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Reentry plasma sheath diagnostic plays extremely important roles in the research of the blackout problem. In this paper, a broadband microwave reflectometer based on the invariant point of reflection data has been designed and developed for the reentry plasma sheath diagnostic. The invariant point Y(ωp, 1) is derivable from the broadband reflection data. The electron density and collision frequency are measured simultaneously. The diagnostic algorithm was verified by the simulation analysis and diagnostic experiment. The algorithm has low computational complexity and relatively high precision. This algorithm offers a certain reference value for the plasma sheath diagnostic of reentry vehicles or hypersonic vehicles in the future. Especially, the design of broadband VVD antenna with heat-resistant wave-transparent composites has certain practical values. [ABSTRACT FROM AUTHOR]

Many high power electronic devices operate in a regime where the current they draw is limited by the self-fields of the particles. This space charge limited current poses particular challenges for numerical modeling where common techniques like over-emission or Gauss' Law are computationally inefficient or produce nonphysical effects. In this paper, we show an algorithm using the value of the electric field in front of the surface instead of attempting to zero the field at the surface, making the algorithm particularly well suited to both electromagnetic and parallel implementations of the particle-in-cell algorithm. We show how the algorithm is self-consistent within the framework of finite difference (for both electrostatics and electromagnetics). We show several 1D and 2D benchmarks against both theory and previous computational results. Finally, we show the application in 3D to high power microwave generation in a 13 GHz magnetically insulated line oscillator. [ABSTRACT FROM AUTHOR]

This paper discusses the modeling of experiments that measure iron opacity in local thermodynamic equilibrium (LTE) using laser-driven hohlraums at the National Ignition Facility (NIF). A previous set of experiments fielded at Sandia's Z facility [Bailey et al., Nature 517, 56 (2015)] have shown up to factors of two discrepancies between the theory and experiment, casting doubt on the validity of the opacity models. The purpose of the new experiments is to make corroborating measurements at the same densities and temperatures, with the initial measurements made at a temperature of 160 eV and an electron density of 0.7 × 1022 cm−3. The X-ray hot spots of a laser-driven hohlraum are not in LTE, and the iron must be shielded from a direct line-of-sight to obtain the data [Perry et al., Phys. Rev. B 54, 5617 (1996)]. This shielding is provided either with the internal structure (e.g., baffles) or external wall shapes that divide the hohlraum into a laser-heated portion and an LTE portion. In contrast, most inertial confinement fusion hohlraums are simple cylinders lacking complex gold walls, and the design codes are not typically applied to targets like those for the opacity experiments. We will discuss the initial basis for the modeling using LASNEX, and the subsequent modeling of five different hohlraum geometries that have been fielded on the NIF to date. This includes a comparison of calculated and measured radiation temperatures. [ABSTRACT FROM AUTHOR]

The simplified δf mixed-variable/pullback electromagnetic simulation algorithm implemented in XGC for core plasma simulations by Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total-f electromagnetic algorithm that can include, for the first time, the boundary plasma in diverted magnetic geometry with neutral particle recycling, turbulence, and neoclassical physics. The δf mixed-variable/pullback electromagnetic implementation is based on the pioneering work by Kleiber and Mischenko et al. [Kleiber et al., Phys. Plasmas 23, 032501 (2016); Mishchenko et al., Comput. Phys. Commun. 238, 194 (2019)]. An electromagnetic demonstration simulation is performed in a DIII-D-like, H-mode boundary plasma, including a corresponding comparative electrostatic simulation, which confirms that the electromagnetic simulation is necessary for a higher fidelity understanding of the electron particle and heat transport even at the low-β pedestal foot in the vicinity of the magnetic separatrix. [ABSTRACT FROM AUTHOR]

More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions. [ABSTRACT FROM AUTHOR]

We propose a multi-particle self-consistent Hamiltonian (derived from an N-body description) that is applicable for periodic structures, such as traveling-wave tubes (TWTs), gyrotrons, free-electron lasers, or particle accelerators. We build a one-dimension symplectic multi-particle algorithm to simulate the nonlinear wave–particle interaction in the time domain occurring in an experimental 3-m-long helix TWT. Our algorithm is efficient thanks to a drastic reduction model. A 3D helix version of our reduction model is provided. Finally, we establish an explicit expression of the electromagnetic power in the time domain and in non-monochromatic (non-"continuous waveform") regime. [ABSTRACT FROM AUTHOR]

