Maxwellian Component Research Articles

Collisional-radiative calculations for the J = 0−1 lasing line of neon-like germanium under anisotropic excitation conditions

A new asymmetry parameter characterizing the differences between the polarized π and σ gain components of the soft-x-ray J = 0–1 lasing line of neon-like ions is calculated in the case of Ge22+ assuming an electron distribution which is a weighted sum of an isotropic Maxwellian and a monoenergetic beam. Using a quasi steady-state collisional-radiative model, we determine in the weak amplification regime the relative populations of the upper M = 0 and lower magnetic sublevels of the lasing line as a function of electron density from 1020 to cm−3. This model includes inelastic and elastic collisional transitions, as well as spontaneous radiative decay between all the 337 M-sublevels arising from the 75 lowest-lying Ge22+ J-levels. The computations were performed for a temperature of the Maxwellian component between and K, a kinetic energy E0 and a fraction f of the beam component in the ranges and , respectively. The basic atomic data, such as level energies, radiative decay probabilities and inelastic collision strengths, were calculated with the flexible atomic code. However, some modifications of this code were made to get the collision strengths for transitions between M-sublevels due to impact with isotropic electrons as well as due to impact with an electron beam in the case of de-excitation. We find that the newly introduced asymmetry parameter may become significant under certain conditions of electron distribution corresponding to relatively low ( K) and E0 (3–6 keV). The results reported here may be useful in the evaluation of the polarization degree of the J = 0–1 x-ray laser output from a germanium plasma in the presence of fast directional electrons.

Inferring divertor plasma properties from hydrogen Balmer and Paschen series spectroscopy in JET-ILW

A parametrised spectral line profile model is formulated to investigate the diagnostic scope for recovering plasma parameters from hydrogenic Balmer and Paschen series spectroscopy in the context of JET-ILW divertor plasmas. The separate treatment of Zeeman and Stark contributions in the line model is tested against the PPP-B code which accounts for their combined influence on the spectral line shape. The proposed simplified model does not fully reproduce the Stark–Zeeman features for the α and β transitions, but good agreement is observed in the line width and wing profiles, especially for n > 5. The line model has been applied to infer radial density profiles in the JET-ILW divertor with generally good agreement between the D , , , and lines for high recycling and detached conditions. In an L-mode detached plasma pulse the Langmuir probe measurements typically underestimated the density by a factor 2–3 and overestimated the electron temperature by a factor of 5–10 compared to spectroscopically derived values. The line model is further used to generate synthetic high-resolution spectra for low-n transitions to assess the potential for parameter recovery using a multi-parametric fitting technique. In cases with 4 parameter fits with a single Maxwellian neutral temperature component the D line yields the best results with parameter estimates within 10% of the input values. For cases with 9 parameter fits inclusive of a multi-component neutral velocity distribution function the quality of the fits is degraded. Simultaneous fitting of the D and profiles improves the fit quality significantly, highlighting the importance of complementary spectroscopic measurements for divertor plasma emission studies.

Ne IX line G-ratio in a non-Maxwellian and anisotropic plasma

We have theoretically studied how the presence of a small proportion of energetic beam electrons mixed to a bulk of Maxwellian electrons in a hot plasma affects the temperature-dependent intensity ratio G = (x + y + z)/w of the helium-like triplet intercombination (x, y) and forbidden (z) lines to the singlet resonance line (w). By modelling the electron distribution function as a combination of a Maxwellian isotropic component and a monoenergetic beam component, detailed calculations of the G ratio of the Ne8 + lines have been performed for temperatures Te of the Maxwellian component and kinetic energies e0 of the beam component in the ranges 106–107 K and 1.5–25 keV, respectively. A magnetic sublevel-to-magnetic sublevel collisional-radiative model has been used for determining the populations of the upper magnetic sublevels of the four lines at an electron density below 1013 cm−3. Excitations from the ground 1s2 1S0 and metastable 1s2s 3S1 magnetic sublevels to the 1snl (n = 2–4) magnetic sublevels as well as the inner-shell ionization of the lithium-like ion in its ground level were taken into account. All basic atomic data, including the radiative transition probabilities and the collisional excitation and ionization cross sections, were computed using the flexible atomic code. It is found that the contribution of a 5% fraction of the beam component can reduce the G ratio by a factor of 30 at Te = 106 K and of 2.4 at Te = 3 × 106 K. Our calculations also indicate that the effect of directionality of the beam component on G is negligible for e0 above ∼10 keV and that for a given Te, G is practically insensitive to variations in e0 above ∼7 keV.

