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We present the results of a joint experimental and theoretical study of plasma expansion arising from Nd:YAG laser ablation (laser wavelength λ = 1.064 μm) of tin microdroplets in the context of extreme ultraviolet lithography. Measurements of the ion energy distribution reveal a near-plateau in the distribution for kinetic energies in the range 0.03-1 keV and a peak near 2 keV followed by a sharp fall-off in the distribution for energies above 2 keV. Charge-state resolved measurements attribute this peak to the existence of peaks centered near 2 keV in the Sn3+-Sn8+ ion energy distributions. To better understand the physical processes governing the shape of the ion energy distribution, we have modelled the laser-droplet interaction and subsequent plasma expansion using two-dimensional radiation hydrodynamic simulations. We find excellent agreement between the simulated ion energy distribution and the measurements both in terms of the shape of the distribution and the absolute number of detected ions. We attribute a peak in the distribution near 2 keV to a quasi-spherical expanding shell formed at early times in the expansion.

Experiments aimed at investigation of X-ray self-emission of plasma of heated targets consisting of layers of different materials (Mylar, polypropylene, In, Sn, and Au) exposed to the action of energy flux of X‑ray radiation (the so-called energy exposure of the target) of up to 10 kJ/cm2 were carried out. A Z-pinch induced by implosion of a tungsten wire-array by current of up to 4 MA in Angara-5-1 facility was used as a source of high-power X-ray radiation. The temporal dynamics of intensity of self-emission of heated targets was studied. In the process, contribution of expanding layer of a material with high atomic number Z to self-emission of the target dominates that of a Mylar film with effective charge Zeff ≈ 4.5. It is demonstrated that the 1/e decay time of target emission depends on expansion dynamics of target plasma. The latter, in turn, depends on orientation of the layer characterized by high atomic number relative to the source of radiation. New data on spectral composition of self-emission of targets and its changes with time is obtained. This data is compared with the results of numerical simulation of target heating and scatter by means of RALEF-2D two-dimensional radiation gas-dynamic code.

Extreme ultraviolet (EUV) lithography is currently entering high-volume manufacturing to enable the continued miniaturization of semiconductor devices. The required EUV light, at 13.5 nm wavelength, is produced in a hot and dense laser-driven tin plasma. The atomic origins of this light are demonstrably poorly understood. Here we calculate detailed tin opacity spectra using the Los Alamos atomic physics suite ATOMIC and validate these calculations with experimental comparisons. Our key finding is that EUV light largely originates from transitions between multiply-excited states, and not from the singly-excited states decaying to the ground state as is the current paradigm. Moreover, we find that transitions between these multiply-excited states also contribute in the same narrow window around 13.5 nm as those originating from singly-excited states, and this striking property holds over a wide range of charge states. We thus reveal the doubly magic behavior of tin and the origins of the EUV light., Extreme ultraviolet (EUV) light is entering use in nanolithography. Here the authors discuss experimental and theoretical results about the prominent role of multiply-excited states in highly charged tin ions in the mechanism of EUV light emission from laser-produced plasma.

We explore the deformation of tin microdroplets of various diameters induced by two consecutive laser pulses having pulse durations of 0.4 ns. Impact of laser pulses with this duration mainly leads to shock-wave-induced cavitation and spallation. The main result obtained in this work is the observation of a strong reduction of the spall velocity that depends on the time delay between the two pulses. This reduction reveals a complex interplay between plasma recoil pressure and shock-wave-driven deformation, and enables an estimation of the moment of spall formation and the average shock-wave propagation velocity. We find that the shock wave traverses the droplet with an average velocity ranging from 1.2 to 1.6 times the speed of sound. We study the effects of the energy of the second pulse on the deformation and qualitatively discuss the formation of microjets. Crucially, we demonstrate the ability to manipulate the microdroplet expansion and spallation with double-pulse sequences, thereby increasing the portfolio of obtainable target shapes for droplet-based extreme ultraviolet light sources.

