Arbitrary Plasma Research Articles

Tokamak plasma equilibria with n=1 toroidal asymmetry

A general approach of how to construct plasma equilibrium in a tokamak with n=1 violation of toroidal symmetry is proposed. For an arbitrary axisymmetric tokamak plasma equilibrium, there exists the small n=1 deformation of the initial magnetic configuration that keeps the nesting of the magnetic surfaces (as in the initial configuration) and provides plasma equilibrium; such deformation and final equilibrium configuration are calculated analytically. The asymmetric analogue of the Solov'ev's equilibrium with non-degenerated plasma pressure and current density profiles is presented as an example of the application of the developed algorithm.

Stellarator equilibrium axis-expansion to all orders in distance from the axis for arbitrary plasma beta

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

FLIPEC, an ideal MHD free-boundary axisymmetric equilibrium solver in the presence of macroscopic flows

The most relevant features of FLIPEC (Free fLow Iterative Plasma Equilibrium Code) are presented. This new code iteratively calculates free-boundary, axisymmetric ideal MHD equilibria with arbitrary poloidal and toroidal plasma flows. FLIPEC is a mature code that has emerged from a complete overhaul of a previous version (F-Torija Daza 2022 et al Nucl. Fusion 62 126044). It uses a (inverse) curvilinear coordinate representation for the Grad–Shafranov–Bernoulli equation system, which allows FLIPEC to extend its free-boundary capabilities to arbitrary plasma shapes and removes many limitations with regards to the distance between plasma and external coils. Run-time stabilization of vertical modes has also been implemented by means of artificial feedback coils. Finally, active targeting schemes have also been included. These capabilities are illustrated on two very different cases: the ITER tokamak baseline configuration and a NSTX spherical tokamak equilibrium.

Higher order contribution to ion-acoustic Korteweg–de Vries (KdV) soliton in unmagnetized quantum plasmas with arbitrary degeneracy of electrons

The propagation of nonlinear ion-acoustic Korteweg–de Vries (KdV) solitons and dressed solitons (with higher order contribution term) in unmagnetized quantum plasmas with arbitrary degeneracy of electrons is investigated using quantum hydrodynamic model. The reductive perturbation method is used to derive the first order nonlinear ion-acoustic KdV equation and also higher order contribution of inhomogeneous differential equation is obtained for the dressed ion-acoustic wave soliton in arbitrary degenerate electron plasmas. Moreover, the higher order inhomogeneous differential equation is solved (nonsecular solution is obtained) using the renormalization method. The conditions for the validity of the higher order correction are also discussed in detail for ion-acoustic solitons in unmagnetized arbitrary degenerate electrons plasma case. The effects of chosen values of electron temperature, equilibrium fugacity and corresponding electron density of a physical quantum plasma system and quantum diffraction parameter H (for two conditions i.e., H < 2 or H > 2) on the amplitude and width of the KdV and dressed ion-acoustic wave solitons for both electrostatic potential hump (compressive) or dip (rarefactive) structures are investigated. The numerical plots are also presented for illustration with numerical values of a physical partially degenerate electrons plasma system exist in the astrophysical or laboratory conditions.

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalized kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving the finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, Bϑ/B, it generalizes the drift kinetic theory of Hazeltine [Phys. Plasmas 15, 77 (1973)] to the limit of Bϑ/B∼1 (e.g., to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalized gyrokinetic formalism of Dudkovskaia et al. [Plasma Phys. Controlled Fusion 65, 045010 (2023)], derived specifically to capture neoclassical equilibrium currents in the gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of Dudkovskaia et al. [Nucl. Fusion 63, 016020 (2023)] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. Resolving ρ∼ρϑ (or Bϑ∼B), where ρϑ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

The Effects of Nonequilibrium Velocity Distributions on Alfvén Ion-cyclotron Waves in the Solar Wind

