Density effects of heavy-ion stopping power in high temperature matter

Abstract

The stopping power and range for Xe ions in high temperature matter (partially ionized plasmas) have been calculated using the dielectric response function method. Calculations have been made for a target matter Al (Z = 13) over a wide range of temperatures and densities considering a finite temperature model. The stopping powers obtained have smaller values in comparison with those of a zero temperature model. The stopping power strongly depends on the density and temperature of the target material, and the projectile ion energy.     

A globally convergent method for computing the electron density of a partially ionized plasma

A stable, globally convergent method for computing the equilibrium electron density of a partially ionized plasma is presented. Since the Newton-Raphson method is used, the convergence is quadratic. In addition, global convergence is guaranteed in local thermodynamic equilibrium. The applicability of the method to non-LTE plasmas is discussed.     

Spectroscopic diagnostics of carbon and aluminum laser-produced plasmas

VUV emission spectra of plasmas produced by focusing laser radiation with intensity of 10¹⁰–10¹¹ W/cm² on carbon and aluminum targets were studied. Using the partial local thermodynamic equilibrium model for an electron density exceeding 10¹⁷ cm^?3, the spectroscopic diagnostics and the analysis of ion composition of plasmas were carried out. The electron temperatures determined for carbon and aluminum plasmas from the ratio of intensities of ionic lines were found to be 8±3 eV and 11±4 eV, respectively. Stark broadening of aluminum lines was measured and parameters of electron broadening were determined. Using the spatially resolved measurement of Stark line broadening, the spatial density distribution and the law of electron gas expansion were found. The electron gas in the hot region of size 5 mm with an average density of (5±2) 10₁₇cm ^?3 experienced one-dimensional expansion according to the law 1/z ^1.1 with increasing distance z from the target.     

Quantum molecular dynamics of partially ionized plasmas

We study a partially ionized hydrogen plasma by means of quantum molecular dynamics, which is based on wave packets. We introduce a new model which distinguishes between free and bound electrons. The free electrons are modelled as Gaussian wave packets with fixed width. For the bound states the 1s-wave function of the hydrogen atom is assumed. In our simulations we obtain thermodynamic properties in the equilibrium such as the internal energy and the degree of ionization. The degree of ionization is in good agreement with theoretical predictions. The thermodynamic functions agree well with results from quantum statistics for 10000 K ≲ T ≲ 40000 K.     

强激光部分离化等离子体成丝不稳定性

从部分离化等离子体和通常的全离化等离子体的差异是存在束缚电子出发,分析强激光在部分离化等离子体中的传播和折射指数,其束缚电子加强成丝不稳定性的发展.对钕玻璃三倍频激光金靶等离子体的原子成丝不稳定性进行了计算和分析.结果表明强激光部分离化等离子体的原子成丝不稳定性显著高于相对论成丝不稳定性. 关键词： 激光等离子体相互作用 部分离化等离子体 成丝不稳定性     

Experimental observation of excited state muon transfer in mixtures of hydrogen isotopes

Molecular dynamic (MD) computer simulations are used to investigate the stopping of heavy ions in strongly coupled electron plasmas. Our results show, that in this regime collisions between the electrons as well as non-linear screening effects yield at low ion velocities a dependence of the stopping power on the ion chargeZ which scales like Z^1.43 instead of the usual Z² ln(const/Z)-scaling for weak coupling. This is connected with an enhanced local density of electrons around a highly charged, slow ion.Supported by the Bundesministerium für Bildung und Forschung (BMBF), the Gesellschaft für Schwerionenforschung Darmstadt (GSI) and the European Community.     

Ionization Energies of Ions in Hot and Dense Plasma: Beryllium-Like Ions for Z=26-36

Ionization energies of beryllium-like ions for Z = 26 - 36 in hot ana aense plasmas （ne=10^22 -10^24 cm^-3,kT= 500 - 2000 eV） are obtained by using an approach developed for electronic structure and transition property of ions in hot and dense plasmas based on the multi-configuration Dirac-Fock model. Influence of the plasma environment is considered by introducing a correction to the one-electron potential to account for the screening of the ionized electrons. This correction is calculated from the ionized electron micro-space distribution, which is obtained based on an ＂average atom model for the temperature and density-dependent average ionization of atoms in plasmas. Comparison between the present and the ion sphere models is made to display the significance of the ionized electron micro-space distribution.     

