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Peter J. Catto - One of the best experts on this subject based on the ideXlab platform.
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Electromagnetic Zonal Flow residual responses
Journal of Plasma Physics, 2017Co-Authors: Peter J. Catto, Felix I. Parra, Istvan PusztaiAbstract:The collisionless axisymmetric Zonal Flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value Zonal Flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the Zonal Flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.
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Zonal Flow in a tokamak pedestal
Physics of Plasmas, 2009Co-Authors: Grigory Kagan, Peter J. CattoAbstract:Neoclassical shielding is the dominant mechanism reducing the collisionless Zonal Flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the Zonal Flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefore the pedestal neoclassical polarization and the Zonal Flow residual differ from the conventional results. This change is due to the strong electric field intrinsic to a subsonic pedestal that modifies neoclassical ion orbits so that their response to a Zonal Flow perturbation is qualitatively different from that in the core. In addition to orbit squeezing, we find a spatial phase shift between the initial and final Zonal Flow potentials—an effect absent in previous works. Moreover, we demonstrate that because of orbit modification neoclassical phenomena disappear in the large electric field limit making the residual close to one.
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Zonal Flow in a tokamak pedestal
Physics of Plasmas, 2009Co-Authors: Grigory Kagan, Peter J. CattoAbstract:Neoclassical shielding is the dominant mechanism reducing the collisionless Zonal Flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the Zonal Flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefore the pedestal neoclassical polarization and the Zonal Flow residual differ from the conventional results. This change is due to the strong electric field intrinsic to a subsonic pedestal that modifies neoclassical ion orbits so that their response to a Zonal Flow perturbation is qualitatively different from that in the core. In addition to orbit squeezing, we find a spatial phase shift between the initial and final Zonal Flow potentials—an effect absent in previous works. Moreover, we demonstrate that because of orbit modification neoclassical phenomena disappear in the large electric field limit making the residua...
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effects of finite poloidal gyroradius shaping and collisions on the Zonal Flow residual
Physics of Plasmas, 2007Co-Authors: Yong Xiao, Peter J. Catto, W DorlandAbstract:Zonal Flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that Zonal Flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent Zonal Flow advances are summarized including the evaluation of the effects on the Zonal Flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the Zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes.
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collisional damping for ion temperature gradient mode driven Zonal Flow
Physics of Plasmas, 2007Co-Authors: Yong Xiao, Peter J. Catto, Kim MolvigAbstract:Zonal Flow helps reduce and control the level of ion temperature gradient turbulence in a tokamak. The collisional damping of Zonal Flow has been estimated by Hinton and Rosenbluth (HR) in the large radial wavelength limit. Their calculation shows that the damping of Zonal Flow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, HR calculated the neoclassical polarization in the low and high collisionality limits. A new approach, based on an eigenfunction expansion of the collision operator, is employed to evaluate the neoclassical polarization and the Zonal Flow residual for arbitrary collisionality. An analytical expression for the temporal behavior of the Zonal Flow is also given showing that the damping rate tends to be somewhat slower than previously thought. These results are expected to be useful extensions of the original HR collisional work that can provide an effective benchmark for numerical codes for all regimes of collisionality.
P H Diamond - One of the best experts on this subject based on the ideXlab platform.
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nonlinear phase bores in drift wave Zonal Flow dynamics
Physics of Plasmas, 2019Co-Authors: H Kang, P H DiamondAbstract:A minimal model of nonlinear phase dynamics in drift waves is shown to support phase bore solutions. Coupled nonlinear equations for amplitude, phase, and Zonal Flow are derived for the Hasegawa-Mima system and specialized to the case of spatiotemporally constant amplitude. In that limit, phase curvature (finite second derivative of the phase with respect to the radius) alone generates propagating shear Flows. The phase field evolves nonlinearly by a competition between phase steepening and dispersion. The analytical solution of the model reveals that the phase bore solutions so obtained realize the concept of a phase slip in a concrete dynamical model of drift wave dynamics. The implications for phase turbulence are discussed.A minimal model of nonlinear phase dynamics in drift waves is shown to support phase bore solutions. Coupled nonlinear equations for amplitude, phase, and Zonal Flow are derived for the Hasegawa-Mima system and specialized to the case of spatiotemporally constant amplitude. In that limit, phase curvature (finite second derivative of the phase with respect to the radius) alone generates propagating shear Flows. The phase field evolves nonlinearly by a competition between phase steepening and dispersion. The analytical solution of the model reveals that the phase bore solutions so obtained realize the concept of a phase slip in a concrete dynamical model of drift wave dynamics. The implications for phase turbulence are discussed.
