Fluid Code Research Articles

Modeling the time evolution of laser-induced plasmas for various pulse durations and fluences

In this paper, the expansion in ambient air of a plasma produced by laser ablation from an aluminum target is studied with the help of a one-dimensional fluid code that includes a consistent description of ablation and of the subsequent plasma expansion. Two limiting cases for the expansion geometry have been considered: Cartesian and hemispheric. The plasma temperature and electron density as a function of the space coordinate and time have been obtained for laser pulse durations of 100 fs, 200 ps, and 5 ns, and laser fluences up to a few tens of J/cm2. Simulation results are in good agreement with experiments. The code shows that for times typically longer than 1 μs, the plasma space-averaged temperature and electron density are nearly independent of the laser parameters and of the chosen expansion geometry. For a given pulse duration the plasma temperature first increases with the fluence and then reaches a saturation value. It is shown that most of the observed plasma behavior can be explained by radiative cooling.

Understanding transport barriers through modelling

Models of radial electric field formation are discussed and compared with the results of numerical simulations from fluid transport codes and Monte Carlo codes. A comparison of the fluid and Monte Carlo codes is presented. A conclusion is arrived at that all the simulations do not predict any bifurcation of the electric field, i.e. no bifurcation of poloidal rotation from low to high Mach number values is obtained. In most of the simulations, the radial electric field is close to the neoclassical electric field. The deviation from neoclassical electric field at the separatrix due to the existence of a transitional viscous layer is discussed. Scalings for the shear of the poloidal rotation are checked versus simulation results. It is demonstrated that assuming the critical shear to be of the order of 105 s−1, it is possible to obtain a L–H transition power scaling close to that observed in the experiment. The dependence of the threshold on the magnetic field direction, pellet injection, aspect ratio and other factors are discussed on the basis of existing simulations. Transport codes where transport coefficients depend on the turbulence level and scenario simulations of L–H transition are analysed. However, the details of gyrofluid and gyrokinetic modelling should be discussed elsewhere. Simulations of internal transport barrier (ITB) formation are discussed as well as factors responsible for ITB formation.

Extensions of the 3‐Dimensional Plasma Transport Code E3D

AbstractOne important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2‐D code packages like B2‐Eirene or UEDGE are under development. A 3‐dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm.The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra‐variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A New Mechanism Explaining the Asymmetric X‐Ray Emission from Supernova Remnant PKS 1209−52

The interaction of a supernova remnant with its surrounding environment is a powerful source of radiation in various spectral regions and at different stages in its development. The study of these emissions can therefore help to investigate the interstellar medium surrounding a supernova. For example, the highly asymmetric X-ray emission from PKS 1209-52 has previously been described as resulting from the supernova shock front on the eastern side of the remnant interacting with a small, dense interstellar cloud (or cloud core). In this paper we describe a possible mechanism through which the kinetic energy of the expanding shock is converted to energetic electrons. The particular interaction is a plasma streaming instability known as the modified two-stream instability that creates plasma waves in the lower hybrid frequency range that can then go on to accelerate electrons to high energy. A Fokker-Planck equation describing the diffusion of the electrons to high energies by lower hybrid waves is solved for both Gaussian and Lorentzian wave spectral distributions. We also simulate the interaction between the supernova remnant with the dense interstellar cloud using a two-dimensional fluid code. The nonthermal electrons can then generate X-ray emission via bremsstrahlung and also line radiation through interactions with the ambient medium. The maximum energy of these electrons is limited to the few keV energy range and therefore does not lead to any synchrotron radio emission that would otherwise lead to a radio asymmetry in the remnant that is not seen.

HL-2A Tokamak Edge Modeling with B2

The outer divertor plasma of HL-2A and its associated scrape-off plasma have been simulated using a two-dimensional multi-species fluid code of Braams with a simplified neutral gas model. HL-2A has a double-null closed divertor in separate divertor chambers above and below the nearly circular plasma tours. The computed numerical grid is developed according to an ideal magnetic surface. The calculation is involved only with pure hydrogen plasma. The emphasis has been focused on parametric studies involving variation of the assumptions made for the core plasma. The peak temperatures and the heat flux near the target are of the principal concern.