Scattering of ultrashort laser pulses on “ion‐sphere” in dense plasmas

Scattering of ultrashort electromagnetic pulses on the dense strongly coupled plasma is under consideration in the frame of hard ion sphere model. The electron distribution inside the ion sphere is obtained from self‐consistent solution of the Shrodinger equation for bound electrons and the Poisson equation for free electrons. The electron density distribution is determined by plasma electron temperatures. The ion density of Al plasmas under consideration is of the order of 10²⁰–10²² cm^?3, the electron temperature changes between 54 and 816 eV. Dynamical polarizability of the hard sphere determining the scattering cross sections is calculated using the modified local plasma frequency approximation. The spectrum of scattering cross section has maxima in the vicinity of the mean plasma frequency. Dependencies of scattering probability on carrier frequency and pulse duration are analysed in detail. The transition of the total scattering probabilities from nonlinear time dependence at small times to standard linear ones with the increase of pulse duration is demonstrated.     

Kinetic analysis of the ionization ratio effects on a three‐species plasma

In partially ionized plasmas, the energy transferred to electrically charged species by the electromagnetic field can be partly channelized to the population of neutrals, due to interspecies collisional processes. Depending on the relative density of neutrals, these effects may govern the collective plasma dynamics by drastically modifying particle dynamics and energy‐transport processes with respect to the fully ionized plasma‐approximation models. In this work, the influence of the ionization ratio r_i on a partially ionized plasma is analysed by means of a three‐species one‐dimensional kinetic model to compute transient and steady state velocity‐dependent distribution functions. The conservative collision operators accounting for charge–charge and charge–neutral interactions allow studying several plasma scenarios with the same entire number of particles per unit of volume but for an increasing r_i parameter, in the presence of a modulated signal‐like electric field. For a sequence of plasma scenarios of fixed r_i, ranging from typical weakly ionized to highly ionized plasma values r_i ～ 10^?7–10^?4, the mass species flows are examined. These flows behave linearly with respect to r_i up to a value r_i ? 10^?5 from which the quasi‐linear dependence is critically altered. The convection–diffusion equations are solved with the semianalytical Propagator Integral Method, which behaves well to deal with conservative operators, density, and field discontinuities, allowing for the use of collision terms of disparate time and spatial characteristic scales. The results can be relevant to a wide class of plasma systems and to analyse the ionization ratio effects on transport coefficients.     

Nucleus-electron model for states changing from a liquid metal to a plasma and the Saha equation

We extend the quantal hypernetted-chain (QHNC) method, which has been proved to yield accurate results for liquid metals, to treat a partially ionized plasma. In a plasma, the electrons change from a quantum to a classical fluid gradually with increasing temperature; the QHNC method applied to the electron gas is in fact able to provide the electron-electron correlation at an arbitrary temperature. As an illustrating example of this approach, we investigate how liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV at a fixed normal ion density 1.03x10(22)/cm(3). The electron-ion radial distribution function (RDF) in liquid Rb has distinct inner-core and outer-core parts. Even at a temperature of 1 eV, this clear distinction remains as a characteristic of a liquid metal. At a temperature of 3 eV, this distinction disappears, and rubidium becomes a plasma with the ionization 1.21. The temperature variations of bound levels in each ion and the average ionization are calculated in Rb plasmas at the same time. Using the density-functional theory, we also derive the Saha equation applicable even to a high-density plasma at low temperatures. The QHNC method provides a procedure to solve this Saha equation with ease by using a recursive formula; the charge population of differently ionized species are obtained in Rb plasmas at several temperatures. In this way, it is shown that, with the atomic number as the only input, the QHNC method produces the average ionization, the electron-ion and ion-ion RDF's, and the charge population that are consistent with the atomic structure of each ion for a partially ionized plasma.     

