Optical properties and one-particle spectral function in non-ideal plasmas
Carsten Fortmann, Gerd Röpke, August Wierling
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13 pages, 7 figures, 52 references. Submitted to Contrib. Plasma Phys. Results presented at the International Workshop on Physics of Non-ideal Plasmas (PNP12), Darmstadt, sept. 4.-8. 2006
A basic concept to calculate physical features of non-ideal plasmas, such as optical properties, is the spectral function which is linked to the self-energy. We calculate the spectral function for a non-relativistic hydrogen plasma in $GW$-approximation. In order to go beyond $GW$ approximation, we include self-energy and vertex correction to the polarization function in lowest order. Partial compensation is observed. The relation of our approach to $GW$ and $GWΓ$ calculations in other fields, such as the band-structure calculations in semiconductor physics, is discussed. From the spectral function we derive the absorption coefficient due to inverse bremsstrahlung via the polarization function. As a result, a significant reduction of the absorption as compared to the Bethe-Heitler formula for bremsstrahlung is obtained.
The magnetic connection theorem of ideal Magnetohydrodynamics by Newcomb [Newcomb W.A., Ann. Phys., 3, 347 (1958)] and its covariant formulation are rederived and reinterpreted in terms of a "time resetting" projection that accounts for the loss of simultaneity in different reference frames between spatially separated events.
Idealized merging argon plasma jets are simulated in 2D using both gas dynamic and MHD models. Results indicate that peak pressures of several hundred kilobar can be achieved for high Mach number jets. Including a simple optically thin Brehmstrahlung radiation model and plasma targets shows that extremely high densities and magnetic fields can be achieved during jet merging on the order of ~1000 times the initial density/field. Further investigations should include detailed ionization processes and more accurate radiation modeling to properly capture the radiation transport and subsequent targ…
Lorentz invariant scalar functions of the magnetic field are defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the {\it potential magnetic field} introduced by R. Hide in Ann. Geophys. 1, 59 (1983) on the line of Ertel's theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the Eulerian-Lagrangian variable mapping. In addition the adopted procedure allows us to formulate Alfvèn theorem for the conservation of the magnetic flux through a surface comoving with the plasma in a Loren…
The expansion of non-ideal copper plasma into vacuum is analyzed for the conditions typical to explosive electron emission in vacuum arcs. The gas-dynamic model solves the Euler equations with an equation of state (EoS) for weakly non-ideal plasma taking into account the ionization energy correction due to electron-ion Coulomb coupling. We have obtained that the EoS has insignificant influence on the plasma expansion, when the plasma properties and composition change drastically. Based on our simulation results, the validity of the 'frozen' state theory often used in the vacuum arcs plasma dia…
The quantum diffraction and symmetry effects on the entanglement fidelity (EF) of different elastic electron-electron, ion-ion and electron-ion interactions are investigated in non-ideal dense plasma. The partial wave analysis and an effective screened interaction potential including quantum mechanical diffraction and symmetry effects are employed to obtain the EF in a non-ideal dense plasma. We show that collision energy and temperatures of electron and ion have a destroying role in the entanglement. In fact, by decreasing the temperature of any kind of particles, the quantum effects become d…
In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly-coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.
The asymptotic behavior of the equilibrium radiation in Maxwellian plasma is studied for the low--frequency region. It is shown, that the equilibrium radiation can essentially deviate from the Planck law even for a weakly non-ideal plasma. The deviation from the Planck distribution is described by the transverse dielectric permittivity which takes into account both frequency and spatial dispersion. The influence of plasma non-ideality increases with the non-ideality parameter in the dielectric permittivity. The spectral energy distribution of the equilibrium radiation essentially changes in th…
A new model method for describing of the electrostatic screening in two-component systems (electron-ion plasmas, dusty plasmas, electrolytes, etc) is developed. The method is applicable to the systems of higher non-ideality degree. The expressions for all the screening parameters introduced in the previous paper (Part 1) of this work, as well as for an additional parameter characteristic for multi-component systems, are obtained. All these parameters are presented in a simple analytic form suitable for operative laboratory usage, especially for theoretical interpretation of experimental data.