Three-dimensional modeling of a surface type alternating current plasma display panel cell: the effect of cell geometry on the discharge characteristics

Three-dimensional fluid code was used to investigate the effects of discharge cell's geometrical parameters on the characteristics of the addressing and the sustaining discharges. The main parameters investigated in this study are the cell pitch, the address electrode width, and the barrier rib height. The investigated discharge characteristics are the sustain voltage range, the luminance and efficiency, and the minimum applied voltage needed for the successful addressing. In this study, it was found that a larger cell pitch or a higher barrier rib can lower the sustain voltage range and a wider address electrode can lower the addressing voltage. Also, we obtained that the luminance and efficiency dependence on the sustain voltage for various values of each parameter. Especially for the analysis of the barrier rib height effect, we developed a ray-optics code where the luminance and efficiency can be calculated in terms of the visible light. From this analysis, we found that although cells with a higher barrier rib generate more VUV photons, there exists an optimal barrier rib height for a given cell pitch that gives the highest visible luminance and efficiency because of the shadow effect by the barrier ribs.

Complex leak-before-break analysis demonstrated on RBMK-1500 austenitic piping

Application of the Leak-Before-Break (LBB) concept to nuclear reactor cooling system piping requires satisfaction of regulatory requirements. When performing LBB deterministic analysis, it should be demonstrated that leak monitoring systems would be able to detect a leak before a crack reaches the critical size. Many countries use the US Nuclear Regulatory Commission based LBB evaluation procedure. In these regulations the target leak rate and leakage flaw size are given values that should be satisfied if the LBB concept is going to be applied. For many cases these strict limitations can lead to LBB not being demonstrated for piping systems if sensitivity aspects are not taken into account. This paper presents a LBB application demonstrated by complex analysis of RBMK-1500 austenitic piping. The analysis consists of 3D finite element calculations for crack opening and fracture parameter evaluations, leak rate determination performed using analytical and state-of-art fluid codes and thermohydraulic parameter response in compartment evaluation. The study of the influence of load, material fracture parameter and crack length safety factor on calculated leak rate and the influence on leakage to compartments of thermohydraulic parameters is demonstrated.

Hydrodynamic Implosion Simulation Including Relativistic Effects on Petawatt-Class Pulse Heating

A spherically symmetric fluid code that includes the relativistic effects of hot electrons has been newly developed. In the present simulations, I attempt to implode a target shell of laser fusion using a nanosecond pulse; then, an additional heating short pulse is injected into the coronal plasma surrounding a highly compressed core. I found that the relativistic effects of hot electrons on electron transport are likely to inhibit the heat flows, and to reduce thermonuclear fusion neutrons significantly. This feature may be important for off-center fast ignition and burn of fusion targets.

Operating regime for a backward Raman laser amplifier in preformed plasma

A critical issue in the generation of ultraintense, ultrashort laser pulses by backward Raman scattering in plasma is the stability of the pumping pulse to premature backscatter from thermal fluctuations in the preformed plasma. Malkin et al. [Phys. Rev. Lett. 84, 1208 (2000)] demonstrated that density gradients may be used to detune the Raman resonance in such a way that backscatter of the pump from thermal noise can be stabilized while useful Raman amplification persists. Here plasma conditions for which the pump is stable to thermal Raman backscatter in a homogeneous plasma and the density gradients necessary to stabilize the pump for other plasma conditions are quantified. Other ancillary constraints on a Raman amplifier are also considered to determine a specific region in the Te–ne plane where Raman amplification is feasible. By determining an operability region, the degree of uncertainty in density or temperature tolerable for an experimental Raman amplifier is thus also identified. The fluid code F3D [R. L. Berger et al., Phys. Plasmas 5, 4337 (1998)], which includes the effects of thermal fluctuations, is used to verify these analytic estimates.

The low-field density peak in helicon discharges

Although the density n in helicon discharges increases monotonically with magnetic field B for B larger than a few hundred gauss, as expected from theory, a pronounced density peak is often observed at B∼50 G or below. A peak in antenna loading is indeed found in computations using a fluid code as long as reflections from an endplate are taken into account. Various tests show that this peak is caused by constructive interference from the reflected wave. This effect can be used in the design of compact helicon plasma injectors. In addition, it can be the cause of density enhancements previously observed using cusped magnetic fields or aperture limiters.

Neoclassical nature of the radial electric field at the low-to-high confinement transition

The radial electric field Er at the tokamak plasma edge is simulated both with a two-dimensional (2D) fluid code solving the most complete system of transport equations and with five-dimensional (three-dimensional in configuration space and 2D in velocity space) Monte Carlo particle following code. At low to high confinement transition conditions, the E⃗r×B⃗ shearing rate is found to be high enough for turbulence suppression even though the field is essentially neoclassical. Here, B⃗ is the magnetic field. No bifurcation of Er is found.