The electric field at the surface of a curved emitter is necessary to calculate the field emission current. For smooth parabolic emitting tips where space charge is negligible, variation of the electric field at the surface is known to follow the generalized cosine law. Here, we investigate the validity of the cosine law in the regime, where space charge due to emitted electrons is important. Particle-in-cell (PIC) simulations with an emission algorithm based on the cosine law are employed for this study. It is shown that if EP and EL be the field at the apex of tip with and without space charge, respectively, then for ϑ = E P / E L ≥ 0.9 , the average relative deviation of the electric field from the cosine law is less than 3% over the endcap. Thus, an emission scheme based on the cosine law may be used in PIC simulations of field emission of electrons from curved emitter tips in the weak space charge regime. The relation between ϑ and normalized current ζ for curved emitters in this regime is also investigated. A linear relation, ϑ = 1 − δ ζ (where δ is a constant), similar to that obtained theoretically for flat emitting surfaces is observed, but the value of δ indicates that the extension of the theory for curved emitters may require incorporation of the field enhancement factor. [ABSTRACT FROM AUTHOR]

Upon inclusion of collisions, the speed-limited particle-in-cell (SLPIC) simulation method successfully computed the Paschen curve for argon. The 1D3V simulations modeled an electron cascade across an argon-filled capacitor, including electron-neutral ionization, electron-neutral elastic collisions, electron-neutral excitation, and ion-induced secondary electron emission. In electrical breakdown, the timescale difference between ion and electron motion makes traditional PIC methods computationally slow. To decrease this timescale difference and speed up computation, we used SLPIC, a time-domain algorithm that limits the speed of the fastest electrons in the simulation. The SLPIC algorithm facilitates a straightforward, fully kinetic treatment of dynamics and collisions. SLPIC was as accurate as PIC, but ran up to 200 times faster. SLPIC accurately computed the Paschen curve for argon over three orders of magnitude in pressure. [ABSTRACT FROM AUTHOR]

In this paper, we study the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein bracket. We develop Hamiltonian particle-in-cell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semi-discrete system that possesses a discrete non-canonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nedelec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semi-discrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structure-preserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time. [ABSTRACT FROM AUTHOR]

A numerical algorithm is developed and tested that implements the kinetic treatment of electromagnetic radiation propagating through plasmas whose properties have small scale fluctuations, which was developed in a companion paper. This method incorporates the effects of refraction, damping, mode structure, and other aspects of large-scale propagation of electromagnetic waves on the distribution function of quanta in position and wave vector, with small-scale effects of nonuniformities, including scattering and mode conversion approximated as causing drift and diffusion in wave vector. Numerical solution of the kinetic equation yields the distribution function of radiation quanta in space, time, and wave vector. Simulations verify the convergence, accuracy, and speed of the methods used to treat each term in the equation. The simulations also illustrate the main physical effects and place the results in a form that can be used in future applications. [ABSTRACT FROM AUTHOR]

Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets. [ABSTRACT FROM AUTHOR]

The 1953 publication, “Equation of State Calculations by Very Fast Computing Machines” by N. Metropolis, A. W. Rosenbluth and M. N. Rosenbluth, and M. Teller and E. Teller [J. Chem. Phys. 21, 1087 (1953)] marked the beginning of the use of the Monte Carlo method for solving problems in the physical sciences. The method described in this publication subsequently became known as the Metropolis algorithm, undoubtedly the most famous and most widely used Monte Carlo algorithm ever published. As none of the authors made subsequent use of the algorithm, they became unknown to the large simulation physics community that grew from this publication and their roles in its development became the subject of mystery and legend. At a conference marking the 50th anniversary of the 1953 publication, Marshall Rosenbluth gave his recollections of the algorithm’s development. The present paper describes the algorithm, reconstructs the historical context in which it was developed, and summarizes Marshall’s recollections. [ABSTRACT FROM AUTHOR]

Two schemes for coupling gyrokinetic simulations of microturbulence in tokamaks are proposed. The first scheme is based on an additive Schwarz domain decomposition. We show that, because the goal of turbulence is long-time averages of the dynamics rather than temporal accuracy, the iteration to self-consistency across domains, which is typically required by Schwarz schemes, can be avoided, thereby accelerating the computation. Second, we propose a coupling scheme that relies entirely on the addition of source terms, leaving the boundary conditions arbitrary. The practical motivations for such a scheme are discussed, and forms of the source terms that ensure consistency and stability are derived. The schemes are tested on a nonlinear, one-dimensional model problem, and the first scheme is further tested on the Hasegawa–Wakatani model. [ABSTRACT FROM AUTHOR]

Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times. [ABSTRACT FROM AUTHOR]

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations. [ABSTRACT FROM AUTHOR]

