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Journal articles on the topic 'Plasma distribution function'

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Author: Grafiati

Published: 6 September 2023

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1

Levko, Dmitry, Rochan R. Upadhyay, Laxminarayan L. Raja, Alok Ranjan, and Peter Ventzek. "Influence of electron energy distribution on fluid models of a low-pressure inductively coupled plasma discharge." Physics of Plasmas 29, no. 4 (April 2022): 043510. http://dx.doi.org/10.1063/5.0083274.

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The aim of the present paper is to examine the influence of assumption on the electron energy distribution function on the relation between the plasma potential and the electron temperature for both electropositive (argon) and electronegative (chlorine) plasmas. A one-dimensional fluid model is used for simplicity although similar results were obtained using a self-consistent two-dimensional fluid model coupled with the Maxwell's equations for inductively coupled plasmas. We find that for electropositive plasma only a bi-Maxwellian electron energy distribution function provides reasonable results compared to measurements in low-pressure inductively coupled plasmas, namely, the increasing plasma potential for increasing electron temperature. For electronegative plasma, the plasma potential is an increasing function of the electron temperature for all electron distributions considered in the model. However, the scaling factors do not agree with the conventional plasma theory. We explain these results by the deviation of electrons from a Boltzmann distribution, which is due to non-equilibrium and non-local nature of plasma at the low-pressure conditions.

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2

Orefice, A. "Relativistic theory of absorption and emission of electron cyclotron waves in anisotropic plasmas." Journal of Plasma Physics 39, no. 1 (February 1988): 61–70. http://dx.doi.org/10.1017/s002237780001285x.

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The weakly relativistic theory of absorption and emission of electron cyclotron waves in hot magnetized plasmas is developed for a large class of anisotropic electron distribution functions. The results are expressed in terms of the weakly relativistic plasma dispersion functions, and therefore of the well-known plasma Z-function. The particular case of a loss-cone electron distribution function is presented as a simple example.

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3

Saito, S., F. R. E. Forme, S. C. Buchert, S. Nozawa, and R. Fujii. "Effects of a kappa distribution function of electrons on incoherent scatter spectra." Annales Geophysicae 18, no. 9 (September 30, 2000): 1216–23. http://dx.doi.org/10.1007/s00585-000-1216-2.

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Abstract. In usual incoherent scatter data analysis, the plasma distribution function is assumed to be Maxwellian. In space plasmas, however, distribution functions with a high energy tail which can be well modeled by a generalized Lorentzian distribution function with spectral index kappa (kappa distribution) have been observed. We have theoretically calculated incoherent scatter spectra for a plasma that consists of electrons with kappa distribution function and ions with Maxwellian neglecting the effects of the magnetic field and collisions. The ion line spectra have a double-humped shape similar to those from a Maxwellian plasma. The electron temperatures are underestimated, however, by up to 40% when interpreted assuming Maxwellian distribution. Ion temperatures and electron densities are affected little. Accordingly, actual electron temperatures might be underestimated when an energy input maintaining a high energy tail exists. We have also calculated plasma lines with the kappa distribution function. They are enhanced in total strength, and the peak frequencies appear to be slightly shifted to the transmitter frequency compared to the peak frequencies for a Maxwellian distribution. The damping rate depends on the electron temperature. For lower electron temperatures, plasma lines for electrons with a κ distribution function are more strongly damped than for a Maxwellian distribution. For higher electron temperatures, however, they have a relatively sharp peak.Key words: Ionosphere (auroral ionosphere; plasma waves and instabilities) – Space plasma physics (kinetic and MHD theory)

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4

Nicolaou, Georgios, George Livadiotis, and Robert T. Wicks. "On the Determination of Kappa Distribution Functions from Space Plasma Observations." Entropy 22, no. 2 (February 13, 2020): 212. http://dx.doi.org/10.3390/e22020212.

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The velocities of space plasma particles, often follow kappa distribution functions. The kappa index, which labels and governs these distributions, is an important parameter in understanding the plasma dynamics. Space science missions often carry plasma instruments on board which observe the plasma particles and construct their velocity distribution functions. A proper analysis of the velocity distribution functions derives the plasma bulk parameters, such as the plasma density, speed, temperature, and kappa index. Commonly, the plasma bulk density, velocity, and temperature are determined from the velocity moments of the observed distribution function. Interestingly, recent studies demonstrated the calculation of the kappa index from the speed (kinetic energy) moments of the distribution function. Such a novel calculation could be very useful in future analyses and applications. This study examines the accuracy of the specific method using synthetic plasma proton observations by a typical electrostatic analyzer. We analyze the modeled observations in order to derive the plasma bulk parameters, which we compare with the parameters we used to model the observations in the first place. Through this comparison, we quantify the systematic and statistical errors in the derived moments, and we discuss their possible sources.

