Two-temperature Electron Distribution Research Articles

Radial acceleration of ions during adiabatic expansion of a multicomponent cylindrical plasma

The methods of modern group analysis allow an analytic solution of the Cauchy problem to be constructed for the system of kinetic equations for a fully ionised electron – ion plasma, describing the acceleration of ions during the adiabatic expansion of a cylindrical plasma. Time and spatial dependences of the distribution functions of particles are obtained and their integral characteristics, such as density, average velocity, temperature, and energy spectrum, are found. The formation of the energy spectrum of accelerated ions, asymptotically repeating the spatial distribution of their density, and the cooling of electrons in the process of ion acceleration are analytically described. Particular attention is paid to the investigation of the influence of the heavy ionic component on the dynamics of the light component. The features of ion acceleration in the case of a two-temperature electron distribution function that describes the presence of hot and cold electron components are studied, which corresponds to the typical conditions of the experiment on plasma heating by intense laser radiation.

Characterization of intense laser-produced fast electrons using hard x-rays via bremsstrahlung

Energy distribution of high-power, short-pulse laser produced fast electrons was experimentally and numerically studied using high-energy bremsstrahlung x-rays. The hard x-ray photons and escaping electrons from various metal foils, irradiated by the 50 TW Leopard laser at Nevada Terawatt Facility, were recorded with a differential filter stack spectrometer that is sensitive to photons produced by mainly 0.5–2 MeV electrons and an electron spectrometer measuring >2 MeV electrons. The experimental bremsstrahlung and the slope of the measured escaped electrons were compared with an analytic calculation using an input electron spectrum estimated with the ponderomotive scaling. The result shows that the electron spectrum entering a Cu foil could be continuous single slope with the slope temperature of ∼1.5 MeV in the detector range. The experiment and analytic calculation were then compared with a 2D particle-in-cell code, PICLS, including a newly developed radiation transport module. The simulation shows that a two-temperature electron distribution is generated at the laser interaction region, but only the hot component of the fast electrons flow into the target during the interaction because the low energy electron component is trapped by self-generated magnetic field in the preformed plasma. A significant amount of the photons less than 100 keV observed in the experiment could be attributed to the low energy electrons entering the foil a few picoseconds later after the gating field disappears.

Planar sheath model in dusty plasmas with a two-temperature electron distribution

The two-temperature electron distribution is found to affect significantly the dust grain surface potential or the dust grain charge. Based on the Sagdeev potential approach, a modified sheath criterion including the effect of a two-temperature electron distribution is established theoretically. A one-dimensional fluid model is utilized to describe the sheath at a plasma-wall boundary in dusty plasmas with a two-temperature electron distribution. The effects of the population ratio of hot to cold electrons and of the temperature ratio of hot to cold electrons on the characteristics of the dusty plasma-plane wall (or probe) boundary are investigated. The spatial distributions of the electric potential and of the velocities and densities of the plasma species including those of dust grains, the electric force, and the ion drag force are calculated. With increasing population ratio of hot to cold electrons, the sheath width broadens, and the ion flux to the wall increases whereas the ion drift velocity decreases. An enhanced temperature ratio of hot to cold electrons causes the sheath width to broaden and the ion flux to the wall to increase.

Expansion of a plasma into vacuum with a bi-Maxwellian electron distribution function

A comprehensive theory is developped to describe the expansion of a plasma into a vacuum with a two-temperature electron distribution function. The characteristics of the rarefaction shock which occurs in the plasma when the hot- to the cold-electron temperature ratio is larger than 9.9 are investigated with a semi-infinite plasma. Furthermore by using a finite plasma foil, a possible heating of the cold electrons population is evidenced, for a sufficiently large hot- to the cold-electron density ratio.

Heavy-ion emission from short-pulse laser-plasma interactions with thin foils

A Thomson parabola ion spectrometer, implemented on the Laboratory for Laser Energetics Multi-Terawatt laser facility, has been used to study heavy-ion acceleration from ultra-intense laser-plasma interactions. These studies were conducted using 20 μm-thick flat foil targets with on-target intensities of 4−5×1019 W-cm−2. Several charge states of energetic heavy ions were accelerated from the rear of Al and Cu foils in the presence of hydrocarbon contaminants. In contrast to previous work, we show that the mean and maximum energies of each heavy-ion species scale linearly with only the charge of the ion, and not the charge-to-mass ratio, implying that the space-charge is not readily depleted as ions expand. It has been shown previously and observed here that the maximum heavy-ion energies are lower than that of protons, though a fundamental explanation for this discrepancy has not been provided. We show how a two-temperature electron distribution, observed in these experiments, explains these observations.

