Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time

Blum, Jacques; Boulbe, Cédric; Faugeras, Blaise

doi:10.1016/j.jcp.2011.04.005

Cited by 55 publications

(63 citation statements)

References 30 publications

(37 reference statements)

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“…Real-time magnetic equilibrium reconstruction is an established basis for tokamak control [7,8,9]. The procedure for solving the Grad-Shafranov partial differential equation is based on cyclic reduction [10].…”

Section: Introductionmentioning

confidence: 99%

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Giannone

Fischer

McCarthy

et al. 2015

Fusion Engineering and Design

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Real-time magnetic equilibria are needed for NTM stabilization and disruption avoidance experiments on ASDEX Upgrade. Five improvements to real-time magnetic equilibrium reconstruction on ASDEX upgrade have been investigated. The aim is to include as many features of the offline magnetic equilibrium reconstruction code in the real-time equilibrium reconstruction code. Firstly, spline current density basis functions with regularization are used in the offline equilibrium reconstruction code, CLISTE [1]. It is now possible to have the same number of spline basis functions in the real-time code. Secondly, in the presence of edge localized modes, (ELM's), it is found to be necessary to include the low pass filter effect of the vacuum vessel on the fast position control coil currents to correctly compensate the magnetic probes for current oscillations in these coils. Thirdly, the introduction of ferromagnetic tiles in ASDEX Upgrade means that a real-time algorithm for including the perturbations of the magnetic equilibrium generated by these tiles is required. A methodology based on tile surface currents is described. Fourthly, during current ramps it was seen that the difference between fitted and measured magnetic measurements in the equilibrium reconstruction were larger than in the constant current phase. External loop voltage measurements and magnetic probe pairs inside and outside the vessel wall were used to measure the vacuum vessel wall resistivity. This is the first step towards including vacuum vessel currents during the plasma current ramp in the real-time equilibrium reconstruction. Fifthly, the introduction of a constraint of the safety factor on the magnetic axis is found to be a helpful method to improve the prediction of the location of rational surfaces for NTM stabilization and disruption avoidance experiments. Soft X-ray tomography is used to assess the quality of the real-time magnetic equilibrium reconstruction using this internal constraint.

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Section: Introductionmentioning

confidence: 99%

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Giannone

Fischer

McCarthy

et al. 2015

Fusion Engineering and Design

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“…It is assumed that ρ(ψ) and ψ(R, Z) are known from real-time 2D equilibrium reconstruction (see [51][52][53]). …”

Section: Synthetic Output Equationmentioning

confidence: 99%

Control-oriented modeling of the plasma particle density in tokamaks and application to real-time density profile reconstruction

Blanken

Felici

Rapson

et al. 2018

Fusion Engineering and Design

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“…Методы решения такой некорректно поставленной задачи основываются на следующих подходах: разложение по тороидальным гармоникам [6], использование филаментов (точечных или распределён-ных, подвижных или стационарных) [7][8][9][10], решение интегральных уравнений [5,11,12]. В настоящей работе применяется метод, основанный на интегральных уравнениях, который ранее применялся при моделировании системы магнитной диагностики установки КТМ (Казахстан) [11].…”

Section: система электромагнитной диагностики модернизированной устанunclassified

Numerical Simulation of Electromagnetic Diagnostics System of the Tokamak T-15

Zotov¹,

Белов²,

Sychugov³

et al. 2015

PAST-TF

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В настоящее время проводится модернизация токамака Т-15. Одной из задач исследований на Т-15 является получение разря-дов с вытянутым поперечным сечением плазмы, окружённым сепаратрисой. Присутствие на сепаратрисе Х-точки, где магнит-ное поле обращается в ноль, позволяет использовать данную конфигурацию для создания дивертора -устройства для вывода из плазмы примесей и продуктов реакции. Для оптимизации дивертора и контроля плазмы предполагается в каждый момент разряда проводить реконструкцию границы плазменного шнура. Достоверность такой реконструкции зависит от влияния раз-личных факторов на сигналы электромагнитной диагностики. В работе на основе одного из возможных сценариев разряда в Т-15 проведено исследование точности реконструкции границы плазмы и профиля тока в зависимости от погрешности измере-ний и прочих факторов. Рассматривается задача определения границы плазмы на лимитерной и диверторной стадиях разряда, исследуется влияние распределения тока на сигналы в магнитных датчиках. Так как подобная задача является некорректной, изучается вопрос о выборе параметра регуляризации, в частности, когда погрешность измерений неизвестна. Входными дан-ными задачи являются число магнитных датчиков и их расположение, а также погрешность измерения ими магнитных полей. Исследуется точность восстановления границы плазмы в целом и X-точки сепаратрисы отдельно в зависимости от погрешности измерений и количества датчиков. Моделирование сценария разряда проводилось с помощью кодов TOKAMEQ и DINA. Об-ратные задачи МГД-равновесия решались на основе кода RPB (Reconstruction of Plasma Boundary).Ключевые слова: токамак Т-15, обратная задача МГД-равновесия, электромагнитная диагностика, граница плазмы, профиль тока. The T-15 Tokamak is now under modernisation. One of the objectives of research in the T-15 is obtaining a discharge with an elongated cross-section of the plasma, surrounded with a separatrix. The presence of Х-point on the separatrix, where the magnetic field vanishes, allows to create a divertor-the device for removal of plasma impurities and reaction products. In order to optimize and control the divertor plasma is expected at every moment of the discharge to carry out the reconstruction of the plasma boundary. Reliability of this reconstruction depends on the influence of various factors on the electromagnetic signals of diagnostics. In this paper on the basis of one of the possible scenarios discharge in the T-15 we are interested in the plasma boundary reconstruction accuracy and current profile according to the measurement error and other factors. The problem of determining the plasma boundary on the limiter and divertor discharge stage is studied, examines the impact of the plasma current density at the signals of the magnetic sensors. As this problem is illposed, we study choosing the regularization parameter, in particular for the case when the measurement error is unknown. The problem input data are the number of magnetic sensors and their location and the accuracy of the magnetic fields measurement. We s...

show abstract

Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time

Cited by 55 publications

References 30 publications

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Control-oriented modeling of the plasma particle density in tokamaks and application to real-time density profile reconstruction

Numerical Simulation of Electromagnetic Diagnostics System of the Tokamak T-15

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