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- Weiland, Jan, 1944, et al.
(författare)
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Drift wave theory for transport in tokamaks
- 2019
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Ingår i: Reviews of Modern Plasma Physics. - : Springer Science and Business Media LLC. - 2367-3192. ; 3:8
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Forskningsöversikt (refereegranskat)abstract
- We revisit the theory of tokamak transport due to drift waves. We recall the whole development, starting with simple theories from the 1950s till today advanced theories using advanced fluid models taking full account of kinetic effects in the frequency regime of drift waves, also including the effects of zonal flows, and also fully nonlinear kinetic theory itself. Traditionally drift waves have been described by either kinetic theory or expanded fluid theories. The expansions have usually been made in the ratio of magnetic drift frequency and frequency. As was just shown toroidal drift waves are mainly driven by the magnetic drift resonance so such an expansion is usually not allowed. It is, in fact, natural that toroidal effects play an important role since they originate from bending the system to a torus, thus eliminating the third direction in which the magnetic field does not confine plasma. Due to an exact fluid closure, we are now able to use fluid theory completely without expansion, thus maintaining the fluid resonances due to magnetic drifts in the denominators. This gives us a new normalization of drift wave equations and this enables us to recover nonlinear (Dimits) upshifts, spinup of poloidal rotation in internal transport barriers and the L–H transition. The principle of our reactive closure is that we include all moments with sources in the experiment. Here, it is usually enough to use the diamagnetic heat flow as closure term but more general cases are, of course, possible and remain parts of our general closure. The fact that the model is self-consistent then also leads to the overall experimental power scaling τe∼P−2/3. Using a full transport matrix we are then also able to obtain adequate particle pinches and apparently nonlocal phenomena such as the heat pinch on DIII-D. Recently an extension of the derivation of the fluid closure also showed that quasilinear theory works well for the real part of the eigenfrequency in our fluid description of driftwaves. A fluid description using an exact closure with a fully valid quasilinear approach also lets us cover cases with nonlinear thresholds for gradients then including also sand pile thresholds. Finally, we use a correlation length at the maximum of the E × B drift in k-space. Then we can go beyond the gyro-Bohm scaling if we allow the parameter kρ to vary. Thus, we are, in practice, able to relax all limitations of traditional drift wave theories. This means that we can recover all aspects of low-frequency tokamak transport by a systematic derivation from first principles. Our model is not fitted numerically to any other model.
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- Weiland, Jan, 1944, et al.
(författare)
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Fluid Closure, Theory, Relations to Particle Pinches, Fluid Resonances
- 2011
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Ingår i: AIP Conference Proceedings. - : AIP. - 1551-7616 .- 0094-243X. - 9780735409620 ; 1392, s. 33-41
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The fluid closure in a toroidal plasma is discussed. In particular the relation to particle and temperature pinches is considered. Implications for the radial growth of transport coefficients are given. A particularly significant effect of dissipative kinetic resonances is that they reduce particle pinches. This is shown both for a gyrofluid and a quasilinear kinetic model. In particular the fact that the ITG and Trapped electron modes are resonant modes and that the effect of dissipative kinetic resonanses is ignorable for impurities but not for main ions shows that the closure aspect in a fluid description and strongly nonlinear effects in a kinetic description are instrumental for a proper description of particle pinches. We assume here that only the ITG mode due to main ions is unstable. The ITG mode due to impurities would, of course, be sensitive to the resonance with impurities. This also addresses the question of sources in the Fokker-Planck equation. The point is that we need only to worry about resonant sources for the wave dynamics, since RF heating with phase velocity or NBI heating with beam velocity far from the drift waves will appear only as ideal heat sources. The difference in phase velocity between drift waves and RF waves is much larger than the difference in thermal velocity of main ions and typical impurity ions.
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- Weiland, Jan, 1944, et al.
(författare)
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On the normalization of transport from ITG modes
- 2016
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 23:10, s. Art no 102307-
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Tidskriftsartikel (refereegranskat)abstract
- We have analyzed the interplay of ITG turbulence and zonal flows as derived by the reductiveperturbation method. Not surprisingly, the overall transport level depends strongly on the physicsdescription of ITG modes. In particular, the fluid resonance turns out to play a dominant role forthe excitation of zonal flows. This is the mechanism recently found to lead to the L-H transitionand to the nonlinear Dimits upshift in transport code simulations. It is important that we have heretaken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagneticflow. This has turned out to be the most relevant effect as found in transport simulations of the L-Htransition, internal transport barriers, and Dimits shift.
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- Zagorodny, Anatoly, 1951, et al.
(författare)
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Non-Markovian Effects in Drift-type Turbulence
- 2009
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Ingår i: American Institute of Physics Proceedings. ; From Leonardo to ITER, s. 72-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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- Zagorodny, Anatoly, 1951, et al.
(författare)
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Non-Markovian effects in turbulent diffusion in magnetized plasmas
- 2009
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Ingår i: AIP Conference Proceedings. - : AIP. - 1551-7616 .- 0094-243X. - 9780735407169 ; 1177, s. 72-84
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Konferensbidrag (refereegranskat)abstract
- The derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is presented. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.
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- Zagorodny, Anatoly, 1951, et al.
(författare)
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Non-Markovian renormalization of kinetic coefficients for drift-type turbulence in magnetized plasmas
- 2009
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 16:5, s. 052308-
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Tidskriftsartikel (refereegranskat)abstract
- The problem of derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is considered. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. Kinetic calculations of the dielectric response function are also performed with regard to the influence of turbulent fields on particle motion. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.
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- Zasenko, V.I., et al.
(författare)
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Permittivity of Plasma in Random Fields of Moderate Intensity
- 2011
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Ingår i: Ukrainian Journal of Physics. - 2071-0194. ; 56:7, s. 654-658
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Tidskriftsartikel (refereegranskat)abstract
- The permittivity of plasma in the electric field of randomwaves of moderate intensity is given in terms of theparticle transition probability between two points of thephase space. The transition probability was found asan approximate solution of the Fokker–Planck equation.Validity of this analytical approximation was verified bythe direct simulation of the particle diffusion in a field of random waves.
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