When applying the standard δf particle-in-cell simulation method to simulate linear and nonlinear collective instabilities with coherent structures, wave-particle interaction may result in large weight growth for resonant or nearly resonant simulation particles. In this paper, we demonstrate that the large noise associated with the large weight of nearly resonant simulation particles can produce significant error fields at the nonlinear stage of the instability. To overcome this deleterious effect, we have developed a modified δf method that contains a smooth switching algorithm between the δf and total-f methods. Before the switch, the simulation effectively makes use of the desirable low-noise feature of the δf method for small weight to accurately follow unstable mode structures. When the weight function becomes large during the nonlinear phase, the low-noise advantage of the δf method ceases to be significant and the simulation is switched to the total-f method to avoid the large noise induced by nearly resonant simulation particles. This algorithm has been successfully applied to simulation studies of the electrostatic Harris instability driven by large temperature anisotropy in high-intensity charged particle beams typical of applications in high current accelerators, including high-energy density physics and heavy ion fusion. [ABSTRACT FROM AUTHOR]

It has long been acknowledged that the well known and frequently used stability criterion βp<0.3 for the toroidal ideal magnetohydrodynamic internal kink mode in a tokamak is inaccurate for an empirically relevant safety factor. The present paper outlines the severity of the usual approximation, and presents improved analytical approximations of the general solution in M. N. Bussac, R. Pellat, D. Edery, and J. L. Soulé, Phys. Rev. Lett. 35, 1638 (1975), thus providing new insights into the nature of the instability, together with simple formulas that can be incorporated into transport codes with sawtooth cycle algorithms. [ABSTRACT FROM AUTHOR]

In this paper, algorithms for the solution of two-fluid plasma equations are presented and applied to the study of field-reversed configurations (FRCs). The two-fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia, charge separation, and the full electromagnetic field equations, and it allows for separate electron and ion motion. The algorithm presented is the high-resolution wave propagation scheme. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. The algorithms are benchmarked against the Geospace Environmental Modeling Reconnection Challenge problem. Equilibrium of FRC is studied. It is shown that starting from a MHD equilibrium produces a relaxed two-fluid equilibrium with strong flows at the FRC edges due to diamagnetic drift. The azimuthal electron flow causes lower-hybrid drift instabilities (LHDI), which can be captured if the ion gyroradius is well resolved. The LHDI is known to be a possible source of anomalous resistivity in many plasma configurations. LHDI simulations are performed in slab geometries and are compared to recent experimental results. [ABSTRACT FROM AUTHOR]

Kinetic plasma simulation typically requires to handle a multiplicity of space and time scales. The implicit moment particle in cell (PIC) method provides a possible route to address the presence of multiple scales effectively. Here, a new implementation of the implicit moment method is described. The present paper has two goals. First, the most modern implementation of the implicit moment method is described. While many of the algorithms involved have been developed in the past, the present paper reports for the first time how the implicit moment method is currently implemented and what specific algorithms have been found to work best. Second, we present the CELESTE3D code, a fully electromagnetic and fully kinetic PIC code, based on the implicit moment method. The code has been in use for a number of years but no previous complete description of its implementation has been provided. The present work fills this gap and introduces a number of new methods not previously presented: a new implementation of the Maxwell solver and a new particle mover based on a Newton-Krylov nonlinear solver for the discretized Newton’s equations. A number of benchmarks of CELESTE3D are presented to shown the typical application and to investigate the improvements introduced by the new solver and the new mover. [ABSTRACT FROM AUTHOR]

Large-amplitude, intermittent fluctuations are ubiquitous in the boundary region of magnetically confined plasmas and lead to detrimental plasma-wall interactions in next-generation, high duty cycle fusion power experiments. Using gas puff imaging data time series from the scrape-off layer in the Alcator C-Mod device, it is here demonstrated that the large-amplitude fluctuations can be described as a super-position of pulses with a fixed shape and a constant duration. By applying a new deconvolution algorithm on the data time series with a two-sided exponential pulse function, the arrival times and amplitudes of the pulses can be estimated, and the measurement time series can be reconstructed with high accuracy. The pulse amplitudes are shown to follow an exponential distribution. The waiting times between pulses are uncorrelated, their distribution has an exponential tail, and the number of arrivals is a linear function of time. This demonstrates that pulse arrivals follow a homogeneous Poisson process. Identical statistical properties apply to both ohmic and high confinement mode plasmas, clearly demonstrating the universality of the fluctuation statistics in the boundary region of Alcator C-Mod. [ABSTRACT FROM AUTHOR]