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5

Benisti, D., A. Friou, and L. Gremillet. "Nonlinear Electron Distribution Function in a Plasma." Interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 3, no. 4 (December 2014): 435–44. http://dx.doi.org/10.5890/dnc.2014.12.006.

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6

SHAIKH, DASTGEER, and B. DASGUPTA. "An analytic model of plasma-neutral coupling in the heliosphere plasma." Journal of Plasma Physics 76, no. 6 (June 30, 2010): 919–27. http://dx.doi.org/10.1017/s0022377810000310.

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AbstractWe have developed an analytic model to describe coupling of plasma and neutral fluids in the partially ionized heliosphere plasma medium. The sources employed in our analytic model are based on a κ-distribution as opposed to the Maxwellian distribution function. Our model uses the κ-distribution to analytically model the energetic neutral atoms that result in the heliosphere partially ionized plasma from charge exchange with the protons and subsequently produce a long tail, which is otherwise not describable by the Maxwellian distribution. We present our analytic formulation and describe major differences in the sources emerging from these two distinct distributions.

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7

Lago, V., A. Lebehot, Michel A. Dudeck, and Z. Szymanski. "ELECTRON ENERGY DISTRIBUTION FUNCTION IN PLASMA ARC JETS." High Temperature Material Processes (An International Quarterly of High-Technology Plasma Processes) 6, no. 1 (2002): 8. http://dx.doi.org/10.1615/hightempmatproc.v6.i1.20.

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8

Maslov, S. A., S. Ya Bronin, N. G. Gusein-zade, and S. A. Trigger. "Photon Distribution Function in Weakly Coupled Maxwellian Plasma." Bulletin of the Lebedev Physics Institute 46, no. 8 (August 2019): 263–66. http://dx.doi.org/10.3103/s1068335619080062.

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9

Hasegawa, Akira, Kunioki Mima, and Minh Duong-van. "Plasma Distribution Function in a Superthermal Radiation Field." Physical Review Letters 54, no. 24 (June 17, 1985): 2608–10. http://dx.doi.org/10.1103/physrevlett.54.2608.

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10

Melrose, D. B., and A. Mushtaq. "Plasma dispersion function for a Fermi–Dirac distribution." Physics of Plasmas 17, no. 12 (December 2010): 122103. http://dx.doi.org/10.1063/1.3528272.

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11

Abid, A. A., S. Ali, J. Du, and A. A. Mamun. "Vasyliunas–Cairns distribution function for space plasma species." Physics of Plasmas 22, no. 8 (August 2015): 084507. http://dx.doi.org/10.1063/1.4928886.

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12

Malinovsky, V. S., A. E. Belikov, O. V. Kuznetsov, and R. G. Sharafutdinov. "Electron distribution function in an electron-beam plasma." Physical Review E 51, no. 4 (April 1, 1995): 3498–503. http://dx.doi.org/10.1103/physreve.51.3498.

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13

Guio, P., J. Lilensten, W. Kofman, and N. Bjørnå. "Electron velocity distribution function in a plasma with temperature gradient and in the presence of suprathermal electrons: application to incoherent-scatter plasma lines." Annales Geophysicae 16, no. 10 (October 31, 1998): 1226–40. http://dx.doi.org/10.1007/s00585-998-1226-z.

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Abstract. The plasma dispersion function and the reduced velocity distribution function are calculated numerically for any arbitrary velocity distribution function with cylindrical symmetry along the magnetic field. The electron velocity distribution is separated into two distributions representing the distribution of the ambient electrons and the suprathermal electrons. The velocity distribution function of the ambient electrons is modelled by a near-Maxwellian distribution function in presence of a temperature gradient and a potential electric field. The velocity distribution function of the suprathermal electrons is derived from a numerical model of the angular energy flux spectrum obtained by solving the transport equation of electrons. The numerical method used to calculate the plasma dispersion function and the reduced velocity distribution is described. The numerical code is used with simulated data to evaluate the Doppler frequency asymmetry between the up- and downshifted plasma lines of the incoherent-scatter plasma lines at different wave vectors. It is shown that the observed Doppler asymmetry is more dependent on deviation from the Maxwellian through the thermal part for high-frequency radars, while for low-frequency radars the Doppler asymmetry depends more on the presence of a suprathermal population. It is also seen that the full evaluation of the plasma dispersion function gives larger Doppler asymmetry than the heat flow approximation for Langmuir waves with phase velocity about three to six times the mean thermal velocity. For such waves the moment expansion of the dispersion function is not fully valid and the full calculation of the dispersion function is needed.Key words. Non-Maxwellian electron velocity distribution · Incoherent scatter plasma lines · EISCAT · Dielectric response function

