Plasma Pressure Profiles Research Articles

Modeling, measurement, and 3-D equilibrium reconstruction of the bootstrap current in the Helically Symmetric Experiment

The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the reconstruction is constrained by the measured data from a diagnostic array that is internal to the vacuum chamber.

Pressure profiles of plasmas confined in the field of a magnetic dipole

Equilibrium pressure profiles of plasmas confined in the field of a dipole magnet are reconstructed using magnetic and x-ray measurements on the levitated dipole experiment (LDX). LDX operates in two distinct modes: with the dipole mechanically supported and with the dipole magnetically levitated. When the dipole is mechanically supported, thermal particles are lost along the field to the supports, and the plasma pressure is highly peaked and consists of energetic, mirror-trapped electrons that are created by electron cyclotron resonance heating. By contrast, when the dipole is magnetically levitated losses to the supports are eliminated and particles are lost via slower cross-field transport that results in broader, but still peaked, plasma pressure profiles.

Alfvén modes in the Madison Symmetric Torus

This work presents a theoretical and computational analysis of core-localized energetic particle driven modes observed near the magnetic axis in the Madison Symmetric Torus [L. Lin, W. X. Ding, D. L. Brower et al., Phys. Plasmas 20, 030701 (2013)]. Using measured safety factor and plasma pressure profiles as input, the linear ideal MHD code Adaptive EiGenfunction Independent Solution (AEGIS) [L. J. Zheng and M. Kotschenreuther, J. Comput. Phys. 211, 748 (2006)] reveals Alfvénic modes close to the measured frequencies. The AEGIS results together with a reduced analytical model demonstrate that the modes are essentially “cylindrical” and dominated by a single poloidal component (m = 1). The modes are localized at the plasma core where the magnetic shear is weak and continuum damping is minimal. Detailed analysis establishes constraints on the safety factor and plasma pressure, under which two modes can exist simultaneously.

Stable anisotropic plasma confinement in magnetic configurations with convex–concave field lines

It is shown that a combination of the convex and the concave part of a field line provides a strong stabilizing action against convective (flute-interchange) plasma instability (Tsventoukh 2011 Nucl. Fusion 51 112002). This results in internal peaking of the stable plasma pressure profile that is calculated from the collisionless kinetic stability criterion for any magnetic confinement system with combination of mirrors and cusps. Connection of the convex and concave field line parts results in a reduction of the space charge that drives the unstable E × B motion, as there is an opposite direction of the particle drift in a non-uniform field at convex and concave field lines. The pressure peaking arises at the minimum of the second adiabatic invariant J that takes place at the ‘middle’ of a tandem mirror–cusp transverse cross-section. The position of the minimum in J varies with the particle pitch angle that results in a shift of the peaking position depending on plasma anisotropy. This allows one to improve a stable peaked pressure profile at a convex–concave field by changing the plasma anisotropy over the trap cross-section. Examples of such anisotropic distribution functions are found that give an additional substantial enhancement in the maximal central pressure. Furthermore, the shape of new calculated stable profiles has a wide central plasma layer instead of a narrow peak.

Characteristics of plasma ring, surrounding the Earth at geocentric distances ∼7–10RE, and magnetospheric current systems

There are strong experimental evidences of the existence of plasma domain forming a closed plasma ring around the Earth at geocentric distances ∼7–10RE. In this work, we analyze the main properties of this ring, using the data of the THEMIS satellite mission, acquired between April 2007 and September 2011. We also analyze the contribution of this ring to the storm dynamics. In particular, it is shown that the distribution of plasma pressure at ∼7–10RE is nearly azimuthally symmetric. However, the daytime compression of the magnetic field lines and the shift of the minimal value of the magnetic field to higher latitudes lead to the spreading of the transverse current along field lines and splitting of the daytime integral transverse current into two branches in Z direction. The CRC is the high latitude continuation of the ordinary ring current (RC), generated by plasma pressure gradients, directed to the Earth. We evaluated the contribution of the azimuthally symmetric part of the plasma ring to the Dst index for strong geomagnetic storms using the AMPTE/CCE radial profiles of plasma pressure published before, and showed that the contribution of the ring current including both RC and CRC is sufficient to obtain the observed Dst variation without the necessity to include the tail current system.

