Collisionless Flow Research Articles

Rarefication Effects on Jet Impingement Loads

Rarefication effects on jet impingement loads are studied by comparing recent new formulas at the collisionless flow limit and numerical simulations. The jet exit size is finite, and can be either planar or round. In the simulations, the jets have different degrees of rarefication, with a Knudsen (Kn) number ranging from 0 to infinity; i.e., the jet flows can be continuum, collisional, or collisionless. The comparison results indicate that (1) the new surface load formulas are accurate at the collisionless flow limit; (2) in general, the formulas offer upper limits for the peak loads; (3) however, it is improper to assert that local loads always decrease. The new formulas can offer fast estimations of impingement loads. This may be quite helpful for applications in space engineering by significantly reducing the amount of simulations and experiment costs. Those expressions explicitly include non-dimensional parameters, and their contribution and influence on the loads can be studied in a systematic manner (e.g., with a swift parameter study).

Electromagnetic zonal flow residual responses

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.

Transition from Collisional to Collisionless Regimes in Interpenetrating Plasma Flows on the National Ignition Facility.

A study of the transition from collisional to collisionless plasma flows has been carried out at the National Ignition Facility using high Mach number (M>4) counterstreaming plasmas. In these experiments, CD-CD and CD-CH planar foils separated by 6-10mm are irradiated with laser energies of 250kJ per foil, generating ∼1000 km/s plasma flows. Varying the foil separation distance scales the ion density and average bulk velocity and, therefore, the ion-ion Coulomb mean free path, at the interaction region at the midplane. The characteristics of the flow interaction have been inferred from the neutrons and protons generated by deuteron-deuteron interactions and by x-ray emission from the hot, interpenetrating, and interacting plasmas. A localized burst of neutrons and bright x-ray emission near the midpoint of the counterstreaming flows was observed, suggesting strong heating and the initial stages of shock formation. As the separation of the CD-CH foils increases we observe enhanced neutron production compared to particle-in-cell simulations that include Coulomb collisions, but do not include collective collisionless plasma instabilities. The observed plasma heating and enhanced neutron production is consistent with the initial stages of collisionless shock formation, mediated by the Weibel filamentation instability.

Kinetic and radiative power from optically thin accretion flows

We perform a set of general relativistic, radiative, magneto-hydrodynamical simulations (GR-RMHD) to study the transition from radiatively inefficient to efficient state of accretion on a non-rotating black hole. We study ion to electron temperature ratios ranging from $T_{\rm i}/T_{\rm e}=10$ to $100$, and simulate flows corresponding to accretion rates as low as $10^{-6}\dot M_{\rm Edd}$, and as high as $10^{-2}\dot M_{\rm Edd}$. We have found that the radiative output of accretion flows increases with accretion rate, and that the transition occurs earlier for hotter electrons (lower $T_{\rm i}/T_{\rm e}$ ratio). At the same time, the mechanical efficiency hardly changes and accounts to ${\approx}\,3\%$ of the accreted rest mass energy flux, even at the highest simulated accretion rates. This is particularly important for the mechanical AGN feedback regulating massive galaxies, groups, and clusters. Comparison with recent observations of radiative and mechanical AGN luminosities suggests that the ion to electron temperature ratio in the inner, collisionless accretion flow should fall within $10<T_{\rm i}/T_{\rm e}<30$, i.e., the electron temperature should be several percent of the ion temperature.

A New Gaskinetic Model to Analyze Background Flow Effects on Weak Gaseous Jet Flows from Electric Propulsion Devices

Recent work on studying rarefied background and jet flow interactions is reported. A new gaskinetic method is developed to investigate two closely related problems. The first problem is how a collisionless background flow can affect a highly rarefied jet flow. The rarefied jet and background flow conditions are assumed available and described with seven parameters. Gaskinetic theories are applied and formulas are obtained for the mixture properties. Simulations are performed to validate these expressions, and excellent agreement is obtained. The second problem is to recover the collisionless background and jet flow parameters with limited measurements. A group of linearized equations are derived for the flowfield properties. The solving process includes initial estimations on the seven parameters, followed with iterations. Numerical tests are performed and the results indicate the procedure is accurate and efficient. The new method and expressions can reduce the amount of experimental work and numerical simulations to analyze facility effects. Parameter studies with particle simulations may require several months; however, the new methods may require minutes. These methods can be used to quantify and predict jet performance, vacuum chamber designs and optimization. Applications may be for many societies using vacuum conditions.

