TJ-II:Transport analysis by means of the Transfer Entropy

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Experimental campaign

2018 Spring

Proposal title

Transport analysis by means of the Transfer Entropy

Name and affiliation of proponent

B.P. van Milligen, T. Estrada, B.A. Carreras, A. Cappa, HIBP Group and 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)

Recently, radial heat transport has been explored by means of the Transfer Entropy in TJ-II.[1] This work makes use of spontaneously arising core electron temperature (Te) perturbations that propagate outward and shows that heat transport is not a smooth and continuous (diffusive) process, but involves mini-transport barriers associated with low-order rational surfaces and rapid non-local radial ‘jumps’.

The Transfer Entropy has some remarkable properties. First, it is directional, a fact that provides an additional filter that preferentially selects information components related to (directional) propagation. Second, it is a fully non-linear measure of the (causal) relationship between two signals. Hence, unlike linear tools such as the cross correlation or the conditional average, it does not depend on the temporal waveform or even the amplitude of the fluctuations, but merely on the time lag between the two signals. This converts the technique in a sensitive tool to study the propagation of perturbations in highly non-linear systems (such as fusion plasmas), in which perturbations tend to be deformed or change shape quickly as they propagate.

In the proposed experiments, we intend to explore these initial observations further.

1 Power scan experiments and heat transport

In this experiment, we repeat the study reported in[2], consisting of an ECRH power scan in a different magnetic configuration (i.e., different from the standard configuration); ECRH power is deposited centrally and is varied from its minimum (∼200 kW) to its maximum (∼500 kW) values in around 10 steps.

We will use configurations with a relatively important low-order rational at mid radius. Electron Cyclotron Emission (ECE) data are used to study heat propagation.

Possible configurations:

  • Configuration 100_44 (8/5 at ρ = 0.76) – completed already, see [2]
  • Configuration 100_46 (8/5 at ρ = 0.60)
  • Configuration 100_48 (8/5 at ρ = 0.30)
  • Configuration 100_36 (3/2 at ρ = 0.62) – only if time permits

Ideally, Doppler Reflectometry (DR) and Heavy Ion beam Probe (HIBP) should be operational (see point 3 below).

2 The effect of local shear on heat propagation

Following the same method reported in [1], we again use ECE to study the propagation of heat. We can modify the iota profile using the induction of Ohmic current[3] to study the impact of magnetic shear on the propagation of heat pulses. The induced Ohmic current will also lead to outward radial motion of the rational surfaces, allowing to track the effect of the low-order rational as it crosses the measurement locations of the ECE channels (and the DR).

Unlike the discharges reported in [3], it is possible, using C-mode, to obtain a stationary period of modified shear.

3 Velocity shear and transport

The above proposals can be combined with Doppler Reflectometry (v) and/or HIBP (φ) measurements in order to check whether a velocity shear layer in the plasma indeed affects the radial propagation (of particles and/or heat), as expected. DR measurements are restricted to the density gradient region, near ρ = 0.7, whereas ECE measurements are limited to ρ < 0.73, typically. The DR reflection layer can be placed further inward only in very low density discharges, where ECE may not be very reliable. Overlap between HIBP and ECE may be easier to obtain.

4 Density perturbations

Using the Heavy Ion beam Probe (HIBP), we can place the 5-slit HIBP probe such that the slits are placed nearly radially at mid radius (or in the gradient region). The other HIBP probe (2 slits) can be placed near the core (to provide a reference signal, maybe). This would allow studying the radial propagation of density (and potential) perturbations in the mid-radius region. Several discharges can be analysed, each time placing the 5-slit observation region at a different radial position in order to explore (nearly) the full radius on a shot-by-shot basis.

This is totally new, hence very interesting, but success is not guaranteed.

If applicable, International or National funding project or entity

Generación de Conocimiento: PGC2018-097279-B-I00

Description of required resources

Required resources:

  • Number of plasma discharges or days of operation: 2 for power scan in various configurations (point 1)
  • Essential diagnostic systems: ECE; optional Doppler Reflectometry and HIBP
  • Type of plasmas (heating configuration): ECRH only; C-mode if point 2 is attempted

Preferred dates and degree of flexibility

Preferred dates: any


  1. 1.0 1.1 B. van Milligen, J. Nicolau, L. García, B. Carreras, C. Hidalgo, and the TJ-II Team, The impact of rational surfaces on radial heat transport in TJ-II, Nucl. Fusion, 57(5):056028, 2017
  2. 2.0 2.1 B. van Milligen et al, A possible mechanism for confinement power degradation in the TJ-II stellarator, Submitted (2018)
  3. 3.0 3.1 B. van Milligen, T. Estrada, L. García, D. López-Bruna, B. Carreras, Y. Xu, M. Ochando, C. Hidalgo, J. Reynolds-Barredo, and A. López-Fraguas, The role of magnetic islands in modifying long range temporal correlations of density fluctuations and local heat transport, Nucl. Fusion, 56(1):016013, 2016

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