Thin-foil expansion into a vacuum with a two-temperature electron distribution function

A kinetic theory of the expansion into a vacuum of a plasma thin foil with initially a hot and a cold Maxwellian electron population is examined with a one-dimensional kinetic code. Whereas hot electrons always lose energy to expanding ions, cold electrons can either gain or lose energy depending on the initial temperature and density ratios and on time. When the cold electrons' density is not too large, they experience initially an adiabatic compression by the electric field associated with the rarefaction wave. The corresponding temperature increase can be as large as a factor of a few tens. Later on, as expected, the cold electrons eventually lose energy to the expansion. When cold electrons are numerically dominant, a rarefaction shock appears during the first phase of the expansion. Hot electrons cool down faster than cold electrons, thus reducing the effective temperature ratio. Furthermore, the amplitude of the rarefaction shock and the dip that it causes on the ion velocity spectrum tend to be smoothed out by the expansion.

Mach probe interpretation in the presence of suprathermal electrons

The collisionless theory of Mach probes assuming isothermal, Maxwellian electrons is extended to include an isotropic, two-temperature electron distribution function. The kinetic equations for ion and electron motion in the probe wake are solved using a quasineutral particle-in-cell method, which compares qualitatively well with the results of a simple fluid model. The measured Mach number decreases slightly with increasing hot electron concentration, but the main effect is on the measured electron temperature. Due to the fact that the probe is sensitive to even a tiny population of hot electrons, the resulting ion sound speed can be overestimated by up to a factor of 2, leading to measurements of absolute flow speed that are too large.

Thin-foil expansion into a vacuum

The collisionless expansion into a vacuum of a thin foil heated by an ultrashort laser pulse and adiabatically cooling down is studied with a particular emphasis on the structure of the accelerating field and on the resultant ion energy spectrum. For late times, a double layer structure at the ion front becomes the dominant feature. The dependence of the maximum ion velocity on the thin foil width is established. The effect of a two-temperature electron distribution function is discussed.

Ultra hard x rays from krypton clusters heated by intense laser fields

The interaction of ultrashort laser pulses with krypton clusters at intensity up to 1.3×1018 Wcm−2 has been investigated. Intense Kα and Kβ emission from krypton at 12.66 and 14.1 keV, respectively, has been observed using conventional solid state x-ray detectors. The measured x-ray spectra have broad bremsstrahlung continuum reaching to photon energies up to 45 keV, with evidence that approximately 10% of electrons that are heated to very high electron temperatures, which is consistent with a two-temperature electron distribution. This is ascribed to the presence of a hot electron population, similar to that found in laser–solid interactions. The highest laser energy to x-ray conversion efficiency observed is 9.2×10−7, which is equivalent to 45 nJ x-ray pulse energy from the 12.66 keV krypton Kα transition.

Shape of ion energy spectra in ultra-short and intense laser?matter interaction

Structured proton spectra and a two-temperature electron distribution were simulated using a 1D3V particle-in-cell code for a plasma created by 35-fs laser pulses with an intensity of I≥1019 W/cm2. Such a two-temperature electron distribution was used as a prerequisite for a fluid dynamical model allowing us to describe the experimentally measured deep dips in the proton energy spectra of laser-produced plasmas from water-droplet targets.

Charge separation effects in solid targets and ion acceleration with a two-temperature electron distribution.

The electrostatic field at the solid-vacuum interface generated by two electron populations with different thermal energies, each following a Boltzmann distribution, is analytically derived from the Poisson equation and studied in terms of plasma parameters. In particular, the effect of the pressure of each of the two populations on the amplitude of the electric field and on its spatial extension is described. In order to evaluate the cold electron temperature, an analytical model for the Ohmic heating of the background electron population by laser generated fast electrons is developed and the consequences on ion detachment, ionization, and acceleration processes in laser-solid experiments are discussed. The efficiency of ion acceleration is shown to be controlled by the heating rate of the background electrons.

How wrong is collisional Monte Carlo modeling of fast electron transport in high-intensity laser-solid interactions?