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14

Kucinski, M. Y., I. L. Caldas, L. H. A. Monteiro, and V. Okano. "Toroidal plasma equilibrium with arbitrary current distribution." Journal of Plasma Physics 44, no. 2 (October 1990): 303–11. http://dx.doi.org/10.1017/s0022377800015191.

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A new System of co-ordinates is found and a method developed to determine the toroidal equilibrium of plasmas with arbitrary current distribution and plasma cross-section. The method depends on knowledge of the equilibrium of a straight plasma column of similar cross-section and similar current distribution. A large aspect ratio is assumed. By successive approximations, better solutions can be obtained. An explicit formula is presented for the poloidal flux of a nearly circular plasma. This can be written in terms of a function related to the asymmetry of the poloidal field due to toroidality. The method works provided that there is only one magnetic axis.

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15

Hussein, N. A., D. A. Eisa, A. N. A. Osman, and R. A. Abbas. "Quantum Binary and Triplet Distribution Functions of Plasma by using Green's Function." Contributions to Plasma Physics 54, no. 10 (November 2014): 815–26. http://dx.doi.org/10.1002/ctpp.201400016.

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16

Hamilton, Jason, and Charles E. Seyler. "Plasma thermal transport with a generalized 8-moment distribution function." Physics of Plasmas 29, no. 3 (March 2022): 034502. http://dx.doi.org/10.1063/5.0081656.

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Moment equations that model plasma transport require an ansatz distribution function to close the system of equations. The resulting transport is sensitive to the specific closure used, and several options have been proposed in the literature. Two different 8-moment distribution functions can be generalized to form a single-parameter family of distribution functions. The transport coefficients resulting from this generalized distribution function can be expressed in terms of this free parameter. This provides the flexibility of matching the 8-moment model to some validating result at a given magnetization value, such as Braginskii's transport, or the more recent results of Davies et al. [Phys. Plasma, 28, 012305 (2021)]. This process can be thought of as a solution for the 8-moment distribution function that matches the value of a transport coefficient given by a Chapman–Enskog expansion while retaining the improved physical properties, such as finite propagation speeds and time dependence, which belong to the hyperbolic moment models. Since the presented generalized distribution function only has a single free parameter, only a single transport coefficient can be matched at a time. However, this generalization process may be extended to provide multiple free parameters. The focus of this Brief Communication is on the dramatically improved thermal conductivity of the proposed model compared to the two base moment models.

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17

Muñoz, V. "A nonextensive statistics approach for Langmuir waves in relativistic plasmas." Nonlinear Processes in Geophysics 13, no. 2 (June 29, 2006): 237–41. http://dx.doi.org/10.5194/npg-13-237-2006.

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Abstract. The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.

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18

SINGHAL, R. P., and A. K. TRIPATHI. "Loss-cone index in distribution function in a hot magnetized plasma." Journal of Plasma Physics 73, no. 2 (April 2007): 207–14. http://dx.doi.org/10.1017/s0022377806004491.

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Abstract.The components of the dielectric tensor for the distribution function given by Leubner and Schupfer have been obtained. The effect of the loss-cone index appearing in the particle distribution function in a hot magnetized plasma has been studied. A case study has been performed to calculate temporal growth rates of Bernstein waves using the distribution function given by Summers and Thorne and Leubner and Schupfer. The effect of the loss-cone index on growth rates is found to be quite different for the two distribution functions.

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19

Bronin, S. Ya, E. V. Vikhrov, B. B. Zelener, and B. V. Zelener. "General expression for the probability distribution function of electric field in a spatially inhomogeneous non-neutral plasma." Physics of Plasmas 30, no. 1 (January 2023): 010702. http://dx.doi.org/10.1063/5.0129560.