A finite-difference algorithm is proposed for numerical modeling of hydrodynamic flows with rarefaction shocks, in which the fluid undergoes a jump-like liquid-gas phase transition. This new type of flow discontinuity, unexplored so far in computational fluid dynamics, arises in the approximation of phase-flip (PF) hydrodynamics, where a highly dynamic fluid is allowed to reach the innermost limit of metastability at the spinodal, upon which an instantaneous relaxation to the full phase equilibrium (EQ) is assumed. A new element in the proposed method is artificial kinetics of the phase transition, represented by an artificial relaxation term in the energy equation for a “hidden” component of the internal energy, temporarily withdrawn from the fluid at the moment of the PF transition. When combined with an appropriate variant of artificial viscosity in the Lagrangian framework, the latter ensures convergence to exact discontinuous solutions, which is demonstrated with several test cases.

The hybrid model of laser energy deposition is a combination of the geometrical-optics ray-tracing method with the one-dimensional (1D) solution of the Helmholtz wave equation in regions where the geometrical optics becomes inapplicable. We propose an improved version of this model, where a new physically consistent criterion for transition to the 1D wave optics is derived, and a special rescaling procedure of the wave-optics deposition profile is introduced. The model is intended for applications in large-scale two- and three-dimensional hydrodynamic codes. Comparison with exact 1D solutions demonstrates that it can fairly accurately reproduce the absorption fraction in both the s - and p -polarizations on arbitrarily steep density gradients, provided that a sufficiently accurate algorithm for gradient evaluation is used. The accuracy of the model becomes questionable for long laser pulses simulated on too fine grids, where the hydrodynamic self-focusing instability strongly manifests itself.

Dynamics and spectral transmission of Al plasma produced by extreme ultraviolet (EUV) irradiation of 0.75-μm thick Al foil is investigated. The EUV radiation with the peak power density in the range of 0.19–0.54 TW/cm2 is provided by Z-pinch formed by W multiwire array implosion in the Angara-5-1 facility. Geometry of the experiment ensures that there are no plasma fluxes from the pinch toward the Al foil and plasma. The same EUV source is used as a back illuminator for obtaining the absorption spectrum of Al plasma in the wavelength range of 5–24 nm. It comprises absorption lines of ions Al4+, Al5+, Al6+, Al7+. Analysis of relative intensities of the lines shows that those ions are formed in dense Al plasma with a temperature of ∼20 eV. Dynamics of Al plasma has been investigated with transverse laser probing. We have also performed radiation-gas-dynamics simulations of plasma dynamics affected by external radiation, which includes self-consistent radiation transport in a plasma shell. The simulations show good agreement with an experimental absorption spectrum and with experimental data concerning plasma dynamics, as well as with the analysis of line absorption spectrum. This confirms the correctness of the physical model underlying these simulations.

We present mathematical models and methods of the computational experiment using a three-dimensional RMHD model simulating the implosion of Z-pinches formed by an imploding cylindrical array of thin tungsten wires. The calculations take into account the discrete structure of the array and the extended plasma formation at the evaporation of the wire material and they yield the estimated values of the output power and X-ray spectrum. The data are presented on the spatio-temporal distribution in the parameters of the Z-pinch plasma, including the velocity, electron and ion temperatures, ionization degree, and the power output integrated over space. We have also calculated the characteristics of the Z- pinch X-ray spectrum depending on the photon energy at different times after the discharge current starts. It has been found that the trailing mass of tungsten on the periphery affects the emission intensity of the central part of the pinch in the radial direction, which can be explained by the emission absorption in the peripheral plasma layers of the trailing tungsten mass. A detailed model has been constructed of the central pinch formed by the electric current implosion of the material of multiwire tungsten arrays. This model enables one to calculate the intensity of the soft X-ray emission with a temporal, spatial, angular, and spectral resolution for specific experiments on the Angara-5-1 experimental complex intended to study the implosion of cylindrical multiwire arrays, for which there is sufficient information about the time profile of the absolute emission intensity in the low-energy range of the X-ray emission. The obtained numerical results can be directly compared with the experimental values. The RMHD model simulating the implosion of Z-pinches has been verified by comparing its results with the experimental implosion indicators.

The effect of induced transparency of thin Al foils radiatively heated by intense extreme ultraviolet (EVU) radiation has been observed. The radiation of the plasma of Z-pinches appearing under the compression of tungsten liners at the Angara-5-1 facility has been used as the radiation that heats the Al foil (peak illumination on the foil ~0.55 TW/cm2) and is transmitted through it. The photoabsorption has been studied in the formed aluminum plasma at temperatures of ~10–30 eV in the density range of ~1–20 mg/cm3 in the wavelength range of ~5–24 nm. Absorption lines of Al4+...7+ ions have been identified in the experimental spectrum. In addition, radiative gas-dynamic simulations of the foil heating and expansion have been performed taking into account radiation transfer processes.