Numerical study on rarefied unsteady jet flow expanding into vacuum using the Gas-Kinetic Unified Algorithm

The unsteady process of rarefied jet flows expanding into a vacuum is numerically solved by the Gas-Kinetic Unified Algorithm (GKUA) based on the Boltzmann model equations. The discrete velocity ordinate method (DVOM) is adopted to discretize the velocity space of the molecular velocity distribution function, while the corresponding numerical integral technique is developed to evaluate macroscopic flow variables, including number density, flow velocity, temperature and so on. The time-explicit finite difference scheme is constructed to capture the unsteady evolution of the discrete velocity distribution functions at each DVO point by using the unsteady time-splitting method. The multi-block docking grid technique is designed for different regions of flow field in physical space with self-adaptive adjustment. Then, the supersonic planar jet flows with the wide range of Knudsen numbers, from 100 to 0.1, are solved numerically and discussed, including startup to steady state and shutting down. The GKUA results of free-molecule jet flows are analyzed and compared with the Maxwellian analytical solutions for collisionless plume flows, in which good agreement shows the validity and accuracy of the present numerical method. When taking the collision effect into account, the unsteady jet flows with different Knudsen numbers are computed by the present GKUA method. It is shown that the collision term of the Boltzmann model equation plays an important role in this rarefied gas diffusion into the back flow when Kn ≤ 10. However, the colliding relaxation term have a little influence on the kernel region in the startup process for Kn ≥ 0.1. In general, the convective transport term of the Boltzmann model equation dominates the kernel region of the jet flow during the unsteady process of gas expanding into a vacuum. The numerical experience indicates that the present GKUA can provide a vital tool for solving unsteady flow problems covering various flow regimes by directly tracing the time evolution of the Boltzmann-type velocity distribution function.

The residual zonal flows in anisotropic tokamak plasmas

The gyro-kinetic equation is analytically solved based on the anisotropic two-temperature distribution, in which the ions' parallel temperature is a flux function while the perpendicular temperature depends on the poloidal angle. The residual level of collisionless zonal flows (ZFs) is derived and calculated in the large aspect circular limit. Our result shows that the anisotropy plays a remarkable role in determining the residual value of ZFs. Even weak anisotropy can significantly change the residual level.

Evolution of velocity dispersion along cold collisionless flows

The infall of cold dark matter onto a galaxy produces cold collisionless flows and caustics in its halo. If a signal is found in the cavity detector of dark matter axions, the flows will be readily apparent as peaks in the energy spectrum of photons from axion conversion, allowing the densities, velocity vectors and velocity dispersions of the flows to be determined. We discuss the evolution of velocity dispersion along cold collisionless flows in one and two dimensions. A technique is presented for obtaining the leading behaviour of the velocity dispersion near caustics. The results are used to derive an upper limit on the energy dispersion of the Big Flow from the sharpness of its nearby caustic, and a prediction for the dispersions in its velocity components.

The Modeling of Pickup Ion or Energetic Particle Mediated Plasmas

Suprathermal energetic particles, such as solar energetic particles (SEPs) in the inner heliosphere and pickup ions (PUIs) in the outer heliosphere and the very local interstellar medium, often form a thermodynamically dominant component in their various environments. In the supersonic solar wind beyond > 10 AU, in the inner heliosheath (IHS), and in the very local interstellar medium (VLISM), PUIs do not equilibrate collisionally with the background plasma. Similarly, SEPs do not equilibrate collisionally with the background solar wind in the inner heliosphere. In the absence of equilibration between plasma components, a separate coupled plasma description for the energetic particles is necessary. Using a collisionless Chapman-Enskog expansion, we derive a closed system of multi-component equations for a plasma comprised of thermal protons and electrons, and suprathermal particles (SEPs, PUIs). The energetic particles contribute an isotropic scalar pressure to leading order, a collisionless heat flux at the next order, and a collisionless stress tensor at the second-order. The collisionless heat conduction and viscosity in the multi-fluid description results from a nonisotropic energetic particle distribution. A simpler single-fluid MHD-like system of equations with distinct equations of state for both the background plasma and the suprathermal particles is derived. We note briefly potential pitfalls that can emerge in the numerical modeling of collisionless plasma flows that contain a dynamically important energetic particle component.