The asymptotic behavior of the equilibrium radiation in Maxwellian plasma is investigated for the region of low frequencies. It is shown, that already for a weakly non-ideal plasma the equilibrium radiation can essentially deviate from the Planck law. The deviation from the Planck distribution is described by the transverse dielectric permittivity which takes into account both frequency and spatial dispersion. The influence of plasma non-ideality increases with increase of the non-ideality parameter in the in the dielectric permittivity. The spectral energy distribution of the equilibrium radi…
Thomson scattering in non-ideal (collision-dominated) two-component plasmas is calculated accounting for electron-ion collisions as well as electron-electron correlations. This is achieved by using a novel interpolation scheme for the electron-electron response function generalizing the traditional Mermin approach. Also, ions are treated as randomly distributed inert scattering centers. The collision frequency is taken as a dynamic and complex quantity and is calculated from a microscopic quantum-statistical approach. Implications due to different approximations for the electron-electron corre…
The problem of calculation of the reflectivity of non-ideal shock-compressed plasmas is revisited. The dielectric formalism based on the method of moments incorporating exact asymptotic forms and sum rules is applied to the new experimental data. The approach is based on the Ansatz of reflection of laser radiation from a thin shock-front and possesses one adjustable parameter which depends only on the thermodynamic conditions of the experiment. A self-consistent agreement with all available experimental data is achieved.
A high explosive shock tube of non-ideal gaseous plasma for proton radiography is described. The gas dynamic flow in the shock compressed xenon at initial pressure of 7 bar was investigated in the tube. The velocity of the shock wave in xenon and the associated particle velocity were measured by a high-speed rotating mirror streak camera. Experimental time-distance data was used for approximation of the velocities by exponential decay functions. The shock tube is intended for generation of non-ideal plasma of xenon at the pressure of 5-12 kbar, the density of 0.24-0.3 g/cm3 when the initial pr…
The physical sense and the properties of a group screening parameters which are determined in the previous papers (Part~1 and Part~2) for single- and two-component systems is discussed in this paper. On the base of data from the mentioned papers are determined two new characteristic lengths which complete a new hierarchy system of screening lengths in plasma. It was shown that the methods developed in Part~1 and Part~2 generates results which are applicable to the strongly non-ideal gaseous and dusty plasmas, and manifest a very good agreement with the existing experimental data.
Conditions of Velikhov-Chandrasekhar magneto-rotational instability in ideal and non-ideal plasmas are examined. Linear WKB analysis of hydromagnetic axially symmetric flows shows that in the Rayleigh-unstable hydrodynamic case where the angular momentum decreases with radius, the MRI branch becomes stable, and the magnetic field suppresses the Rayleigh instability at small wavelengths. We investigate the limiting transition from hydromagnetic flows to hydrodynamic flows. The Rayleigh mode smoothly transits to the hydrodynamic case, while the Velikhov-Chandrasekhar MRI mode completely disappea…
This work presents scaling relations for the peak thermal pressure and stagnation time (over which peak pressure is sustained) for an imploding spherical plasma liner formed by an array of merging plasma jets. Results were derived from three-dimensional (3D) ideal hydrodynamic simulation results obtained using the smoothed particle hydrodynamics code SPHC. The 3D results were compared to equivalent one-dimensional (1D) simulation results. It is found that peak thermal pressure scales linearly with the number of jets and initial jet density and Mach number, quadratically with initial jet radius…
In this paper a new model method for describing of the electrostatic screening in single-component systems which is free of Debye-Huckel's non-physical properties is presented. The method is appropriate for the determination of screening parameters in the case of the systems of higher non-ideality degree. The obtained screening characteristics are presented in a simple analytic form. The presented results make basic elements of a method for determination of screening characteristics in dense two-component plasmas, which are discussed in Part2 and Part 3 of this work.
An effective approach for construction of simple approximation for description of non-ideality effects in classical one- and two-component plasma model is under discussion. General constraints i.e. positiveness and exponential type for radial distribution functions F2(r) combined with normalizing (local electroneutrality) conditions, which validity is independent on degree of non-ideality, are used for effective correction of several well-known approximated forms of F(r). Resulting corrected forms F*(r) leads to non-ideality corrections, which are asymptotically exact in the weak non-ideality …
The method of molecular dynamics is used to study behavior of a ultracold non-ideal ion-electron Be plasma in a uniform magnetic field. Our simulations yield an estimate for the rate of electron-ion collisions which is non-monotonicallydependent on the magnetic field magnitude. Also they explicitly show that there are two types of diffusion: classical one, corresponding to Brownian motion of particles, and Bohm diffusion when the trajectory of particles (guiding centers) includes substantial lengths of drift motion.