In this work, we investigate how the complex structure found in solar wind proton velocity distribution functions (VDFs), rather than the commonly assumed two-component bi-Maxwellian structure, affects the onset and evolution of parallel-propagating microinstabilities. We use the Arbitrary Linear Plasma Solver, a numerical dispersion solver, to find the real frequencies and growth/damping rates of the Alfvén modes calculated for proton VDFs extracted from Wind spacecraft observations of the solar wind. We compare this wave behavior to that obtained by applying the same procedure to core-and-beam bi-Maxwellian fits of the Wind proton VDFs. We find several significant differences in the plasma waves obtained for the extracted data and bi-Maxwellian fits, including a strong dependence of the growth/damping rate on the shape of the VDF. By applying the quasilinear diffusion operator to these VDFs, we pinpoint resonantly interacting regions in velocity space where differences in VDF structure significantly affect the wave growth and damping rates. This demonstration of the sensitive dependence of Alfvén mode behavior on VDF structure may explain why the Alfvén ion-cyclotron instability thresholds predicted by linear theory for bi-Maxwellian models of solar wind proton background VDFs do not entirely constrain spacecraft observations of solar wind proton VDFs, such as those made by the Wind spacecraft.

A collisional global sheath – Bulk model of argon plasma for semiconductor scale manufacturing

Plasma processes enhance the high-quality, semiconductor fabrication employed in large-scale industries. A crucial element in this process are the many gases that generate different reactive species at low temperatures. Capacitive plasma discharge radio frequency CCPs play a major role in semiconductor scale fabrication. The analysis of nonlinear dynamics in CCPs are complicated even under simple approaches. Therefore, we study self consistent collision fluid model, particle in cell simulation PIC, step approximation and finally the global model to find the accurate solution of merging plasma sheath -bulk region. For this purpose we study the self consistent collisional fluid model to find the accurate charge–voltage distribution V(Q) which controls the nonlinear dynamics of CCPs. The results against the PIC simulations and the more elaborate model step approximation is accomplished with higher accuracy. Consequently, the cubic polynomial formula V(Q) are applied in the global model. Accurate analytical global sheath-bulk calculations of the higher harmonic effect-exhibiting average power distributions, bulk potentials, and currents are obtained. This study provides an effective solution of collision regime for any arbitrary plasma reactor designs, including single-frequency and double frequency CCPs. Moreover, we used the argon gas as a good example in our study for a good ion etching. Finally, we can assist in achieving effective results that are consistent with experimental data and in large-scale applications in the semiconductor sector.

Whistler Waves as a Signature of Converging Magnetic Holes in Space Plasmas

Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA’s Magnetospheric Multiscale Mission enable us to study the particle dynamics in magnetic holes in the Earth’s magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave–particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole converges, a pair of counter-streaming electron beams form near the hole’s center as a consequence of the combined action of betatron and Fermi effects. The beams trigger the generation of slightly oblique whistler waves. Our conceptual prediction is supported by a remarkable agreement between our observations and numerical predictions from the Arbitrary Linear Plasma Solver. Our study shows that wave–particle interactions are fundamental to the evolution of magnetic holes in space and astrophysical plasmas.

Implementation of multi-component Zhdanov closure in SOLEDGE3X

The multi-component fluid closure derived by Zhdanov (2002 Transport Processes in Multicomponent Plasma (London: Taylor and Francis)) is implemented in the fluid code SOLEDGE3X-EIRENE to deal with arbitrary edge plasma composition. The closure assumes no distinction between species such as light versus heavy species separation. The work of Zhdanov is rewritten in a matricial form in order to clearly link friction forces and heat fluxes to the different species velocities and temperature gradients.

Time-resolved study of holeboring in realistic experimental conditions

The evolution of dense plasmas prior to the arrival of the peak of the laser irradiation is critical to understanding relativistic laser plasma interactions. The spectral properties of a reflected laser pulse after the interaction with a plasma can be used to gain insights about the interaction itself, whereas the effect of holeboring has a predominant role. Here we developed an analytical model, describing the non-relativistic temporal evolution of the holeboring velocity in the presence of an arbitrary overdense plasma density and laser intensity profile. We verify this using two-dimensional particle-in-cell simulations, showing a major influence on the holeboring dynamic depending on the density profile. The influence on the reflected laser pulse has been verified during an experiment at the PHELIX laser. We show that this enables the possibility to determine the sub-micrometer scale length of the preplasma by measuring the maximum holeboring velocity and acceleration during the laser-plasma interaction.

