Poloidal Beta Research Articles

Plasma Equilibrium in Tokamaks

This lecture treats the magnetohydrodynamic (MHD) equilibrium of axisymmetric plasmas, as given by the Grad-Shafranov equation. In a brief introduction, equilibrium parameters such as the q-profile, the internal inductance, and the poloidal beta are introduced. The properties of these quantities will be illustrated in the case of the tokamak, by applying the large aspect ratio tokamak approximation. The properties of a non-circular plasma cross-section and the role of the vertical field will also be discussed in this approximation. Some attention is given to the (numerical) problem of solving the equilibrium equation and of reconstructing a plasma equilibrium from external measurements.

RETRACTED ARTICLE: Comparative Measurements of the Asymmetry Factor in Tokamaks Using the Magnetic Probes, Poloidal and Toroidal Flux Loops

Measurement of the Asymmetry factor (Shafranov parameter) is essential in tokamak plasma experiments. The purpose of this paper is comparing of the magnetic probes, poloidal flux loops, and diamagnetic loops techniques in determination of the Asymmetry factor in tokamaks. For this reason, array of magnetic probes, flux loops, and diamagnetic loop with its compensation coil, were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber, and then the Asymmetry factor and poloidal beta measured. Moreover, a few approximate values of the internal inductance for the different plasma current density profiles are also calculated. Experimental results compared.

Measurements of the Plasma Current Density and Q-Profiles in IR-T1 Tokamak

The purposes of this paper are determination of the current density and safety factor profiles, J(r) and q(r), in IR-T1 tokamak. For these purposes, a diamagnetic loop with its compensation coil, and also an array of magnetic probes were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber, and then the poloidal beta and poloidal and radial magnetic fields measured. Moreover, a few approximate values of the internal inductance for the different possible profiles of the plasma current density are also calculated. From the results, current density and q-profiles obtained.

RETRACTED ARTICLE: Differences Between the Toroidal and Poloidal Flux Loops in the Measurement of Plasma Position in Tokamaks

We presented two magnetic techniques for the measurement of plasma position in IR-T1 tokamak: a poloidal flux loops and toroidal flux loop (diamagnetic loop) methods. In the first method, two poloidal flux loops were designed and installed on outer surface of the IR-T1 tokamak chamber, and then displacement of the plasma column center (Shafranov shift) determined from them. To compare the result, the diamagnetic loop with its compensation coil were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber, and then the poloidal beta obtained from them. Moreover a few approximate values of the internal inductance for the different possible profiles of the plasma current density are also determined. Then the Shafranov parameter and therefore the Shafranov shift were obtained. Experimental results compared and discussed. Comparison of results shows that plasma current density should have a flat profile that is acceptable for the ohmically heated tokamaks as IR-T1.

RETRACTED ARTICLE: Relations Between the Plasma Diamagnetic Effect and Plasma Basic Parameters in IR-T1 Tokamak

Precise determination of the poloidal Beta, internal inductance, plasma energy, plasma pressure, plasma temperature, plasma resistance, plasma effective atomic number, and plasma energy confinement time are essential for tokamak experiments. In this paper an experimental method especially based on the plasma diamagnetic effect for measurements of these parameters in IR-T1 tokamak are presented. For these purposes a diamagnetic loop with its compensation coil, and also an array of magnetic probes designed, constructed, and installed on outer surface of the IR-T1. Also in this work we measured the Shafranov parameter, plasma current, plasma voltage, and the plasma density by the magnetic probes, Rogowski coil, poloidal flux loop, and the Langmuir probe measurements, respectively.

RETRACTED ARTICLE: Determination of the Plasma Internal Inductance and Evaluation of its Effects on Plasma Horizontal Displacement in IR-T1 Tokamak

In this paper we presented comparison between two techniques in order to investigate the effects of the plasma internal inductance on plasma horizontal displacement in IR-T1 tokamak. For this purpose, a diamagnetic loop with its compensation coil, and also an array of magnetic probes were designed, constructed, and installed on outer surface of the IR-T1 tokamak chamber, and then the poloidal beta and poloidal and radial magnetic fields measured. Moreover, a few approximate values of the internal inductance for different possible profiles of the plasma current density are also calculated. Then, the Shafranov parameter and also the plasma horizontal displacement were determined. Experimental results compared. Comparing of the results on IR-T1, show that (1) by increasing the internal inductance from one, plasma column shifted inward, and also (2) IR-T1 plasma current density profile relate to the power of υ = 3.