Slow down of a globally neutral relativistic e−e+ beam shearing the vacuum

The microphysics of relativistic collisionless shear flows is investigated in a configuration consisting of a globally neutral, relativistic beam streaming through a hollow plasma/dielectric channel. We show through multidimensional particle-in-cell simulations that this scenario excites the mushroom instability (MI), a transverse shear instability on the electron-scale, when there is no overlap (no contact) between the beam and the walls of the hollow plasma channel. The onset of the MI leads to the conversion of the beam’s kinetic energy into magnetic (and electric) field energy, effectively slowing down a globally neutral body in the absence of contact. The collisionless shear physics explored in this configuration may operate in astrophysical environments, particularly in highly relativistic and supersonic settings where macroscopic shear processes are stable.

Collisionless Gas Flow over a Cylinder and a Sphere

In this paper, the problems of collisionless flows over a cylinder or a sphere are investigated. New flowfield formulas for the specular surface scenario are obtained, whereas past formulas to the scenario of a diffuse surface are simplified. All formulas are evaluated with a computer code. Several simulations with the direct simulation Monte–Carlo are performed, and the results are compared with these analytical results. In general, the agreement is satisfactory. These analytical results are quite complex; however, they explicitly illustrate the effects from several parameters, such as the specific heat and temperature ratios, and several geometry factors.

Thrust and efficiency model for electron-driven magnetic nozzles

A performance model is presented for magnetic nozzle plasmas driven by electron thermal expansion to investigate how the thrust coefficient and beam divergence efficiency scale with the incoming plasma flow and magnetic field geometry. Using a transformation from cylindrical to magnetic coordinates, an approximate analytical solution is derived to the axisymmetric two-fluid equations for a collisionless plasma flow along an applied magnetic field. This solution yields an expression for the half-width at half-maximum of the plasma density profile in the far-downstream region, from which simple scaling relations for the thrust coefficient and beam divergence efficiency are derived. It is found that the beam divergence efficiency is most sensitive to the density profile of the flow into the nozzle throat, with the highest efficiencies occurring for plasmas concentrated along the nozzle axis. Increasing the expansion ratio of the magnetic field leads to efficiency improvements that are more pronounced for incoming plasmas that are not concentrated along the axis. This implies that the additional magnet required to increase the expansion ratio may be worth the added complexity for plasma sources that exhibit poor confinement.

Stagnation point properties for non-continuum gaseous jet impinging at a flat plate surface from a planar exit

In this paper, we investigate highly rarefied gaseous jet flows out of a planar exit and impinging at a normally set flat plate. Especially, we concentrate on the plate center stagnation point pressure and heat flux coefficients. For a specular reflective plate, the stagnation point pressure coefficient can be represented using two non-dimensional factors: the characteristic gas exit speed ratio S0 and the geometry ratio of H/L, where H is the planar exit semi-height and L is the center-to-center distance from the exit to the plate. For a diffuse reflective plate, the stagnation point pressure and heat flux coefficients involve an extra factor of T0/Tw, i.e., the ratio of exit gas temperature to the plate wall temperature. These results allow us to develop four diagrams, from which we can conveniently obtain the pressure and heat flux coefficients for the stagnation impingement point, at the collisionless flow limit. After normalization with these maximum coefficients, the pressure and heat flux coefficient distributions along the surface essentially degenerate to almost identical curves. As a result, with known plate surface pressure coefficient distributions and these diagrams, we can conveniently construct the heat flux coefficient distributions along the plate surface, and vice versa.

Asymptotic Solutions of Pressure and Heat Flux of Highly Rarefied Gas Flows in Vacuum Packaged Micro-Electro-Mechanical System Devices

This study analyzed a highly rarefied gas flow fields inside an enclosure. The enclosure is formed by four plates with two different temperatures. The plate surfaces are assumed completely diffuse; at the final steady flow stage for any point inside the enclosure or at the surface, the velocity distribution function was determined and all the macroscopic properties was determined by integrating the velocity distribution function. First, the collisionless flow solution was considered as the base solution, and then based on the Bhatnagar-Gross-Krook model, the characteristic relaxation time scale τ was used as a small parameter, and obtained general asymptotic analytical solutions for the flow fields and heat transfer expressions. To validate these asymptotic solutions, a series of numerical simulations with the direct simulation Monte Carlo method were performed and compared with the analytical results. In general, as Knudsen number decreases, the solutions for the pressure, temperature, and density fields deteriorate; the temperature fields had relatively better agreement than the density and pressure fields.

