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Electromagnetic microinstabilities in tokamak plasmas are studied by means of a linear global eigenvalue numerical code. Ion dynamics is described by the gyrokinetic equation, so that finite ion Larmor radius effects are taken into account to all orders. Nonadiabatic electrons are included in the model, with passing particles described by the drift-kinetic equation and trapped particles through the bounce averaged drift-kinetic equation. A large aspect ratio plasma with circular shifted surfaces is considered for the numerical implementation. The effects of an electromagnetic perturbation on toroidal ion temperature gradient driven modes are studied, confirming the stabilization of these modes with increasing β (parameter identifying the ratio of the plasma pressure to the magnetic pressure). The threshold for the destabilization of an electromagnetic mode, the so-called kinetic ballooning mode or Alfvénic ion temperature gradient mode is identified. Moreover, owing to the global formulation, the radial structure of these electromagnetic modes is observed for the first time. Finally, the contributions of trapped electron dynamics and the effects of the Shafranov shift are addressed. [ABSTRACT FROM AUTHOR]

Strong electric fields generate an ExB rotation of the equilibrium plasma. Experiments have shown that this effect could lower the anomalous transport in tokamaks. The study of the effect of these flows on the linear stability of ion temperature gradient (ITG) modes has therefore been undertaken. The question is addressed solving the spectrum of the gyrokinetic equation in the full two-dimensional poloidal plane for a large aspect ratio tokamak with concentric circular magnetic surfaces. Results show a strong stabilizing effect of ExB flows on the ITG modes. Study with respect to different profiles of the flow shows that the so-called curvature of flow (second derivative) has no effect, while the intensity of flow itself produces the strongest effect. Study with respect to different magnetic shears did not allow the discovery of any particular behavior of the negative magnetic shear cases. Eventually, an experimental comparison was conducted. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Kinetic theory is used to develop equations describing dynamics of small-amplitude electromagnetic perturbations in toroidal axisymmetric plasmas. The closed Vlasov–Maxwell equations are first solved for a hot stationary plasma using the expansion in the small parameter εe=ρ/L, where ρ is the Larmor radius and L a characteristic length scale of the stationary state. The ordering and additional assumptions are specified so as to obtain the well-known Grad–Shafranov equation. The dielectric tensor of such a plasma is then derived. The Vlasov equation for the perturbed distribution function is solved by the expansion in the small parameters εe and εp=ρ/λ, where λ is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in εe and the second order in εp. By integrating the resulting distribution function over velocity space, an explicit expression for the tensor is derived in the form of a two-dimensional partial differential operator. The operator is shown to possess the proper symmetry corresponding to the energy conservation law. [ABSTRACT FROM AUTHOR]

A numerical code, seal, solving the full form of a second-order integrodifferential equation that describes electrostatic waves in a slab plasma is presented. No expansion in the smallness of the ion Larmor radius is made. The plasma may have arbitrary density and temperature profiles and is immersed in a nonuniform magnetic field. Only small magnetic field gradients, Maxwellian equilibrium distribution functions, and ky =0 are assumed. First the integral equation is derived in Fourier space using the linearized Vlasov and Poisson equations, and then it is transformed back into real space, which enables us to treat the case of bounded plasmas. The two boundary conditions specified simulate an antenna at one end of the plasma and wave-reflecting walls. Solutions having wavelengths smaller than the ion Larmor radius have been found. Comparison with experiments where ion Bernstein waves are launched in argon and barium plasmas shows very good agreement with the solution of the code seal. A positive-definite formula for the local power absorption is also derived and computed. [ABSTRACT FROM AUTHOR]

The ponderomotive force acting on a magnetized plasma resulting from a radio-frequency (rf) electric field is studied both theoretically and experimentally. The fundamental difference between the predictions of the single-particle and fluid approaches is emphasized and its origin elucidated. An experiment is described that illustrates the collective interaction of a fluid with an rf field. This collective behavior manifests itself in the perpendicular ponderomotive force by the interaction of the fi-induced magnetization current with the magnetic field. [ABSTRACT FROM AUTHOR]

