Analytical eigenvalue solution for ηi modes of general modewidth

Weiland, Jan

doi:10.1063/1.1738648

Cited by 17 publications

(13 citation statements)

References 12 publications

(17 reference statements)

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“…Here, since our eigenfunction is varying slowly in the interior we can use this eigenfunction everywhere. In fact, the solution ( 23) turned out to be in excellent agreement with shooting code results (Weiland 2004). Small shear was also important in obtaining internal transport barriers on JET (Weiland et al 2011).…”

Section: Parallel Ion Motionsupporting

confidence: 65%

“…We start by observing that the confinement of plasma means that we have to maintain gradients of the most central plasma properties such as pressure, density, etc. (Kadomtsev 1965;Dupree 1967;Liu 1969;Chandrasekhar 1943;Lehnert 1966;Dupree 1966;Kadomtsev and Pogutse 1970;Liu and Bhadra 1970;Taylor and McNamara 1971;Okuda and Dawson 1973;Hasegawa 1975;Weiland and Wilhelmsson 1977;Coppi and Pegoraro 1977;Horton et al 1981;Hasegawa and Mima 1978;Sagdeev et al 1978;Hassam and Kulsrud 1979;Hasegawa et al 1979;Weiland 1980Weiland , 2004Weiland , 2010Weiland , 2012Weiland , 2014Weiland , 2015Weiland , 2016Weiland , 2018Wakatani and Hasegawa 1984;Liewer 1985;Weiland and Nordman 1988, 1991Weiland et al 1989;Wootton et al 1990;Scott et al 1990;Kardaun et al 1992;Wagner and Stroth 1993;LeBrun et al 1993;Luce et al 1992;Nilsson and Weiland 1994;Waltz et al 1995;Staebler et al 1997;Mattor and Parker 1997;…”

Section: Introductionmentioning

confidence: 99%

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Drift wave theory for transport in tokamaks

Weiland

Zagorodny

2019

Rev. Mod. Plasma Phys.

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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 e ∼ 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 k 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 Extended author information available on the last page of the article Reviews of Modern Plasma Physics (2019) 3:8 1 3 8 Page 2 of 21transport by a systematic derivation from first principles. Our model is not fitted numerically to any other model.

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Section: Parallel Ion Motionsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Drift wave theory for transport in tokamaks

Weiland

Zagorodny

2019

Rev. Mod. Plasma Phys.

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“…15 as "Weiland19" in an effort to combine several effects described in individual papers. [17][18][19][20] Growth rates and frequencies of ITG modes and trapped electron modes ͑TEMs͒ are computed assuming only one poloidal wave number ͑ITG/TEM range͒. The equilibrium is also approximated by shifted circular magnetic surfaces.…”

Section: The Glf23 and Weiland Theory-based Modelsmentioning

confidence: 99%

Simulation of Joint European Torus beta scan experiments using theory-based models

et al. 2008

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Transport modeling of beta (β) scaling experiments performed in the Joint European Torus (JET) [P. H. Rebut et al., Nucl. Fusion 25 1011 (1985)] is presented. Two theory-based models are used: the Weiland model [F. D. Halpern et al., Phys. Plasmas 15, 012304 (2008)] and the gyro-Landau-fluid model GLF23 [J. E. Kinsey et al., Phys. Plasmas 12, 062302 (2005)]. First, the β dependence of energy transport in each model is illustrated by running them stand-alone with imposed plasma profiles obtained in JET β scaling experiments. Both models show a stabilization of ion temperature gradient modes with increasing β up to a critical β value for which ballooning modes become unstable, leading to a strong degradation of the core confinement. Second, the models are used in predictive simulations of heat transport in order to test the capability of the models to reproduce experimental results. A good agreement between the Weiland model and experimental results is found, but the model sensitivity to dimensionless parameters mismatches throughout the experimental scan strongly affects the apparent scaling. This is tested by running predictive simulations using modified input parameters in order to correct the mismatch. In order to identify which dimensionless parameter mismatches are responsible for the apparent scaling, a sensitivity analysis of the Weiland model is performed. A comparison with modeling of previous experimental results is also presented.

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“…[26][27][28]. In this contribution, however, a semilocal mode approximation 10,35 has been used in order to avoid a system of equations higher than second order.…”

Section: Introductionmentioning

confidence: 99%