The interaction of a high-intensity laser with a solid target generates a large current of fast electrons flowing into the target. Due to the large value of the current, the fast electrons generate significant electric and magnetic fields in the target and rapidly heat it to high temperatures. However, these effects were neglected in interpreting x-ray emission experiments, so the details of the fast electron generation that were inferred could be incorrect. This is considered, theoretically, for layered target, Kalpha emission experiments, by using a hybrid Monte Carlo code that includes field generation. The code is used to model such experiments with aluminum and plastic targets, using fast electron parameters taken from experimental results for average intensities of around 10(18) W cm(-2). These numerical results are then interpreted in the same manner as previous experiments, using only the Monte Carlo part of the code. The field generation leads to lower total emission and to an apparent two-temperature fast electron distribution. The laser absorption into fast electrons inferred by Monte Carlo modeling is consistently lower than the actual value. The mean fast electron energy inferred could be either higher or lower than the actual value, depending on the experimental setup and the cone angle and energy distribution used in the Monte Carlo modeling. The errors caused by neglecting the fields are, in general, greater for plastic than aluminum targets, leading to inconsistencies in results obtained by Monte Carlo modeling.

Inverse bremsstrahlung in a plasma with electron temperature anisotropy

Inverse bremsstrahlung absorption of electromagnetic radiation in plasma with anisotropic two-temperature bi-Maxwellian electron distribution function over velocities is investigated. In the case of a weak field, absorption is more effective if the radiation field is polarized in the plane in which the plasma electrons have the smaller of the two temperatures. In the case when the distribution function is highly anisotropic, absorption changes strongly when the field polarization changes its direction with respect to the temperature anisotropy axis. In the intermediate domain, when the field is strong in directions not very close to that of the larger temperature, both absorption efficiency and degree of its anisotropy decrease. The conditions when the absorbed power practically does not depend on the field are established. Finally, in the case of a strong field, absorption decreases further while the degree of anisotropy is a weakly changing logarithmic function of effective electron temperatures.

Ion acceleration during adiabatic plasma expansion: Renormalization group approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.

Effect of two-temperature electron distribution on the Bohm sheath criterion

The effect of two-temperature electron distribution on the Bohm sheath criterion is studied in a collisionless sheath layer in contact with a perfectly absorbing wall. A modified Maxwell-Boltzmann model is used for the electron distribution functions, which considers the effect that the electrons above the sheath potential energy do not reflect back into the plasma. The present model shows that the Bohm velocity at the sheath edge is much more independent of the hotter species than what was understood previously with a simple Maxwell-Boltzmann electron model. {copyright} {ital 1996} {ital The American Physical Society}

Modeling electronegative plasma discharges

A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane rf driven oxygen plasma for two cases: (1) p=50 mTorr, ne0=2.4×1015 m−3, and (2) 10 mTorr, ne0=1.0×1016 m−3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be α0≊8, while in the higher power case α0≊1.3. Using an electron energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of α0 are found to be close to, but somewhat larger than, the simulation values. The average electron temperature found self-cosistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.

Bohm velocity with a two-temperature distribution of negative particles

A one-dimensional simulation of a low-pressure RF-driven discharge is used to verify the theoretical prediction of the Bohm velocity of ions at the sheath edge for a two-temperature electron distribution. Simulation results indicate that the Bohm velocity is geared to the cooler species, provided that it contains most of the electrons. A similar comparison is performed for an electronegative plasma. >

Magnetic field behavior beyond the laser spot

A self-consistent, analytic solution for the two-dimensional, rotationally symmetric, time varying problem of the interaction of a laser plasma with its self-generated magnetic field has been determined at lateral locations away from the laser spot. The plasma is described by a two-fluid model, with the magnitude of the electron velocity much greater than the ion velocity. Increased spatial gradients in the density and velocity around the magnetic field maximum have been found. This leads to a double humped ion-velocity spectrum, which could be interpreted in terms of a two-temperature electron distribution, in qualitative agreement with experiment.

Cyclotron emission from a toroidal plasma with an isotropic two-temperature electron distribution

A modified Kirchhoff law is applied to the evaluation of the cyclotron emission from a toroidal plasma with a suprathermal electron component with Maxwellian distribution. The radiation temperature is obtained for the ordinary wave at the first cyclotron harmonic and for the extraordinary wave at the second cyclotron harmonic, both for transverse and oblique propagation with respect to the toroidal magnetic field.