The equations of quasilinear theory are derived for a uniformly magnetized inhomogeneous plasma interacting with electromagnetic field fluctuations. The derivation avoids the use of the random phase approximation, and requires no assumption on the ratio of the Larmor radius to the fluctuation wavelength. These equations are used to obtain the transport equations for each plasma component. The latter satisfy the necessary conservation properties, and yield explicit expressions for various fluxes. [ABSTRACT FROM AUTHOR]

Presents global gyrokinetic equation to solve the spectral problem of microinstabilities in a cylindrical plasma. Computation of the full unstable spectrum of ion temperature gradient type modes; Applicability of equation to the two-dimensional equation of the tokamak configurations; Use of an elaborated Nyquist technique.

Studies global Alfven eigenmodes using two different models for the plasma and compares the results with the instability threshold measured experimentally. Consideration of the ion Larmor radius and the resonant Landau interactions between the particles and the wavefield; Power transfers between the wave and the transfers.

An abstract on electrophilic polyfluoroalkylation from the synthesis of quaternary a-perfluoroalkyl lactams is presented.

In the scope of the study of low-frequency electrostatic microinstabilities in tokamak plasmas, attention has been focused on the effect of trapped ions. The ballooning transform has been applied to the gyrokinetic equation, for the case of a large aspect ratio plasma with circular magnetic surfaces. A new eigenvalue code has been developed to solve the resulting integral equation, for the case of adiabatic electrons and full ion dynamics, thus taking into account both circulating and trapped ions. The goal has been to assess the validity of the ballooning transform for trapped ion modes. A scan over the parameter k[sub θ]ρ[sub L] has been carried out to determine a lower threshold for applicability of the ballooning representation. Illustrative results of trapped ion modes (TIM) are presented, together with the comparison with the ones obtained using a global gyrokinetic code, for low toroidal wave numbers, and a local kinetic dispersion relation. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effect of trapped electrons on the ion temperature gradient (ITG) mode in a regime where its wavelength is shorter than the conventional ITG mode (k⊥ρLi≤1) has been studied. Such a mode propagates in the ion diamagnetic direction with a typical scale length k⊥ρLi>1 and is termed as the short wavelength ITG (SWITG) mode. The effect of the trapped electrons on this SWITG mode is investigated, for the first time, using a global and local linear gyrokinetic model. The trapped electrons are observed to destabilize the mode strongly. Comparison of the various parameter scans for the SWITG mode with and without the trapped electrons is presented. One important result obtained is that, while in the absence of the trapped electrons the mode was found to subside with increasing value of εn=Ln/R exhibiting the character of a slablike mode, the presence of the trapped electrons has been observed to enhance the εn=Ln/R window of the existence of the SWITG mode making the mode more toroidal like. [ABSTRACT FROM AUTHOR]

Linear, fully gyrokinetic, full radius (global), large aspect ratio studies of Alfvén-ion temperature gradient mode (AITG) or kinetic ballooning modes or beta-induced Alfvén eigenmodes considering only “passing” species is presented. Effects hitherto completely neglected in a full radius approach such as B∥-fluctuations and the ones which have been treated partly [Phys. Plasmas 10, 1424 (2003)] such as Shafranov shifts are included. To this end, an existing code EM-GLOGYSTO has been upgraded to incorporate these effects. Among others, the most interesting results include: (i) For relatively large positive magnetic shear s⁁ [1.25

Collisionless microtearing modes have recently been found linearly unstable in sharp temperature gradient regions of large aspect ratio tokamaks. The magnetic drift resonance of passing electrons has been found to be sufficient to destabilise these modes above a threshold plasma β. A global gyrokinetic study, including both passing electrons as well as trapped electrons, shows that the non-adiabatic contribution of the trapped electrons provides a resonant destabilization, especially at large toroidal mode numbers, for a given aspect ratio. The global 2D mode structures show important changes to the destabilising electrostatic potential. The β threshold for the onset of the instability is found to be generally downshifted by the inclusion of trapped electrons. A scan in the aspect ratio of the tokamak configuration, from medium to large but finite values, clearly indicates a significant destabilizing contribution from trapped electrons at small aspect ratio, with a diminishing role at larger aspect ratios. [ABSTRACT FROM AUTHOR]

