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.     

Plasma Horizontal Displacement Measurement Using Flux Loops in IR-T1 Tokamak

In this paper we presented poloidal flux loops technique for measurement of plasma horizontal displacement in the IR-T1 tokamak. In this technique, two poloidal flux loops were designed and installed on outer surface of the IR-T1 tokamak chamber, and then the plasma displacement was obtained from them. To compare the result obtained using this method, analytical solution is also experimented on the IR-T1. Results of the two methods are in good agreement with each other.     

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.     

Multivariable Online Adaptive PID Controller for Plasma Current,Shape, and Position in Tokamaks

Nuclear fusion is one of the newest and most promising clean and safe energies hence, it imposes a new research area of control. In this paper, the design of a multivariable adaptive proportional-integral-derivative (PID) controller for the control of the plasma current, shape and position to ensure the safe operation of the fusion reactor is successfully developed. The recursive least square algorithm is used in an alternative way as an adaptation mechanism for tuning PID controller gains. Since stability is a vital issue in the evaluation of control systems, therefore stability analysis of the proposed controller is developed using the Lyapunov stability theory. The main objective of plasma current, shape and position controller in fusion reactors is to improve the stability and the performance of tokamak magnetic systems without contravening the limits imposed by the actuating coils voltages physical limitations. The proposed APID (adaptive PID) controller tunes online its parameters to cope with the presence of the disturbance or any parameters changes occur during the operation. The results of the proposed APID on a simulation code of a tokamak show a noteworthy improvement with respect to those obtained with other control techniques in the cases of changing the initial controller gains, adding disturbance signal and variation in the reactor model parameters.     

Multipole Moments Based Study on Determination of Toroidal Plasma Equilibrium Position and Shift

The multipole moments based technique studied for the determination of toroidal plasma column shift. First, we presented analytical details for using this technique. Then, principle of two different models based on this technique for design and fabrication of a modified Rogowski coil (MRC) and Saddle Sine coil (SSC) will be presented. Because of continuous measurements of magnetic field distribution around the toroidal plasma using the MRC and SSC, this technique is the good method for the determination of toroidal plasma column shift.     

Effects of Alfvenic Poloidal Flow and External Vertical Field on Plasma Position in IR-T1 Tokamak

We analyzed dynamic equilibrium properties of a large aspect ratio and low Beta tokamaks, in particular deriving a modified relation for the Shafranov shift in the presence of poloidal flow and external vertical field, and demonstrate it experimentally on the IR-T1 tokamak. Poloidal flow can produce modifications in the equilibrium properties. By increasing Alfvenic Mach number from zero, flow produce outward force, and plasma shifted in outward direction. If the poloidal Alfvenic Mach number equal to one, singularity will observe in the solution of generalized Grad–Shafranov equation. Also inversion of Shafranov shift in the transition of flow speed between sub-Alfvenic to super-Alfvenic speeds can be observed due to inward force produced by flow.     

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.     

Simulation of Toroidal Rotation Effect on Heat Flux Transport in the Edge Plasma of Small Size Divertor Tokamak

The effect of toroidal rotation on heat flux transport in the edge plasma of small size divertor was simulated by B2SOLP0.5.2D transport code. The main results of simulation shows that, the following: (1) the radial heat flux is strongly influenced by toroidal rotation. (2) The amplification of conduction part of radial heat flux imposes nonresilient profile of ion temperature, under which the effect of toroidal rotation on ion temperature profile is strong. (3) The ion distribution and its gradients are lower for counter-injection neutral beam than for co-injection neutral beam. (4) Reversal of toroidal rotation during using neutral beam injection result in reverses of radial electric field and E × B drift velocity. (5) The toroidal rotation strong influence on the ion temperature scale length of the ion temperature gradient (ITG). (6) Switch on and off all drifts leads to higher change in the ion density distribution in edge plasma of small size divertor tokamak when the unbalance neutral beam injection are considered (7) the comparison between radial heat flux at different momentum input shows that, the radial ion heat flux with larger ion temperature scale length in the case of co-injection neutral beam is larger than the ion heat flux with smaller ion temperature scale length in the case of counter-injection neutral beam.     