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Zonal Flow patterns how toroidal coupling induces phase jumps and shear layers
Physical Review Letters, 2016Co-Authors: Z B Guo, P H DiamondAbstract:A new, frequency modulation mechanism for Zonal Flow pattern formation is presented. The model predicts the probability distribution function of the Flow strength as well as the evolution of the characteristic spatial scale. Magnetic toroidicity-induced global phase dynamics is shown to determine the spatial structure of the Flow. A key result is the observation that global phase patterning can lead to Zonal Flow formation in the absence of turbulence inhomogeneity.
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small scale coherent vortex generation in drift wave Zonal Flow turbulence
Physics of Plasmas, 2015Co-Authors: Z B Guo, T S Hahm, P H DiamondAbstract:We present a paradigm for the generation of small scale coherent vortex (SSCV) in drift wave-Zonal Flow (DW-ZF) turbulence. We demonstrate that phases of DWs can couple coherently, mediated by the ZF shearing. A SSCV is formed when the phases of the DWs are “attracted” to form a stable “phase cluster.” We show that the ZF shearing induces asymmetry between “attractive” and “repulsive” phase couplings, so that a net attractive phase coupling results. The turbulent DWs will (partially)synchronize into a stable SSCV at locations, where the attractive phase coupling induced by the ZF shearing exceeds the “detuning” effects by the DW dispersion and random phase scattering. We also discuss the “self-binding” effect of the newly formed SSCV.
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elasticity in drift wave Zonal Flow turbulence
Physical Review E, 2014Co-Authors: Z B Guo, Yusuke Kosuga, P H Diamond, O D GurcanAbstract:We present a theory of turbulent elasticity, a property of drift-wave--Zonal-Flow (DW-ZF) turbulence, which follows from the time delay in the response of DWs to ZF shears. An emergent dimensionless parameter ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is found to be a measure of the degree of Fickian flux-gradient relation breaking, where ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|$ is the ZF shearing rate and $\ensuremath{\Delta}{\ensuremath{\omega}}_{k}$ is the turbulence decorrelation rate. For ${|\ensuremath{\langle}v\ensuremath{\rangle}}^{\ensuremath{'}}|/\ensuremath{\Delta}{\ensuremath{\omega}}_{k}g1$, we show that the ZF evolution equation is converted from a diffusion equation, usually assumed, to a telegraph equation, i.e., the turbulent momentum transport changes from a diffusive process to wavelike propagation. This scenario corresponds to a state very close to the marginal instability of the DW-ZF system, e.g., the Dimits shift regime. The frequency of the ZF wave is ${\ensuremath{\Omega}}_{\mathrm{ZF}}=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\gamma}}_{d}^{1/2}{\ensuremath{\gamma}}_{\mathrm{modu}}^{1/2}$, where ${\ensuremath{\gamma}}_{d}$ is the ZF friction coefficient and ${\ensuremath{\gamma}}_{\mathrm{modu}}$ is the net ZF growth rate for the case of the Fickian flux-gradient relation. This insight provides a natural framework for understanding temporally periodic ZF structures in the Dimits shift regime and in the transition from low confined mode to high confined mode in confined plasmas.
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Coherent structures in ion temperature gradient turbulence-Zonal Flow
Physics of Plasmas, 2014Co-Authors: P. Kaw, Rameswar Singh, Özgür D. Gürcan, P H DiamondAbstract:Nonlinear stationary structure formation in the coupled ion temperature gradient (ITG)-Zonal Flow system is investigated. The ITG turbulence is described by a wave-kinetic equation for the action density of the ITG mode, and the longer scale Zonal mode is described by a dynamic equation for the m = n = 0 component of the potential. Two populations of trapped and untrapped drift wave trajectories are shown to exist in a moving frame of reference. This novel effect leads to the formation of nonlinear stationary structures. It is shown that the ITG turbulence can self-consistently sustain coherent, radially propagating modulation envelope structures such as solitons, shocks, and nonlinear wave trains.