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We discuss the influence of micro- and macro-fields on spectral lines of ions as it takes place for spatially inhomogeneous plasma. A distribution function of an electric field is obtained. The function accounts for inhomogeneity and non-neutrality of plasma. The results of calculations of this function for various regimes are presented. Experimental results for ultracold plasma are used to compare theory with experiment. Dependence of the absorption coefficient on the function is shown. These results may be useful for diagnostics of various types of plasmas. One of the methods of plasma diagnostics is the analysis of the influence of its electric field on the shape of the spectral lines of atoms and ions (the Stark effect).

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20

Nicolaou, Georgios, and George Livadiotis. "Statistical Uncertainties of Space Plasma Properties Described by Kappa Distributions." Entropy 22, no. 5 (May 13, 2020): 541. http://dx.doi.org/10.3390/e22050541.

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The velocities of space plasma particles often follow kappa distribution functions, which have characteristic high energy tails. The tails of these distributions are associated with low particle flux and, therefore, it is challenging to precisely resolve them in plasma measurements. On the other hand, the accurate determination of kappa distribution functions within a broad range of energies is crucial for the understanding of physical mechanisms. Standard analyses of the plasma observations determine the plasma bulk parameters from the statistical moments of the underlined distribution. It is important, however, to also quantify the uncertainties of the derived plasma bulk parameters, which determine the confidence level of scientific conclusions. We investigate the determination of the plasma bulk parameters from observations by an ideal electrostatic analyzer. We derive simple formulas to estimate the statistical uncertainties of the calculated bulk parameters. We then use the forward modelling method to simulate plasma observations by a typical top-hat electrostatic analyzer. We analyze the simulated observations in order to derive the plasma bulk parameters and their uncertainties. Our simulations validate our simplified formulas. We further examine the statistical errors of the plasma bulk parameters for several shapes of the plasma velocity distribution function.

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21

Caron, D., R. John, E. E. Scime, and T. E. Steinberger. "Ion velocity distribution functions across a plasma meniscus." Journal of Vacuum Science & Technology A 41, no. 3 (May 2023): 033001. http://dx.doi.org/10.1116/6.0002439.

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Here, we present laser-induced fluorescence measurements of an ion beam extraction angle and speed through a plasma-vacuum boundary as a function of plasma source parameters and bias potential applied to a wafer simulacrum outside the plasma. Ion temperature, velocity, and relative density are calculated from the measured ion velocity distribution function and are compared to a particle-in-cell model of the system. The measurements demonstrate that beam steering is feasible by varying plasma source density and extraction bias voltage. The focal point of the extracted beam, resulting from the plasma meniscus at the plasma-vacuum interface, depends on source density and extraction bias in a manner consistent with computational predictions.

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22

Meng, Zhaoyue, Richard M. Thorne, and Danny Summers. "Ion-acoustic wave instability driven by drifting electrons in a generalized Lorentzian distribution." Journal of Plasma Physics 47, no. 3 (June 1992): 445–64. http://dx.doi.org/10.1017/s002237780002434x.

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A generalized Lorentzian (kappa) particle distribution function is useful for modelling plasma distributions with a high-energy tail that typically occur in space. The modified plasma dispersion function is employed to study the instability of ion-acoustic waves driven by electron drift in a hot isotropic unmagnetized plasma modelled by a kappa distribution. The real and imaginary parts of the wave frequency ω0 + ιγ are obtained as functions of the normalized wavenumber kλD, where λD is the electron Debye length. Marginal stability conditions for instability are obtained for different ion-to-electron temperature ratios. The results for a kappa distribution are compared with the classical results for a Maxwellian. In all cases studied the ion-acoustic waves are strongly damped at short wavelengths, kλD ≫ 1, but they can be destabilized at long wavelengths. The instability for both the kappa and Maxwellian distributions can be quenched by increasing the ion-electron temperature ratio Ti/Te. However, both the marginally unstable electron drift velocities and the growth rates of unstable waves can differ significantly between a generalized Lorentzian and a Maxwellian plasma; these differences are also influenced by the value of Ti/Te.

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Orefice, A. "Resonant interaction of electron cyclotron waves with a plasma containing arbitrarily drifting suprathermal electrons." Journal of Plasma Physics 34, no. 2 (October 1985): 319–26. http://dx.doi.org/10.1017/s0022377800002890.

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A relativistic treatment of the plasma dispersion functions and of the dielectric tensor for electron cyclotron electromagnetic waves is given for non-thermal plasmas where the electron distribution function can be represented as a combination of Maxwellians with arbitrary drifts along the magnetic field.