Bernstein instability driven by suprathermal protons in the ring current

[1] Kinetic linear dispersion theory for electromagnetic fluctuations in a homogeneous collisionless plasma is used to study the properties of a proton Bernstein mode instability driven by a proton velocity distribution fp(v) such that ∂fp(v⊥)/∂v⊥ > 0 at suprathermal values of v⊥ and v∥ ≃ 0, where ∥ and ⊥ denote directions parallel and perpendicular to the background magnetic field Bo, respectively. The model uses a three-component proton velocity distribution with fp(v) = f1(v) + f2(v∥, v⊥) − f3(v∥, v⊥), where f1(v) represents a Maxwellian thermal component. Here f2 and f3 are bi-Maxwellians with T⊥p > T∥p and slightly different densities and temperatures to represent a suprathermal component consistent with proton perpendicular velocity distributions observed in the magnetospheric ring current. As is well established, the growth rate of the resulting instability has relative maxima near harmonics of the proton cyclotron frequency, the wave vector k satisfies 0 < k∥ ≪ k⊥, and wavelengths are of the order of or smaller than the proton gyroradius. The instability growth rate decreases as the electron/thermal proton temperature ratio increases and, for the dimensionless parameters chosen here, has a maximum value for the thermal proton β of about 10%.

Suppression of longitudinal losses in a gas-dynamic trap by using an ambipolar mirror

The efficiency of utilizing ambipolar mirrors for suppression of longitudinal losses of particles and energy in a gas-dynamic trap (GDT) was investigated. An additional relatively small axisymmetric mirror cell was installed in one of the facility ends. Hydrogen or deuterium atomic beams with an energy of 22 keV and equivalent current density of up to 1 A/cm2 were injected into the additional cell at an angle of 90° to the facility axis. Trapping of the beams with a total power of 800 kW by the plasma in the additional cell leads to the formation of a hot ion population with an anisotropic velocity distribution, a mean energy of 13 keV, and a density of up to 4.5 × 1013 cm−3. It is shown that the confinement of hot ions in the additional cell is determined by classical processes, such as charge exchange on the beam atoms and collisional deceleration by electrons, in spite of the onset of Alfven ion-cyclotron instability at fast ion densities higher than 2.5 × 1013 cm−3. The effect of ambipolar confinement manifests itself in that, at hot ion densities higher than 3 × 1013 cm−3, the flux density of ions escaping from the trap in the mode with beam injection decreases fivefold as compared to that without injection. In this case, the density of the Maxwellian plasma component in the central cell is about 2.5 × 1013 cm−3. The efficiency of suppression of longitudinal particle losses by the ambipolar mirror substantially exceeds estimates obtained for both collisional (gas-dynamic) and collisionless (adiabatic) confinement modes. Qualitatively, this is because, in the GDT experiments, the mode of warm plasma confinement is transitional between the gas-dynamic and adiabatic modes and the use of an ambipolar mirror facilitates a transition from the lossy gas-dynamic mode into a nearly adiabatic one.