Transport in complex magnetic geometries: 3D modelling of ergodic edge plasmas in fusion experiments

Both stellarators and tokamaks can have quite complex magnetic topologies in the plasma edge. Special complexity is introduced by ergodic effects producing stochastic domains. Conventional numerical methods from fluid dynamics are not applicable in this case. In the present paper, we discuss two alternative possibilities. Our multiple coordinate system approach (MCSA) [Phys. Plasmas 8 (2001) 916] originally developed for the TEXTOR DED allows modelling of plasma transport in general magnetic field structures. The main idea of the concept is: magnetic field lines can exhibit truly stochastic behavior only for large distances (compared to the Kolmogorov length), while for smaller distances, the field remains regular. Thus, one can divide the computational domain into a finite set of sub-domains, introduce local magnetic coordinate systems in each and use an ‘interpolated cell mapping’ technique to switch between the neighboring coordinate systems. A 3D plasma fluid code (E3D, based upon MCSA) is applied to realistic geometries. We also introduce here some new details of the algorithm (stellarator option). The results obtained both for intrinsic (stellarator) and external (tokamak with ergodic divertor) perturbations of the magnetic field are discussed. Another approach, also using local coordinate systems, but based on more conventional finite difference methods, is also under development. Here, we present the outline of the algorithm and discuss its potential as compared to the Lagrangian Monte-Carlo approach.

Role of neutrals in core fueling and pedestal structure in H-mode DIII-D discharges

The 2-D fluid code UEDGE was used to analyze DIII-D experiments to determine the role of neutrals in core fueling, core impurities, and also the H-mode pedestal structure. We compared the effects of divertor closure on the fueling rate and impurity density of high-triangularity, H-mode plasmas. UEDGE simulations indicate that the decrease in both deuterium core fueling (≈15–20%) and core carbon density (≈15–30%) with the closed divertor compared to the open divertor configuration is due to greater divertor screening of neutrals. We also compared UEDGE results with a simple analytic model of the H-mode pedestal structure [Nucl. Fusion 42 (2002) 52]. The model predicts both the width and gradient of the transport barrier in n e as a function of the pedestal density. The more sophisticated UEDGE simulations of H-mode discharges corroborate the simple analytic model, which is consistent with the hypothesis that fueling processes play a role in H-mode transport barrier formation.

Development of Large Scale Fusion Plasma Simulation and Storage Grid on JAERI Origin3800 System.

Under the Numerical EXperiment of Tokamak (NEXT) research project, various fluid, particle, and hybrid codes have been developed. These codes require a computational environment which consists of high performance processors, high speed storage system, and high speed parallelized visualization system. In this paper, the performance of the JAERI Origin3800 system is examined from a point of view of these requests. In the performance tests, it is shown that the representative particle and fluid codes operate with 15˜40% of processing efficiency up to 512 processors. A storage area network (SAN) provides high speed parallel datatransfer. A parallel visualization system enables order of magnitude faster visualization of a large scale simulation data compared with the previous graphic workstations. Accordingly, an extremely advanced simulation environment is realized on the JAERI Origin3800 system. Recently, development of a storage grid is underway in order to improve a computational environment of remote users. The storage grid is constructed by a combination of SAN and a wavelength division multiplexer (WDM). The preliminary tests show that compared with the existing data transfer methods, it enables dramically high speed data transfer ˜100 Gbps over a wide area network.

Modelling of DC Electric Fields Induced by RF Sheath in Front of ICRF Antenna

Reducing the ICRH (ion cyclotron range frequency) antenna-plasma interaction is one of the key points for reaching very long tokamak discharges. One problem which limits such discharges, is the appearance of hot spots on the surface of the antenna: Radio Frequency (RF) sheaths modify the properties of the edge plasma by rectifying the RF potential along open magnetic field lines and can induce hot spots. This paper investigates the corrections to sheath potentials introduced by the interactions between adjacent flux tubes. Our theoretical study started from an oscillating double Langmuir probe model, in which a transverse influx of current was included. This model was confronted with 1D PIC simulations along a magnetic field line, and demonstrated that current exchanges can decrease mean potentials. A 2D electrostatic fluid code was then developed, which couples adjacent flux tubes in a poloidal cross section with collisional conductivity or polarization currents. It showed that transverse currents are able to smooth structures smaller than a characteristic size in the sheath potential maps (results for Tore Supra). These computed rectified potentials can be used to obtain the DC electric fields in front of the antenna. And then, it gives an estimate of the particle drift and the energy flux on the antenna structure, which can explain hot spots.

Fluid modeling of the laser ablation depth as a function of the pulse duration for conductors.