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Vega, Cristian, Stanislav Boldyrev, and Vadim Roytershteyn. "Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence." Astrophysical Journal 949, no. 2 (June 1, 2023): 98. http://dx.doi.org/10.3847/1538-4357/accd73.

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Abstract Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f(γ)d γ ∝ γ −α d γ, where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n, has a power-law distribution function, P ( n ) dn ∝ n − β dn . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

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Asseo, Estelle, and Alain Riazuelo. "The Pulsar Pair Plasma." International Astronomical Union Colloquium 177 (2000): 455–56. http://dx.doi.org/10.1017/s0252921100060280.

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AbstractThe anisotropic and relativistic features of the pulsar pair plasma are adequately modelled using relativistic one-dimensional Jűttner-Synge distribution functions. The dispersion relation for wave propagation in such a plasma involves coefficients that specifically depend on the distribution function of its particles. An analytical determination of these coefficients allows us to obtain characteristics of quasi-longitudinal waves together with the conditions for the unstable interaction of ultrarelativistic beam and plasma. Similar derivations concern electromagnetic waves.

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26

Bespalov, Peter, and Olga Savina. "Pancake-like and tablet-like distribution functions of energetic electrons in the middle magnetosphere." Annales Geophysicae 35, no. 1 (January 24, 2017): 133–38. http://dx.doi.org/10.5194/angeo-35-133-2017.

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Abstract. We propose a simple explanation of the prolonged existence of pancake-like electron velocity distributions in the radiation belts. The pancake-like distribution function is characterized by a longitudinal particle velocity (along the magnetic field) of the order of the thermal velocity of the background plasma. The parameters of the tablet-like distribution function with a characteristic longitudinal particle velocity of the order of 20 Alfvèn velocities are refined. Such distribution functions can occur in the middle magnetosphere near the magnetic equator with appropriate sources of energetic particles. The stability of these distributions is examined. The results agree with known experimental data.

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Sufi, Muhammad, Saktioto, and Jalil Ali. "Distribution Function for Nonlinear Potential Gradient High Pressure Plasma." Applied Mechanics and Materials 511-512 (February 2014): 85–93. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.85.

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The effect of carbon ion species distribution in arc discharge process becomes significant for the formation of carbon nanomaterial. It is essential to account for the velocity distribution of each carbon ion species to determine the greatest contribution from the kinetic energy possesses by each species that govern the binding energy for carbon formation. The resultant speed of the particle as a result of collisions determines the resultant force exerted by the particles which consider in non-conservative force. The variation of velocity distribution is investigated while the reaction rate for carbon species during kinematic process, the transient condition for carbon species is analyzed. Collision rate of carbon ion species is underway to derive carbon ion motion in electrode gap region where the external electric field is constant. The theoretical development has shown that at constant pressure and temperature, carbon ion species possess the resultant speed due to collision frequency affecting the distribution function quantified for each species.

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Mustafaev, A. S., and A. Yu Grabovskii. "Probe diagnostics of anisotropic electrons distribution function in plasma." High Temperature 50, no. 6 (November 2012): 785–805. http://dx.doi.org/10.1134/s0018151x12060077.

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Roudaki, F. S., A. Salar Elahi, and M. Ghoranneviss. "Determination of Electron Energy Distribution Function in Tokamak Plasma." Journal of Fusion Energy 34, no. 4 (March 8, 2015): 911–17. http://dx.doi.org/10.1007/s10894-015-9898-3.

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Gasteiger, M., and D. Tskhakaya. "On the Electron Distribution Function in the Edge Plasma." Contributions to Plasma Physics 54, no. 4-6 (June 2014): 503–7. http://dx.doi.org/10.1002/ctpp.201410048.

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TJULIN, ANDERS, ANDERS I. ERIKSSON, and MATS ANDRÉ. "Physical interpretation of the Padé approximation of the plasma dispersion function." Journal of Plasma Physics 64, no. 3 (September 2000): 287–96. http://dx.doi.org/10.1017/s0022377800008606.

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It is shown that using Padé approximants in the evaluation of the plasma dispersion function Z for a Maxwellian plasma is equivalent to the exact treatment for a plasma described by a ‘simple-pole distribution’, i.e. a distribution function that is a sum of simple poles in the complex velocity plane (v plane). In general, such a distribution function will have several zeros on the real v axis, and negative values in some ranges of v. This is shown to be true for the Padé approximant of Z commonly used in numerical packages such as WHAMP. The realization that an approximation of Z is equivalent to an approximation of f(v) leads the way to the study of more general distribution functions, and we compare the distribution corresponding to the Padé approximant used in WHAMP with a strictly positive and monotonically decreasing approximation of a Maxwellian.