Signatures of a Maxwellian component in shock-accelerated electrons in GRBs

Recent particle-in-cell simulations suggest that a large fraction of the energy dissipated in a relativistic shock is deposited into a Maxwellian distribution of electrons that is connected to the high-energy power-law tail. Here, we explore the observational implications of such a mixed thermal-nonthermal particle distribution for the afterglow and prompt emission of gamma-ray bursts. When the Maxwellian component dominates the energy budget, the afterglow lightcurves show a very steep decline phase followed by a more shallow decay when the characteristic synchrotron frequency crosses the observed band. The steep decay appears in the X-rays at ~100 sec after the burst and is accompanied by a characteristic hard-soft-hard spectral evolution that has been observed in a large number of early afterglows. If internal shocks produce a similar mixed electron distribution, a bump is expected at the synchrotron peak of the nu*f_nu spectrum.

Effect of directional energetic electrons on the density diagnostic of hot plasmas

We have theoretically investigated how a small fraction of energetic beamed electrons influences the diagnostics of the electron density in hot plasmas, based on the intensity ratio R of the helium-like forbidden line to the intercombination lines. Elaborate calculations of the intensity ratio R have been performed for Ne8+ ions over the range of electron densities 109–1013 cm−3 using an electron distribution (model) that includes both Maxwellian isotropic and monoenergetic beam components. By taking into account all important transitions among the 117 magnetic sublevels of the and 1snl (n = 2–4) configurations, a collisional-radiative model has been applied for determining the populations of the upper-magnetic sublevels of lines. The required collision strengths due to both electron components were computed semi-relativistically in the complementary distorted-wave and Coulomb–Bethe methods. The results are given for temperatures Te of the Maxwellian electron component in the range 2–5 × 106 K and for kinetic energies e0 of the monoenergetic electron component between 0.95 and 4 keV. At low Te and e0 not too high, the anisotropy of the intensity angular distribution of lines is found to have an appreciable effect on the R ratio. The electron density inferred from the intensity ratio R without including the beam effect can be significantly overestimated or underestimated depending upon the emission angle relative to the electron beam direction.

Wave damping as a critical phenomenon

The evolution of a monochromatic Langmuir wave in a collisionless plasma is studied using Vlasov simulations for a wide range of initial amplitudes. Three types of initial electron distributions are considered: Maxwellian, Lorentzian, and dilute warm Maxwellian plus dense cold component. It is shown that there exists a critical initial amplitude ε* that separates the damping and nondamping asymptotic regimes. Depending on the initial amplitude there are three main types of asymptotic evolution: (i) monotonic linear Landau damping below the threshold, ε≪ε*; (ii) the critical case ε≈ε*, when the field damps algebraically as E(t)∝t−3.26; (iii) at ε&amp;gt;ε* initial damping followed by a period of subsequent exponential growth and then irregular oscillations about a nonzero amplitude. This threshold is well described as a critical phenomenon, showing power-law dependencies on the distance from the threshold not only for field quantities, which are expected of second-order phase transitions in thermodynamics, but also for temporal ones. The critical exponent for both the initial damping and growth phases differ from those expected if the threshold is caused by O’Neil’s particle trapping in the wave potential. However, trapping affects the critical exponents well above the threshold and explains the characteristic frequency of oscillations above the threshold. It is found that for a Maxwellian plasma the threshold amplitude ε* corresponds to the condition that the trapping (bounce) frequency ωb equals the modulus of the theoretical Landau damping rate |γL|; at the threshold, qc=ωb/|γL|≈1. For Lorentzian and Maxwellian-plus-cold component plasmas this ratio is qLor≈0.84 and qCM≈0.83, respectively. The temporal and the field scalings are thus interrelated, suggesting that the inclusion of the temporal dimension is vital for critical phenomena in collisionless plasmas, in contrast to thermodynamic systems where the very small characteristic time to achieve equilibrium removes time from the scaling.

