Toroidal and poloidal momentum transport studies in tokamaks

Abstract

This paper reports on recent studies of toroidal and poloidal momentum transport in tokamaks. The ratio of the global energy confinement time to the momentum confinement is found to be close to τ E /τ φ = 1 among several tokamaks. On the other hand, local transport analysis in the core plasma shows a larger scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χ φ,eff / χ i,eff among different tokamaks, for example the value of effective Prandtl number being typically around χ φ,eff / χ i,eff ≈ 0.2 on JET. Perturbative NBI modulation experiments on JET have indicated, however, that the Prandtl number (calculated only with diffusive terms) χ φ / χ i is around 1, and in addition, a significant inward momentum pinch is needed to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. Concerning the poloidal velocity, the experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the neo-classical estimate within the ITB. This significantly affects the calculated radial electric field and therefore, the E×B flow shear used for example in transport simulations. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and being dominantly caused by flow due to the Reynold's stress. It is important to note that both codes treat the equilibrium in a simplified way and this affects the geodesic curvature effects and Geodesic Acoustic Modes (GAMs). The neo-classical equilibrium is calculated more accurately in the GEM code and interestingly, the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, with poloidal velocity tight to the 2D neo-classical equilibrium and following in particular the growth of the toroidal velocity within the ITB.

JET intrinsic rotation studies in plasmas with a high normalized beta and varying toroidal field ripple

“…Early JET intrinsic rotation studies have used this technique [11,23]. The JET intrinsic rotation data included in the multi-machine study of [2] is from XCS measurements from 1994-95, when the wavelength scale had for the first time been calibrated by comparison with the angular frequency derived during NBI from charge exchange recombination spectroscopy of 6 C + . For newer pulses XCS intrinsic rotation measurements are not always available as there isn't enough Ni in the JET machine in X-point plasmas.…”

“…[4] do not include any contribution from a momentum pinch which is found to exist in JET NBI discharges [6,7] and other tokamaks [8,9]. This inward pinch will modify the rotation profile in ITER, in particular the peaking of the rotation profile will increase.…”

Overview of physics results from MAST

“…Plasmas in NBI heated spherical tokamaks show a fast toroidal rotation with thermal Mach numbers measured on MAST of up to M th = v φ /v th 0.8 [48]. On many tokamaks a link between momentum confinement and energy confinement has been observed [49], with the so called Prandtl number P φ = χ φ /χ i ≈ 1 relating ion momentum and ion energy diffusivity. This is consistent with theoretical studies of ITG transport.…”

Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

“…Modulation at a suitable frequency has the advantage of optimizing the S/N ratio by averaging over several cycles and has been used successfully to study electron and more recently ion heat transport, and also particle and impurity transport (see [18] for a recent review). Its application to momentum transport studies using Neutral Beam Injection (NBI) modulation is a recent development, with a couple of studies reported in JT-60U [19,20], one experiment reported in JET [21,22,23] and one in DIII-D [24]. The use of magnetic perturbations to brake the plasma was reported in DIII-D [25] and NSTX [24,26,27] as another means to induce a transient from which it is possible to infer diffusivity and convection separately.…”

“…This paper describes momentum perturbative experiments using Neutral Beam Injection (NBI) modulation at JET, presenting both new experiments and more refined analysis and modelling with respect to previous work [21,22,23] and including detailed comparison of the results with recent gyro-kinetic and fluid theory predictions. Sect.2 illustrates the experiments, Sect.3 discusses the calculations of the time dependent torque deposition, Sect.4 illustrates the rather heavy experimental methodology, based on transport modelling required to extract from the data the estimates of momentum diffusivity and pinch, Sect.5 summarizes the linear gyro-kinetic predictions, Sect.6 describes first attempts to perform time-dependent modelling of the rotation dynamic response with 1D quasilinear fluid transport models.…”