Ballooning theory of the second kind-two dimensional tokamak modes

Journal Article · Sun Jul 15 00:00:00 EDT 2012 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4731724· OSTI ID:22072524

Xie, T; Wang, A K ^[1]; Zhang, Y Z ^[2]; Mahajan, S M ^[3]

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1. Southwestern Institute of Physics, Chengdu (China)
2. Center for Magnetic Fusion Theory, Chinese Academy of Sciences, Hefei (China)
3. Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)

The 2-D ballooning transform, devised to study local high toroidal number (n) fluctuations in axisymmetric toroidal system (like tokamaks), yields a well-defined partial differential equation for the linear eigenmodes. In this paper, such a ballooning equation of the second kind is set up for ion temperature gradient driven modes pertinent to a 2-D non-dissipative fluid plasma; the resulting partial differential equation is numerically solved, to calculate the global eigenvalues, and the 2-D mode structure is presented graphically along with analytical companions. The radial localization of the mode results from translational symmetry breaking for growing modes and is a vivid manifestation of spontaneous symmetry breaking in tokamak physics. The eigenmode, poloidally ballooned at {theta}={+-}{pi}/2, is radially shifted from associated rational surface. The global eigenvalue is found to be very close to the value obtained in 1-D parameterized ({lambda}={+-}{pi}/2) case. The 2-D eigenmode theory is applied to estimate the toroidal seed Reynolds stress [Y. Z. Zhang, Nucl. Fusion Plasma Phys. 30, 193 (2010)]. The solution obtained from the relatively simplified ballooning theory is compared to the solution of the basic equation in original coordinate system (evaluated via FFTs); the agreement is rather good.

• OSTI ID: 22072524
• Journal Information: Physics of Plasmas, Vol. 19, Issue 7; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
AXIAL SYMMETRY
BALLOONING INSTABILITY
EIGENVALUES
FLUCTUATIONS
ION TEMPERATURE
MATHEMATICAL SOLUTIONS
MODE RATIONAL SURFACES
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
REYNOLDS NUMBER
STRESSES
SYMMETRY BREAKING
TEMPERATURE GRADIENTS
TOKAMAK DEVICES
TOROIDAL CONFIGURATION
TWO-DIMENSIONAL CALCULATIONS