F Zonca - One of the best experts on this subject based on the ideXlab platform.
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effects of energetic particles on Zonal Flow generation by toroidal alfven eigenmode
Physics of Plasmas, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Generation of Zonal Flow (ZF) by energetic particle (EP) driven toroidal Alfven eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and micro-scale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.
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fine structure Zonal Flow excitation by beta induced alfven eigenmode
Nuclear Fusion, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Author(s): Qiu, Z; Chen, L; Zonca, F | Abstract: © 2016 IAEA, Vienna. Nonlinear excitation of low frequency Zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic Zonal Flow (ZF), rather than Zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the Zonal electric field has an even mode structure at the rational surface where radial envelope peaks.
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fine structure Zonal Flow excitation by beta induced alfven eigenmode
arXiv: Plasma Physics, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Nonlinear excitation of low frequency Zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic Zonal Flow (ZF), rather than Zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the Zonal electric field has an even mode structure at the rational surface where radial envelope peaks.
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radial spreading of drift wave Zonal Flow turbulence via soliton formation
Physical Review Letters, 2009Co-Authors: Zehua Guo, Liu Chen, F ZoncaAbstract:The self-consistent spatiotemporal evolution of a drift-wave (DW) radial envelope and a Zonal-Flow (ZF) amplitude is investigated in a slab model. The stationary solution of the coupled partial differential equations in a simple limit yields the formation of DW-ZF soliton structures, which propagate radially with speed depending on the envelope peak amplitude. Additional interesting physics, e.g., the generation, destruction, collision, and reflection of solitons, as well as turbulence bursting can also be observed due to the effects of linear growth or damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling with the system size by broadening of the turbulent region. The correspondence of the present analysis with the description of DW-ZF interactions in toroidal geometry is also discussed.
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radial spreading of drift wave Zonal Flow turbulence via soliton formation
arXiv: Plasma Physics, 2009Co-Authors: Zehua Guo, Liu Chen, F ZoncaAbstract:The self-consistent spatiotemporal evolution of drift wave (DW) radial envelope and Zonal Flow (ZF) amplitude is investigated in a slab model [1]. Stationary solution of the coupled partial differential equations in a simple limit yields formation of DW-ZF soliton structures, which propagate at group velocity depending on the envelope peak amplitude. Additional interesting physics, e.g. generation, destruction, collision and reflection of solitons, as well as turbulence bursting can also be observed due to effects of linear growth/damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling with system size by broadening of the turbulent region. Correspondence of the present analysis with the description of DW-ZF interactions in toroidal geometry [2, 3] is also elucidated.
Liu Chen - One of the best experts on this subject based on the ideXlab platform.
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effects of energetic particles on Zonal Flow generation by toroidal alfven eigenmode
Physics of Plasmas, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Generation of Zonal Flow (ZF) by energetic particle (EP) driven toroidal Alfven eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and micro-scale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.
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fine structure Zonal Flow excitation by beta induced alfven eigenmode
Nuclear Fusion, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Author(s): Qiu, Z; Chen, L; Zonca, F | Abstract: © 2016 IAEA, Vienna. Nonlinear excitation of low frequency Zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic Zonal Flow (ZF), rather than Zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the Zonal electric field has an even mode structure at the rational surface where radial envelope peaks.
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fine structure Zonal Flow excitation by beta induced alfven eigenmode
arXiv: Plasma Physics, 2016Co-Authors: Zhiyong Qiu, Liu Chen, F ZoncaAbstract:Nonlinear excitation of low frequency Zonal structure (LFZS) by beta-induced Alfven eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic Zonal Flow (ZF), rather than Zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the Zonal electric field has an even mode structure at the rational surface where radial envelope peaks.
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radial spreading of drift wave Zonal Flow turbulence via soliton formation
Physical Review Letters, 2009Co-Authors: Zehua Guo, Liu Chen, F ZoncaAbstract:The self-consistent spatiotemporal evolution of a drift-wave (DW) radial envelope and a Zonal-Flow (ZF) amplitude is investigated in a slab model. The stationary solution of the coupled partial differential equations in a simple limit yields the formation of DW-ZF soliton structures, which propagate radially with speed depending on the envelope peak amplitude. Additional interesting physics, e.g., the generation, destruction, collision, and reflection of solitons, as well as turbulence bursting can also be observed due to the effects of linear growth or damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling with the system size by broadening of the turbulent region. The correspondence of the present analysis with the description of DW-ZF interactions in toroidal geometry is also discussed.