Thomson scattering measurement of a shock in laser-produced counter-streaming plasmas

We report the first direct measurement of temporally and spatially resolved plasma temperatures at a shock as well as its spatial structure and propagation in laser-produced counter-streaming plasmas. Two shocks are formed in counter-streaming collisionless plasmas early in time, and they propagate opposite directions. This indicates the existence of counter-streaming collisionless flows to keep exciting the shocks, even though the collisional effects increase later in time. The shock images are observed with optical diagnostics, and the upstream and downstream plasma parameters of one of the shocks are measured using Thomson scattering technique.

Collisionless coupling of ion and electron temperatures in counterstreaming plasma flows.

Rapid electron and ion heating is observed in collisionless counterstreaming plasma flows and explained via a novel heating mechanism that couples the electron and ion temperatures. Recent experiments measure plasma conditions 4 mm from the surface of single foil (single plasma stream) and double foils (two counterstreaming plasmas) targets using Thomson scattering. Significant increases in electron and ion temperatures (from <100 eV to >1 keV) compared to the single foil geometry are observed. While electrons are heated by friction on opposite going ions, ion-ion collisions cannot explain the observed ion heating. Also, density and flow velocity measurements show negligible slow down and rule out stagnation. The nonlinear saturation of an acoustic two-stream electrostatic instability is predicted to couple the ion temperature to the electron temperature through the dynamic evolution of the instability threshold. Particle-in-cell simulations including both collisional and collisionless effects are compared to the experimental measurements and show rapid electron and ion heating consistent with the experimental measurements.

Complex wakes behind objects in multispecies plasmas

Many space, astrophysical, technological and laboratory plasmas are multispecies. Using particle-in-cell (PIC) numerical simulations, the novel features of the wake structures behind finite-sized objects in multispecies collisionless plasma flows are studied. In electropositive plasmas, different ion species can form separate wakes with distinct ion focus regions, and give rise to polarization of the plasma. In electronegative plasmas, with a large fraction of heavy negative ions, the polarization can be stronger due to substantial ion density reduction in the wake.

Dynamics of the ion flow in a discharge with crossed E and H fields

The experimental and theoretical results of the investigation of an ion flow in a low-pressure discharge in crossed E and H fields are presented. It is shown that two quasi-stationary current states can be realized in a transonic collisionless flow of ions in a cold plasma.

Effects of equilibrium-scale radial electric fields on zonal flows and turbulence in helical configurations

Effects of equilibrium-scale radial electric fields (Er0) on the zonal flow response and the ion temperature gradient (ITG) instability in magnetically confined plasma with helical configurations are investigated by gyrokinetic simulations. Poloidally global simulations of the collisionless zonal flow damping manifest enhancement of the residual amplitude by the uniform and constant Er0, and show agreement with the zonal flow response function in the long wavelength limit analytically derived from the theory for helical plasmas with multiple-helicity confinement field components. A higher zonal flow response is found with heavier ion mass for the same ion temperature and Er0, that is, the isotope effect, while the ITG mode frequency is Doppler shifted. Accordingly, the isotope dependence of the zonal flow response through Er0 possibly leads to the ion mass (or the poloidal Mach number) dependence of the turbulent transport and fluctuations.

Surface properties for rarefied circular jet impingement on a flat plate

In this paper, we investigate rarefied jet gas flows out of a circular exit impinging on a vertical flat plate. We employ a constraint relation about the velocity components of gas particles leaving a nozzle exit point and arriving at a given spatial point outside the nozzle. This relation leads to several analytical expressions for collisionless flow property distributions on the plate surface, including density, slip-velocity, temperature, pressure, shear stress, and heat flux. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical collisionless flow solutions. The impingement properties on the plate surface are accurate when the Knudsen number is large.