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma-β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient ge. Scans at different β values show an inverse relationship between the ge threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM. [ABSTRACT FROM AUTHOR]

An electron density gradient driven instability identified as the toroidal branch of the universal drift instability is studied using a global gyrokinetic model treating both electrons and ions fully nonadiabatically and valid at all orders in the ratio of the Larmor radius to the wavelength. The physics of the magnetic drift resonance, Landau resonance and transit resonance, which are considered to be important for the toroidal universal mode, are kept for both species. A systematic parametric study is carried out for the mode. The toroidal universal drift mode is observed to sustain finite temperature gradient and can thus coexist with the temperature gradient driven modes and may contribute to the observed particle transport along with other drift modes. Especially at intermediate scales between the ion temperature gradient driven mode and electron temperature gradient driven mode, this branch of the drift instability can also be a plausible candidate for the observed particle loss. The effect of magnetic fluctuations on the mode is also investigated. In contrast to the slab mode, the toroidal branch of the universal drift mode is found to be strongly stabilized by electromagnetic effects at finite plasma β. Finally, the effect of trapped electrons on the universal mode is studied and compared with the other possible modes in the same parameter regime, namely, ion temperature gradient mode in the presence of trapped electrons and pure trapped electron modes. [ABSTRACT FROM AUTHOR]

It is believed that low frequency microinstabilities such as ion temperature gradient (ITG) driven modes and trapped electron modes (TEMs) are largely responsible for the experimentally observed anomalous transport via the ion and electron channels in a tokamak. In the present work, a comprehensive global linear gyrokinetic model incorporating fully kinetic (trapped and passing) electrons and ions, actual ion to electron mass ratio, radial coupling, and profile variation is used to investigate the ITG driven modes and pure TEMs. These modes are found to exhibit multiscale structures in the presence of nonadiabatic passing electrons. The multiscale structure is related to the large nonadiabaticity of electrons in the vicinity of mode rational magnetic surfaces and leads to reduced mixing length estimates of transport compared to those obtained from adiabatic electron models. [ABSTRACT FROM AUTHOR]

In this work, role of nonadiabatic untrapped electrons in the context of a global ion temperature gradient driven mode has been investigated. In past studies, untrapped electrons have been assumed to be able to respond “instantaneously” to a disturbance. It is proposed that such adiabatic electron models should be reexamined for two important reasons: (i) It is known that global modes with n in the range of 3≤n≤15 (n is the toroidal mode number) have eigenmode widths spanning several mode-rational surfaces. It is being argued that close to these mode-rational surfaces, adiabatic electron models fail and a consistent treatment of nonadiabatic electrons is crucial for global modes. (ii) Electromagnetic effects depend on passing nonadiabatic electron dynamics. A minimal nontrivial model for the benchmarking of global linear and nonlinear gyrokinetic codes in the future becomes necessary, which can treat both passing ions and electrons on the same physics footing. As a first step, a study of the effect of nonadiabatic passing electrons in global electrostatic ion temperature gradients is presented. Interesting results include a demonstration of multiscale structure, downshift in critical ηi with increasing ηe, and a reduction in mixing-length based transport. [ABSTRACT FROM AUTHOR]

Abstract: A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r, θ, z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been validated in the linear and non-linear regimes. The GYSELA code is found to be stable over long simulation times (more than 20 times the linear growth rate of the most unstable mode), including for cases with a high resolution mesh (δr ∼0.1 Larmor radius, δz ∼10 Larmor radius). [Copyright &y& Elsevier]

A common feature of the Vlasov equation is that it develops fine‐scale filamentation as time evolves, as observed, for example, in global nonlinear simulations of the ion‐temperature‐gradient instability. From a numerical point of view, it is not trivial to simulate nonlinear regimes characterized by increasingly smaller scales, which eventually become smaller than the (finite) grid size. When very small structures occur, higher order interpolation schemes have a tendency to produce overshoots and negative‐density regions unless some additional dissipative procedure is applied. Different interpolation schemes for the distribution function are compared and discussed. [ABSTRACT FROM AUTHOR]

