Abstract
A comparison is made between two versions of the Weiland model for computing anomalous transport driven by drift modes such as the ion temperature gradient(ITG) and trapped electron mode (TEM) in tokamak plasmas. Both are quasilinear fluid models that include physical effects resulting from finite , magnetic shear, electronion collisions, impurities, and fast ions. An outline of the derivation is presented for the newer Weiland19 model, which includes a more accurate description of the effects of finite , low and negative magnetic shear, plasma elongation, varying correlation lengths, particle pinch, and momentum transport. It is shown that the two models produce nearly the same ion thermal diffusivity as a function of normalized temperature gradient in a circular plasma with moderate magnetic shear, low , and moderately low density gradient. The models differ significantly at low magnetic shear and in elongated plasmas with high . In addition, the two models differ significantly in the behavior of the transition between moderate transport driven by ITG/TEM modes at low and large transport driven by magnetohydrodynamic instabilities at high . In the older Weiland14 model, the transition occurs at a low value of that is insensitive to plasma elongation and magnetic shear. In the newer Weiland19 model, the transition occurs at a relatively large value of that is a sensitive function of plasma elongation and magnetic shear.
I. INTRODUCTION
II. OVERVIEW OF THE PHYSICS BASIS OF THE WEILAND14 AND WEILAND19 MODELS FOR ANOMALOUS TRANSPORT
A. Fluid equations for the ionic species
B. Magnetic vector potential and ballooning parameter
C. Poloidal averaging of magnetic shear and geometry effects
D. Nonlinear iteration to determine mode width
E. Computation of correlation lengths and transport levels
III. COMPARISON OF ION THERMAL DIFFUSIVITIES PREDICTED BY THE WEILAND14 AND WEILAND19 MODELS
A. Comparison of models in the electrostatic limit at low and moderate positive magnetic shear
B. Effect of collisions
C. Effect of magnetic shear
D. Effect of plasma elongation
E. Effect of plasma
F. Combined effect of magnetic shear, elongation, and plasma
IV. SUMMARY AND CONCLUSION
Key Topics
 Ion temperature gradient mode
 38.0
 Thermal models
 22.0
 Plasma transport properties
 21.0
 Magnetohydrodynamics
 17.0
 Thermal diffusion
 16.0
Figures
Ion thermal diffusivity is shown as a function of normalized ion temperature gradient for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) for the plasma parameters listed in Table I. For these parameters, the eigenfunctions for both models are in the strong ballooning limit.
Ion thermal diffusivity is shown as a function of normalized ion temperature gradient for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) for the plasma parameters listed in Table I. For these parameters, the eigenfunctions for both models are in the strong ballooning limit.
Ion thermal diffusivity is shown as a function of collisionality for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . The value of is varied while , , , and are held constant at the values used for the baseline case. These constants and other parameters are listed in Table I. The thermal diffusivity is divided by to remove the dependence introduced by in the gyroBohm normalization factor.
Ion thermal diffusivity is shown as a function of collisionality for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . The value of is varied while , , , and are held constant at the values used for the baseline case. These constants and other parameters are listed in Table I. The thermal diffusivity is divided by to remove the dependence introduced by in the gyroBohm normalization factor.
Ion thermal diffusivity is shown as a function of magnetic shear for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . Magnetic shear is varied from to while , , are held constant. These constants and other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of magnetic shear for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . Magnetic shear is varied from to while , , are held constant. These constants and other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of elongation for the Weiland14 model (solid line) and for the Weiland19 model (dashed line). In addition, for the Weiland19 model, the largest ion (ITG) mode growth rate and the largest electron (MHD) mode growth rate , normalized by , are plotted as a function of . It is found that for , the MHD mode growth rate is dominant. The scans were carried out at fixed temperature gradients , , and . Other dimensionless parameters are held constant at the baseline values given in Table I.
Ion thermal diffusivity is shown as a function of elongation for the Weiland14 model (solid line) and for the Weiland19 model (dashed line). In addition, for the Weiland19 model, the largest ion (ITG) mode growth rate and the largest electron (MHD) mode growth rate , normalized by , are plotted as a function of . It is found that for , the MHD mode growth rate is dominant. The scans were carried out at fixed temperature gradients , , and . Other dimensionless parameters are held constant at the baseline values given in Table I.
Ion thermal diffusivity is shown as a function of plasma for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . Plasma is varied while , , are held constant at the values given in Table I.
Ion thermal diffusivity is shown as a function of plasma for the Weiland14 model (solid line) and for the Weiland19 model (dashed line) at fixed temperature gradients . Plasma is varied while , , are held constant at the values given in Table I.
Ion thermal diffusivity is shown as a function of magnetic shear for . The curve corresponding to the Weiland14 model is represented with a solid line. There are four curves for the Weiland19 model, each one corresponding to a different value of elongation. For the results shown in this figure, the plasma is increased from the base case value of to . The plasma density, temperature, and magnetic field are changed from the values given in Table I (, , and ) so that dimensionless parameters and are held constant at the baseline values. These constants and the other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of magnetic shear for . The curve corresponding to the Weiland14 model is represented with a solid line. There are four curves for the Weiland19 model, each one corresponding to a different value of elongation. For the results shown in this figure, the plasma is increased from the base case value of to . The plasma density, temperature, and magnetic field are changed from the values given in Table I (, , and ) so that dimensionless parameters and are held constant at the baseline values. These constants and the other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of magnetic shear . The results are for the same conditions used for the plots in Fig. 6 except that rather than . The curve corresponding to the Weiland14 model is represented with a solid line. There are four curves for the Weiland19 model, each one corresponding to a different value of elongation.
Ion thermal diffusivity is shown as a function of magnetic shear . The results are for the same conditions used for the plots in Fig. 6 except that rather than . The curve corresponding to the Weiland14 model is represented with a solid line. There are four curves for the Weiland19 model, each one corresponding to a different value of elongation.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid lines) and for the Weiland19 model (nonsolid lines) at fixed temperature gradients . The computations are carried out using weak elongation and three different magnetic shear values . Plasma is varied while and are held constant at the baselines values. These constants and other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid lines) and for the Weiland19 model (nonsolid lines) at fixed temperature gradients . The computations are carried out using weak elongation and three different magnetic shear values . Plasma is varied while and are held constant at the baselines values. These constants and other parameters are given in Table I.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid line) and for the Weiland19 model (dashed lines) for weak magnetic shear . The computations are carried out at four different elongation values with fixed temperature gradients . Plasma is varied while and are held constant at the values given in Table I.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid line) and for the Weiland19 model (dashed lines) for weak magnetic shear . The computations are carried out at four different elongation values with fixed temperature gradients . Plasma is varied while and are held constant at the values given in Table I.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid line) and for the Weiland19 model (nonsolid lines) for strong magnetic shear . The computations are carried out at four different elongation values with fixed temperature gradients . Plasma is varied while and are held constant at the values given in Table I.
Ion thermal diffusivity is shown as a function of for the Weiland14 model (solid line) and for the Weiland19 model (nonsolid lines) for strong magnetic shear . The computations are carried out at four different elongation values with fixed temperature gradients . Plasma is varied while and are held constant at the values given in Table I.
Tables
Parameters and nomenclature used.
Parameters and nomenclature used.
Differences in the implementation of physics effects.
Differences in the implementation of physics effects.
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