It is proposed to evaluate the effects of thermodynamic metastability on fluid dynamics by comparing two different ideal-hydrodynamics solutions --- one obtained with the fully equilibrium equation of state using the Maxwell construction, and the other in what we call the phase-flip approximation. The latter is based on the assumption of instantaneous decay of metastable states upon reaching the spinodal. The proposed method is applied to the classical problem of the centered rarefaction wave by expansion into vacuum, for which exact analytical solutions exist in both approximations. It is shown that the rapid decay of metastable states leads to the formation of a rarefaction shock in the expanding flow. Implications for the laser-heating experiments are discussed.

The measurement of the propulsion of metallic microdroplets exposed to nanosecond laser pulses provides an elegant method for probing the ablation pressure in dense laser-produced plasma. We present the measurements of the propulsion velocity over three decades in the driving Nd:YAG laser pulse energy, and observe a near-perfect power law dependence. Simulations performed with the RALEF-2D radiation-hydrodynamic code are shown to be in good agreement with the power law above a specific threshold energy. The simulations highlight the importance of radiative losses which significantly modify the power of the pressure scaling. Having found a good agreement between the experiment and the simulations, we investigate the analytic origins of the obtained power law and conclude that none of the available analytic theories is directly applicable for explaining our power exponent., Comment: 11 pages, 8 figures

We present a new double hohlraum target for the creation of a moderately coupled ( 0.1 Γ 1 ) carbon plasma for energy loss and charge state measurements of projectile ions interacting with this plasma. A spherical cavity of 600 μ m in diameter is heated with a 150-J laser pulse ( λ L = 527 nm ) within 1.2 ns to produce a quasi-Planckian X-ray source with a radiation temperature of T r ≈ 100 eV . These X-rays are then used to heat volumetrically two thin carbon foils in a secondary cylindrical hohlraum to a dense plasma state. An axi-symmetric plasma column with a free-electron density of up to 8 × 10 21 cm - 3 , a temperature of T ≈ 10 eV, and an average ionization degree of Z ≈ 3 is generated. This plasma stays in a dense and an almost uniform state for about 5 ns . Ultimately, such targets are supposed to be used in experiments where a heavy ion beam is launched through the sample plasma, and the ion energy losses as well as the charge distributions are to be measured. The present paper is in a certain sense a symbiotic one, where the theoretical analysis and the experimental results are combined to investigate the basic properties and the prospects of this type of plasma targets.

The energy deposition of ions in dense plasmas is a key process in inertial confinement fusion that determines the α-particle heating expected to trigger a burn wave in the hydrogen pellet and resulting in high thermonuclear gain. However, measurements of ion stopping in plasmas are scarce and mostly restricted to high ion velocities where theory agrees with the data. Here, we report experimental data at low projectile velocities near the Bragg peak, where the stopping force reaches its maximum. This parameter range features the largest theoretical uncertainties and conclusive data are missing until today. The precision of our measurements, combined with a reliable knowledge of the plasma parameters, allows to disprove several standard models for the stopping power for beam velocities typically encountered in inertial fusion. On the other hand, our data support theories that include a detailed treatment of strong ion-electron collisions., The energy loss of ions in plasma is a challenging issue in inertial confinement fusion and many theoretical models exist on ion-stopping power. Here, the authors use laser-generated plasma probed by accelerator-produced ions in experiments to discriminate various ion stopping models near the Bragg peak.

Remaining within the pure hydrodynamic approach, we formulate a self-consistent model for simulating the dynamic behavior of matter passing through metastable states in the two-phase liquid-vapor region of the phase diagram. The model is based on the local criterion of explosive boiling, derived by applying the theory of homogeneous bubble nucleation in superheated liquids. Practical application of the proposed model is illustrated with hydrodynamic simulations of a volumetrically uniformly heated planar layer of fused silica SiO2. Implications for experimentally measurable quantities are briefly discussed. A newly developed equation of state, based on the well known QEOS model and capable of handling homogeneous mixtures of elements, was used in the numerical simulations., 14 pages, 9 figures

Simulations have been performed to study the energy loss of carbon ions in a hot, laser-generated plasma in the velocity region of the stopping-power maximum. In this parameter range, discrepancies of up to 30% exist between the various stopping theories and hardly any experimental data are available. The considered plasma, created by irradiating a thin carbon foil with two high-energy laser beams, is fully-ionized with a temperature of nearly 200 eV. To study the interaction at the maximum stopping power, Monte-Carlo calculations of the ion charge state in the plasma are carried out at a projectile energy of 0.5 MeV per nucleon. The predictions of various stopping-power theories are compared and experimental campaigns are planned for a first-time theory benchmarking in this low-velocity range.

