Johan Anderson

Influence of the radio frequency ponderomotive force on anomalous impurity transport in tokamaks

Trace impurity transport in tokamaks is studied using an electrostatic, collisionless fluid model for ion-temperature-gradient and trapped-electron mode driven turbulence in the presence of radio frequency (rf) fields, and the results are compared with neoclassical predictions. It is shown that the inward impurity convective velocity (pinch) that is usually obtained can be reduced by the rf fields, in particular close to the wave resonance location where the rf ponderomotive force may be significant. However, the impurity diffusivity and convective velocity are usually similarly affected by the ponderomotive force, and hence the steady-state impurity density peaking factor −∇nz∕nz is only moderately affected by the rf fields.Trace impurity transport in tokamaks is studied using an electrostatic, collisionless fluid model for ion-temperature-gradient and trapped-electron mode driven turbulence in the presence of radio frequency (rf) fields, and the results are compared with neoclassical predictions. It is shown that the inward impurity convective velocity (pinch) that is usually obtained can be reduced by the rf fields, in particular close to the wave resonance location where the rf ponderomotive force may be significant. However, the impurity diffusivity and convective velocity are usually similarly affected by the ponderomotive force, and hence the steady-state impurity density peaking factor −∇nz∕nz is only moderately affected by the rf fields.

Structure based statistical theory of intermittency

A general statistical theory of the intermittency in turbulence based on short-lived coherent structures (instantons) is presented. The probability density functions (PDFs) of the flux R are shown to have an exponential scaling P(R)∝exp(−cRs) in the tails, with the exponent s=(n+1)∕m. Here, n and m are the order of the highest nonlinear interaction term and moments for which the PDFs are computed, respectively; c is constant depending on spatial profile of the coherent structure. The results can have important implications for understanding the universality often observed in simulations and experiments.A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate earlier measurements of edge transport, further confirming the strongly non-Gaussian feature of edge transport. It is found that increasing the cross sectional spatial scale length (Lx and Ly) of the blob results in larger transport whereas increasing the toroidal scale length (Lz) decreases the PDF. The results imply that the PDF decreases for larger blob speed vb. anderson.johan@gmail.com 1

Analytical theory of the probability distribution function of structure formation

The probability distribution function (PDF) tails of the zonal flow structure formation and the PDF tails of momentum flux are computed by incorporating the effect of a shear flow in ion-temperature-gradient (ITG) turbulence. The bipolar vortex soliton (modon) is assumed to be the coherent structure responsible for bursty and intermittent events driving the PDF tails. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa–Mima turbulence, as well as further from marginal stability. This suggests that although ITG turbulence has a higher level of heat flux, it also more likely generates stronger zonal flows, leading to a self-regulating system. It is also shown that shear flows can significantly reduce the PDF tails of Reynolds stress and structure formation.

The momentum flux probability distribution function for ion-temperature-gradient turbulence

There has been overwhelming evidence that coherent structures play a critical role in determining the overall transport in a variety of systems. We compute the probability distribution function (PDF) tails of momentum flux and heat flux in ion-temperature-gradient turbulence, by taking into account the interaction among modons, which are assumed to be coherent structures responsible for bursty and intermittent events, contributing to the PDF tails. The tail of PDF of momentum flux R=⟨vxvy⟩ is shown to be exponential with the form exp{−ξR3∕2}, which is broader than a Gaussian, similar to what was found in the previous local studies. An analogous expression with the same functional dependence is found for the PDF tails of heat flux. Furthermore, we present a detailed numerical study of the dependence of the PDF tail on the temperature and density scale lengths and other physical parameters through the coefficient ξ.

Non-perturbative statistical theory of intermittency in ITG drift wave turbulence with zonal flows

The probability distribution functions (PDFs) of momentum flux and zonal flow formation in ion-temperature-gradient (ITG) turbulence are investigated in two different models. The first is a general five-field model (ni, , Ti, Te, vi∥) where a reductive perturbation method is used to derive dynamical equations for drift waves and a zonal flow. The second is a reduced two-field model (, Ti) that has an exact non-linear solution (bipolar vortex soliton). In both models the exponential tails of the zonal flow PDFs are found with the same scaling ( ), but with different coefficients cZF. The PDFs of momentum flux is, however, found to be qualitatively different with the scaling (PDF ~ exp{−cMRs}), where s = 2 and s = 3/2 in the five and two-field models, respectively.

Intermittency and self-organization in turbulent flows

We present a statistical theory of self-organization of shear flows, modeled by a nonlinear diffusion equation with a stochastic forcing. A non-perturbative method based on a coherent structure is utilized for the prediction of probability distribution functions (PDFs), showing strong intermittency with exponential tails. We confirm these results by numerical simulations. Furthermore, the results reveal a significant probability of super-critical states due to stochastic perturbation. To elucidate the crucial role of relative time scales of relaxation and disturbance in the determination of PDFs, we present numerical simulation results obtained in a threshold model where the diffusion is given by discontinuous values. Our results highlight the importance of a statistical description of gradients.

Nonperturbative models of intermittency in edge turbulence

A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate earlier measurements of edge transport, further confirming the strongly non-Gaussian feature of edge transport. It is found that increasing the cross-sectional spatial scale length (Lx and Ly) of the blob results in larger transport, whereas increasing the toroidal scale length (Lz) decreases the PDF. The results imply that the PDF decreases for larger blob speed vb.

Quasilinear analysis of the zonal flow back-reaction on ion-temperature-gradient mode turbulence

There is strong evidence in favor of zonal flow suppression in the Ion-Temperature-Gradient (ITG) mode turbulence, specifically close to the linear stability threshold. The present Letter attempts to analytically calculate the effects of zonal flow suppression of the ITG turbulence by deriving a modified dispersion relation including the back-reaction of the zonal flows on the ITG turbulence based on the quasilinear theory. The results are manifested in a reduction of the linear growth rate and an increase in the effective linear ITG threshold.

Statistical Theory of Plasmas Turbulence

We present a statistical theory of intermittency in plasma turbulence based on short-lived coherent structures (instantons). In general, the probability density functions (PDFs) of the flux R are shown to have an exponential scaling P(R) ∝ exp (-cRs ) in the tails. In ion-temperature-gradient turbulence, the exponent takes the value s = 3/2 for momentum flux and s = 3 for zonal flow formation. The value of s follows from the order of the highest nonlinear interaction term and the moments for which the PDFs are computed. The constant c depends on the spatial profile of the coherent structure and other physical parameters in the model. Our theory provides a powerful mechanism for ubiquitous exponential scalings of PDFs, often observed in various tokamaks. Implications of the results, in particular, on structure formation are further discussed.

Model of intermittent zonal flow structure formation

We present a theory the PDF tails of the zonal flow formation by assuming that a modon (a bipolar vortex) drives a zonal flow through the generalized Reynolds stress. We show that the PDF tails of zonal flow formation have exponential behavior ≃e−ξφZF3, with the overall amplitude ξ severely quenched by strong flow shear. It is found that stronger zonal flows are generated in ITG turbulence than Hasegawa‐Mima (HM) turbulence as well as further from marginal stability. This suggests that although ITG turbulence has a higher level of heat flux, it also more likely generates stronger zonal flows, leading to a self‐regulating system. It is also shown that shear flows can significantly reduce the PDF tails of structure formation.