Cauchy Condition Surface Method Research Articles

Equilibrium Reconstruction and Equilibrium Properties in QUEST Tokamak

Plasma shape reconstruction is an important part of tokamak data analysis. An off-line plasma shape reconstruction, based on the EFIT code in Linux system, can be carried out in Q-shu Univ. Experiment in Steady-State Spherical Tokamak (QUEST). In this paper, the algorithm about equilibrium reconstruction is described in detail. Magnetic reconstruction in QUEST, which is calculated by the EFIT code according to the external magnetic measurements, is introduced and the results are presented in detail. It is known that the eddy current effect is large in QUEST experiment, the eddy current effect is first considered into equilibrium reconstruction. Fourier expansion is applied to reconstruct the vessel current distribution in EFIT code. To test the accuracy of the result, a comparison with the result of Cauchy condition surface method has made, which suggests the reliability of the result. A visualization interface is made, which is convenient for physicists and operators to analyze the behavior of plasma. At the same time, the operation space of elongated discharges is discussed based on the QUEST database. The real time EFIT will be applied to the plasma control system of QUEST in the future.

Reconstruction of plasma shape and eddy current profile based on modified cauchy condition surface method in merging spherical tokamak

The spherical tokamak merging start-up is one of the central solenoid-free start-up method. For controlling the merging actively, it is essential to identify the plasma shapes during the merging process. In the present work, the modified Cauchy condition surface method is applied to demonstrate the reconstruction of the plasma boundary shapes as well as the eddy current profiles at three different representative phases in the merging start-up process (a. initial phase, b. merging phase, c. after merging). Profiles of magnetic flux and plasma boundary have been reconstructed accurately using noiseless magnetic sensor signals and reconstructed with a fairly good accuracy using sensor signals with 3% noise. The eddy current profile have been also reconstructed with a fairly accuracy.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA.

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

Shape Reconstruction of RF-Driven Divertor Plasma on QUEST

In the present RF-driven plasma with a lot of high-energy electrons, there may be anisotropic plasma pressure, which makes the usual equilibrium analysis difficult, but the Cauchy condition surface method can reconstruct the plasma shape precisely regardless of the anisotropy. In addition, the plasma current effect in the open magnetic surfaces outside of the closed magnetic surfaces is considered in the RF-driven divertor plasma. In the reconstruction process, singular value (SV) decomposition is used and optimal criterion function for generalized cross validation is estimated concerning truncation or reduction of the small-SV components.

Validation of plasma shape reconstruction by Cauchy condition surface method in KSTAR

Cauchy Condition Surface (CCS) method is a numerical approach to reconstruct the plasma boundary and calculate the quantities related to plasma shape using the magnetic diagnostics in real time. It has been applied to the KSTAR plasma in order to establish the plasma shape reconstruction with the high elongation of plasma shape and the large effect of eddy currents flowing in the tokamak structures for the first time. For applying the CCS calculation to the KSTAR plasma, the effects by the eddy currents and the ferromagnetic materials on the plasma shape reconstruction are studied. The CCS calculation includes the effect of eddy currents and excludes the magnetic diagnostics, which is expected to be influenced largely by ferromagnetic materials. Calculations have been performed to validate the plasma shape reconstruction in 2012 KSTAR experimental campaign. Comparison between the CCS calculation and non-magnetic measurements revealed that the CCS calculation can reconstruct the accurate plasma shape even with a small IP.

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals

For the MHD equilibrium reconstruction of a reverse field pinch device, it is a big issue to identify accurately the strong eddy current flow on the shell. In the present work, boundary integrals of the eddy current along the shell are added to the conventional Cauchy-condition surface method formulation. The eddy current profile is unknown in advance but straightforwardly identified using only the signals from magnetic sensors located outside the plasma. Two ideas are introduced to overcome the numerical difficulties encountered in the problem. One is an accurate boundary integral scheme to damp out the near singularity occurring at the sensor position very close to the shell. The other is the modified truncated singular value decomposition technique to solve an illconditioned matrix equation when a large number of nodal points exist on the shell. The capability of the new method is demonstrated for a test problem modeling the RELAX device. c

Three-dimensional Cauchy-condition surface method to identify the shape of the last closed magnetic surface in the Large Helical Device

Kurihara's Cauchy-condition surface (CCS) method, originally developed for axisymmetric tokamak plasma, has been expanded to reconstruct the 3D magnetic field profile outside the non- axisymmetric plasma in the Large Helical Device (LHD). The boundary integral equations (BIEs) in terms of 3D vector potential for magnetic field sensors, flux loops and points along the CCS are solved simultaneously. In the BIE for a flux loop, the portions related to the fundamental solution are integrated along the loop. The rotational symmetry of the plasma is incorporated into the formulation to reduce the number of unknowns. The reconstructed magnetic field caused only by the plasma current agrees fairly well with the reference solution for the LHD, while good agreement is observed when adding the coil current effect to the magnetic field. The magnetic field line tracing using the reconstructed field indicates the plasma boundary (the outer surface of the stochastic region) precisely and the last closed magnetic surface agrees fairly well with the reference one.