Balance of the stored energies sustained by the internal and edge transport barriers and effects of ELMs and L–H transitions in JT-60U

To understand key physics processes determining radial profiles of the kinetic plasma parameters in the advanced tokamak operation scenarios, correlations between the edge transport barrier (ETB) and the internal transport barrier (ITB) have been studied in the JT-60U tokamak device. It has been found that the edge pedestal poloidal beta, βp-ped, increases almost linearly with the total poloidal beta, βp-tot, over a wide range of the plasma current for type I ELMing H-mode plasmas, and this dependence becomes stronger with increasing triangularity. This dependence is not due to the profile stiffness, since the dependence is the same regardless of the existence of ITB. As the stored energy inside the ITB-foot radius (WITB) increases, the total thermal stored energy (Wth) increases and then the pedestal stored energy (Wped) increases. On the other hand, as Wped increases, the ELM penetration expands more inwards and finally reaches the ITB-foot radius. At this situation, the ITB-foot radius cannot move outwards because of the erosion by ELMs. Then the fractions of WITB/Wth and Wped/Wth become almost constant. It has also been found that the type I ELM expels/decreases the edge toroidal momentum larger than the edge ion thermal energy. The ELM penetration for the toroidal rotation tends to be deeper than that for the ion temperature and can exceed the ITB-foot radius. The ELM penetration is deeper for CO-rotating plasmas than CTR rotating plasmas. In both cases, the ELM penetration is deeper in the order of the toroidal rotation (Vt), the ion temperature (Ti) and then the electron temperature (Te). The L–H transition also changes the Vt profile more significantly than the Ti profile. At the L–H transition, the pedestal Vt shifts into the CTR-direction deeply and suddenly without a change in Ti, and then the pedestal Vt grows further together with a growth of the pedestal Ti in a slower timescale. Such changes in Vt by ELMs and L–H transitions may affect degradation/evolution of ITBs.

Progress towards a predictive model for pedestal height in DIII-D

Recent DIII-D pedestal studies provide improved characterization of pedestal scaling for comparison with models. A new pedestal model accurately predicts the maximum achieved pedestal width and height in type I ELMing discharges over a large range of DIII-D operational space, including ITER demonstration discharges. The model is a combination of the peeling–ballooning theory for the MHD stability limits on the pedestal with a simple pedestal width scaling in which the width is proportional to the square root of the pedestal poloidal beta. Width scalings based on the ion toroidal or poloidal gyroradius are much poorer descriptions of DIII-D data. A mass scaling experiment in H and D provides support for a poloidal beta scaling and is not consistent with an ion poloidal gyroradius scaling. Studies of pedestal evolution during the inter-ELM cycle provide evidence that both the pedestal width and height increase during pedestal buildup. Model studies with a 1D kinetic neutrals calculation show that the temporal increase in density width cannot be explained in terms of increased neutral penetration depth. These studies show a correlation of pedestal width with both the square root of the pedestal poloidal beta and the square root of the pedestal ion temperature during the pedestal buildup.

Experimental Study of Effects of the Internal Inductance on the Energy Confinement Time in IR-T1 Tokamak

In this paper we present an experimental study of effects of the internal inductance on the energy confinement time, in IR-T1 tokamak. For this purpose, four magnetic pickup coils were designed, constructed, and installed on the outer surface of the IR-T1, and Then Shafranov parameter (asymmetry factor) is obtained from them. On the other hand, also diamagnetic loop were constructed and installed on IR-T1, and poloidal Beta is determined from it. Therefore, the internal inductance obtained. Also, energy confinement time is obtained using diamagnetic loop. Experimental Results show that maximum energy confinement time (which correspond to minimum collisions, minimum microinstabilities, and minimum transport) in IR-T1, relate to the low values of internal inductance (\( 0.61 \, < \, li \, < \, 0.72 \)). This is agreement with theoretical approach.

RETRACTED ARTICLE: Investigation of Effects of Toroidal Field Ripple on Plasma Poloidal Beta in IR-T1 Tokamak

We present an investigation of effect of Toroidal Field (TF) ripple (due to finite number of the toroidal field coils) on the plasma poloidal Beta in IR-T1 Tokamak. For this purpose, array of magnetic probes and also a diamagnetic loop with its compensation coil were designed, constructed, and installed on the outer surface of IR-T1. Amplitude of the TF ripple is obtained 0.01, and also the effect of the TF ripple on the poloidal Beta discussed. In the high field side region of tokamak chamber, the TF ripple effect is decreasing of the poloidal Beta, whereas the low field side has inverse situation.