Influence of gas pressure and cathode composition on ion energy distributions in filtered cathodic vacuum arcs

We report measurements of ion energy distributions of ionized species in titanium and aluminium filtered cathodic vacuum arcs operating in oxygen and nitrogen gas atmospheres. The ion energy distributions were recorded using a Hiden mass selected ion energy analyzer. The results show that a significant reduction in ion energies and a change in the shape of ion energy distributions occurs as the gas pressure is increased. The degree of the energy reduction depends on both the type of gas and the metal ions making up the arc plasma. This has important implications for the deposition of thin films, such as titanium nitride, commonly produced using vacuum arcs in reactive gas atmospheres. The ion energy distributions of the cathode ion species in the absence of background gas and at low gas pressures are well fitted by shifted Maxwellian distributions. As the gas pressure rises the distributions consist of a progressively increasing thermalized Maxwellian component and a decreasing shifted Maxwellian. An investigation of energy distributions of species in arcs triggered on alloyed cathodes showed that the relative abundance of ions of different charge states and their energy distributions varied as alloy metals were introduced. This indicates that the electron temperature in the cathode spot and hence the cathode spot dynamics is affected by the presence of the alloy metal.

BIMODAL ANGULAR AND VELOCITY DISTRIBUTIONS OF CO2 DESORBING AFTER OXIDATION OF CO ON Pt(111)

Time-of-flight (TOF) distributions of CO 2 molecules desorbing after the oxidation of CO on Pt (111) were investigated at various desorption angles ϑ for surface temperatures Ts in the range 550–800 K. The Pt (111) surface was exposed to a continuous flow of O 2 from a doser and to a chopped CO nozzle beam. Surface residence-time effects proved to be unimportant or were elucidated. Bimodal TOF distributions composed of two parts were obtained: molecules with a Maxwellian velocity distribution corresponding to Ts appeared in a cosine-shaped angular distribution and molecules with appreciably higher kinetic energies (mean kinetic energy normal to the surface &lt;E kin &gt;⊥≈9kTs) were observed in a narrow angular distribution proportional to cos 8 ϑ. The partition of the total desorbing CO 2 flux to these two channels depended on Ts and ϑ and the total oxygen dose d0 accumulated during an experiment. With increasing d0 the Maxwellian component markedly increased at the expense of the fast component. The observed trends suggest almost only fast desorption from clean Pt (111). We therefore assume Maxwellian desorption to occur mainly from surface sites gradually produced under the influence of oxygen.

Electron Distribution Functions in a Sputtering Magnetron Discharge

The electron distribution function g(vz) in a cylindrically symmetric, planar, sputtering magnetron has been characterized using a one-sided, planar Langmuir probe. Measurements were made above the magnetic trap at six radial locations in the direction normal to the cathode. The distribution function is found to be non-Maxwellian, with a shape that depends sensitively on radial position. Near the symmetry axis, g(vz) is anisotropic and exhibits a strong electron drift from the cathode to the anode. Off axis, g(vz) is nearly symmetric and has two components: a dense, cold Maxwellian component, and a tenuous, energetic shell component.

Electron behavior during electron cyclotron resonance heating in a stellarator

Experimental and theoretical studies of the electron energy distribution during electron cyclotron resonant heating of a target plasma in the Interchangeable Module Stellarator (IMS) [IEEE Trans. Plasma Sci. PS-9, 212 (1981)] have been made. The experimental results show an electron energy distribution with a bulk Maxwellian component (f0) with a temperature of 10–25 eV, and a warm component (f1) with an average energy of 140–160 eV. The electron energy distribution is obtained numerically with a particle-following Monte Carlo simulation. To model the electron cyclotron heating interactions with the electrons, an rf collision model based on stochastic electron–wave interactions is used. Results from this simulation are compared to experimental results. The experimental measurements and the calculated distributions agree well, to within experimental error.