A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. By choosing an appropriate gauge, we show that the plasma displacement satisfies the same Euler-Lagrange equation in ideal and relaxed regions, except in the neighbourhood of magnetic surfaces. The difference at singular surfaces is analysed in cylindrical geometry: in ideal MHD only Newcomb's [W. A. Newcomb (2006) Ann. Phys., 10, 232] small solutions are allowed, whereas in relaxed MHD only the odd-parity large solution and even-pa…
The screening of a test charge by partially degenerate non-ideal free electrons at conditions related to warm dense matter and dense plasmas is investigated using linear response theory and the local field correction based on ab inito Quantum Monte-Carlo simulations data. The analysis of the obtained results is performed by comparing to the random phase approximation and the Singwi-Tosi-Land-Sjölander approximation. The applicability of the long-wavelength approximation for the description of screening is investigated. The impact of electronic exchange-correlations effects on structural proper…
The method of moments is used to calculate the dynamic conductivity of strongly coupled fully ionized hydrogen plasmas. The electron density $n_{e}$ and temperature $T$ vary in the domains $ 10^{21} < n_{e} < 10^{24} {\rm cm}^{-3}$, $10^{4} {\rm K} < T < 10^{6} {\rm K}$. The results are compared to some theoretical data.
The screened ion potential in non-ideal dense quantum plasmas is investigated by invoking the Singwi-Tosi-Land-Sjölander approximation for the electronic local field correction at densities $r_s\lesssim 2$ and degeneracy parameters $θ\lesssim 1$, where $r_s$ is the ratio of the mean inter-particle distance to the first Bohr radius, and $θ$ is the ratio of the thermal energy to the Fermi energy of the electrons. Various cross-checks with ion potentials obtained from ground state quantum Monte-Carlo data, the random phase approximation, as well as with existing analytical models are presented. F…
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock and existing numerical solutions to the GEM challenge magnetic reconnection problem. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based …
In this paper we introduce an algebraic form of the dispersion relation for a non ideal inhomogeneous dusty plasma in order to improve drastically the calculation of the drift instability growth rate. This method makes use of the multipole approximation of the Z dispersion function, previously published, and valid for the entire range. A careful analysis of the solutions spectra of this kind of polynomial equation permits us to calculate easily the growth rate of the drift instability for the ion-dust and dust acoustic mode. The value of the parallel to magnetic field wavelength for which the …
The wide use of a speed-independent distance as a cut-off impact parameter together with Rutherford's scattering formula, within the cut-off theory, to account for charge screening in plasma environment embodies a clear inconsistency. A new physically justified choice of the cut-off distance is introduced and used to derive a closed form expression for the effective momentum transport cross section. A simple approximation for the present Coulomb logarithm, free of special functions, is also presented and assessed. A comparison with experimentally recovered data for the reduced Coulomb conducti…
We present results from three-dimensional ideal magnetohydrodynamic simulations of unmagnetized dense plasma jet injection into a uniform hot strongly magnetized plasma, with the aim of providing insight into core fueling of a tokamak with parameters relevant for ITER and NSTX (National Spherical Torus Experiment). Unmagnetized dense plasma jet injection is similar to compact toroid injection but with much higher plasma density and total mass, and consequently lower required injection velocity. Mass deposition of the jet into the background appears to be facilitated via magnetic reconnection a…
Active plasma resonance spectroscopy (APRS) is a process-compatible plasma diagnostic method which utilizes the natural ability of plasmas to resonate on or near the electron plasma frequency. The Multipole Resonance Probe (MRP) is a particular design of APRS that has a high degree of geometric and electric symmetry. The principle of the MRP can be described on the basis of an idealized geometry that is particularly suited for theoretical investigations. In a pressure regime of a few Pa or lower, kinetic effects become important, which can not be predicted by the Drude model. Therefore, in thi…
This paper presents both rigorous results and physical theory on the breakdown of magnetic flux conservation for ideal plasmas, by nonlinear effects. Our analysis is based upon an effective equation for magnetohydrodynamic (MHD) modes at length-scales $>\ell,$ with smaller scales eliminated, as in renormalization-group methodology. We prove that flux-conservation can be violated for an arbitrarily small length-scale $\ell,$ and in the absence of any non-ideality, but only if singular current sheets and vortex sheets both exist and intersect in sets of large enough dimension. This result gives …
Ideal MHD relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important tool for investigating plasma equilibria and is often used to study the magnetic configurations in fusion devices and astrophysical plasmas. We study the equilibrium reached by a localized magnetic field through the topology conserving relaxation of a magnetic field based on the Hopf fibration in which magnetic field lines are closed circles that are all linked…
Plasma-based electron and positron wakefield acceleration has made great strides in the past decade. However one major challenge for its applications to coherent light sources and colliders is the relatively large energy spread of the accelerated beams, currently at a few percent level. This energy spread is usually correlated with particle position in the beam arising from the longitudinal chirp of the wakefield amplitude. Therefore a dechirper is highly desirable for reducing this spread down to $\sim0.1\%$ level, while at the same time for maintaining the emittance of the accelerated beam. …
In the article an ultracold electron-ion plasma created by photoionization of cooled atoms is investigated. We obtained analitical expressions for non-ideality parameters which establish due to correlation heating. In the work the nearest neighbour and the Wigner-Seitz cell approximations were used, the recombination heating of electrons was taken into account. We have got a good agreement with the experiment results. The possibility of creation of strongly non-ideal electron subsystem has been shown and conditions of this process have been determined.