RETRACTED ARTICLE: Effects of Resonant Helical Field on Plasma Internal Inductance in IR-T1 Tokamak

Measurement of plasma internal inductance is important in tokamak plasma experiments (plasma internal inductance relates to the plasma current profile). In this paper we present an experimental investigation of effects of Resonant Helical Field (RHF) on the plasma internal inductance in IR-T1 tokamak. For this purpose, four magnetic probes and also a diamagnetic loop with its compensation coil were constructed and installed on outer surface of the IR-T1 tokamak, and Shafranov parameter, poloidal Beta, and then the internal inductance determined. In order to investigate the effects of RHF on internal inductance, we measured it in presence and also in absence of different modes of the RHF (L = 2, L = 3, L = 2&3). Experimental results show that L = 3 mode can flat the plasma current and increase the plasma internal inductance.

RETRACTED ARTICLE: Measurement of Plasma Poloidal Beta in Presence of Resonant Helical Field in IR-T1 Tokamak

Precise measurements of poloidal beta and internal inductance are essential for tokamak plasma experiments. In this paper we present an experimental investigation of effects of Resonant Helical Field (RHF) on the poloidal beta in IR-T1 tokamak. For this purpose, a diamagnetic loop with its compensation coil were constructed and installed on outer surface of the IR-T1 tokamak, and then poloidal beta measured. In order to investigate the effects of RHF on the poloidal beta, we measured it with and without introducing of different modes of the RHF (L = 2, L = 3, L = 2 & 3). Experimental results discussed.

The stability margin on EAST tokamak

The experimental advanced superconducting tokamak (EAST) is the first full superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. Its poloidal coils are relatively far from the plasma due to the necessary thermal isolation from the superconducting magnets, which leads to relatively weaker coupling between plasma and poloidal field. This may cause more difficulties in controlling the vertical instability by using the poloidal coils. The measured growth rates of vertical stability are compared with theoretical calculations, based on a rigid plasma model. Poloidal beta and internal inductance are varied to investigate their effects on the stability margin by changing the values of parameters αn and γn (Howl et al 1992 Phys. Fluids B 4 1724), with plasma shape fixed to be a configuration with k = 1.9 and δ = 0.5. A number of ways of studying the stability margin are investigated. Among them, changing the values of parameters κ and li is shown to be the most effective way to increase the stability margin. Finally, a guideline of stability margin Ms(κ, li, A) to a new discharge scenario showing whether plasmas can be stabilized is also presented in this paper.

Diamagnetic measurements in the STOR-M tokamak by a flux loop system exterior to the vacuum vessel

Diamagnetic measurements of poloidal beta have been performed in the STOR-M tokamak by a flux loop placed exterior to the vacuum chamber with compensation for the vacuum toroidal field using a nonenclosing coplanar coil, and vibrational compensation from auxiliary coils. It was found that in STOR-M conditions (20% toroidal magnetic field decay over discharge) there is significant influence on the diamagnetic flux measurements from strong residual signals, presumably from image currents being induced by the toroidal field coils, requiring further compensation. A blank (nonplasma) shot is used specifically to eliminate the residual component which is not proportional to the toroidal magnetic field. Data from normal Ohmic discharge operation is presented and calculations of poloidal beta from coil data (beta(theta) approximately 0.5) is found to be in reasonable agreement with the values of poloidal beta obtained from measurements of electron density and Spitzer temperature with neoclassical corrections for trapped electrons. Contributions present in the blank shot (residual) signal and the limitations of this method are discussed.

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.

Temporal evolution of H-mode pedestal in DIII-D

The temporal evolution of pedestal parameters is examined in the initial edge localized mode (ELM)-free phase and inter-ELM phases of H-mode discharges in the DIII-D tokamak. These discharges are heated by deuterium neutral beam injection and achieve type-I ELMing conditions. Pedestal parameters exhibit qualitatively similar behaviour in both the ELM-free and inter-ELM phases. There is a trend for the widths and heights of pedestals for electron density, temperature and pressure to increase during these phases; the increase in width is most pronounced in the density and least pronounced in electron temperature. Near the separatrix, the ion temperature achieves higher values but a flatter profile as compared with the electron temperature. Higher heating powers lead to a faster evolution of the pedestal and to a shorter period until the onset of an ELM. For sufficiently long ELM-free or inter-ELM periods, some parameters, particularly gradients, approach a steady state. However, a simultaneous steady state in all parameters is not observed. The simultaneous increase in density width and pedestal density is opposite to the predictions of a simple model, which predicts that the density width is set by neutral penetration. Thus, additional physics must be added to the simple model to provide a more general description of pedestal behaviour. However, the barrier growth is qualitatively consistent with time-dependent theoretical models that predict a self-consistent temporal growth of the pedestal due to E × B shearing effects. In addition, an approximate linear correlation is observed between the density width and the square root of the pedestal ion temperature and also between the density width and the square root of the pedestal beta poloidal. These pedestal studies suggest that a complete model of the pedestal width in type-I ELMing discharges must be time dependent, include transport physics during inter-ELM periods and include the limits to pedestal evolution imposed by the ELM instability.