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Micca Longo, Gaia, Luca Vialetto, Paola Diomede, Savino Longo, and Vincenzo Laporta. "Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives." Molecules 26, no. 12 (June 16, 2021): 3663. http://dx.doi.org/10.3390/molecules26123663.

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We review the recent progress in the modeling of plasmas or ionized gases, with compositions compatible with that of primordial atmospheres. The plasma kinetics involves elementary processes by which free electrons ultimately activate weakly reactive molecules, such as carbon dioxide or methane, thereby potentially starting prebiotic reaction chains. These processes include electron–molecule reactions and energy exchanges between molecules. They are basic processes, for example, in the famous Miller-Urey experiment, and become relevant in any prebiotic scenario where the primordial atmosphere is significantly ionized by electrical activity, photoionization or meteor phenomena. The kinetics of plasma displays remarkable complexity due to the non-equilibrium features of the energy distributions involved. In particular, we argue that two concepts developed by the plasma modeling community, the electron velocity distribution function and the vibrational distribution function, may unlock much new information and provide insight into prebiotic processes initiated by electron–molecule collisions.

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Chen, L. F., and S. R. Liang. "A Modified Pulsar Model Green Function Period Distribution." Symposium - International Astronomical Union 125 (1987): 62. http://dx.doi.org/10.1017/s0074180900160486.

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The downward accelerated e− in the “unfavorable” zone, like that in the “favorable” one, will emit γ-photons, which in turn convert into e± pairs in some places near the surface of stars. But what happens, which is different from that in the “favorable” zone, is that some γ-photons will travel through a long distance before their conversion. This makes it possible that some γ-photons arrive at the “diode” district in the “favorable” zone. The magnetic conversion of pairs is much easier to happen than that occured in the “favorable” zone, where the γ-photons are created by the primary e− beam. The existence of dense e± plasma near the surface of stars makes the E, vanish at places where such plasma is present.

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Godyak, V. A., R. B. Piejak, and B. M. Alexandrovich. "Electron energy distribution function measurements and plasma parameters in inductively coupled argon plasma." Plasma Sources Science and Technology 11, no. 4 (November 1, 2002): 525–43. http://dx.doi.org/10.1088/0963-0252/11/4/320.

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35

Hellberg, M. A., and R. L. Mace. "Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution." Physics of Plasmas 9, no. 5 (May 2002): 1495–504. http://dx.doi.org/10.1063/1.1462636.

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Gonzalez, F. J., J. I. Gonzalez, S. Soler, C. E. Repetto, B. J. Gómez, and D. B. Berdichevsky. "New procedure to estimate plasma parameters through the q-Weibull distribution by using a Langmuir probe in a cold plasma." Plasma Research Express 4, no. 1 (February 3, 2022): 015003. http://dx.doi.org/10.1088/2516-1067/ac4f35.

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Abstract We describe a procedure to obtain the plasma parameters from the I-V Langmuir curve by using the Druyvesteyn equation. We propose to include two new parameters, q and r, to the usual plasma parameters: plasma potential (V p ), floating potential (V f ), electron density (n), and electron temperature (T). These new parameters can be particularly useful to represent non-Maxwellian distributions. The procedure is based on the fit of the I-V Langmuir curve with the q-Weibull distribution function, and is motivated by recent works which use the q-exponential distribution function derived from Tsallis statistics. We obtain the usual plasma parameters employing three techniques: the numerical differentiation using Savitzky Golay (SG) filters, the q-exponential distribution function, and the q-Weibull distribution function. We explain the limitations of the q-exponential function, where the experimental data V > V p needs to be trimmed beforehand, and this results in a lower accuracy compared to the numerical differentiation with SG. To overcome this difficulty, the q-Weibull function is introduced as a natural generalization to the q-exponential distribution, and it has greater flexibility in order to represent the concavity change around V p . We apply this procedure to analyze the measurements corresponding to a nitrogen N 2 cold plasma obtained by using a single Langmuir probe located at different heights from the cathode. We show that the q parameter has a very stable numerical value with the height. This work may contribute to clarify some advantages and limitations of the use of non-extensive statistics in plasma diagnostics, but the physical interpretation of the non-extensive parameters in plasma physics remains not fully clarified, and requires further research.

