Poloidal Beta Βp Research Articles

Stability nature of ohmic discharges with hollow current profiles on the HL-2A tokamak

The equilibrium configurations with hollow current density profiles can effectively improve plasma confinement. The stability of the ohmic discharges with hollow current density profiles on the HL-2A tokamak was studied for various parameters, such as plasma poloidal beta βp, the axial and edge safety factors q0 and qs, as well as the minimum safety factor . The results suggest that the restriction to the parameters of discharges with hollow current density profiles is stricter than that of conventional discharges with peaked current density profiles. In the case of q profile with reverse shear, the instability of the configuration is significantly improved with higher βp. As a result, the configuration with a hollow toroidal current profile is stable for high βp operations. Only if q0, qs and satisfy the specific limitations, i.e. on HL-2A, only if both and hold, together with and , may the configurations with the reverse shears be stable for hollow-current-type Ohmic discharge. The results may give hints for the role of the discharges with hollow toroidal current densities in the coming advanced tokamak operations.

Optimization of Magnetic Confinement for Quasi-Snowflake Divertor Configuration

To realize the commercialized operation, it is preferable that tokamak devices achieve the operating scenarios with steady-state, long-pulse, H-mode and high magnetic confinement plasma current. For enhancing the magnetic confinement capability and improving the poloidal beta βp in quasi-snowflake configuration, under the consideration of the effect on other performance parameters, the method of shifting magnetic axis is employed. According to the calculated method proposed in this paper, the plasma current density distribution is modified to realize the supposed radial movement of the magnetic axis. Then the value of βp, the coordinates of X2 point, the flux expansion of outside and inside strike points (fmout and fmin), poloidal field currents and safety factor q profile are formulated, the relations between these parameters and the horizontal displacement of the magnetic axis are analyzed. Finally, in lower single-null quasi-snowflake configuration, by shifting the magnetic axis from 1.9242 to 1.9412m, βp has an increase of 86.96 %, the confinement capability of the plasma is significantly enhanced, Meanwhile, the position of X2 point is varied from (2.6789 m, −1.6439 m) to (2.2955 m, −1.6039 m), which is closer to X1 point and the plasma. Therefore, fmout is enlarged from 6.646 to 7.706, which has an increase of 15.9%. And fmin has a decrease of 0.62%, which can be neglected. The safety factor at magnetic axis q0 is decreased by 1.75%, from 1.0897 to 1.0701, which is larger than 1 and satisfies the requirement of magnetohydrodynamic stability. In addition, EFIT code is used to verify the feasibility and the accuracy of the optimized results.

A novel code for the simulation of plasma equilibrium and evolution implemented in ANSYS

The simulation of the plasma equilibrium and its evolution is important for the study of plasma physics and for the correct design of fusion devices. For this purpose, a novel code, based on the solution of the Grad-Shafranov equation, has been fully implemented in ANSYS. It exploits the finite element method using the magnetic potential vector formulation. In this approach plasma pressure and current density profiles are described by means of two main parameters: the internal plasma inductance li and the poloidal beta βp. Several ITER equilibria of limiter and diverted plasma configurations have been reproduced and benchmarked with validated codes (e.g. DINA). Being fully implemented in ANSYS this code will easily allow the coupling of the 2D axisymmetric plasma equilibrium equations, describing the plasma behavior, with the full 3D eddy currents equations, describing the surrounding three-dimensional structures. Moreover it will also allow the coupling with the ANSYS mechanical module to perform self-consistent coupled electro-mechanical analyses.