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem “degenerate variational integration.” Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms. [ABSTRACT FROM AUTHOR]

We present a numerical model and a set of conservative algorithms for Non-Maxwellian plasma kinetics with inelastic collisions. These algorithms self-consistently solve for the time evolution of an isotropic electron energy distribution function interacting with an atomic state distribution function of an arbitrary number of levels through collisional excitation, deexcitation, as well as ionization and recombination. Electron-electron collisions, responsible for thermalization of the electron distribution, are also included in the model. The proposed algorithms guarantee mass/charge and energy conservation in a single step, and is applied to the case of non-uniform gridding of the energy axis in the phase space of the electron distribution function. Numerical test cases are shown to demonstrate the accuracy of the method and its conservation properties. [ABSTRACT FROM AUTHOR]

Quasineutral particle-in-cell models of ions must fulfill the kinetic Bohm criterion, in its inequality form, at the domain boundary in order to match correctly with solutions of the Debye sheaths tied to the walls. The simple, fluid form of the Bohm criterion is shown to be a bad approximation of the exact, kinetic form when the ion velocity distribution function has a significant dispersion and involves different charge numbers. The fulfillment of the Bohm criterion is measured by a weighting algorithm at the boundary, but linear weighting algorithms have difficulties to reproduce the nonlinear behavior around the sheath edge. A surface weighting algorithm with an extended temporal weighting is proposed and shown to behave better than the standard volumetric weighting. Still, this must be supplemented by a forcing algorithm of the kinetic Bohm criterion. This postulates a small potential fall in a supplementary, thin, transition layer. The electron-wall interaction is shown to be of little relevance in the fulfillment of the Bohm criterion. [ABSTRACT FROM AUTHOR]

The properties of Bishop-Taylor equilibria and the algorithm of their calculations, implemented into numerical code Cbbsh, are described. These equilibria are unique in having the shape of magnetic surfaces not dependent on the poloidal flux distribution, which, in its turn, determines both the current and pressure profiles in this case. These equilibria can be calculated with any precision, using only 3 ordinary differential equations. Possessing a free profile, they can be used for calibrating equilibrium and stability codes. They are also especially valuable for equilibrium reconstruction as a precise example of a configuration where the external magnetic field does not depend on the current density. [ABSTRACT FROM AUTHOR]

A new method to implement low-noise collision operators in particle-in-cell simulations is presented. The method is based on the fact that relevant collision operators can be included naturally in the Lagrangian formulation that exemplifies the particle-in-cell simulation method. Numerical simulations show that the momentum and energy conservation properties of the simulated plasma associated with the low-noise collision operator are improved as compared with standard collision algorithms based on random numbers. [ABSTRACT FROM AUTHOR]

The self-adapting algorithms are improved to optimize a beam configuration in the direct drive laser fusion system with the solid state lasers. A configuration of 32 laser beams is proposed for achieving a high uniformity illumination, with a root-mean-square deviation at 10-4 level. In our optimization, the parameters such as beam number, beam arrangement, and beam intensity profile are taken into account. The illumination uniformity robustness versus the parameters such as intensity profile deviations, power imbalance, intensity profile noise, the pointing error, and the target position error is also discussed. In this study, the model is assumed a solid-sphere illumination, and refraction effects of incident light on the corona are not considered. Our results may have a potential application in the design of the direct-drive laser fusion of the Shen Guang-II Upgrading facility (SG-II-U, China). [ABSTRACT FROM AUTHOR]

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte- Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted- Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms. [ABSTRACT FROM AUTHOR]

Ion cyclotron range of frequency (ICRF) heating is foreseen as an integral component of the initial ITER operation. The status of ICRF preparations for ITER and supporting research were updated in the 2007 [Gormezano et al., Nucl. Fusion 47, S285 (2007)] report on the ITER physics basis. In this report, we summarize progress made toward the successful application of ICRF power on ITER since that time. Significant advances have been made in support of the technical design by development of new techniques for arc protection, new algorithms for tuning and matching, carrying out experimental tests of more ITER like antennas and demonstration on mockups that the design assumptions are correct. In addition, new applications of the ICRF system, beyond just bulk heating, have been proposed and explored. [ABSTRACT FROM AUTHOR]