Eddy current-adjusted plasma shape reconstruction by Cauchy condition surface method on QUEST

CCS (Cauchy Condition Surface) method is a numerical approach to reproduce plasma shape, which has good precision in conventional tokamaks. In order to apply it in plasma shape reproduction of ST (Spherical Tokamak), the calculation precision of the CCS method in a spherical tokamak CPD (Compact PWI experimental Device) ( B t = 0.25 T, R = 0.3 m, a = 0.2 m) has been analyzed. The precision was confirmed also in ST and decided to be applied to a spherical tokamak QUEST ( B t = 0.25 T, R = 0.68 m, a = 0.40 m).. In present stage from the magnetic measurement, it is known that the eddy current effect is large in QUEST experiment, and there are no special magnetic measurements for eddy current now, so some proper model should be selected to evaluate the eddy current effect. The eddy current density by not only CS (Center Solenoid) coil but also plasma current is calculated using EDDYCAL (JAEA). The eddy current magnitudes are taken as unknown variables and solved together with plasma shape reconstruction in ohmic discharge and ECCD (Electron Cyclotron Current Drive) discharge.

Study of current decay time during disruption in JT-60U tokamak

An L/R model that predicts the current decay time from the circuit equation is essentially used for the design of the International Thermonuclear Experimental Reactor. In order to verify the validity of the L/R model in the determination of current decay time during disruption, the plasma current decay time in the JT-60U tokamak is studied using experimental plasma resistance and inductance. The plasma resistance during the initial phase of current quench is estimated from the electron temperature profile measured using the electron cyclotron emission diagnostic system and by measuring the He I line emission intensity ratios and plasma inductance is estimated by the Cauchy-Condition surface method using magnetic sensor signals. Further, the radiation-induced disruptive plasma discharges with massive neon gas puffing are also analysed. The observed area-normalized current decay times have a weak dependence on the electron temperature, particularly in a small decay time region (5–10 ms m−2). The observed decay times are lesser by one order of magnitude than the decay times estimated by the L/R model. However, a novel model for decay time prediction, which takes into account the time derivative of the plasma inductance, wields results that are extremely consistent with the experimental decay time.

Plasma Shape Reconstruction of Spherical Tokamak using CCS Method

Plasma shape reconstruction is important for plasma control of tokamak. Cauchy-Condition Surface (CCS) method is a numerical approach to reproduce plasma shape which has good precision in conventional tokamak. In order to apply it in the plasma shape reproduction of Compact PWI experimental Device (CPD) which is a new spherical tokamak in Kyushu University, the calculation precision of CCS method in CPD is analyzed in the paper.

Boundary integral equation approach based on a polynomial expansion of the current distribution to reconstruct the current density profile in tokamak plasmas

A new approach has been proposed to reconstruct the current density profile in tokamak plasmas. The boundary-only integral equation derived from the Grad–Shafranov equation, under the assumption of polynomial expansion of current density, will have no unknowns except for the polynomial expansion coefficients, once the magnetic flux and its derivative have been given along the plasma boundary with the aid of Kurihara's Cauchy-condition surface method based on magnetic sensor data. In addition to the discretized form of the equation, some constraints are taken into account: the total plasma current, zero-current along the plasma boundary and a scalar relationship derived from the MHD equilibrium to relate the current density to the magnetic flux. It is also assumed that the poloidal field, as a quantity closely related to the current density, can be measured at a certain number of points inside the plasma. The whole set of linear equations is solved using the singular value decomposition technique to determine the polynomial expansion coefficients. The validity of the present technique and the quality of the current density solution have been investigated through test calculations for some plasma configurations.

A tokamak with nearly uniform coil stress based on the virial theorem

A novel tokamak design with a new type of toroidal field (TF) coil and a central solenoid (CS) whose stress is reduced greatly to the theoretical limit determined by the virial theorem, has been devised, and plasma production and confinement experiments in a new small tokamak based on this design are presented. According to the virial theorem, the best TF coil for producing the strongest magnetic field under the weakest stress requires equal averaged principal stresses in all directions. Applying this condition to a helical coil, its pitch number is determined as a function of the aspect ratio. The helical winding according to this condition is modulated in such a way that the poloidal field exists only outside of the torus, which reduces the torsional force on the helical coil and makes plasma breakdown possible. Moreover, a helical coil with this modulation and a low aspect ratio is similar to CS and TF coil systems in conventional tokamaks since its helical winding is nearly vertical in the outer part of the torus. With the aspect ratio A = 2, our optimal coil theoretically reduces the working stress in the coil to about one-third less than that of conventional TF coils. On the basis of the design, a small prototype, ‘Todoroki-II’, with a major radius of 0.3 m, a minor radius of 0.08 m, toroidal magnetic field strengths of BT < 1.5 T and plasma currents of IP < 40 kA, was made. An external vertical field increased the plasma pulse length and the current to 1 ms and 11 kA, respectively, while they were restricted with no vertical field control. Using a Cauchy-condition surface method, the shape and displacement of the plasma boundary were reconstructed, and position control using the vetical field was confirmed.