The DTEQ Code for Toroidal MHD Equilibria with Diamagnetic Current Modeling Using the deal.II Finite Element Library

The Deal Two Equilibrium (DTEQ) code solves the Grad-Shafranov (GS) equation for magnetohydrodynamics equilibrium in the axisymmetric toroidal geometry using the deal.II finite element library. In this paper, we introduce DTEQ that can solve the GS equation both linearly and nonlinearly. The linear solution obtained from this code is verified by comparing with a known analytic solution of the linear GS equation. For the nonlinear solution, DTEQ requires two input profiles, p(ψ) and F(ψ), to be specified as a function of the normalized minor radius ρ. The pressure profile p(ψ) is specified based on Thomson scattering, charge exchange spectroscopy data, and an energetic particle pressure model. The toroidal field profile F(ψ) is obtained from our model that makes the diamagnetic current play a significant role when the poloidal beta βp is greater than one. With these two input profiles, the nonlinear GS equation can be solved using Picard iteration within the plasma boundary from EFIT. Using this newly developed code, we obtain several meaningful results that show its validity. The calculated poloidal current density is very large in the transport barrier due to the diamagnetic current, and the characteristics of the Pfirsch-Schlüter current appear in the toroidal current density. In addition, the results obtained from this code agree well with those from EFIT, and the calculated safety factor values in the center are well correlated with the sawtooth activity in the discharge.

On virial analysis at low aspect ratio

The validity of virial analysis to infer global MHD equilibrium poloidal beta βp and internal inductance ℓi from external magnetics measurements is examined for low aspect ratio configurations with A<2. Numerical equilibrium studies at varied aspect ratio are utilized to validate the technique at finite aspect ratio. The effect of applying high-A approximations to low-A experimental data is quantified and demonstrates significant over-estimation of stored energy (factors of 2–10) in spherical tokamak geometry. Experimental approximations to equilibrium-dependent volume integral terms in the analysis are evaluated at low-A. Highly paramagnetic configurations are found to be inadequately represented through the virial mean radius parameter RT. Alternate formulations for inferring βp and ℓi that are independent of RT to avoid this difficulty are presented for the static isotropic limit. These formulations are suitable for fast estimation of tokamak stored energy components at low aspect ratio using virial analysis.

Study of the poloidal beta and internal inductance by solving the simplest Grad-Shafranov equation for a tokamak with a circular cross section

In this work, we present the poloidal beta βp and internal inductance li by solving the simplest Grad-Shafranov equation (GSE), using the Solov’ev assumption for an HT-7 tokamak with a circular cross section. The poloidal beta and internal inductance are measured by using diamagnetic and compensation loops, combined with poloidal magnetic probe array signals. In this paper, theoretical and experimental results of determining βp and li are presented. The calculated poloidal beta and internal inductance are demonstrated to depend on the kind of the discharge or plasma current.

RETRACTED ARTICLE: Theoretical and Experimental Approach in Poloidal Beta and Internal Inductance Measurement on IR-T1 Tokamak

Measurements of poloidal beta βp and internal inductance li are essential in tokamak plasma research. Much more plasma parameters such as the plasma current density profile, magnetohydrodynamics instability, and plasma energy confinement time are determined by using these parameters. Discrete poloidal magnetic probes along with the diamagnetic loop can be utilized in measurement of the plasma poloidal beta βp and internal inductance li. In this paper, theoretical and experimental results in determining βp and li are presented and discussed.

Numerical study of the resonant magnetic perturbations for Type I edge localized modes control in ITER

A number of possible designs of external and in-vessel coils generating resonant magnetic perturbations (RMPs) for Type I edge localized modes (ELMs) control in ITER are analysed for the reference scenarios (H-mode, Hybrid and Steady-State) taking into account physical, technical and spatial constraints. The level of stochasticity (Chirikov parameter ∼1 at ψ1/2 ∼ 0.95) generated by the I-coils in the DIII-D experiments on ELMs suppression was taken as a reference. Designs with a toroidal symmetry n = 3 were considered to avoid lower n numbers producing larger central islands, a potential trigger of MHD instabilities. The evaluation of RMP coils designs is done with respect to the RMPs spectrum that should produce enough edge ergodisation and minimum central perturbations at minimum current. The proposed designs include in-vessel, mid-ports and external coils. Changes in the equilibrium due to changes in the internal inductance li, the poloidal beta βp and the edge magnetic shear in a reasonable range for ITER scenarios were demonstrated to have a small effect on the edge ergodisation. Present estimations were done without margins and for vacuum fields neglecting plasma response on RMPs. The validity of the vacuum approach was estimated analytically in the visco-resistive linear response regime using [1]. The typical radial magnetic field amplitudes produced by RMP coils in DIII-D and ITER are an order of magnitude or slightly above the critical values for the ‘downward’ bifurcation to the reconnected stage indicating the possibility of the islands formation in the pedestal region. Central islands (from the top of the pedestal) are expected to be screened.