We derive an equation for energy transfer from relativistic charged particles to a cold background plasma appropriate for finite-size particles that are used in particle-in-cell simulation codes. Expressions for one-, two-, and three-dimensional particles are presented, with special attention given to the two-dimensional case. This energy transfer is due to the electric field of the wake set up in the background plasma by the relativistic particle. The enhanced stopping is dependent on the q2/m, where q is the charge and m is the mass of the relativistic particle, and therefore simulation macro-particles with large charge but identical q/m will stop more rapidly. The stopping power also depends on the effective particle shape of the macro-particle. These conclusions are verified in particle-in-cell simulations. We present 2D simulations of test particles, relaxation of high-energy tails, and integrated fast ignition simulations showing that the enhanced drag on macro-particles may adversely affect the results of these simulations in a wide range of high-energy density plasma scenarios. We also describe a particle splitting algorithm which can potentially overcome this problem and show its effect in controlling the stopping of macro-particles. [ABSTRACT FROM AUTHOR]

A previous publication [R. V. Bravenec et al., Phys. Plasmas 18, 122505 (2011)] presented favorable comparisons of linear frequencies and nonlinear fluxes from the Eulerian gyrokinetic codes gyro [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and gs2 [W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)]. The motivation was to verify the codes, i.e., demonstrate that they correctly solve the gyrokinetic-Maxwell equations. The premise was that it is highly unlikely for both codes to yield the same incorrect results. In this work, we add the Lagrangian particle-in-cell code gem [Y. Chen and S. Parker, J. Comput. Phys. 220, 839 (2007)] to the comparisons, not simply to add another code, but also to demonstrate that the codes' algorithms do not matter. We find good agreement of gem with gyro and gs2 for the plasma conditions considered earlier, thus establishing confidence that the codes are verified and that ongoing validation efforts for these plasma parameters are warranted. [ABSTRACT FROM AUTHOR]

We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k∥/k⊥<1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length LTi0, instability requires that either k⊥ρi or ρi/LTi0 be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the complex eigenvalue ω=ωr+iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid kinetic δf code that assumes six-dimensional Vlasov ions and isothermal fluid electrons, as functions of k⊥ρi and ρi/LTi0 using a spatially dependent equilibrium. These solutions are compared with each other, and with the predictions of the local kinetic and fluid dispersion relations. Kinetic and fluid calculations agree well at and near the marginal stability point, but diverge as k⊥ρi or ρi/LTi0 increases. There is good qualitative agreement between the models for the shape of the unstable global eigenfunction for LTi0/ρi=30 and 20. The results quantify how far fluid calculations can be extended accurately into the kinetic regime. We conclude that for the linear ITG problem in slab geometry with unsheared magnetic field when k∥/k⊥<1, the extended MHD model may be a reliable physical model for this problem when ρi/LTi0<10-2 and k⊥ρi<0.2. [ABSTRACT FROM AUTHOR]

A multi-hierarchy simulation model aimed at magnetic reconnection studies has been developed, in which macroscopic and microscopic physics are solved self-consistently and simultaneously. In this work, the previous multi-hierarchy model by these authors is extended to a more realistic one with non-uniform space grids. Based on the domain decomposition method, the multi-hierarchy model consists of three parts: a magnetohydrodynamics algorithm to express the macroscopic global dynamics, a particle-in-cell algorithm to describe the microscopic kinetic physics, and an interface algorithm to interlock macro and micro hierarchies. For its verification, plasma flow injection is simulated in this multi-hierarchy model and it is confirmed that the interlocking method can describe the correct physics. Furthermore, this model is applied to collisionless driven reconnection in an open system. Magnetic reconnection is found to occur in a micro hierarchy by injecting plasma from a macro hierarchy. [ABSTRACT FROM AUTHOR]

An improved Monte Carlo collisional scheme modeling both elastic and inelastic interactions has been implemented into the particle-in-cell code CALDER [E. Lefebvre et al., Nucl. Fusion 43, 629 (2003)]. Based on the technique proposed by Nanbu and Yonemura [J. Comput. Phys. 145, 639 (1998)] allowing to handle arbitrarily weighted macro-particles, this binary collision scheme uses a more compact and accurate relativistic formulation than the algorithm recently worked out by Sentoku and Kemp [J. Comput. Phys. 227, 6846 (2008)]. Our scheme is validated through several test cases, demonstrating, in particular, its capability of modeling the electrical resistivity and stopping power of a solid-density plasma over a broad parameter range. A relativistic collisional ionization scheme is developed within the same framework, and tested in several physical scenarios. Finally, our scheme is applied in a set of integrated particle-in-cell simulations of laser-driven fast electron transport. [ABSTRACT FROM AUTHOR]

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t→0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the 'antisymmetric discretization gauge,' in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law [J. Squire, H. Qin, and W. Tang (to be published)]. [ABSTRACT FROM AUTHOR]