Scattering processes and electrical conductivity of partially ionized hydrogen plasma

We consider partially ionized hydrogen plasma for the density region n_e = (10¹⁸ ÷ 10²²) cm^—3. The cross sections for scattering processes between the particles are calculated within the partial wave method. Charged particles in the system (electrons, protons) interact via an effective potential that takes into account threeparticle correlations. The Buckingham polarization potential is used to describe electron‐atom and proton‐atom interactions. The electrical conductivity is determined using the Chapman‐Enskog method. The results are compared with other available data.     

部分电离金属钛和银等离子体输运性质的计算

金属等离子体的组分为计算热力学、光学和辐射输运特性研究提供了基本的输入参数.为获得此参数,本文用部分电离等离子体模型,在考虑金属发生三次电离,以及电子与中性粒子的极化作用、离子与离子之间、电子与离子之间、电子与电子之间库仑相互作用下,计算得到了等离子体组分,进而用线性响应理论计算了金属钛和银的电导率.并与已有的实验数据进行了比较,验证了模型的可靠性.在此基础上进一步预测了密度在0.001—2.0 g/cm³、温度在1.5×10⁴—2.5×10^{4关键词： 等离子体 线性响应理论 电离度 输运系数}     

Losses and nonlinear steady-state particle distribution functions for fully ionized tokamak-plasmas in the collisional transport regimes

Fully ionized L-mode tokamak plasmas in the fully collisional (Pfirsch-Schlüter) and in the low-collisional (banana) nonlinear transport regimes are analyzed. We derive the expressions for particles and heat losses together with the steady-state particle distribution functions in the several collisional transport regimes. The validity of the nonlinear closure equations, previously derived, has been indirectly tested by checking that the obtained particle distribution functions are indeed solutions of the nonlinear, steady-state, Vlasov-Landau gyro-kinetic equations. A quite encouraging result is the fact that, for L-mode tokamak plasmas a dissymmetry appears between the ion and electron transport coefficients: the latter submits to a nonlinear correction, which makes the radial electron coefficients much larger than the former. In particular we show that when the L-mode JET plasma is out of the linear region, the Pfirsch-Schlüter electron transport coefficients are corrected by an amplification factor, which may reach values of order 10². Such a correction is absent for ions. On the contrary, in the banana regime, the ion transport coefficients are increased by a factor 2 and the nonlinear corrections for electrons are negligible. These results are in line with experiments.     

Fusion burning waves in degenerate plasmas

The outcome of fusion burning waves in non-degenerate plasmas is limited by the strength of ion–electron Coulomb collisions and subsequent energy loss mechanisms as electron heat conduction and radiation emission. In this Letter, an analysis is presented on the degeneracy effects in the stopping power of suprathermal charged particles and in the energy transmitted from ions to electrons by Coulomb collision. Main results of this analysis is that very powerful fusion burning waves can be launched into previously compressed degenerate plasmas. This can be specially suitable for proton–boron fusion, but it also applicable to any type of fusion reaction, where ignition can be triggered by an incoming ion beam or another external source of energy deposited in a small fraction of the compressed plasma (fast ignition).     

Fullerene C60 formation in partially ionized carbon vapor

The assembling rate of a fullerene C₆₀ molecule has been theoretically studied as a function of electron concentration and temperature in partially ionized carbon vapor. For C⁶⁰ formation via one or two intermediate stages of cluster collisions, it has been shown that there is a region of plasma parameters (the temperature and electron concentration) in which fullerene C₆₀ is formed more efficiently. The C₆₀ formation rate versus temperature and electron concentration relationships have been found to correlate with the trends in the collision cross-section of carbon clusters as functions of these parameters.     