Io plasma torus electrons: Voyager 1

The analysis of in situ plasma electron observations in the Io plasma torus by the plasma science experiment during the Voyager 1 encounter with Jupiter is presented in terms of two components: a thermal (c) Maxwellian component and suprathermal (H) non‐Maxwellian component of the electron distribution function. Average electron temperatures are Te &lt; 1 eV in the cold torus (L &lt; 5.5), with Te ≃ 5–6 eV in the hot torus (5.5 &lt; L &lt; 7.6); Te rises abruptly to Te ≃ 30 eV just outside the hot torus (L &gt; 7.6) and then continues to rise to Te &gt; 100 eV at r &gt; 12 RJ. In the cold torus the density ratio of the suprathermal component nH to that of the cold component nc was &lt;10−4; but in the hot torus, nH/nC ∼ 10−3 was observed, and outside the torus, nH/nc can exceed 10−1. We present evidence that suprathermal electrons are locally produced in the hot torus. Throughout the hot torus the electron temperature Te is a factor of 10 less than the thermal ion temperature. A large difference in the hot electron pressure PH is observed between the inbound and the outbound data which is interpreted as a latitudinal gradient with PH being a maximum at the magnetic equator. If one imposes the theoretical and observational constraint that (T⊥/T∥)EQ ≤ 2 for the hot electrons, then one requires the presence of a parallel electric field E∥ &gt; 2.5 µV/m which exceeds the ambipolar electric field E∥ &lt; 1 µV/m produced by the centrifugally confined ions. However, if unacceptable charge imbalances in the thermal plasma are not to occur from this larger E∥, then sufficient wave turbulence in the plasma must be present to adequately scatter the thermal electrons. We infer the presence of a neutral corona around Io from the observed decrease and symmetry with respect to Io of Tc. The energy input to the torus by charge exchange and ionization in this neutral corona followed by pickup is ∼2 × 1011 W, substantially less than the EUV luminosity. In the hot torus, suprathermal electrons contribute significantly to the ionization of the more highly ionized ions (O+, O2+, S2+, and S3+).

Pioneer Venus suprathermal electron flux measurements in the Venus umbra

Statistical properties of the two Maxwellian electron densities and temperatures characterizing the differential suprathermal electron fluxes measured by the Pioneer‐Venus Lockheed‐IPW retarding potential analyzer in the Venus umbra between approximately 1000 and 2000 km altitude and nightward of 130° solar zenith angle are reported. We find that the median density n2 and temperature T2 of the principal Maxwellian component are 3 cm−3 and 14 eV, respectively, and do not exhibit an altitude or solar zenith angle dependence within the umbra region studied. Two thirds of the measured values of n2 and T2 typically fall within plus or minus a factor of 2 of the median values. The second suprathermal component density n3 is less well defined but has a median density of 0.06 cm−3 and similarly exhibits no clear altitude or solar zenith angle dependence. Two thirds of the n3 values fall within plus or minus a factor of 2 of the median value. The temperature T3 of the second component is assumed constant and equal to 200 eV. The median integral flux measured in this study between 15 and 45 eV energy is consistent with that reported earlier for the Venus nightside ionosphere by Spenner et al. (1981) at altitudes below 1000 km. The integral flux measured by the Pioneer‐Venus retarding potential analyzer appears to be larger than the Venera measured median flux by a factor of approximately 2 in the energy range of the Pioneer‐Venus retarding potential analyzer.

Whistler-mode electron cyclotron emission as an electron temperature diagnostic for magnetic mirror devices

A non-relativistic formulation has been developed which calculates the whistler-mode electron cyclotron emission spectrum in the direction parallel to the magnetic field for a plasma containing an isotropic Maxwellian electron component and an anisotropic bi-Maxwellian electron component. The formulation is valid for arbitrary densities of both components and the model utilizes the radiation transfer equation to obtain the intensity of the emitted radiation. The calculations are intended for use with mirror devices and the motivation is to use cyclotron emission as an electron temperature diagnostic. The projected plasma parameters for the TMX-Upgrade machine have been considered as an example, where the plasma is assumed to have a cold- and a hot-electron component (ne ∼ 1012 – 1013 cm−3, Tcold ∼ 1 keV, Thot ∼ 50 keV). A procedure is described by which the axial cold-electron temperature profile can be obtained from spectral measurements of the cyclotron emission. The effect of the hot-electron population has been considered in detail and it is shown that in certain circumstances their influence on the emitted spectrum is small. For those cases where hot electrons dominate the emission, the model can be used to obtain important information about hot-electron behaviour.