A general method for deriving electromagnetic particle in cell (EMPIC) algorithms has been given by Eastwood [Comput. Phys. Commun. 64, 252 (1991)]. This method devises variation of the action-integral to find discrete governing equations. The most important advantage of this method is automatic inclusion of the time coordinate via the action integral into the computational domain. This inclusion is inevitable because electromagnetic algorithms are based on time evolution of the system from its initial state. The drawback of this method is that it is rather abstract. This causes obscurity of particle-mesh interactions and makes it hard to analyze physical treatments of the computational model. This analysis is crucial both for finding error sources and for conformity of the computational model with the actual physical system. Errors are responsible for unphysical heating and/or cooling of the plasma. We have obtained EMPIC algorithms based on an objective model. This model consists of the shaped charged-particles. The particle shape has explicit time dependence as well as space dependence. Discrete field equations are obtained by appropriate integration of the actual continuous equations over a time-space mesh. The method of particle source assignment into the mesh has been derived by implying particle-charge conservation. The interaction of the shaped particles with self-consistent fields is briefly discussed. The effects of computational errors in unphysical behaviors of the system are studied. To show how theoretical results appear in application, results of a 2D PIC code in simulation of free expansion of collisionless plasma into a vacuum are presented. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional complex (dusty) plasma crystal excited by an electrostatically-induced shock wave. Dust particle kinematics in such a system are usually determined using particle tracking velocimetry. In this work we present a particle tracking algorithm which determines the dust particle kinematics with significantly higher accuracy than particle tracking velocimetry. The algorithm uses multiple extended Kalman filters to estimate the particle states and an interacting multiple model to assign probabilities to the different filters. This enables the determination of relevant physical properties of the dust, such as kinetic energy and kinetic temperature, with high precision. We use a Hugoniot shock-jump relation to calculate a pressure-volume diagram from the shocked dust kinematics. Calculation of the full pressure-volume diagram was possible with our tracking algorithm, but not with particle tracking velocimetry. [ABSTRACT FROM AUTHOR]

We describe a new particle-based two-fluid fully electromagnetic algorithm suitable for modeling high density (ni ∼ 1017 cm-3) and high Mach number laboratory plasma jets. In this parameter regime, traditional particle-in-cell (PIC) techniques are challenging due to electron timescale and lengthscale constraints. In this new approach, an implicit field solve allows the use of large timesteps while an Eulerian particle remap procedure allows simulations to be run with very few particles per cell. Hall physics and charge separation effects are included self-consistently. A detailed equation of state (EOS) model is used to evolve the ion charge state and introduce non-ideal gas behavior. Electron cooling due to radiation emission is included in the model as well. We demonstrate the use of these new algorithms in 1D and 2D Cartesian simulations of railgun (parallel plate) jet accelerators using He and Ar gases. The inclusion of EOS and radiation physics reduces the electron temperature, resulting in higher calculated jet Mach numbers in the simulations. We also introduce a surface physics model for jet accelerators in which a frictional drag along the walls leads to axial spreading of the emerging jet. The simulations demonstrate that high Mach number jets can be produced by railgun accelerators for a variety of applications, including high energy density physics experiments. [ABSTRACT FROM AUTHOR]

Axisymmetric equilibrium of a magnetically confined plasma with multiple ion species is considered. To describe hot plasmas with isothermal surfaces, we adopt a formulation consistent with zero poloidal ion flow. This formulation includes all magnetic field components and also correctly includes all effects of toroidal ion rotation. There are two free surface functions for each species and a third which is determined by a differential equation relating surface functions per species. We have developed and implemented an algorithm for the solution of the resulting nonlinear equations and found solutions with large charge and mass contrast among the ion species for both compact (r = 0 included) and annular (r = 0 excluded) domains. Our solution method allows for arbitrary domain shapes, includes far-field conditions, and treats any combination of electrically conducting or insulating walls. Appropriate surface functions are used to describe the transition from closed to open field plasma in a reasonable manner. Solutions for advanced fuel cycle fusion systems (both D-3He and p-11B) are presented to illustrate the power of the method. Finally, we briefly discuss the special issues associated with obtaining very elongated solutions and describe the algorithm for implementing these features. [ABSTRACT FROM AUTHOR]

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately calculate the particles'orbits for an arbitrary long simulating time with good conservation property. When a time-independent convection and corotation electric field is considered, the VSI method can give the accurate single particle orbit, while the RK4 method gives an incorrect orbit due to its intrinsic error accumulation over a long integrating time. [ABSTRACT FROM AUTHOR]