Experimental Measurement of Asymmetric Fluctuations of Poloidal Magnetic Field in Damavand Tokomak at Different Plasma Currents

Toroidal and Poloidal magnetic fields have an important effect on the tokomak topology. Damavand Tokomak is a small size tokomak characterized with k?=?1.2, B _t?=?1T, R ₀?=?36?cm, maximum plasma current is about 35?KA with a discharge time of 21?ms. In this experimental work, the variation of poloidal magnetic field on the torodial cross section is measured and analyzed. In order to measure the polodial magnetic field, 18 probes were installed on the edge of tokomak plasma with ?θ?=?18°, while a limiter was installed inside the torus. Plasma current, I _p, induces a polodial magnetic field, B _p, smaller than the torodial magnetic field B _t. Magnetic lines B produced as a combination of B _t and B _p, are localized on the nested toroidal magnetic surfaces. The presence of polodial magnetic field is necessary for particles confinement. Mirnov oscillations are the fluctuations of polodial magnetic field, detected by magnetic probes. Disrupted instability in Tokomak typically starts with mirnov oscillations which appear as fluctuations of polodial magnetic field and is detected by magnetic probes. Minor disruptions inside the plasma can contain principal magnetic islands and their satellites can cause the annihilation of plasma confinement. Production of thin layer of turbulent magnetic field lines cause minor disruption. Magnetic limiter may cause the deformation of symmetric equilibrium configuration and chaotic magnetic islands reveal in plasma occurring in thin region of chaotic field lines close to their separatrix. The width of this chaotic layer in the right side of poloidal profile of Damavand Tokomak is smaller than the width in the left side profile because of Shafranov displacement. Ergodic region in the left side of profile develops a perturbation on the magnetic polodial field lines, B _p, that are greater in magnitude than that in the right side, although the values of B _p on the left side are smaller than that on the right side of the profile. The Left side of profile is close to the principal magnetic axis and the right side is away from Z axis of Tokamak.     

Plasma modeling and first wall interaction phenomena in Tokamaks

Fluxes of neutral hydrogenic particles, alpha particles and electromagnetic radiation to the liner or first wall of both two component tokamaks and large ignited tokamak fusion reactors are estimated using space and time dependent models of tokamak plasmas. Data requirements and the effects of uncertainties in the areas of first wall interaction phenomenon and plasma transport coefficients are described.     

Comparison Autocorrelation Method and SVD Method for Plasma Mode Analysis in Tokamaks

Autocorrelation method (Single time series) is new method for analysis of plasma mode in Tokamaks. In this article autocorrelation method has been compared with SVD method. Energy of the modes which obtained by SVD analysis showed that the autocorrelation method is a cited method for mode detection.     

Comparison Study of Fourier and SVD Method for Plasma Mode Analysis in Tokamaks

Fourier analysis and Singular Value Decomposition (SVD) are two familiar methods for mode detection in tokamaks. In this article this two methods, fourier and SVD, have compared. The results show fourier analysis in m ≥ 3 and when the energy is balanced between modes could not recognize the correct mode number. The SVD analysis is cited method for all modes.     

Effect of Plasma Rotation on Neutral Beam Heating and Current Drive in Tokamaks

For a rapidly rotating plasma, the effects of the resulting Doppler shift have to be included in the neoclassical theory of neutral beam heating, current drive, and plasma transport. In this paper, an improved simulation of neutral beam injection (NBI) and current drive in rotating plasmas is introduced. NBI is simulated using the Monte Carlo code NUBEAM along with the transport code ONETWO. The physical characteristics of heating and current drive for co- and counter-NBI are investigated for non-rotating, co-rotating, and counter-rotating plasmas, all of which can take place in the experiments. In general, it is found that rotation of the plasma can increase the NBI power deposition on the plasma electrons but has little effect on the ions. Moreover, plasma heating by co-NBI is more efficient than that by counter-NBI. For neutral beam current drive, because of the Doppler shift, co-rotation (counter-rotation) of the bulk plasma tends to decrease the co-NBI (counter-NBI) driven current. On the other hand, due to trapping and orbit loss of the fast ions, co-rotation (counter-rotation) has little effect on the counter-NBI (co-NBI) driven current. The results are applied to the forthcoming NBI heating and current drive experiments of the EAST tokamak and should also be useful in the design of experiments in ITER.     