Structure, force balance, and evolution of incompressible cross-tail current sheet thinning

[1] THEMIS five-point observations on April 8, 2009 were used to study thinning of the current sheet in the near-Earth tail that led to the onset of a small substorm. Taking advantage of a fortuitous alignment of the five spacecraft near 2300 LT and 11 RE and within 1.5 RE of the current sheet center, latitudinal gradients are analyzed. A significant latitudinal pressure gradient is present indicating the necessity of a (J × B)z force to maintain the pre-onset equilibrium state. During thinning the total pressure remained approximately constant at all spacecraft rather than increasing. Within the plasma sheet, magnetic field strength increased while plasma pressure decreased due to decreasing temperature. We present a comprehensive explanation for the relationship between the thinning, the stretched structure, and development of intense current density. Our analysis of this event suggests that (1) the thinning in this event is an MHD force-balanced self-evolving process and is not a forced process due to an increased lobe field; (2) the thinning changes flux tube structure in length and curvature but not significantly in volume; (3) the thinning evolves with a change of the radial plasma pressure profile in the near-Earth tail, which is associated with a locally intensified current sheet. The conclusion is that the increased lobe field strength is not the necessary and the primary cause for cross tail current sheet thinning but rather thinning can occur within the plasma sheet as a result of unknown internal processes.

Shock pressure induced by glass-confined laser shock peening: Experiments, modeling and simulation

The shock pressure generated by the glass confined regime in laser shock peening and its attenuation in the target material are investigated. First, the particle velocity of the target back free surface induced by laser generated shock pressure of this regime is measured using a photonic Doppler velocimetry system. The temporal profile of the particle velocity at the back free surface, where the elastic precursor is captured, manifests a powerful diagnostic capability of this newly developed photonic Doppler velocimetry system for tracking the velocity on short time scales in shock-wave experiments. Second, a coupling pressure analytical model, in which the material constitutive models of confined layers and target material are considered, is proposed to predict the plasma pressure profile at the surface of target. Furthermore, using the predicted shock pressure profile as the input condition, the dynamic response of the target under the shock pressure is simulated by LS-DYNA. The simulated back free surface velocity profile agrees well with that measured by the photonic Doppler velocimetry system. Finally, the attenuation behavior of stress waves and particle velocities in the depth of the target is analyzed, and it indicates an exponential decay. The corresponding empirical formulas for the attenuation behavior are given based on the numerical results.

Note: Multi-point measurement of |B| in the gas-dynamic trap with a spectral motional Stark effect diagnostic

An upgraded spectral motional Stark effect diagnostic has been installed on the gas-dynamic trap (GDT) experiment to enable spatially resolved measurement of |B|. A new low-noise charge-coupled device detector, combined with enhancements of the diagnostic neutral beam, allows single-shot profile measurements. Previously only single-point motional Stark effect measurements were possible, and detector noise severely limited measurement precision, requiring multi-shot averaging. The plasma pressure profile in GDT is derived from the measured diamagnetic modification of |B| and used to examine the conditions of stable plasma confinement at high plasma pressure.

Modeling of Saturn's magnetosphere during Voyager 1 and Voyager 2 encounters

We model Saturn's magnetosphere during the Voyager 1 encounter on days 317 and 318 in 1980 and the Voyager 2 encounter on days 237 and 238 in 1981, respectively. The rotating magnetosphere of Saturn is modeled by two‐dimensional axisymmetric equilibrium solutions of the Grad‐Shafranov type equation, which includes effects of the plasma pressure gradient force and the centrifugal force due to plasma toroidal rotation, by prescribing the radial profiles of plasma density and temperature in the equatorial plane. By varying the equatorial plasma profiles the equilibrium solutions are obtained with reasonably good fit to the observed plasma and magnetic field data along the orbits of the Voyager 1 encounter with the Saturn's magnetosphere on days 317 and 318 in 1980 and the Voyager 2 encounter on days 237 and 238 in 1981. The numerical equilibrium solutions provide detailed information of the global distribution of plasma environment and magnetic field structure of the Saturn's inner magnetosphere (for L < 24), and the results show that the plasma environment and the magnetic field configuration of the Saturn's magnetosphere are very different between these two spacecraft encounters with the Saturn. In particular, the meridian distributions of heavy ion density, azimuthal current density, and heavy ion beta have thin disk‐like shapes centered at the equator for the Voyager 1 case, but have fat torus shapes for the Voyager 2 case. The difference results from the difference in the equatorial plasma pressure profile which decreases with R for R > 5RS for the Voyager 1 case, but is quite flat between R ≃ 5 and 17RS for the Voyager 2 case.