The influence of binary Coulomb collisions on trapped particle nonlinearities related to stimulated Raman scatter (SRS) in a single laser speckle is examined using one-dimensional particle-in-cell simulations. Binary Coulomb collisions are incorporated using a numerical particle-pairing algorithm that reproduces a collision integral of the Landau form. The onset of nonlinearly enhanced levels of SRS reflectivity is shown to coincide with electron trapping in the daughter plasma wave and is sensitive to the collisional scattering rate. Relaxation of trapping-induced perturbations to the electron velocity distribution via collisional velocity space diffusion is predicted to have the largest effect on the onset of SRS when the amplitude of the daughter plasma wave is smallest, and trapping-induced perturbations to the electron velocity distribution function are also small. In the absence of higher dimensional detrapping mechanisms (e.g., electron side-loss), it is shown that the onset threshold for enhanced SRS reflectivity is determined predominantly by the parallel diffusion of trapped electrons scattering from bulk thermal electrons, and that for the conditions studied here, the contribution to detrapping from perpendicular diffusion is non-negligible. Additionally, inverse bremsstrahlung heating of the bulk electrons is shown to shift the daughter plasma wave spectrum upward along the Stoke's resonance to larger wave frequency and smaller wave number, changing the linear parametric coupling conditions to SRS backscatter as a function of time. The reduction in SRS reflectivity from binary Coulomb collisions is greatest for laser intensities near the collisionless onset threshold, ulimately leading to an increase in the onset threshold laser intensity for enhanced SRS reflectivity in the kinetic regime. [ABSTRACT FROM AUTHOR]

A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a 'source-correction' term to be defined, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria. [ABSTRACT FROM AUTHOR]

Magnetized jets are important features of many systems of physical interest. To date, most interest has focused on solar and space physics and astrophysical applications, and hence the unbounded magnetized jet, and its cousin, the unbounded magnetized wake, have received the most attention. This work presents calculations of a bounded, magnetized jet for a laboratory experiments in the Helimak device [K. W. Gentle and H. He, Plasma Sci. Technol. 10, 284 (2008)]. The Helimak device has a toroidal magnetic field with a controlled velocity flow that represents jets in bounded systems. Experimental and theoretical features include three spatial dimensions, the inclusion of resistivity and viscosity, and the presence of no-slip walls. The results of the linearized model are computed with a Chebyshev-τ algorithm. The bounding walls stabilize the ideal varicose mode found in unbounded magnetized jets. The ideal sinuous mode persists in the bounded system. A comparison theorem is proved showing that two-dimensional modes are more unstable than the corresponding three-dimensional modes for any given set of system parameters. This result is a generalization of the hydrodynamic Squires theorem. An energy-stress theorem indicates that the Maxwell stress is crucial for the growth of the instability. The results of the analysis are consistent with the observed plasma fluctuations with in the limits of using a simple model for the more complex measured jet velocity flow profile. The working gas is singly ionized argon and the jet velocity profile is accurately measured with Doppler shift spectroscopy. [ABSTRACT FROM AUTHOR]

An implicitly charge-conserving algorithm has been developed for solving the nonlinear Poisson equation that results from the use of Boltzmann electrons. The new algorithm solves for the Boltzmann density parameter and, in the case of a Neumann boundary condition, the surface-charge density, simultaneously as it solves for the discretized electrostatic potential. Numerical stability is demonstrated for time steps exceeding the electron plasma period and spatial resolutions much coarser than the Debye length. [ABSTRACT FROM AUTHOR]

The theory of variances of equilibrium reconstruction is presented. It complements existing practices with information regarding what kind of plasma characteristics can be reconstructed, how accurately, and what remains beyond the abilities of diagnostic systems. The σ-curves, introduced by the present theory, give a quantitative assessment of quality of effectiveness of diagnostic systems in constraining equilibrium reconstructions. The theory also suggests a method for aligning the accuracy of measurements of different physical nature and for improvements of numerical algorithms used in reconstruction. [ABSTRACT FROM AUTHOR]

Because experiment/model comparisons in magnetic confinement fusion have not yet satisfied the requirements for validation as understood broadly, approaches to validating mathematical models and numerical algorithms are recommended as good practices. Previously identified procedures, such as, verification, qualification, and analysis of errors from uncertainties and deficiencies, remain important. However, particular challenges intrinsic to fusion plasmas and physical measurement therein lead to identification of new or less familiar concepts that are also critical in validation. These include the primacy hierarchy, which tracks the integration of measurable quantities, and sensitivity analysis, which assesses how model output is apportioned to different sources of variation. The use of validation metrics for individual measurements is extended to multiple measurements, with provisions for the primacy hierarchy and sensitivity. This composite validation metric is essential for quantitatively evaluating comparisons with experiments. To mount successful and credible validation in magnetic fusion, a new culture of validation is envisaged. [ABSTRACT FROM AUTHOR]