Plasma Parameters Measurement in IR-T1 Tokamak with Langmuir Probe and the Simulation of the Lower Hybrid Waves in IR-T1, JET and NSTX Tokamaks

Ohmic heating is not enough for ignition mode in plasma and fusion reactions. Therefore additional methods, has been used, such as wave injection into plasma. Radio frequency wave injection into fusion plasma is more considered. Interaction between waves and plasma is described by Fokker–Planck equation with an added quasi-linear term. This paper is composed of three sections. At first, required experimental parameters for LSC program such as temperature and density measured by a Movable Langmuir Probe in IR-T1, and then we presented Computational solution of Fokker–Planck equation with Adjoint method and Rosenbluth potentials to achieve distribution function in velocity space and at least, we simulated Lower Hybrid Waves and quasi-linear term for NSTX, JET and IR-T1 tokamak. The results of this simulation showed higher efficiency of NSTX, in comparison with JET and IR-T1.     

Adaptive Grids in Simulations of Toroidal Plasma Starting from Magneto-Hydrodynamic Equilibrium

This paper introduces the notion of Tokamak Magneto-Hydrodynamics(TMHD),which explicitly reflects the anisotropy of a high temperature tokamak plasma.The set of TMHD equations is formulated for simulation of macroscopic plasma dynamics and disruptions in tokamaks.Free from the Courant restriction on the time step,this set of equations is adequate to plasma dynamics with realistic parameters of high performance plasmas and does not require any extension of the MHD plasma model.At the same time,TMHD requires the use of magnetic field aligned numerical grids.Examples of their use in 2-dimensional cases of tokamak equilibria and dynamics of the wall touching kink mode are presented.For the 3-dimensional case of an ergodic magnetic field,this paper introduces the reference magnetic coordinates as a practical algorithm for generating adaptive grids for TMHD.     

Simulation Study of Heat Flux Deposition Pattern on the Surface of HT-7 Toroidal Limiters

The heat flux deposition pattern on the toroidal limiters installed in HT-7 was simulated with ANSYS code. The simulation model was established with the ripple of the magnetic field. The heat deposition pattern and temperature distribution on the surface of the toroidal linfiters were obtained. A comparison of the results obtained with and without the shaped tiles, used to reduce the heat flux on the leading edge of the limiters, was made. The maximum heat load allowed at the leading edge was about 1.8 MW/m2 because of the poor power removing capacity on the ends of the limiters. This approach can also be applied to other devices with a limiter configuration in a circular cross-section shape.     

The Finite Beta Effects on the Toroidal Field Ripple in a Tokamak Plasma

The efficiency of energetic ion confinement is reduced in a tokamak plasma by the non-axisymmetric field, namely the ripple field. The ripple field is produced by a finite number of toroidal field coils. It is affected by the non-axisymmetric finite beta effect. The three-dimensional MHD equilibrium calculation code VMEC is used to analyze the non-axisymmetric finite beta effect in a ripple tokamak. In the VMEC code, the flux coordinates are used, so the calculation region is limited to the area of plasma. To calculate the orbit outside the plasma, we develop a field calculation code, which is based on the Biot-Savart law. The details of the method and results are described in this paper.     

Shaping Effects of the E-Fishbone in Tokamaks

Shaping effects of the E-fishbone in tokamaks are investigated. Coordinates related to the Solov’ev configuration are used to calculate the precession frequency and kinetic contribution. It is shown that elongation does not change the precession frequency and the kinetic energy. Growth rates of the E-fishbone vary with elongation which essentially has destabilizing effects. For elongated tokamaks, triangularity has a stabilizing effect on the modes which play a compensative role. The results may apply to Sunist.     

The Behavior of Radial Electric Field and Toroidal Rotation in the Edge Plasma of Divertor Tokamak

A new method for describing the nature of radial electric field and its relation with toroidal rotation in edge plasma of small size divertor tokamak is proposed in this work. The expression of radial electric field in the edge plasma of small size divertor tokamak can be divided into two parts. The first part E _r ⁽⁰⁾ is related to electrostatic potential of plasma in edge plasma of this tokamak. The second part E _r ⁽¹⁾ is related to contribution of toroidal rotation of radial current in edge plasma of this tokamak. The results of this work provide the following: (1) A new one-dimensional ordinary differential equation for toroidal velocity is obtained. The one-dimensional ordinary differential equation suggest new tool to explaining tokamak experiments involving measurements of plasma rotation and radial electric field. (2) Also the results of this work shows that, the main contribution to the radial electric field inside separatrix (plasma core) gives the term E _r ⁽¹⁾.