Analytic description of high poloidal beta equilibrium with a natural inboard poloidal field null

Analytical high poloidal beta equilibria for toroidally axisymmetric plasmas with arbitrary aspect ratio and elongation are described. These equilibria that can describe a transition from nondivertor to divertor configuration are exact solutions of the Grad-Shafranov equation when the toroidal current density is quasiuniform. Generally, these are high poloidal beta equilibria, limited by the appearance of a natural inboard poloidal field null. Some of their properties, including the nonuniformity of the poloidal magnetic field in the poloidal direction, the safety factor profile and the magnetic shear profile near the separatrix, the parameter dependence of the poloidal beta βp and εβp, as well as the toroidal beta βT on the aspect ratio and the elongation of the magnetic surface, are discussed. Applications to experiments of the Tokamak Fusion Test Reactor (TFTR) [Sabbagh et al., Phys. Fluids B3, 2277 (1991)] are particularly analyzed.

Diagnostics of Internal Inductance in HT-7

Two arrays of Mirnov coils and a pair of concentric loops have been installed to superconducting tokamak HT-7. Software compensation and digital Fourier series expansion are the two techniques that have been applied successfully in measuring diamagnetic flux of concentric loops and internal inductance. The internal inductance of plasma li, poloidal beta βp, Grad Shafranov parameter Λ, plasma minor radius ap and the center of the outermost magnetic flux surface Δg are determined.

First measurement of confinement properties in TPE-RX reversed field pinch

Electron and ion temperatures Te0 and Ti, respectively, are measured and global confinement properties are estimated at Ip ⩽ 400 kA for the first time in the TPE-RX reversed field pinch (RFP) using a single point Thomson scattering system and a single chord neutral particle energy analyser, respectively. The values of Te0 and Ti range from 0.2 to 1 keV and from 0.2 to 0.4 keV, respectively, at Ip ∼350 kA. The I/N value (N is the line density) is relatively high ( = 12 × 10-14A m) in comparison with those of other RFP machines. The poloidal beta βp and energy confinement time τE are comparable to those in similarly sized RFP plasmas such as the MST and RFX plasmas, namely, βp = 5-10% and τE = 0.5-1.0 ms. The behaviour of the global confinement properties and the implication of thisresult are discussed.

The new phase of the Joint European Torus and prospects for future operation

The Joint European Torus (JET) [Fusion Technol. 11, 1 (1987)] restarted operations in its new pumped divertor configuration. The main elements of the new configuration are four divertor coils, an inertially cooled divertor structure, and an internal cryogenic vacuum pump. Two major differences were observed with respect to the ‘‘old’’ JET. First, the heat load capability of the divertor is dramatically improved. Second, in the high confinement mode (H mode) the occurrence of edge localized modes (ELMs), is more prevalent. Quasi-steady-state ELMy H modes are now obtained in a wide variety of conditions. In the 1994 experimental campaign maximum plasma currents of 4 MA have been obtained. Steady-state H-mode operation has been obtained for a duration of 20 s. Detached divertor operation was established in Ohmic and L-mode plasmas, but not yet in H mode. In low current discharges a poloidal beta βP=2.6 has been obtained in transient. The high βP regime has been extended to long pulse ELMy H mode. Preliminary experiments have not shown an effect of magnitude shear reversal on the confinement. Using the new internal saddle coils, powered by high-frequency amplifiers, toroidal Alfvén eigenmodes (TAE) were excited. The first direct measurements of the damping of TAE modes were carried out.