The gyrokinetic approach for arbitrary frequency dynamics in magnetized plasmas is explored, using the gyrocenter-gauge kinetic theory. Contrary to low-frequency gyrokinetics, which views each particle as a rigid charged ring, arbitrary frequency response of a particle is described by a quickly changing Kruskal ring. This approach allows the separation of gyrocenter and gyrophase responses and thus allows for, in many situations, larger time steps for the gyrocenter push than for the gyrophase push. The gyrophase response which determines the shape of Kruskal rings can be described by a Fourier series in gyrophase for some problems, thus allowing control over the cyclotron harmonics at which the plasma responds. A computational algorithm for particle-in-cell simulation based on this concept has been developed. An example of the ion Bernstein wave is used to illustrate its numerical properties, and comparison with a direct Lorentz-force approach is presented. [ABSTRACT FROM AUTHOR]

Magnetic pickup loops on the vacuum vessel (VV) can provide an abundance of equilibrium information for stellarators. A substantial effort has gone into designing flux loops for the National Compact Stellarator Experiment (NCSX) [Zarnstorff et al., Plasma Phys. Controlled Fusion 43, A237 (2001)], a three-field period quasi-axisymmetric stellarator under construction at the Princeton Plasma Physics Laboratory. The design philosophy, to measure all of the magnetic field distributions normal to the VV that can be measured, has necessitated the development of singular value decomposition algorithms for identifying efficient loop locations. Fields are expected to be predominantly stellarator symmetric (SS)—the symmetry of the machine design—with toroidal mode numbers per torus (n) equal to a multiple of 3 and possessing reflection symmetry in a period. However, plasma instabilities and coil imperfections will generate non-SS fields that must also be diagnosed. The measured symmetric fields will yield important information on the plasma current and pressure profile as well as on the plasma shape. All fields that obey the design symmetries could be measured by placing flux loops in a single half-period of the VV, but accurate resolution of nonsymmetric modes, quantified by the condition number of a matrix, requires repositioning loops to equivalent locations on the full torus. A subarray of loops located along the inside wall of the vertically elongated cross section was designed to detect n=3, m=5 or 6 resonant field perturbations that can cause important islands. Additional subarrays included are continuous in the toroidal and poloidal directions. Loops are also placed at symmetry points of the VV to obtain maximal sensitivity to asymmetric perturbations. Combining results from various calculations which have made extensive use of a database of 2500 free-boundary VMEC equilibria, has led to the choice of 225 flux loops for NCSX, of which 151 have distinct shapes. [ABSTRACT FROM AUTHOR]

Using a newly developed algorithm, the nonlinear transfer of internal fluctuation energy |ñ|2 due to convection of drift-wave turbulence by a geodesic acoustic mode (GAM, a finite-frequency zonal flow) has now been measured directly in a high-temperature plasma. By combining spatially resolved density fluctuation measurements obtained via an upgraded beam emission spectroscopy system in the edge region of the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] with a velocity inference algorithm, the convection of turbulent fluctuations by the GAM has been measured. Taken together, the results strongly suggest that GAM convection of turbulence leads to a transfer of internal fluctuation energy from low to high frequencies, in agreement with expectations from theory and simulation. In addition, the GAM is found to modulate the intensity of the density fluctuations. Calculations of the measured nonlinear interactions in the gyrokinetic code GYRO are found to be in good qualitative agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell’s equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibel instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions. [ABSTRACT FROM AUTHOR]

In ion cyclotron range of frequency experiments, we have simultaneously measured the incident fast wave and the mode converted waves in the mode conversion region in D(3He) plasmas using an upgraded phase contrast imaging diagnostic in the Alcator C-Mod tokamak [I. H. Hutchinson, R. Boivin, F. Bombarida et al., Phys. Plasmas 1, 1511 (1994)]. To experimentally validate the full wave TORIC [M. Brambilla, Nucl. Fusion 38, 1805 (1998)] physics kernel, the simulated power deposition and line integrated perturbed density profiles were compared with experimental profiles and are found to be in remarkably good agreement with the experimentally determined profiles. This suggests the physics model and computation algorithm used in TORIC, particularly for the mode converted waves, model the mode conversion physics well. We also report results from initial mode conversion current drive experiments where the modification of the sawtooth period was clearly observed and was shown to depend on antenna phasing suggesting the presence of a localized driven current. [ABSTRACT FROM AUTHOR]