Computer simulation of auroral kilometric radiation

We study the generation of auroral kilometric radiation (AKR) using relativistic, electromagnetic, particle simulations. The AKR source region is modeled by two electron populations in the simulation: a cold (200ev) Maxwellian component and a hot (5‐20kev) population possessing a loss‐cone feature. The loss‐cone distribution is found to be unstable to the cyclotron maser instability. The fast extraordinary (X‐mode) waves dominate the radiation and saturate when resonant particles diffuse into the loss‐cone via turbulent scattering of the particles by the amplified X‐mode radiation.

A simulation study of cold electron heating by loss cone instabilities

We present results of a computer simulation study of electron cyclotron harmonic waves. We model the initial electrons velocity distribution function as a hot ring perpendicular to the ambient magnetic field and a cold Maxwellian component. We identify nonlinear cyclotron resonance as the saturation mechanism of the unstable waves and as the heating mechanism of the cold electrons.

Warm plasma effects on drift cyclotron loss cone mode

Although plasma density gradients in mirror machines are larger than the theoretical threshold for the drift cyclotron loss cone instability, turbulence is experimentally observed only at low harmonics of the ion cyclotron frequency. The evolution of the drift cyclotron loss cone instability as the loss cone velocity distribution is progressively filled with a warm Maxwellian component is studied. The addition of the warm plasma results in both a lowering of the growth rate and a distortion and narrowing of the frequency spectrum. Under conditions typical of an almost filled loss cone, the numerical result shows that the growth rate is largest for the lower ion cyclotron harmonics and is quite consistent with experimental observations.

Characteristics of a large-volume rf-grid discharge plasma

The properties of a large-volume rf (75 MHz) -grid discharge plasma have been determined. Measurements in the steady state and in the afterglow indicate that the rf grid produces a plasma with two electron components—a secondary Maxwellian component of density 2×1010 electrons/cm3 and temperature 4.5 eV and a ’’primary’’ component of density 1×1010 electrons/cm3 and temperature approximately 15 eV. The ion temperature is ?0.3 eV. A useful 35-liter argon plasma with a noise level on the order of 1% is easily produced in neutral pressure backgrounds as low as 4×10−5 Torr.

Theory and computer simulation of whistler turbulence and velocity space diffusion in the magnetospheric plasma

The nonlinear development of unstable whistler waves and their interaction with electrons in an anisotropic, collisionless, magnetospheric-type plasma is investigated by theory and computer simulation experiments. A two-component plasma is considered; a hot electron Maxwellian component with 60° loss cone is superimposed on a cold isotropic electron background. The linear and quasi-linear theory is developed, and quasi-linear theory is used to obtain equations for the temporal evolution of the parallel and perpendicular energy for the hot and cold plasma components. The computer code follows the nonrelativistic dynamics of a large number of charges in their self-consistent electromagnetic fields. Three velocity and one spatial dimension are used. The simulation automatically includes energy as well as pitch angle diffusion. The 6.5 × 104 electrons, which were followed, were distributed into the two components. Initially, the wave magnetic energy grows according to linear theory; the hot electrons diffuse into the loss cone, gaining parallel and losing perpendicular kinetic energy by both pitch angle and energy diffusion; and the cold background gains perpendicular energy nonresonantly. The quasi-linear equations for the evolution of parallel and perpendicular energy for the hot and cold components explain the partitioning of energy. A plot of hot particle density in υ⊥ versus υ∥ velocity space shows a hole developing as the particles diffuse, in agreement with theory. We observe that, as the hot electrons isotropize, the initially unstable higher mode numbers sequentially switch off; i.e., the spectrum shifts to lower k values. The growth of the wave magnetic energy saturates in a full nonlinear phase when the average growth rate is of the order of the electron trapping frequency in the whistler spectrum. At this time there exists a large residual kinetic energy anisotropy in the hot particle distribution.