Experimental plasma equilibrium reconstruction from kinetic and magnetic measurements in the FTU tokamak

The behaviour of the FTU tokamak plasma has been analysed by using two reconstructive MHD equilibrium codes: the first code works by using the magnetic data alone and the second one by including as well the shape of the kinetic pressure profile, as obtained from the measured profiles of electron temperature Te and density ne. The code that analyses the magnetic data alone provides a good evaluation of the macroscopic quantities such as the poloidal beta βp and the internal inductance li, if the plasma elongation is greater than 1.04. No detailed information about the toroidal current density profile Jϕ and the safety factor profile q can be obtained from the magnetic data alone. On the other hand, the coupling of magnetic and kinetic data is able to provide a reasonable estimate of the toroidal current density profile and of its behaviour during the plasma discharge. The reliability of the Jϕ and q profile reconstruction has been explored and validated by a detailed comparison with the observed MHD behaviour of the FTU plasma discharges. A good agreement between the appearance of the sawtooth activity and the drop of the safety factor on the magnetic axis go to unity is observed. Also, at least for edge safety factors qψ less than 4, the sawtooth inversion radius is found to be very close to the q=1 surface. A remarkable correspondence between Jϕ and Te3/2 is found in sawtoothing discharges. The structure of the snake oscillation in pellet injected discharges is found to be strictly correlated to the position of the q=1 surface. A cylindrical linear tearing mode stability calculation applied to the reconstructed Jϕ profile has shown qualitative agreement with the appearance of the Mirnov oscillations. Finally, the magnetic reconnections between double resonant surfaces during the rise of the plasma current or after the pellet injection have provided an interesting validation of the Jϕ profile reconstruction

Natural elongation and triangularity of tokamak equilibria

Quasianalytic formulas are calculated for the elongation κ and triangularity δ of the plasma surface of a free-boundary tokamak equilibrium. The final results give κ and δ as functions of five quantities: the inverse aspect ratio ε, the poloidal beta βp, the internal inductance li, and the quadrupole and hexapole moments of the externally applied field. The agreement with numerically computed equilibria is found to be quite good when A≥3, κ≤1.5, and δ≤0.2 and when the plasma is limited by the vacuum vessel wall and not diverted by the presence of a separatrix on the plasma surface.

Second Order Effect of a Toroidal Equilibrium With Anisotropic Pressure

A class of equilibria for a high beta Tokamak with highly anisotropic pressure and circular plasma cross section is solved to second order in the inverse aspect ratio. The effect of anisotropy on the limiting values of the poloidal beta βP is slight. The second order correction increases the limiting values of βP.

677. 高ベー夕・トカマクにおける平衡トロイダル・プラズマのまわりのForce-Free磁場構造

For a sharp boundary equilibrium model of an axisymmetrical-toroidal dense plasma sunounded by a pressureless plasma with force-free fields, structure of force-free magnetic fields is studied by using analytical solutions of the Helmholtz equation for toroidal coordinates and Fourier decomposition. Geometrical form of the magnetic surfaces inside the separatrix surrounding the dense plasma is revealed for the poloidal beta βp and the aspect ratio of the dense plasma Rp/rp=coshσp which are characteristic of a high β tokamak.A condition of the equilibrium is determined and the maximum βp is given by βp=1/4(Rp/rp+rp/Rp)+1/2. The magnetic field equation ∇×H=αH is reduced to the Helmholtz equation(∇∇2+αα2)(Hφeiφ)=0 for the condition α=constant, which is solved without the approximation of the expansion about the inverse aspect ratio. The force-free magnetic fields can be evaluated in a high accuracy under the equilibrium condition of the toroidal dense plasma.For the force-free magnetic surfaces similar to the vacuum magnetic ones, by increasing-α or Rp/rp=coshσp, the separatrix surrounding the dense plasma is expanded and the layers of the magnetic surfaces inside the separatrix are increased. Thus, by decreasing Rp/rp for the fixed separatrix, the layers of the magnetic surfaces inside the separatrix are increased with the increase of -α.