Three‐Dimensional Effects on Stochasticity in Non‐Axisymmetric Tori

AbstractThree‐dimensional (3D) effects on the stochasticity of magnetic field lines in helical devices are investigated. The stochastization due to increased plasma pressure is an intrinsic property of the stellarator/heliotron because the pressure‐gradient driven currents are the source of perturbation fields. The stochastization depends on the plasma pressure profile. In an advanced stellarator, the stochastization due to the 3D effects is smaller. However, magnetic islands in the edge are affected by 3D effects. 3D effects in a tokamak plasma are studied,too, and differences from the vacuum approximation are found (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Observation of Confined Current Ribbon in JET Plasmas

We report the identification of a localized current structure inside the JET plasma. It is a field-aligned closed helical ribbon, carrying current in the same direction as the background current profile (cocurrent), rotating toroidally with the ion velocity (corotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first edge localized mode.

Stabilization of ideal pressure gradient driven edge modes during pulsed parallel current drive in reversed field pinch

Significant improvement of plasma confinement in the Madison Symmetric Torus reversed field pinch (RFP) has been routinely achieved by applying an inductive electric field at the plasma boundary in the direction parallel to the equilibrium magnetic field at the plasma edge. An auxiliary edge current is driven by this electric field with the goal of replacing the dynamo-driven current and modifying the parallel current profile to reduce current-driven instabilities. This current-drive technique is called pulsed parallel current drive (PPCD) in RFP. During PPCD plasma fluctuations are reduced everywhere resulting in tokamak-like confinement parameters, while the edge density profile steepens significantly and plasma beta increases. A steep edge plasma pressure profile, a relatively high plasma beta and a strong unfavourable curvature of equilibrium magnetic field near the edge in RFP could excite pressure-driven fluid turbulence near the edge and worsen plasma confinement, opposite to the experimental observations. In this study stability analysis of edge pressure gradient driven ideal modes in standard-like and in PPCD-like plasma equilibria is performed. An ideal magnetohydrodynamic plasma model in cylindrical RFP equilibrium with a step function plasma pressure profile and a vacuum layer between the plasma boundary and the conducting shell is used. Standard-like and PPCD-like plasma equilibria in the model are defined by the direction of the surface current at the plasma–vacuum interface. The results show that while in standard-like equilibrium the edge pressure gradient driven modes are highly unstable in this model, the transition to PPCD-like equilibrium completely stabilizes these modes. The modes stabilization is primarily due to strengthening of magnetic shear at the location of the pressure gradient during the drive and due to the proximity of this location to the conducting wall. This stabilization mechanism is not specific to RFPs, making PPCD a general method of stabilization of the edge pressure gradient driven instabilities which could be applied in other magnetic confinement systems. Application of PPCD to stabilize the edge localized modes in tokamaks is proposed.

Self-Consistent Pressure and Current Profiles in High-Beta D-3He Tokamak Reactors

D-3He reactor has a great advantage of neutron-poor operation, but it requires higher-beta value and higher bootstrap current fraction than D-T reactor. In this paper, we investigated self-consistent plasma pressure and current profiles in the case of a positive magnetic shear mode (parabolic temperature profile) and a negative magnetic shear mode (ITB temperature profile) using TOTAL-T code including Cytran module. In a negative magnetic shear mode, toroidal beta value βT ∼ 52.4 % and bootstrap current fraction fbs ∼ 0.93 was obtained in a plasma with aspect ratio 1.77, plasma major radius 6.2 m, toroidal field 4.2 T and plasma current 49.3 MA.

Generation of Intermittent Turbulent Events at the Transition from Closed to Open Field Lines in a Toroidal Plasma

Turbulent transport at the transition from closed to open field lines has been investigated in the stellarator experiment TJ-K. It is found that drift-wave turbulence in the confined region is responsible for the generation of intermittent structures (so-called blobs) in the unconfined region. There the character of turbulence changes and a decoupling of density and potential fluctuations is observed. The poloidal propagation of the intermittent events can be understood in the framework of background flows caused by gradients in the equilibrium plasma pressure and potential profiles.

Study of plasma pressure distribution in the inner magnetosphere using the low altitude satellite data and its relevance for magnetospheric dynamics

Plasma pressure distribution in the inner magnetosphere is one of the key parameters for understanding the main magnetospheric processes including geomagnetic storms and substorms. However, the pressure profiles obtained from in-situ particle measurements by the high-altitude satellites inside the plasma sheet do not allow tracking the pressure variations related to the magnetospheric dynamics, because time interval needed to do this generally exceeds the characteristic times of the main magnetospheric processes. On the contrary, fast movement of low-altitude satellites makes it possible to restore quasi-instantaneous profiles of plasma pressure along the satellite trajectory, using the precipitating particle flux data in the regions of isotropic plasma pressure. It was found that during quiet geomagnetic conditions profiles obtained from low-altitude and high-altitude satellites coincide. Nevertheless, the plasma pressure profiles change significantly during the development of storms and substorms, that indicates possibility of the interchange (storm) or modified interchange (substorm) instability development.