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Zhang, Yanzeng, and Xian-Zhu Tang. "On the collisional damping of plasma velocity space instabilities." Physics of Plasmas 30, no. 3 (March 2023): 030701. http://dx.doi.org/10.1063/5.0136739.

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For plasma velocity space instabilities driven by particle distributions significantly deviated from a Maxwellian, weak collisions can damp the instabilities by an amount that is significantly beyond the collisional rate itself. This is attributed to the dual role of collisions that tend to relax the plasma distribution toward a Maxwellian and to suppress the linearly perturbed distribution function. The former effect can dominate in cases where the unstable non-Maxwellian distribution is driven by collisionless transport on a timescale much shorter than that of collisions, and the growth rate of the ideal instability has a sensitive dependence on the distribution function. The whistler instability driven by electrostatically trapped electrons is used as an example to elucidate such a strong collisional damping effect of plasma velocity space instabilities, which is confirmed by first-principles kinetic simulations.

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38

Treumann, R. A., R. Nakamura, and W. Baumjohann. "Relativistic transformation of phase-space distributions." Annales Geophysicae 29, no. 7 (July 19, 2011): 1259–65. http://dx.doi.org/10.5194/angeo-29-1259-2011.

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Abstract. We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the electron-cyclotron maser radiation theory, in the vicinity of high-Mach number shocks where particles are accelerated to high speeds, and generally in solar and astrophysical plasmas. We show that the phase-space volume element is a Lorentz constant and construct the general particle distribution function from first principles. Application to thermal equilibrium lets us derive a modified version of the isotropic relativistic thermal distribution, the modified Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.

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LAZAR, M., A. SMOLYAKOV, R. SCHLICKEISER, and P. K. SHUKLA. "A comparative study of the filamentation and Weibel instabilities and their cumulative effect. I. Non-relativistic theory." Journal of Plasma Physics 75, no. 1 (February 2009): 19–33. http://dx.doi.org/10.1017/s0022377807007015.

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AbstractA comparative study of the electromagnetic instabilities in anisotropic unmagnetized plasmas is undertaken. The instabilities considered are the filamentation and Weibel instability, and their cumulative effect. Dispersion relations are derived and the growth rates are plotted systematically for the representative cases of non-relativistic counterstreaming plasmas with isotropic or anisotropic velocity distributions functions of Maxwellian type. The pure filamentation mode is attenuated by including an isotropic Maxwellian distribution function. Moreover, it is observed that counterstreaming plasmas can be fully stabilized by including bi-Maxellian distributions with a negative thermal anisotropy. This effect is relevant for fusion plasma experiments. Otherwise, for plasma streams with a positive anisotropy the filamentation and Weibel instabilities cumulate leading to a growth rate by orders of magnitude larger than that of a simple filamentation mode. This is noticeable for the quasistatic magnetic field generated in astrophysical sources, and which is expected to saturate at higher values and explain the non-thermal emission observed.

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VEGA, PEDRO, LUIS PALMA, and RENE ELGUETA. "The L mode in electromagnetic proton-cyclotron waves in plasmas modelled by a Lorentzian distribution function." Journal of Plasma Physics 60, no. 1 (August 1998): 29–48. http://dx.doi.org/10.1017/s0022377898006382.

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The L mode in electromagnetic proton-cyclotron waves (EPCWs) propagating parallel to a uniform ambient magnetic field is studied here analytically. A generalized Lorentzian distribution function is used to model the plasma. Analytical expressions for the wavenumber and for both the temporal and convective growth rates for a multi-ion plasma are obtained within the linear theory. This analytical approach is appropiate for β∥<1, which is the ratio of plasma kinetic pressure to magnetic field pressure. The characteristics of the unstable spectrum are found to be independent of high-energy particles. For a plasma composed of electrons plus hot and cold protons, it is shown that the maximum growth rates as functions of cold-proton concentration δ can always decrease, or can increase until δ reaches a certain peak value and decrease thereafter, or can always increase, depending on the thermal anisotropy of the hot protons. This behaviour is similar to that in Maxwellian plasmas. However, for the convective growth rate, the expression for the optimum cold-proton concentration shows a significant dependence on the spectral index κ. Therefore, when cold protons are injected, it is more difficult to obtain optimum amplification in a Lorentzian plasma than in a Maxwellian plasma. It is also shown that the influence of the high-energy tail on the generation and amplification processes of the EPCWs is controlled by thermal anisotropy and cold-ion population. As a consequence of the latter, temporal and convective growth rates can be larger than, equal to or smaller than those of Maxwellian plasmas, depending on the anisotropy of the hot-proton distribution and on the cold-proton concentration.

