Abstract
A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyrokinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are then connected with the poloidal derivative of the ballooning envelope, which are one order smaller in the normalised Larmor radius, compared with the derivative of the eikonal. The mechanism, therefore, does not introduce an inhomogeneity in the radial direction, in contrast with the effect of profile shearing. Numerical simulations of the linear ion temperature gradient mode with adiabatic electrons, retaining the finite effects in the E × B velocity, the drift, and the gyroaverage, are presented. The momentum flux is found to be linear in the normalised Larmor radius ( ) but is, nevertheless, generating a sizeable countercurrent rotation. The total momentum flux scales linear with the aspect ratio of the considered magnetic surface, and increases with increasing magnetic shear, safety factor, and density and temperature gradients.
I. INTRODUCTION
II. THE MODEL
A. Higher order corrections to the E × B velocity
B. Higher order correction in the drift due to the magnetic field inhomogeneity
C. Higher order corrections to the particle trapping
D. Higher order corrections in the gyroaverage as well as polarisation
E. Higher order terms in calculating the fluxes
F. Model set of equations
G. Symmetry breaking
III. RESULTS
IV. DISCUSSION
Key Topics
 Magnetic fields
 17.0
 Maxwell equations
 11.0
 Numerical modeling
 8.0
 Toroidal plasma confinement
 7.0
 Ion temperature gradient mode
 6.0
H05H1/02
Figures
[solid (blue) line with symbol “+”], [dashed (blue) line with symbol ‘x’], [solid (red) line with symbol “o”], and Im[w] [dashed (red) line with symbol “*”]. The top figure gives and w^{A} , while the bottom figure gives and w^{S} . All functions shown in the lower figure are zero in the absence of finite terms.
[solid (blue) line with symbol “+”], [dashed (blue) line with symbol ‘x’], [solid (red) line with symbol “o”], and Im[w] [dashed (red) line with symbol “*”]. The top figure gives and w^{A} , while the bottom figure gives and w^{S} . All functions shown in the lower figure are zero in the absence of finite terms.
calculated directly from the eigenfunction [solid (blue) line with symbol “+”], calculated directly from the eigenfunction [dashed (blue) line with symbol “x”], calculated through numerical differentiation of [solid (green) line with symbol “ ”], and calculated through numerical differentiation of [dashed (green) line with symbol “ ”].
calculated directly from the eigenfunction [solid (blue) line with symbol “+”], calculated directly from the eigenfunction [dashed (blue) line with symbol “x”], calculated through numerical differentiation of [solid (green) line with symbol “ ”], and calculated through numerical differentiation of [dashed (green) line with symbol “ ”].
The momentum flux expressed in the equilibrium as a function of . The letters on the right relate to the symmetry breaking mechanism identified in Eqs. (37)–(43) A: red line with symbol “+,” B_{1}: light blue line with symbol “*,” B_{2}: dark green with symbol “ ,” D: black line with symbol “ ,” E: magenta line with symbol “ .” Additionally, the sum of all individual contributions is given by the (green) curve with the symbol “o,” and the momentum flux calculated including all finite terms is given by the (blue) curve with symbol “x.” The axis contains typical values of three machines: ITER, ^{ 52 } AUG, ^{ 53 } and TCV. ^{ 54 }
The momentum flux expressed in the equilibrium as a function of . The letters on the right relate to the symmetry breaking mechanism identified in Eqs. (37)–(43) A: red line with symbol “+,” B_{1}: light blue line with symbol “*,” B_{2}: dark green with symbol “ ,” D: black line with symbol “ ,” E: magenta line with symbol “ .” Additionally, the sum of all individual contributions is given by the (green) curve with the symbol “o,” and the momentum flux calculated including all finite terms is given by the (blue) curve with symbol “x.” The axis contains typical values of three machines: ITER, ^{ 52 } AUG, ^{ 53 } and TCV. ^{ 54 }
Equilibrium value of as a function of different plasma parameters. From left to right: magnetic shear ( ), safety factor (q), poloidal wave vector ( ), density gradient length , and temperature gradient length . The three curves that are shown in each of the graphs correspond to different values of the inverse aspect ratio: solid (red) line with symbol “x,” dasheddotted (green) line with symbol “+,” and dashed (blue) line with symbol “o.”
Equilibrium value of as a function of different plasma parameters. From left to right: magnetic shear ( ), safety factor (q), poloidal wave vector ( ), density gradient length , and temperature gradient length . The three curves that are shown in each of the graphs correspond to different values of the inverse aspect ratio: solid (red) line with symbol “x,” dasheddotted (green) line with symbol “+,” and dashed (blue) line with symbol “o.”
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