Total ion pressure changes with L shell in the nightside inner magnetosphere

The total ion plasma pressure has been estimated in the equatorial plane of the magnetosphere from the CRRES measurements when the satellite crossed the magnetic shells from L ∼ 2.3 to L ∼ 6.6 in the night sector of ∼20–24 MLT. The data of the LEPA and the EPAS particle detectors as well as the magnetic field data on the CRRES satellite have been used for two events with the AE < 300 nT before the substorm onset. It is found that the gross radial structure of the plasma pressure constructed along the CRRES orbit exhibits a maximum at L ∼ 3 and then a gradual decrease with distance from the Earth. Along with these usual features of the plasma pressure profile, we revealed an additional maximum of the total ion pressure, which appears at L ∼ 4.6–4.9. It is located earthward of the Alfvén boundaries of low‐energy electrons. From the analysis of the energy composition of plasma pressure we conclude that this additional maximum is a result of enhancement of the pressure of ions with energies <30 keV which was observed ∼20 min after a small enhancement of magnetic activity. We suppose that dynamical changes in the electric field and particle density in the plasma sheet are the dominant processes that form the observed peculiarity in the radial profile of the total ion pressure. These dynamical changes lead to a shift of convection boundaries and to acceleration of ion flux which was formed by preexisting quasi‐steady convection.

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.

Full f gyrokinetic method for particle simulation of tokamak transport

A gyrokinetic particle-in-cell approach with direct implicit construction of the coefficient matrix of the Poisson equation from ion polarization and electron parallel nonlinearity is described and applied in global electrostatic toroidal plasma transport simulations. The method is applicable for calculation of the evolution of particle distribution function f including as special cases strong plasma pressure profile evolution by transport and formation of neoclassical flows. This is made feasible by full f formulation and by recording the charge density changes due to the ion polarization drift and electron acceleration along the local magnetic field while particles are advanced. The code has been validated against the linear predictions of the unstable ion temperature gradient mode growth rates and frequencies. Convergence and saturation in both turbulent and neoclassical limit of the ion heat conductivity is obtained with numerical noise well suppressed by a sufficiently large number of simulation particles. A first global full f validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. At high Mach number ( M p ∼ 1 ) of the poloidal flow, the radial electric field is significantly enhanced over the standard neoclassical prediction. The neoclassical radial electric field together with the related GAM oscillations is found to regulate the turbulent heat and particle diffusion levels particularly strongly in a large aspect ratio tokamak at low plasma current.

Advanced tokamak scenario developments for the next step

The objective of advanced tokamak scenario research is to provide a candidate plasma scenario for continuous operation in a fusion power plant. The optimization of the self-generated non-inductive current by the bootstrap mechanism up to a level of 50% and above using high plasma pressure and improved confinement are the necessary conditions to achieve this goal. The two main candidate scenarios for continuous operation, the steady state scenario and long duration (up to 3000 s) high neutron fluency scenario (the hybrid scenario), both face physics challenges in terms of confinement, stability, power exhaust and plasma control. Resistive wall modes and Alfvénic fast ion driven instabilities are the main limitations for operating the steady state scenario at high pressure and low magnetic shear. In addition, this scenario demands a high degree of control over the plasma current and pressure profile and the steady state heat load on in-vessel plasma facing components. Understanding the confinement properties of hybrid scenario is still an outstanding issue as well as its modelling for ITER in particular with regard to the H-mode pedestal parameters. This scenario will also require active current profile control, although, less demanding than for the steady state scenario. To operate advanced tokamak scenario, broad current and pressure profile control appears as a necessary requirement on ITER actuators, in addition to the tools required for instability control such as error field coils or electron cyclotron current drive.

Tokamak Equilibria with Toroidal-Current Reversal in the Plasma Core Consistent with Experimental Data

For the first time, tokamak equilibria with negative toroidal current flowing in the plasma core are computed consistently with available measurements from typical current-hole discharges. The equilibrium reconstruction, which leads to non-nested configurations where a system of axisymmetric magnetic islands unfolds, yields an overall good agreement between the computed and experimental plasma-pressure profiles, together with an excellent fit to motional-Stark-effect data. Therefore, considering the accuracy limits of present-day experimental results, care must be exercised when ruling out the existence of tokamak equilibria with central toroidal-current reversal, particularly if relying on reconstruction tools that cannot cope with non-nested configurations.