It is proved that (a) the solutions of the ideal magnetohydrodynamic equation, which describe the equlibrium states of a cylindrical plasma with purely poloidal flow and arbitrary cross sectional shape [G. N. Throumoulopoulos and G. Pantis, Plasma Phys. and Contr. Fusion 38, 1817 (1996)] are also valid for incompressible equlibrium flows with the axial velocity component being a free surface quantity and (b) for the case of isothermal incompressible equilibria the magnetic surfaces have necessarily circular cross section.
The standard picture of the Coulomb logarithm in the ideal plasma is controversial, the arguments for the lower cut off need revision. The two cases of far subthermal and of far superthermal electron drift motions are accessible to a rigorous analytical treatment. We show that the lower cut off $b_{\min}$ is a function of symmetry and shape of the shielding cloud, it is not universal. In the subthermal case shielding is spherical and $b_{\min}$ is to be identified with the de Broglie wavelength; at superthermal drift the shielding cloud exhibits cylindrical (axial) symmetry and $b_{\min}$ is t…
A self-consistent determination of the spectral function and the self-energy of electrons in a hot and dense plasma is reported. The self-energy is determined within the approximation of the screened potential. It is shown, that the quasi-particle concept is not an adequate concept for hot and dense plasmas, since the width of the spectral function has to be considered. As an example, the solar core plasma is discussed. An effective quasi-particle picture is introduced and results for the solar core plasma as well as for ICF plasmas are presented.
We present results from three-dimensional ideal magnetohydrodynamic simulations of low $β$ compact toroid (CT) injection into a hot strongly magnetized plasma, with the aim of providing insight into CT fueling of a tokamak with parameters relevant for ITER (International Thermonuclear Experimental Reactor). A regime is identified in terms of CT injection speed and CT-to-background magnetic field ratio that appears promising for precise core fueling. Shock-dominated regimes, which are probably unfavorable for tokamak fueling, are also identified. The CT penetration depth is proportional to the …
The common feature of sheared flows of an ideal fluid and plasma in magnetic field is the Kelvin-Helmholtz instability. This instability is described by identical equations in mentioned two cases. The wave equation for the eigenmodes in the plasma obtained by the kinetic method in the long-wave limit coincides with the Rayleigh equation known for an ideal fluid. Velocity profile with a transition layer of finite width is considered. Odd modes are investigated. Localized velocity shear layer is the source of perturbations propagating beyond the transition layer. The conditions of localization o…
Water window emission spectra of two laboratory nitrogen plasma sources were examined with a free standing grating spectrometer (FSGS). The highest line intensities at the wavelength 2.88 nm achievable with the sources were compared. Pulse energies for this line were judged as 0.02 mJ/srad and 0.16 mJ/srad with laser produced plasma system and pinching discharge plasma, respectively. The spectral resolution was found about 0.01 nm at 3rd order of spectral lines around wavelength 2.5 nm.
