau, etc), but in a mixture of regimes, since for a given temperature they are approximately distributed according to a Maxwellian. Studying the parameter dependence of the energy flux can allow to identify to what extent the different regimes contribute to transport in real conditions. This may something relevant, e.g. if, when optimizing a magnetic configuration with respect to neoclassical transport, reducing the transport level of one particular regime is incompatible with reducing that of other regimes. Currently, this kind of analysis is already under development in the W-7X optimized stellarator [5].

As for the Er dependence, it is worth noting that the contribution of the tangential magnetic drift (MTD) in the ion drift kinetic equation at low collisionalities has traditionally been considered negligible for high aspect ratio machines when the radial electric field is large. This assumption has recently been called into question for realistic values of Er, meaning that heat and particle fluxes calculated with NC transport coefficients derived without taking into account the MTD could be inaccurate. This would be specially the case when approaching the root transition, in which Er~0 and the role of MTD becomes particularly relevant. In this situation, conventional calculations predict a clear maximum on radial fluxes around Er=0, e.g. [6], while the peak in ion transport obtained with simulations carried out taking MTD into account [7] [8] is reduced in amplitude and displaced towards Er < 0 (the peak in electron transport should appear then at Er>0). The difference between the two trends could be large enough to be clearly noticeable experimentally, thus representing a good method to evaluate the general validity of the NC transport predictions and the relevance of the MTD in a real-life plasma. It is important to notice that, while this effect should be noted within a wide range of collisionalities, this dependence on the Er does not appear at the plateau regime. Therefore, collisionality must be kept below the threshold for such regime.

With this purpose, we propose to characterize radial electron transport in ECH plasmas of the TJ-II stellarator by realizing density and power scans around the root transition. The objective of these scans would be to obtain a set of shots with comparable Te and ne gradients and different values of Er (comprising a wide range of 0 < Er and Er > 0 values) so that experimental qr,e (Er) can be determined and compared with the corresponding simulations with and without MTD.


In TJ-II, the radial electric field can be measured for a wide radial range by means of Doppler reflectometry (DR). Besides, although qr,e can’t be directly measured, in a stationary plasma, the divergence of qe is determined locally by source terms, which can be evaluated approximately based on data available in TJ-II: the most relevant source terms include radiation (which is considered to be small [3]), ECH power deposition (which will be estimated at the beginning of the experimental day by means of fast modulation of one of the gyrotrons, and should also be small in the radial region probed by the DR) and energy transfer to the ion species, which can be calculated based on density and temperature profiles. In TJ-II, the root transition can be accessed either by a change in density or by a change in heating power. In particular, the Er measured by DR has been observed to change strongly with moderate increases of ne around a critical density determined by the injected heating power. These changes in the electric field seem to have a minor effect on ne and Te profiles, thus providing an scenario in which qr,e (Er) can be obtained experimentally for a range of roughly equivalent ne and Te gradients. This is important in order to allow for a meaningful comparison between measurements and theoretical predictions. Since the plateau regime is to be avoided, when selecting the combination of densities and heating powers for the experiments, collisionality must be minimized whenever possible (i.e., reducing density, or preferably, increasing Te). As well, freshly lithiated walls are required in order to minimize the role of radiation on the electron power balance.

Experiment description

First, the radial electric field will be measured on a series of standard configuration ECH plasmas with constant heating power and increasing densities around the root transition critical density. This scan should provide a set of discharges with constant Te profiles (ECH alignment adjustment may be required to ensure that) and changing ne profiles. The range of densities will be selected by adjusting the heating power value in order to allow the DR in the rho ~ [0.3-0.8] range. Some trade-off maybe necessary to ensure good TS profile data. Ti will be measured at the plasma core by the NPA. At least, 10 different Er profiles should be measured this way, with some intermediate radial region being covered by all density values. Second, a fixed density value will be selected such that an equivalent scan can be carried out by small increments of PECH. In this scan, the radial region probed by the reflectometer remains constant, as density profiles can be made roughly constant, while Te profiles will change. The density must be such that good TS data is collected, the root transition takes place for a power roughly around that of a gyrotron at full power and DR probes the [0.3-0.8] range. Finally, one of the previous scans could be repeated in a high ripple configuration in order to check the impact on the measurements of the increased transport.

Description of required resources

Required resources:

  • Number of plasma discharges or days of operation:

10 Er profiles are required (in order to produce an empirical qe,r (Er) curve with reasonable resolution) for each scan. This means an absolute minimum of 20 discharges. Since fine tunning may required in ECH alignment and fueling in order to achieve constant profiles, two full days of operation will probably be required (one per scan). Ideally, both days would be separated in time in order to properly evaluate the results.

  • Essential diagnostic systems:

The essential diagnostics are those used to measure Er (Doppler reflectometer) and Te and ne profiles (Thomson scattering, plus all other diagnostics involved in the Bayesian profile determination, such as interferometer, ECE, Helium beam, etc).

Ti measurements from the NPA will be useful to estimate the ion temperature profiles used for NC simulations and e-i energy exchange estimations. Bolometry will be used to monitor radiation losses.

  • Type of plasmas (heating configuration):

Standard configuration (100_44_64) with ECH heating. For the high ripple scan, additional shots would be carried out in ECH heated plasmas in 100_32_60 configuration.

  • Specific requirements on wall conditioning if any:

Fresh lithiation is required in order to minimize the effect of impurities in the radiation profile.

Preferred dates and degree of flexibility

Preferred dates:

Any time from 01-05-2018 except:

- 22 to 24-05-2018

- 18 to 25-06-2018


  1. A. Dinklage et al., Inter-machine validation study of neoclassical transport modelling in medium- to high-density stellarator-heliotron plasmas, Nucl. Fusion, 53 (2013), 6.
  2. J. L. Velasco et al., Study of the neoclassical radial electric field of the TJ-II flexible heliac, Plasma Physics and Controlled Fusion 56 (2012) 015005
  3. 3.0 3.1 S. Tallents et al., Transport analysis in an electron cyclotron heating power scan of TJ-II plasmas 2014 Plasma Physics and Controlled Fusion 56 07502
  4. E. Ascasíbar et al., Magnetic configuration and plasma parameter dependence of the energy confinement time in ECR heated plasmas from the TJ-II stellarator, Nucl. Fusion 45 (2005), 276
  5. J. A. Alonso et al., Ion heat transport in low-density W7-X plasmas, 44th EPS Conference on Plasma Physics, Belfast, Northern Ireland, June 26- 30, 2017
  6. J. L. Velasco et al., Study of the neoclassical radial electric field of the TJ-II flexible heliac, Plasma Physics and Controlled Fusion 56 (2012) 015005
  7. S. Matsuoka et al., Effects of magnetic drift tangential to magnetic surfaces on neoclassical transport in non-axisymmetric plasmas, Physics of Plasmas 22 (2015), 072511
  8. B. Huang et al., Benchmark of the local drift-kinetic models for neoclassical transport simulation in helical plasmas, Physics of Plasmas 24 (2017), 022503

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