Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks

Two symmetries of the local nonlinear delta-f gyrokinetic system of equations in tokamaks in the high flow regime are presented. The turbulent transport of toroidal angular momentum changes sign under an up-down reflection of the tokamak and a sign change of both the rotation and the rotation shear. Thus, the turbulent transport of toroidal angular momentum must vanish for up-down symmetric tokamaks in the absence of both rotation and rotation shear. This has important implications for the modeling of spontaneous rotation.Comment: 15 pages, 2 figure

Ion temperature gradient instability at sub-Larmor radius scales with non-zero ballooning angle

Linear gyro-kinetic stability calculations predict unstable toroidal Ion Temperature Gradient modes with normalised poloidal wave vectors well above one ($k_\theta \rho_i > 1$) for standard parameters and with adiabatic electrons. These modes have a maximum amplitude at a poloidal angle $\theta$ that is shifted away from the low field side ($\theta \ne 0$). The physical mechanism is clarified through the use of a fluid model. It is shown that the shift of the mode away from the low field side ($\theta \ne 0$) reduces the effective drift frequency, and allows for the instability to develop. Numerical tests using the gyro-kinetic model confirm this physical mechanism. It is furthermore shown that modes with $\theta \ne 0$ can be important also for $k_\theta \rho_i < 1$ close to the threshold of the ITG. In fact, modes with $\theta \ne 0$ can exist for normalised temperature gradient lengths below the threshold of the ITG obtained for $\theta = 0$

On seed island generation and the non-linear self-consistent interaction of the tearing mode with electromagnetic gyro-kinetic turbulence

The multi-scale interaction of self-consistently driven magnetic islands with electromagnetic turbulence is studied within the three dimensional, toroidal gyro-kinetic framework. It can be seen that, even in the presence of electromagnetic turbulence the linear structure of the mode is retained. Turbulent fluctuations do not destroy the growing island early in its development, which then maintains a coherent form as it grows. The island is seeded by the electromagnetic turbulence fluctuations, which provide an initial island structure through nonlinear interactions and which grows at a rate significantly faster than the linear tearing growth rate. These island structures saturate at a width that is approximately $\rho_{i}$ in size. In the presence of turbulence the island then grows at the linear rate even though the island is significantly wider than the resonant layer width, a regime where the island is expected to grow at a significantly reduced non-linear rate. A large degree of stochastisation around the separatrix, and an almost complete break down of the X-point is seen. This significantly reduces the effective island width.Comment: Joint Varenna - Lausanne International Worksho

Interplay between toroidal rotation and flow shear in turbulence stabilisation

International audienceThe interplay between toroidal rotation u, parallel flow shear u ′ and perpendicular flow shear γE in the stabilisation of tokamak turbulence is investigated in non-linear flux-tube gyrokinetic simulations. The simulations are performed for a reference L-mode DIII-D plasma (the so-called shortfall case) at r/a = 0.8, varying the flow parameters around their nominal values. Depending on the respective signs of u, u ′ and γE, turbulence is found to be enhanced, reduced or unchanged. When the coupling is favorable, the overall effect on the non-linear heat fluxes can be very large, even at moderate flow values. The ion heat flux is for instance decreased by a factor of three when the direction of the parallel flow shear is reversed with respect to its nominal value. Even more surprising, keeping u ′ and γE at their nominal values, the ion heat flux decreases by more than 50% when the toroidal flow is reversed. The relevance of this mechanism in the experiments which depends on the ability to decouple u, u ′ and γE is discussed. The interplay between u and u ′ observed in the non-linear simulations qualitatively follows the linear stability results and is interpreted in the frame of a simple fluid model

Toroidal momentum transport in a tokamak caused by symmetry breaking parallel derivatives