Analytical approach to predict the particle exhausts for arbitrary DEMO divertor configurations

The pumping efficiency, defined as the capability of neutral particles to be exhausted into the pumping system can be assessed analytically based on particle balance requirements valid for arbitrary divertor configurations and plasma performances of fusion reactor. It is shown that the pumping efficiency depends mainly on the ratio of the surface area bounding the divertor plenum from the SOL to the surface at the entrance to the pumping port, on the conductance of the pumping ports and the type of neutrals (atoms, molecules). By varying these parameters the pumping features of SN and SF divertor configurations is assessed. The analytical model can be used for checking the consistency of boundary conditions used in existing numerical codes such as DIVGAS with the necessity to pump out a required particle throughput at given conductance of the divertor port.

Quantum Faraday excitations in degenerate electron-ion plasma

A hydrodynamic two-fluid model encompassing inertialess electrons of arbitrary degree of degeneracy and cold ions using the quasineutrality assumption are reduced to an effective nonlinear Schrödinger equation (NLSE) which is used to investigate driven electrostatic plasma-phonon excitations. The quantized frequency spectrum of these plasma-phonon excitations in a one-dimensional quasineutral electron-ion plasma confined in rectangular potential well is calculated. The spectrum shows a quadratic energy level increase quite similar to that of a single electron confined in a hard box, with much reduced level spacings proportional to the electron-to-ion mass ratio. The parametrically driven NLSE is also used to study the quantum Faraday excitations in both weakly and fully nonlinear regimes by employing the pseudo-potential technique. The quantization criterion for fully nonlinear driven quantum Faraday excitations in an arbitrary degenerate plasma confined in a hard box of length l is derived, and it is shown that these excitations constitute a full frequency spectrum level starting with those of small amplitude, high frequency sinusoidal plasma-phonon up to the topmost zero-frequency level solitary plasma-phonon excitations (plasma-soliton level).

Emittance preservation through density ramp matching sections in a plasma wakefield accelerator

In plasma wakefield acceleration, the witness beam's emittance needs to be preserved when it propagates through a plasma stage. The plasma includes density ramps at both the entrance and the exit. Using the Wentzel-Kramers-Brillouin solution of a single particle's motion, analytical expressions for the evolution of the beam emittance and the Twiss parameters in an arbitrary adiabatic plasma profile are provided neglecting the acceleration of the beam inside the plasma. It is shown that the beam emittance can be preserved under the matching condition even when the beam has an initial energy spread. It is also shown that the emittance growth for an unmatched beam is minimized when it is focused to the same vacuum plane for a matched beam. The emittance evolution from 3D QuickPIC simulation results agree well with the theoretical results. In the some of the proposed experiments on nearly completed FACET II facility, the matching condition may not be perfectly satisfied and the wake may not be perfectly symmetric. It is shown that for a given set of beam parameters that are consistent with FACET II capabilities, even when the assumptions of the theory are not satisfied, the emittance growth can still be minimized by choosing the optimal focal plane. Last, another issue that may cause emittance growth in realistic plasmas is also examined. When using a lithium plasma source in FACET II experiments a helium buffer gas is used. The plasma is formed from field ionization which can lead to a nonlinear focusing force when there are nonuniform helium ions due to its high ionization potential. For an initial beam emittance of $20\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, the helium ionization is found to be small and the witness beam's emittance can be preserved.

Exact Solov'ev equilibrium with an arbitrary boundary

Exact Solov'ev equilibria for arbitrary plasma cross sections are calculated using a constrained least squares method. The boundary, with or without X-points, can be specified with an arbitrarily large number of constraints to ensure an accurate representation. Thus, the order of the polynomial basis functions in the homogeneous solution of the Grad-Shafranov equation becomes an independent parameter determined only by the accuracy requirements of the overall solution. Examples of exact, highly shaped equilibria are presented.

Theoretical demonstration of surface plasmon polaritons in plasma/vacuum interface in GHz frequency

Negative permittivity of the material may lead to the enhanced radiation of an antenna embedded in a finite plasma, which suggests a potential way to solve blackout problem in space technology. However, the enhanced radiation phenomenon is still lack of strict theoretical investigations of surface plasmon polaritons (SPPs) in plasma in GHz frequency. In this paper, we demonstrate the SPPs excited at a plasma/vacuum interface in GHz frequency by the consistency of the simulated and theoretical results. With SPPs, plasma layer thicker than skin depth can be penetrated with which is a complement of wave propagation theory in plasma. We also discuss the influences of thickness d, collision frequency Γ, and different plasma frequencies on SPPs. For plasma frequencies with large difference, common numerical methods have difficulties in result comparison under the same mesh size because of the computer capacity and memory. The analytical multilayer method used in the paper does not need to generate mesh, so the studies of plasma frequencies with large difference can be carried out. The simulation shows that the SPPs can be excited for an arbitrary plasma frequency. We believe the study will be beneficial for the problem of wave propagation in plasma science and technology.