Laser ablation of an aluminum target as a function of the pulse duration, for fluences up to 30 J/cm(2) and a wavelength of 0.8 microm, is investigated by means of a fluid code. For a given fluence, the ablation depth shows a minimum for a pulse duration of approximately 10 ps between a maximum obtained for pulses shorter than approximately 1 ps and a lower maximum obtained for pulses in the nanosecond range, in qualitative agreement with published experimental results. The decrease in ablation depth with increase in pulse duration observed between 1 and 10 ps results from the reduced temperature rise near the surface due to increased inward heat transport. The increase in the ablation depth above approximately 10 ps is due to the increase in electron density gradient length while the laser pulse intensity is close to maximum, which thus enables the plasma to absorb more of the laser pulse energy for increased ablation.

Global numerical study of electron temperature gradient-driven turbulence and transport scaling

A three-dimensional, electromagnetic, fluid code with flux boundaries conditions is used to study the scaling of electron thermal transport caused by electron temperature gradient-driven (ETG) turbulence. It is found that close to the ETG threshold, the thermal transport depends weakly on β, which differs from the heuristic formula χe∝1/β. It is shown also that electron thermal losses scale like gyro-Bohm. The observed electron temperature profiles appear more resilient than the ion temperature profiles obtained from previous ITG simulations in similar conditions.

Progress in ergodic divertor operation on Tore Supra

Upgrade of the Tore Supra ergodic divertor (ED) has led to significant progress in ED physics. Pulse durations of 30 s with LHCD have been achieved demonstrating the heat exhaust capability of both the actively cooled technology at hand and of this specific divertor concept. The disruptive limit governed by the stochastization of the outer magnetic surfaces is found to occur for a value of the Chirikov parameter reaching two on the magnetic surface q = 2+(3/12). This experimentally observed robustness allows one to operate at very low safety factor on the separatrix (q∼2). Numerical analysis of ballooning turbulence in a stochastic layer indicates that the decay of the density fluctuations is associated with an increase of the fluctuating electric drift velocity. This results in an enhanced cross-field transport in the vicinity of the target plates. This lowering of confinement appears to be compensated by an intrinsic transport barrier on the electron temperature. The three-dimensional response of the temperature field is computed with a fluid code. The code can recover the intrinsic transport barrier at the separatrix, reported experimentally, together with small amplitude temperature modulations in the divertor volume. Experimental evidence for the three density regimes (linear, high recycling and detachment) is reported. The low critical density values for transitions between these regimes indicate that similar parallel physics governs the axisymmetric and ED, despite the open configuration of the latter. Measurement and understanding of these density regimes provide a means for feedback control of plasma density and an improvement in ion cyclotron radiofrequency heating coupling scenarios. Experimental data also indicated that particle control with the vented target plates is effective. Increase of both impurity control and radiation efficiency are reviewed. Global power balance has been analysed in order to account for non-axisymmetric radiation. These results, taken together, confirm the large radiation capability of the ED.

General treatment of the interplay between fluid and radiative transportphenomena in symmetric plasmas: the sulphur lamp as a case study

A general ray-trace method for calculating the effects of radiativetransfer in a control volume (CV) fluid code is presented. The method makes useof the structured CV grid of the fluid code, and is suited forgeometries with a point or axis of symmetry. In particular, the specificequations for spherical and cylindrical (without z dependence)configurations are developed. The application of this method to localthermal equilibrium (LTE) and non-LTE plasma models is discussed. Variousopportunities for sacrificing precision for calculation speed are pointedout.As a case study, the effects of radiative transfer in a sulphur lamp arecalculated. Since an LTE description of the molecular radiation yields acomputed spectrum that differs significantly from a measured one, thepossibility of a non-LTE vibrational distribution of the radiating S2-Bstate is investigated. The results indicate that the vibrationalpopulations may be inversed.

Three‐dimensional global MHD simulation code for the Earth's magnetosphere using HPF/JA

AbstractWe have translated a three‐dimensional magnetohydrodynamic (MHD) simulation code of the Earth's magnetosphere from VPP Fortran to HPF/JA on the Fujitsu VPP5000/56 vector‐parallel supercomputer and the MHD code was fully vectorized and fully parallelized in VPP Fortran. The entire performance and capability of the HPF MHD code could be shown to be almost comparable to that of VPP Fortran. A three‐dimensional global MHD simulation of the Earth's magnetosphere was performed at a speed of over 400 Gflops with an efficiency of 76.5% using 56 processing elements of the Fujitsu VPP5000/56 in vector and parallel computation that permitted comparison with catalog values. We have concluded that fluid and MHD codes that are fully vectorized and fully parallelized in VPP Fortran can be translated with relative ease to HPF/JA, and a code in HPF/JA may be expected to perform comparably to the same code written in VPP Fortran. Copyright © 2002 John Wiley & Sons, Ltd.