Toroidal and poloidal momentum transport studies in tokamaks

Tuomas Tala (Corresponding Author), K. Crombe, P.C. De Vries, J. Ferreira, P. Mantica, A.G. Peeters, Y. Andrew, R. Budny, G. Corrigan, A. Eriksson, X. Garbet, C. Giroud, M.-D. Hua, H. Nordman, V. Naulin, M.F.F. Nave, V. Parail, Karin Rantamäki, B.D. Scott, P. Strand & 4 others G. Tardini, A. Thyagaraja, J. Weiland, K.-D. Zastrow

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Abstract

The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper.
Similar energy confinement and momentum confinement times, i.e. τE/τphgr ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χphgreff/χi,eff among different tokamaks can be found.
For example, the value of effective Prandtl number is typically around χphgreff/χi,eff ≈ 0.2 on JET while still τE/τphgr ≈ 1 holds.
Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χphgr/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required 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. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions.

Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress.
It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes.
The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.
Original languageEnglish
Pages (from-to)B291-B302
JournalPlasma Physics and Controlled Fusion
Volume49
Issue number12B
DOIs
Publication statusPublished - 2007
MoE publication typeA1 Journal article-refereed

Fingerprint

Momentum
momentum
Prandtl number
Plasmas
diffusivity
Turbulence
simulation
turbulence
Air cushion vehicles
Reynolds stress
Phase behavior
Shear flow
shear flow
curvature
Electric fields
Modulation
modulation
perturbation
heat
Kinetics

Keywords

  • JET
  • plasma toroidal confinement
  • toroidal momentum transport
  • Tokamak
  • ITER
  • fusion energy
  • fusion reactors
  • plasma

Cite this

Tala, T., Crombe, K., De Vries, P. C., Ferreira, J., Mantica, P., Peeters, A. G., ... Zastrow, K-D. (2007). Toroidal and poloidal momentum transport studies in tokamaks. Plasma Physics and Controlled Fusion, 49(12B), B291-B302. https://doi.org/10.1088/0741-3335/49/12B/S27
Tala, Tuomas ; Crombe, K. ; De Vries, P.C. ; Ferreira, J. ; Mantica, P. ; Peeters, A.G. ; Andrew, Y. ; Budny, R. ; Corrigan, G. ; Eriksson, A. ; Garbet, X. ; Giroud, C. ; Hua, M.-D. ; Nordman, H. ; Naulin, V. ; Nave, M.F.F. ; Parail, V. ; Rantamäki, Karin ; Scott, B.D. ; Strand, P. ; Tardini, G. ; Thyagaraja, A. ; Weiland, J. ; Zastrow, K.-D. / Toroidal and poloidal momentum transport studies in tokamaks. In: Plasma Physics and Controlled Fusion. 2007 ; Vol. 49, No. 12B. pp. B291-B302.
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title = "Toroidal and poloidal momentum transport studies in tokamaks",
abstract = "The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. τE/τphgr ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χphgreff/χi,eff among different tokamaks can be found. For example, the value of effective Prandtl number is typically around χphgreff/χi,eff ≈ 0.2 on JET while still τE/τphgr ≈ 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χphgr/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required 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. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.",
keywords = "JET, plasma toroidal confinement, toroidal momentum transport, Tokamak, ITER, fusion energy, fusion reactors, plasma",
author = "Tuomas Tala and K. Crombe and {De Vries}, P.C. and J. Ferreira and P. Mantica and A.G. Peeters and Y. Andrew and R. Budny and G. Corrigan and A. Eriksson and X. Garbet and C. Giroud and M.-D. Hua and H. Nordman and V. Naulin and M.F.F. Nave and V. Parail and Karin Rantam{\"a}ki and B.D. Scott and P. Strand and G. Tardini and A. Thyagaraja and J. Weiland and K.-D. Zastrow",
year = "2007",
doi = "10.1088/0741-3335/49/12B/S27",
language = "English",
volume = "49",
pages = "B291--B302",
journal = "Plasma Physics and Controlled Fusion",
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Tala, T, Crombe, K, De Vries, PC, Ferreira, J, Mantica, P, Peeters, AG, Andrew, Y, Budny, R, Corrigan, G, Eriksson, A, Garbet, X, Giroud, C, Hua, M-D, Nordman, H, Naulin, V, Nave, MFF, Parail, V, Rantamäki, K, Scott, BD, Strand, P, Tardini, G, Thyagaraja, A, Weiland, J & Zastrow, K-D 2007, 'Toroidal and poloidal momentum transport studies in tokamaks', Plasma Physics and Controlled Fusion, vol. 49, no. 12B, pp. B291-B302. https://doi.org/10.1088/0741-3335/49/12B/S27

Toroidal and poloidal momentum transport studies in tokamaks. / Tala, Tuomas (Corresponding Author); Crombe, K.; De Vries, P.C.; Ferreira, J.; Mantica, P.; Peeters, A.G.; Andrew, Y.; Budny, R.; Corrigan, G.; Eriksson, A.; Garbet, X.; Giroud, C.; Hua, M.-D.; Nordman, H.; Naulin, V.; Nave, M.F.F.; Parail, V.; Rantamäki, Karin; Scott, B.D.; Strand, P.; Tardini, G.; Thyagaraja, A.; Weiland, J.; Zastrow, K.-D.

In: Plasma Physics and Controlled Fusion, Vol. 49, No. 12B, 2007, p. B291-B302.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Toroidal and poloidal momentum transport studies in tokamaks

AU - Tala, Tuomas

AU - Crombe, K.

AU - De Vries, P.C.

AU - Ferreira, J.

AU - Mantica, P.

AU - Peeters, A.G.

AU - Andrew, Y.

AU - Budny, R.

AU - Corrigan, G.

AU - Eriksson, A.

AU - Garbet, X.

AU - Giroud, C.

AU - Hua, M.-D.

AU - Nordman, H.

AU - Naulin, V.

AU - Nave, M.F.F.

AU - Parail, V.

AU - Rantamäki, Karin

AU - Scott, B.D.

AU - Strand, P.

AU - Tardini, G.

AU - Thyagaraja, A.

AU - Weiland, J.

AU - Zastrow, K.-D.

PY - 2007

Y1 - 2007

N2 - The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. τE/τphgr ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χphgreff/χi,eff among different tokamaks can be found. For example, the value of effective Prandtl number is typically around χphgreff/χi,eff ≈ 0.2 on JET while still τE/τphgr ≈ 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χphgr/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required 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. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.

AB - The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. τE/τphgr ≈ 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity χphgreff/χi,eff among different tokamaks can be found. For example, the value of effective Prandtl number is typically around χphgreff/χi,eff ≈ 0.2 on JET while still τE/τphgr ≈ 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number χphgr/χi of around 1 is valid if there is an additional, significant inward momentum pinch which is required 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. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E × B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.

KW - JET

KW - plasma toroidal confinement

KW - toroidal momentum transport

KW - Tokamak

KW - ITER

KW - fusion energy

KW - fusion reactors

KW - plasma

U2 - 10.1088/0741-3335/49/12B/S27

DO - 10.1088/0741-3335/49/12B/S27

M3 - Article

VL - 49

SP - B291-B302

JO - Plasma Physics and Controlled Fusion

JF - Plasma Physics and Controlled Fusion

SN - 0741-3335

IS - 12B

ER -