S. Brunner

Mechanism for blob generation in the TORPEX toroidal plasma

Reference CRPP-CONF-2009-011Afficher la publication dans Web of Science Notice creee le 2009-01-23, modifiee le 2017-05-12

Global approach to the spectral problem of microinstabilities in tokamak plasmas using a gyrokinetic model

A solution to the full two-dimensional eigenvalue problem of electrostatic microinstabilities in a tokamak plasma is presented in the framework of gyrokinetic theory. The approach is the generalization of methods previously developed for a cylindrical system [S. Brunner and J. Vaclavik, Phys. Plasmas 5, 365 (1998)]. By solving the spectral problem in a special Fourier space adapted to the curved geometry, orbit width as well as Larmor radius can be kept to all orders. For a first numerical implementation, a large aspect ratio plasma with circular concentric magnetic surfaces is considered. A root finding algorithm for identifying the eigenfrequencies, based on a higher order Nyquist method, enables straightforward implementation on a parallel computer. Illustrative results for ion temperature gradient-related instabilities are presented. These include scaling studies of the radial width, and toroidicity and magnetic shear scans, as well as the effects of nonadiabatic trapped electron dynamics.

Simulations of electron transport in laser hot spots

Simulations of electron transport are carried out by solving the Fokker–Planck equation in the diffusive approximation. The system of a single laser hot spot, with open boundary conditions, is systematically studied by performing a scan over a wide range of the two relevant parameters. (1) Ratio of the stopping length over the width of the hot spot. (2) Relative importance of the heating through inverse Bremsstrahlung compared to the thermalization through self-collisions. As for uniform illumination [J. P. Matte et al., Plasma Phys. Controlled Fusion 30, 1665 (1988)], the bulk of the velocity distribution functions (VDFs) present a super-Gaussian dependence. However, as a result of spatial transport, the tails are observed to be well represented by a Maxwellian. A similar dependence of the distributions is also found for multiple hot spot systems. For its relevance with respect to stimulated Raman scattering, the linear Landau damping of the electron plasma wave is estimated for such VDFs. Finally, the n...

Dielectric tensor operator of hot plasmas in toroidal axisymmetric systems

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 ee=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 ee and ep=ρ/λ, where λ is a characteristic wavelength of the perturbing electromagnetic field. The solution is obtained up to the first order in ee and the second order in ep. 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 ...

Method for computing protein binding affinity.

A Monte Carlo method is given to compute the binding affinity of a ligand to a protein. The method involves extending configuration space by a discrete variable indicating whether the ligand is bound to the protein and a special Monte Carlo move, which allows transitions between the unbound and bound states. Provided that an accurate protein structure is given, that the protein–ligand binding site is known, and that an accurate chemical force field together with a continuum solvation model is used, this method provides a quantitative estimate of the free energy of binding.

Global approach to the spectral problem of microinstabilities in a cylindrical plasma using a gyrokinetic model

Considering the spectral problem of microinstabilities in a curved system, methods for solving the global gyrokinetic equation are presented for the simple case of a cylindrical plasma. They prove to be efficient for computing the full unstable spectrum of ion temperature gradient (ITG) type modes and have shown to be applicable to the two-dimensional integral equation of tokamak configurations.

Applicability of the ballooning transform to trapped ion modes

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(theta)rho(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

Theoretical Modeling of Recombination Gain in LiIII Transition to Ground State

We present numerical calculation of recombination gain in LiIII transition to ground state (2 → 1). The model includes the initial ionization of the plasma by an intense fs laser pulse, and continues through the expansion and cooling of the plasma simultaneously with the recombination process. We show that although initial estimations of the energy absorption by the plasma from the ionization laser does not allow for recombination gain, the expansion and cooling processes that take place immediately after ionization, in addition to the non‐Maxwellian distribution of electrons in the plasma, give rise to high gain under feasible experimental conditions.

Simulations of Electron Transport in Laser Hot Spots

Simulations of electron transport are carried out by solving the Fokker-Planck equation in the diffusive approximation. The system of a single laser hot spot, with open boundary conditions, is systematically studied by performing a scan over a wide range of the two relevant parameters: (1) Ratio of the stopping length over the width of the hot spot. (2) Relative importance of the heating through inverse Bremsstrahlung compared to the thermalization through self-collisions. As for uniform illumination [J.P. Matte et al., Plasma Phys. Controlled Fusion 30 (1988) 1665], the bulk of the velocity distribution functions (VDFs) present a super-Gaussian dependence. However, as a result of spatial transport, the tails are observed to be well represented by a Maxwellian. A similar dependence of the distributions is also found for multiple hot spot systems. For its relevance with respect to stimulated Raman scattering, the linear Landau damping of the electron plasma wave is estimated for such VD Fs. Finally, the nonlinear Fokker-Planck simulations of the single laser hot spot system are also compared to the results obtained with the linear non-local hydrodynamic approach [A.V. Brantov et al., Phys. Plasmas 5 (1998) 2742], thus providing a quantitative limit to the latter method: The hydrodynamic approach presents more than 10% inaccuracy in the presence of temperature variations of the order delta T/T greater than or equal to 1%, and similar levels of deformation of the Gaussian shape of the Maxwellian background.

Linear delta-f simulations of nonlocal electron heat transport

Nonlocal electron heat transport calculations are carried out by making use of some of the techniques developed previously for extending the delta f method to transport time scale simulations. By considering the relaxation of small amplitude temperature perturbations of a homogeneous Maxwellian background, only the linearized Fokker-Planck equation has to be solved, and direct comparisons can be made with the equivalent, nonlocal hydrodynamic approach. A quasineutrality-conserving algorithm is derived for computing the self-consistent electric fields driving the return currents. In the low-collisionality regime, results illustrate the importance of taking account of nonlocality in both space and time.