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radial spreading of drift wave Zonal Flow turbulence via soliton formation
arXiv: Plasma Physics, 2009Co-Authors: Zehua Guo, Liu Chen, F ZoncaAbstract:The self-consistent spatiotemporal evolution of drift wave (DW) radial envelope and Zonal Flow (ZF) amplitude is investigated in a slab model [1]. Stationary solution of the coupled partial differential equations in a simple limit yields formation of DW-ZF soliton structures, which propagate at group velocity depending on the envelope peak amplitude. Additional interesting physics, e.g. generation, destruction, collision and reflection of solitons, as well as turbulence bursting can also be observed due to effects of linear growth/damping, dissipation, equilibrium nonuniformities and soliton dynamics. The propagation of soliton causes significant radial spreading of DW turbulence and therefore can affect transport scaling with system size by broadening of the turbulent region. Correspondence of the present analysis with the description of DW-ZF interactions in toroidal geometry [2, 3] is also elucidated.
Yong Xiao - One of the best experts on this subject based on the ideXlab platform.
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effects of finite poloidal gyroradius shaping and collisions on the Zonal Flow residual
Physics of Plasmas, 2007Co-Authors: Yong Xiao, Peter J. Catto, W DorlandAbstract:Zonal Flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that Zonal Flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent Zonal Flow advances are summarized including the evaluation of the effects on the Zonal Flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the Zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes.
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collisional damping for ion temperature gradient mode driven Zonal Flow
Physics of Plasmas, 2007Co-Authors: Yong Xiao, Peter J. Catto, Kim MolvigAbstract:Zonal Flow helps reduce and control the level of ion temperature gradient turbulence in a tokamak. The collisional damping of Zonal Flow has been estimated by Hinton and Rosenbluth (HR) in the large radial wavelength limit. Their calculation shows that the damping of Zonal Flow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, HR calculated the neoclassical polarization in the low and high collisionality limits. A new approach, based on an eigenfunction expansion of the collision operator, is employed to evaluate the neoclassical polarization and the Zonal Flow residual for arbitrary collisionality. An analytical expression for the temporal behavior of the Zonal Flow is also given showing that the damping rate tends to be somewhat slower than previously thought. These results are expected to be useful extensions of the original HR collisional work that can provide an effective benchmark for numerical codes for all regimes of collisionality.
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short wavelength effects on the collisionless neoclassical polarization and residual Zonal Flow level
Physics of Plasmas, 2006Co-Authors: Yong Xiao, Peter J. CattoAbstract:Sheared Zonal Flow helps to reduce the turbulent transport caused by the ion temperature gradient mode. Rosenbluth and Hinton (R-H) calculated the residual Zonal Flow level for radial wavelengths that are much larger than the ion poloidal gyroradius. Their calculation is extended to treat arbitrary radial wavelengths. For the radial wavelengths that approach the ion poloidal gyroradius, but are much larger than the ion gyroradius, an analytical formula is obtained. For radial wavelengths that are comparable or shorter than the poloidal ion gyroradius and the ion gyroradius a numerical solution is provided. These small radial wavelength results are then extended into the electron temperature gradient regime, where the residual Zonal Flow level is large but ineffective in regulating the turbulence, indicating that the conventional R-H explanation that Zonal Flow regulates turbulence is incomplete.
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Plasma shaping effects on the collisionless residual Zonal Flow level
Physics of Plasmas, 2006Co-Authors: Yong Xiao, Peter J. CattoAbstract:Plasma shaping effects, such as elongation, triangularity, and Shafranov shift have long been considered important ingredients in improving tokamak performance. It is known that the growth rate of ion temperature gradient (ITG) turbulence can be regulated by these shaping effects and that the ITG turbulence level can also be regulated by Zonal Flow. Moreover, recent numerical simulation shows that the collsionless residual Zonal Flow level can be influenced by these shaping effects. An analytical approach is used to explicitly evaluate plasma shaping effects on the collisionless residual Zonal Flow. The results show that the residual Zonal Flow level increases with elongation, triangularity and the Shafranov shift.