A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyro-kinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are then connected with the poloidal derivative of the ballooning envelope, which are one order smaller in the normalised Larmor radius, compared with the derivative of the eikonal. The mechanism, therefore, does not introduce an inhomogeneity in the radial direction, in contrast with the effect of profile shearing. Numerical simulations of the linear ion temperature gradient mode with adiabatic electrons, retaining the finite rho* effects in the ExB velocity, the drift, and the gyro-average, are presented. The momentum flux is found to be linear in the normalised Larmor radius (\rho*) but is, nevertheless, generating a sizeable counter-current rotation. The total momentum flux scales linear with the aspect ratio of the considered magnetic surface, and increases with increasing magnetic shear, safety factor, and density and temperature gradients

In-Brace versus Out-of-Brace Protocol for Radiographic Follow-Up of Patients with Idiopathic Scoliosis:A Retrospective Study

The purpose of this retrospective study was to compare two standardized protocols for radiological follow-up (in-brace versus out-of-brace radiographs) to study the rate of curve progression over time in surgically treated idiopathic scoliosis (IS) patients after failed brace treatment. In-brace radiographs have the advantage that proper fit of the brace and in-brace correction can be evaluated. However, detection of progression might theoretically be more difficult. Fifty-one IS patients that underwent surgical treatment after failed brace treatment were included. For 25 patients, follow-up radiographs were taken in-brace. For the other 26 patients, brace treatment was temporarily stopped before out-of-brace follow-up radiographs were taken. Both groups showed significant curve progression compared to baseline after a mean follow-up period of 3.4 years. The protocol with in-brace radiographs was noninferior regarding curve progression rate over time. The estimated monthly Cobb angle progression based on the mixed-effect model was 0.5 degrees in both groups. No interaction effect was found for time, and patients' baseline Cobb angle (p = 0.98), and for time and patients' initial in-brace correction (p = 0.32). The results of this study indicate that with both in-brace and out-of-brace protocols for radiographic follow-up, a similar rate of curve progression can be expected over time in IS patients with failed brace treatment

Про маловідомі математичні таблиці Якова Пилипа Кулика

У статті описано маловідомі математичні таблиці професора Пражського університету Якова Пилипа Кулика. Виконано короткий аналіз складу та структури таблиць, що не тільки широко використовувались в арифметиці, алгебрі, теорії чисел і в теорії алгебраїчних рівнянь, але й мали широке практичне застосування.В статье описаны малоизвестные математические таблицы профессора Пражского университета Якова Филиппа Кулика. Произведен короткий анализ содержания и структуры таблиц, которые не только широко использовались в арифметике, алгебре, теории чисел и в теории алгебраических уравнений, но и имели широкое практическое применение.The unknown mathematical tables by Jakob Pilip Kulik – the professor of Prague University, are described in this article. The analysis of the content and structure of tables was conducted, they were not only used widely in arithmetic, algebra, the theory of numbers and in the Theory of equalizations of algebra, but They had a wide practical application

Clinical considerations for the treatment of secondary differentiated thyroid carcinoma in childhood cancer survivors

The incidence of differentiated thyroid carcinoma (DTC) has increased rapidly over the past several years. Thus far, the only conclusively established risk factor for developing DTC is exposure to ionizing radiation, especially when the exposure occurs in childhood. Since the number of childhood cancer survivors (CCS) is increasing due to improvements in treatment and supportive care, the number of patients who will develop DTC after surviving childhood cancer (secondary thyroid cancer) is also expected to rise. Currently, there are no recommendations for management of thyroid cancer specifically for patients who develop DTC as a consequence of cancer therapy during childhood. Since complications or late effects from prior cancer treatment may elevate the risk of toxicity from DTC therapy, the medical history of CCS should be considered carefully in choosing DTC treatment. In this paper, we emphasize how the occurrence and treatment of the initial childhood malignancy affects the medical and psychosocial factors that will play a role in the diagnosis and treatment of a secondary DTC. We present considerations for clinicians to use in the management of patients with secondary DTC, based on the available evidence combined with experience -based opinions of the authors