With the term microinstabilities, we indicate a class of plasma drift waves such as the ion temperature gradient (ITG) mode, the trapped electron mode (TEM), and the electromagnetic Alfvénic ion temperature gradient (AITG) mode. They are usually driven by spatial gradients in the plasma and they are held responsible for anomalous transport and enhanced heat flux in tokamaks. Their understanding is therefore crucial for the development of magnetically confined plasma fusion devices. Our approach is based on the gyrokinetic model (Hahm 1988) for particle dynamics. The gyrokinetic nonlinear Vlasov equation, in the presence of an electromagnetic perturbation (Brizard 1989, 1995), is derived using Lie perturbation theory (Cary and Littlejohn 1983) to average out the fast particle motion around the gyrocenter. We have linearized the gyrokinetic Vlasov equation and added the quasi‐neutrality equation and Ampère's law, providing closure to the system. A temporal spectral formulation is used, ensuring the absence of numerical instabilities due to high frequency modes. The equations are simplified with a large aspect ratio approximation for an axisymmetric toroidal configuration. The fields are expanded in a Fourier series in the three spatial directions (radial, poloidal, and toroidal) reducing the problem in a matrix form. The code EM‐GLOGYSTO (Brunner et al. 1998; Falchetto et al. 2003; Joint Varenna‐Lausanne International Workshop 2002) has been developed to look at its solutions. Recently, we have included in the model an electrostatic equilibrium potential in order to provide E × B sheared flow. The code has been optimized for running in a parallel environment using MPI routines, and it allows us to study frequencies, growth rates, and mode structures of electromagnetic microinstabilities. Results on an AITG mode are shown to illustrate these features. [ABSTRACT FROM AUTHOR]

Electrostatic microinstabilities in ion internal barrier (ITB) and H-mode discharges of the ASDEX Upgrade tokamak [O. Gruber, R. Arslanbekov, C. Atanasiu et al., Nucl. Fusion 41, 1369 (2001)] have been investigated with a full radius gyrokinetic code. The code models linear stability and includes the effect of an equilibrium radial electric field and trapped electrons. In order to simulate plasmas in experimental conditions [k[sub ⊥]ρ[sub L]∼O(1)], the long wavelength approximation in the quasineutrality equation has been replaced by a Padé expansion of the modified Bessel function. Results show that the E×B flow, induced by the radial electric field, changes the linear stability of the dominant ion temperature gradient modes. The electrostatic potential eddies are tilted by the sheared flow thus reducing the radial extent and the growth rate of modes. However, the finite value of the flow has a stabilizing effect too; the most unstable modes are shifted away from the unfavorable curvature region leading to lower linear growth rates. In addition to this at least two other mechanisms give an important contribution to the stabilization in the ITB region; the reverse shear profile itself and, to a lesser degree, the local value of the temperature ratio, τ=T[sub e]/T[sub i]. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effects of applied radial electric fields on the stability of ion temperature gradient (ITG) modes and trapped particle modes are investigated with a full radius gyrokinetic formulation in both axisymmetric and helically symmetric configurations. The validity of a simplified stabilization criterion often applied to experimental analysis (the shearing rate larger than the linear growth rate) is examined for various profiles of E x B flows using an expression for the shearing rate derived for arbitrary quasisymmetric geometries [T. S. Hahm, Phys. Plasmas 4, 4074 (1997)]. The results show that the criterion holds for profiles with finite shearing rate and for toroidal, helical, and slab-like ITG modes. However, it is not always applicable for trapped particle instabilities: a case is shown for which E x B flows are destabilizing. For profiles with zero shearing rate, another stabilizing mechanism is found for toroidal and helical ITG modes but not for slab-like modes. [ABSTRACT FROM AUTHOR]

A correction to the article "On resonance absorption and continuum damping" is presented.