High Beta and High Density Operation in TPE-RX

A high poloidal beta, βp, was achieved using pulsed poloidal current drive (PPCD) in a toroidal pinch experiment-RX (TPE-RX). The plasma electron density and temperature increased, hence improving βp from 5 to 30% during PPCD. βp is almost equal to the total beta in the reversed-field pinch (RFP). D-alpha emission from recycling deuterium by the plasma-wall interaction decreased during the PPCD. An improved particle confinement time was indicated by a ten fold increase in the ratio of the total number of particles to the D-alpha emission. Single pellet injection into the good particle confinement plasma, achieved by the PPCD, produced high density plasma with high beta values. The plasma electron density rapidly increased to triple that of standard plasma, and high density was maintained till the end of the PPCD period. The electron temperature was lower than that of PPCD without ice pellet injection, but βp remained almost the same because the plasma electron density was higher with pellet injection.

Simultaneous evolution of plasma rotation, radial electric field, MHD activity and plasma confinement in the STOR-M tokamak

Radial electric field shear and poloidal plasma rotation are important factors affecting transport and confinement in tokamaks. Alteration of the electric field and plasma rotation in the vicinity of magnetic islands is also an important factor in tokamak plasma confinement. In the STOR-M tokamak, fast (∼1 ms) simultaneous alterations of the radial electric field, plasma rotation (M‖ = 0–0.4 in the plasma current direction), floating potential fluctuations in the periphery and MHD activity generated by rotating islands have been observed experimentally during normal ohmic discharges. The observed time and magnitude of the changes depend on the average electron density and poloidal beta at the beginning of the discharge. In discharges with high initial poloidal beta these changes are accompanied by a reduction in Hα emission and an increase in the line averaged density. Drastic decreases in Hα and increases in line averaged electron density and estimation of poloidal beta suggest that STOR-M confinement is significantly affected in ohmic discharges without an external additional energy input or biasing. MHD activity in STOR-M is damped when a negative electric field is observed at the limiter region of the plasma edge. MHD frequency is observed to decrease with the negative electric field.

Scaling of bootstrap current on equilibrium and plasma profile parameters in tokamak plasmas

A detailed study of the bootstrap current dependence upon some plasma profile parameters is performed and the relations between this intrinsic current with plasma equilibrium quantities such as internal plasma inductance, normalized and poloidal beta values, loop voltage and central safety factor are analysed within an equilibrium calculation valid for arbitrary aspect ratio tokamaks. In the equilibrium model, the total plasma current is given by the sum of the diamagnetic, Pfirsch–Schlüter and the neoclassical ohmic and bootstrap currents. We considered here only cases where the bootstrap current is generated by thermal particles and its profile is calculated by using the fitted formulae proposed by Sauter et al. Strong anisotropies and deep gradients (related to the presence of internal transport barriers) in the plasma pressure profiles are not taken into account. We have also accounted in our analysis for variations of Zeff, plasma elongation, triangularity, magnetic field and plasma current. This study is performed for the spherical tokamak Experimento Tokamak Esférico (ETE), and estimates obtained for the bootstrap current fraction (Ibs/Ip) are compared with a general empirical scaling law proposed by Hoang et al. Due to some deviations observed between Hoang's scaling and our results, a new expression for Ibs/Ip, given in terms of the normalized beta, cylindrical q, internal inductance parameter (li) and peakedness of pressure profile (cp), is proposed. Moreover, a second expression given as a combination of these parameters described in terms of βpol and cp is also presented. Both formulations were obtained from a least-square fitting upon about 350 ETE equilibria, in which some stability criteria were taken into account. Errors mostly up to the order of 10% are obtained when both expressions are compared with the equilibrium estimates for the bootstrap current in ETE.

Plasma Equilibrium in Tokamaks

This lecture treats the magnetohydrodynamic (MHD) equilibrium of axisymmetric plasmas, as given by the Grad-Shafranov equation. In a brief introduction, equilibrium parameters such as the q-profile, the internal inductance, and the poloidal beta are introduced. The properties of these quantities will be illustrated in the case of the tokamak, by applying the large aspect ratio tokamak approximation. The properties of a non-circular plasma cross-section and the role of the vertical field will also be discussed in this approximation. Some attention is given to the (numerical) problem of solving the equilibrium equation and of reconstructing a plasma equilibrium from external measurements.