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Khorashadizadeh, S. M., Sh Abbasi Rostami, A. R. Niknam, S. Vasheghani Farahani, and R. Fallah. "Longitudinal wave instability due to rotating beam-plasma interaction in weakly turbulent astrophysical plasmas." Monthly Notices of the Royal Astronomical Society 489, no. 3 (August 17, 2019): 3059–65. http://dx.doi.org/10.1093/mnras/stz2281.

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ABSTRACTThe aim of this study is to highlight the temporal evolution of the longitudinal wave instability due to the interaction between a rotating electron beam and the magnetoactive plasma region in space plasma structures. The plasma structure which could be either in the solar atmosphere or any active plasma region in space is considered weakly turbulent, where the quasi-linear theory is implemented to enable analytic insight on the wave–particle interaction in the course of the event. It is found that in a weakly turbulent plasma, quasi-linear saturation of the longitudinal wave is accompanied by a significant alteration in the distribution function in the resonant region. In case of a pure electrostatic wave, the wave amplitude experiences elevation due to the energy transfer from the plasma particles. This causes flattening of the bump on tail (BOT) in the electron distribution function. If the gradient of the distribution function is positive, the chance that the beam would excite the wave is probable. In such a situation a plateau on the distribution function (∂f/∂v ≈ 0) is formed that will stop the diffusion of beam particles in the velocity space. Evolution of the electron distribution function experiences a decreases of the instability of the longitudinal wave. It is deduced that the growth rate of the wave instability is inversely proportional to the wave energy. Regarding the Sun, in addition to creating micro-turbulence due to wave–particle interaction, as the wave elevates to higher altitudes it enters a saturated energy state before releasing energy that may be a candidate for the generation of radio bursts.

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Hopkins, M. B., and W. G. Graham. "Electron energy distribution function measurements in a magnetic multipole plasma." Journal of Physics D: Applied Physics 20, no. 7 (July 14, 1987): 838–43. http://dx.doi.org/10.1088/0022-3727/20/7/004.

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Matveyev, A. A., and V. P. Silakov. "Electron energy distribution function in a moderately ionized argon plasma." Plasma Sources Science and Technology 10, no. 2 (March 14, 2001): 134–46. http://dx.doi.org/10.1088/0963-0252/10/2/303.

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Aanesland, A., J. Bredin, P. Chabert, and V. Godyak. "Electron energy distribution function and plasma parameters across magnetic filters." Applied Physics Letters 100, no. 4 (January 23, 2012): 044102. http://dx.doi.org/10.1063/1.3680088.

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Li, Jinming, Igor K. Getmanov, Anatoliy A. Kudryavtsev, Chengxun Yuan, Xiaoou Wang, and Zhongxiang Zhou. "Conductivity and Permittivity in Plasma With Nonequilibrium Electron Distribution Function." IEEE Transactions on Plasma Science 48, no. 2 (February 2020): 388–93. http://dx.doi.org/10.1109/tps.2019.2956731.

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Cappa, A., and F. Castejón. "Electron energy distribution function during second harmonic ECRH plasma breakdown." Nuclear Fusion 44, no. 3 (February 2, 2004): 406–13. http://dx.doi.org/10.1088/0029-5515/44/3/005.

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Lampe, M., T. B. Röcker, G. Joyce, S. K. Zhdanov, A. V. Ivlev, and G. E. Morfill. "Ion distribution function in a plasma with uniform electric field." Physics of Plasmas 19, no. 11 (November 2012): 113703. http://dx.doi.org/10.1063/1.4768456.

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Azooz, A. A. "Extraction of electron plasma energy distribution function using distortion meters." European Physical Journal Applied Physics 34, no. 3 (May 4, 2006): 225–29. http://dx.doi.org/10.1051/epjap:2006040.

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Amemiya, Hiroshi. "Characteristics of the Electron Energy Distribution Function in Nitrogen Plasma." Journal of the Physical Society of Japan 55, no. 1 (January 15, 1986): 169–76. http://dx.doi.org/10.1143/jpsj.55.169.

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Kolobov, V. I., and W. N. G. Hitchon. "Electron distribution function in a low-pressure inductively coupled plasma." Physical Review E 52, no. 1 (July 1, 1995): 972–80. http://dx.doi.org/10.1103/physreve.52.972.

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