An ideal plasma lens can provide the focusing power of a small f-number, solid-state focusing optic at a fraction of the diameter. An ideal plasma lens, however, relies on a steady-state, linear laser pulse-plasma interaction. Ultrashort multi-petawatt (MPW) pulses possess broad bandwidths and extreme intensities, and, as a result, their interaction with the plasma lens is neither steady state nor linear. Here we examine nonlinear and time-dependent modifications to plasma lens focusing, and show that these result in chromatic and phase aberrations and amplitude distortion. We find that a plas…
We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the MHD domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this…
Starting from first principles quantum kinetic theory for ideal plasmas with exchange effects, the quantum hydrodynamic equations are derived taking moments of the corresponding exchange-Vlasov equation. The case of an electron-ion plasma where ions are entirely classical is considered. The linear dispersion relation for ion-acoustic waves is found from the macroscopic equations and compared with exchange quantum kinetic theory, yielding a qualitative agreement apart from a numerical factor of order one in the exchange contribution, assuming a Maxwellian background as a first step, for analyti…
Macroscopic plasma polarization, which is created by gravitation and other mass-acting (inertial) forces in massive astrophysical objects is under discussion. Non-ideality effect due to strong Coulomb interaction of charged particles is introduced into consideration as a new source of such polarization. Simplified situation of totally equilibrium isothermal star without relativistic effects and influence of magnetic field is considered. The study is based on variational approach combined with "local density approximation". It leads to two local forms of thermodynamic equilibrium conditions: co…
We calculate the stability of a multiple relaxation region MHD (MRXMHD) plasma, or stepped-Beltrami plasma, using both variational and tearing mode treatments. The configuration studied is a periodic cylinder. In the variational treatment, the problem reduces to an eigenvalue problem for the interface displacements. For the tearing mode treatment, analytic expressions for the tearing mode stability parameter $Δ'$, being the jump in the logarithm in the helical flux across the resonant surface, are found. The stability of these treatments is compared for $m=1$ displacements of an illustrative R…
There is a well established theory of Ballooning modes in a toroidal plasma. The cornerstone of this is a local eigenvalue lambda on each magnetic surface - which also depends on the ballooning phase angle k. In stationary plasmas lambda(k) is required only near its maximum, but in rotating plasmas its average over k is required. Unfortunately in many case lambda(k) does not exist for some range of k, because the spectrum there contains only a stable continuum. This limits the application of the theory, and raises the important question of whether this "stable interval" gives rise to significa…
We report on the nonlinear turbulent processes associated with electromagnetic waves in plasmas. We focus on low-frequency (in comparison with the electron gyrofrequency) nonlinearly interacting electron whistlers and nonlinearly interacting Hall-magnetohydrodynamic (H-MHD) fluctuations in a magnetized plasma.
In this paper we present the results of the spectral studies of erosive discharge with tin alloy electrodes and of the generated JFs, and experimentally determine internal energy of JFs using the calorimetric technique.
The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for introducing incompressibility are compared in a cylindrical plasma model: In the first method, the limit $γ\to \infty$ is taken, where $γ$ is the ratio of specific heats; in the second, an anisotropic mass tensor $\mathbfρ$ is used, with the component parallel to the magnetic field taken to vanish, $ρ_{\parallel} \to 0$. Use of resistive MHD reveals the nature of the…
A combined theoretical and experimental analysis of the normal modes of three-dimensional spherially confined Yukawa clusters is presented. Particular attention is paid to the breathing mode and the existence of multiple monopole oscillations in Yukawa systems. Finally, the influence of dissipation on the mode spectrum is investigated.
The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a $k$-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phas…
Ordered dusty structures influence plasma conditions. This influence can be revealed, when plasma spectral characteristics change, as dusty particles are injected. For example, a variation in the atomic temperature leads to a variation in the profiles of spectral lines. We studied the profile of a 585 nm neon spectral line in the dusty structures. The structures levitated in a positive column of a glow discharge at a pressure of 50-150 Pa and with a current of 1-9 mA. We scanned the profile with the use of a Fabry-Perot interferometer, by changing the air pressure between the interferometer mi…
Magnetic reconnection is believed to be the driver of many explosive phenomena in Astrophysics, from solar to gamma-ray flares in magnetars and in the Crab nebula. However, reconnection rates from classic MHD models are far too slow to explain such observations. Recently, it was realized that when a current sheet gets sufficiently thin, the reconnection rate of the tearing instability becomes "ideal", in the sense that the current sheet destabilizes on the "macroscopic" Alfvénic timescales, regardless of the Lundquist number of the plasma. Here we present 2D compressible MHD simulations in the…
The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC. The measured amplitudes of the helical displacement around the low field side midplane are in reasonable agreement with the …
A test case, using a similar methodology and experimental set-up than previous test case TC5-Level 1 is presented in this paper. An inductively coupled plasma torch, working at atmospheric pressure, is used to create N2-CH4 Titan-like plasma (98%N2 - 2%CH4). The operating frequency and power are 64 MHz and 3 kW respectively. This kind of apparatus allows obtaining plasma in chemical and quasi-thermal equilibrium The spectral measurements cover the [300-800] nm range and are performed inside the induction coil. Each interesting spectrum is calibrated and compared to the line-by-line spectral co…
In this work, we use a passive advection model for ion temperature fluctuations, in order to investigate their effects on Doppler Spectral line shapes. The relevance of the model is discussed in the framework of the Braginskii equations, and the subsequent Probability Density Function evaluation relies on results obtained in neutral fluids. The resulting Doppler line profiles are shown to exhibit characteristic exponential tails.