Conformity between linear response and binary collision treatments of an ion energy loss in a magnetized quantum plasma

In this paper the energy loss of a heavy ion moving in a magnetized quantum electron plasma is considered within the linear response and binary collision treatments. Treating the electron-ion interaction force as a small perturbation to the electron nth Landau level we show within the second order perturbation theory the conformity between these two models.Received: 8 August 2003PACS: 52.40.Mj Particle beam interactions in plasmas - 34.50.Bw Energy loss and stopping power - 03.65.Nk Scattering theory - 52.20.Hv Atomic, molecular, ion, and heavy-particle collisions     

Classical Molecular Dynamics Model for Coupled Two‐Component Plasmas – Ionization Balance and Time Considerations

The dynamic properties of ion‐electron two‐component plasmas (TCP) are studied by using classical molecular dynamics (MD) simulations. There is a variety of time dependent and structural results that MD is able to provide in complement to other methods, e.g., useful micro‐field sequences can be generated. The method deals with some specific difficulties: the mass ratio between ions and electrons enforces very small time‐steps appropriate to follow electrons motion while, ions must move significantly in order to build, self consistently, their spatial structure. This results in expensive simulations. Electron trajectories are trapped and de‐trapped with multiple electron collisions around ions resulting in the occurrence of quasi metastable bound electron states. An analysis of micro‐fields at neutral in a hydrogen plasma reveals the need to consider a complete hierarchy of time scales extended typically over 7 order of magnitude, i.e., from a time‐step: ～10^‐19s, to a time required to obtain statistical averages, ～10^‐11s. In order to extend the MD capabilities in representing real coupled plasmas a classical ionization/recombination process has been implemented allowing to follow the evolution of plasmas involving several ion stages and model the ionization balance. Here again TCP simulations deal with extended time‐scale providing information about relaxation of non equilibrium plasma states (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Stark broadening of the He I 447.1 nm spectral line

Characteristics of the Stark broadened and overlapping 447.1 nm He I spectral line and its forbidden 447.0 nm components have been measured at electron densities between 4.4×10²² m^-3 and 8.2×10²² m^-3 and electron temperatures between 18 000 K and 33 000 K in plasmas created in five various discharge conditions using the low pressure pulsed arc as an optically thin plasma source operated in helium-nitrogen-oxygen gas mixture. Good agreement was found among our measured line characteristics and their existing calculated values, based on the quasistatic approximation. Possible influence of the singly ionized oxygen impurity atoms (O II) on the intensity values of the dip between allowed and forbidden components was found that can explain the disagreement among some existing experimental and calculated line characteristics data, at higher electron temperatures and densities. On the basis of the observed asymmetry of the 447.1 nm spectral line profile we have obtained the ion contribution parameter at 10²² m^-3 electron density and 8 000 K electron temperature. Received 20 February 2001 and Received in final form 25 April 2001     

Temperature measurements in plasmas generated by using lasers at different intensities

The temperature of laser-generated pulsed plasmas is an important property that depends on many parameters, such as the particle species and the time elapsed from the laser interaction with the matter and the surface characteristics.

Laser-generated plasmas with low intensity (<10¹⁰ W/cm²) at INFN-LNS of Catania and with high intensity (>10¹⁴ W/cm²) in PALS laboratory in Prague have been investigated in terms of temperatures relative to ions, electrons, and neutral species. Time-of-flight (ToF) measurements have been performed with an electrostatic ion energy analyzer (IEA) and with different Faraday cups, in order to measure the ion and electron average velocities. The IEA was also used to measure the ion energy, the ion charge state, and the ion energy distribution.

The Maxwell–Boltzmann function permitted to fit the experimental data and to extrapolate the ion temperature of the plasma core.

The velocity of the neutrals was measured with a special mass quadrupole spectrometer. The Nd:Yag laser operating at low intensity produced an ion temperature core of the order of 400 eV and a neutral temperature of the order of 100 eV for many ablated materials. The ToF of electrons indicates the presence of hot electron emission with an energy of ～1 keV.     

部分离化激光等离子体的受激喇曼散射不稳定性

由于部分离化激光等离子体中存在束缚电子，它可显著改变其参量不稳定性。本文分析了部分离化激光等离子体的受激喇曼散射的非线性色散关系，计算了钕玻璃倍频和三倍频激光受激喇曼散射的增长率，结果表明，前向受激喇曼散射显著增强，后向受激喇曼散射影响不大。