The two-dimensional kinetic ballooning theory for ion temperature gradient mode in tokamak

The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the l...

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Bibliographic Details
Published in:Physics of plasmas 2017-10, Vol.24 (10)
Main Authors: Xie, T., Zhang, Y. Z., Mahajan, S. M., Hu, S. L., He, Hongda, Liu, Z. Y.
Format: Article
Language:English
Subjects:
Basic converters
Computational fluid dynamics
Differential equations
Integral equations
Ion temperature
Iterative methods
Kinetic equations
Mathematical models
Ordinary differential equations
Plasma physics
Plasmas (physics)
Temperature gradients
Tokamak devices
Two dimensional models
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Summary:The two-dimensional (2D) kinetic ballooning theory is developed for the ion temperature gradient mode in an up-down symmetric equilibrium (illustrated via concentric circular magnetic surfaces). The ballooning transform converts the basic 2D linear gyro-kinetic equation into two equations: (1) the lowest order equation (ballooning equation) is an integral equation essentially the same as that reported by Dong et al., [Phys. Fluids B 4, 1867 (1992)] but has an undetermined Floquet phase variable, (2) the higher order equation for the rapid phase envelope is an ordinary differential equation in the same form as the 2D ballooning theory in a fluid model [Xie et al., Phys. Plasmas 23, 042514 (2016)]. The system is numerically solved by an iterative approach to obtain the (phase independent) eigen-value. The new results are compared to the two earlier theories. We find a strongly modified up-down asymmetric mode structure, and non-trivial modifications to the eigen-value.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.5003652