Transverse beam dynamics in a plasma density ramp

An electron beam experiences chromatic emittance growth in a plasma-based accelerator if it is not matched to the focusing force in the plasma wake. A ramped plasma density profile at the entrance and exit of the plasma source can control the focusing of the beam into and out of the plasma accelerator, limiting emittance growth. Here, we present a comprehensive, analytic theory to describe the transverse beam dynamics and emittance growth in a nearly arbitrary plasma ramp profile. For a given incoming beam, this theory can be used to determine the length of the ramp required to correctly focus the electron beam, the optimal location of the beam's vacuum focus, and the chromatic emittance growth in the ramp. In addition, the theory can be used to determine the effect that errors in the beam focusing and plasma profile have on the emittance of the beam. We illustrate two example ramps to demonstrate the theory: one that provides very fast focusing for beam matching, and one that is robust to errors in the plasma density profile.

Spectral–Dynamic Model of the Hot Plasma Layer Expansion

We propose a theoretical model describing the expansion of a plasma layer into vacuum for an arbitrary electron plasma component temperature. Comparison with the known limiting cases of the quasi-neutral outflow and the Coulomb explosion, as well as with the results of the 1D electrostatic simulation, has revealed a high accuracy of the proposed model in the description of the spectral–energy and spatial characteristics of ions accelerated during the plasma expansion. The procedure for obtaining the relations between the characteristics of accelerated ions and the laser pulse and target parameters is described with regard to qualitative predictions and the description of the results of numerical kinetic simulation and experiments on the laser and plasma acceleration of ions.

A computational tool for simulation and design of tangential multi-energy soft x-ray pin-hole cameras for tokamak plasmas.

A new tool has been developed to calculate the spectral, spatial, and temporal responses of multi-energy soft x-ray (ME-SXR) pinhole cameras for arbitrary plasma densities (n e,D), temperature (T e), and impurity densities (n Z). ME-SXR imaging provides a unique opportunity for obtaining important plasma properties (e.g., T e, n Z, and Z eff) by measuring both continuum and line emission in multiple energy ranges. This technique employs a pixelated x-ray detector in which the lower energy threshold for photon detection can be adjusted independently. Simulations assuming a tangential geometry and DIII-D-like plasmas (e.g., n e,0 ≈ 8 × 1019 m-3 and T e,0 ≈ 2.8 keV) for various impurity (e.g., C, O, Ar, Ni, and Mo) density profiles have been performed. The computed brightnesses range from few 102 counts pixel-1 ms-1 depending on the cut-off energy thresholds, while the maximum allowable count rate is 104 counts pixel-1 ms-1. The typical spatial resolution in the mid-plane is ≈0.5 cm with a photon-energy resolution of 500 eV at a 500 Hz frame rate.

ALPS: the Arbitrary Linear Plasma Solver

The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a$(p_{\bot },p_{\Vert })$grid, where$p_{\bot }$and$p_{\Vert }$are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian,$\unicode[STIX]{x1D705}$-distributed and Jüttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments and numerical simulations.

Finite-Difference Time Domain Techniques Applied to Electromagnetic Wave Interactions with Inhomogeneous Plasma Structures

Motivated by the emerging field of plasma antennas, electromagnetic wave propagation in and scattering by inhomogeneous plasma structures are studied through finite-difference time domain (FDTD) techniques. These techniques have been widely used in the past to study propagation near or through the ionosphere, and their extension to plasma devices such as antenna elements is a natural development. Simulation results in this work are validated with comparisons to solutions obtained by eigenfunction expansion techniques well supported by the literature and are shown to have an excellent agreement. The advantages of using FDTD simulations for this type of investigation are also outlined; in particular, FDTD simulations allow for field solutions to be developed at lower computational cost and greater resolution than equivalent eigenfunction methods for inhomogeneous plasmas and are applicable to arbitrary plasma properties such as spatially or time-varying inhomogeneities and collision frequencies, as well as allowing transient effects to be studied as the field solutions are obtained in the time domain.