A new algorithm for solution of diffusion equations in two dimensions on structured quadrilateral grids is proposed. The algorithm is based on a semi-implicit method for the time discretization and has a nine-point local stencil in space. Our scheme is fast, quite accurate and demonstrates good spatial convergence. The presented numerical tests show that it is well suited for hydrocodes with cell-centered principal variables.

Efficient focusing of intense heavy ion beams is an important issue for heavy-ion driven inertial confinement fusion and for investigations of high energy densities in matter produced by heavy ion beams. Here, the description and the results of performance investigation of a plasma lens designed for the heavy-ion accelerator-accumulator facility TWAC-ITEP are presented.

The energy loss of light ions in dense plasmas is investigated with special focus on low to medium projectile energies, i.e., at velocities where the maximum of the stopping power occurs. In this region, exceptionally large theoretical uncertainties remain and no conclusive experimental data are available. We perform simulations of beam-plasma configurations well suited for an experimental test of ion energy loss in highly ionized, laser-generated carbon plasmas. The plasma parameters are extracted from two-dimensional hydrodynamic simulations, and a Monte Carlo calculation of the charge-state distribution of the projectile ion beam determines the dynamics of the ion charge state over the whole plasma profile. We show that the discrepancies in the energy loss predicted by different theoretical models are as high as 20-30%, making these theories well distinguishable in suitable experiments.

New exact results are obtained for relativistic acceleration of test positive ions in the laminar zone of a planar electron sheath evolving from an initially mono-energetic electron distribution. The electron dynamics is calculated against the background of motionless foil ions. The limiting gamma-factor γp∞ of accelerated ions is shown to be determined primarily by the values of the ion-electron charge-over-mass ratio μ=meZp/mp and the initial gamma-factor γ0 of the accelerated electrons. For μ> 1/8 a test ion always overtakes the electron front and attains γp∞> γ0. For μ< 1/8 a test ion can catch up with the electron front only when γ0 is above a certain critical value γcr, which for μ≪1 can most often be evaluated as $\gamma_{cr} = ({1}/{4}) \mu\exp\left(\mu^{-1}-1\right)$ . In this model the protons and heavier test ions, for which γcr> 10398 is enormous, always lag behind the front edge of the electron sheath and have γp∞< γ0; for their maximum energy an appropriate intermediate asymptotic formula is derived. The domain of applicability of the laminar-zone results is analyzed in detail.

A new experimental area has been set up at the RFQ accelerator at ITEP (Moscow) to investigate the interaction of ions with gases and plasmas. The HIPr-ITEP accelerator provides ion beams at a specific energy of 100 keV/u. This energy is particularly suitable for studying the interaction of ions with cold and ionized matter below the maximum of the stopping power. As a first step, the new installation was used to measure the energy loss of copper ions in the nitrogen and hydrogen gases. Equilibrium stopping power values were determined and (as no previous experimental data for the Cu ions below the stopping power maximum existed) compared to the available semiempirical codes SRIM 2000, SRIM 2003, and with the new STIP code based on a clearly defined theoretical model which is now under development at ITEP.

The acceleration of ions by ultra-intense lasers has attracted great attention due to the unique properties and the unmatched intensities of the ion beams. In the early days the prospects for applications were already studied, and first experiments have identified some of the areas where laser accelerated ions can contribute to the ongoing inertial confinement fusion (ICF) research. In addition to the idea of laser driven proton fast ignition (PFI) and its use as a novel diagnostic tool for radiography the strong dependence on the electron transport in the target was found to be helpful in investigating the energy transport by electrons in fast ignitor scenarios. More recently an additional idea has been presented to use laser accelerated ion beams as the next generation ion sources, and taking advantage of the luminosity of the beams, to develop a test bed for heavy ion beam driven inertial confinement fusion physics. We review our recent experiments and simulations relevant to ICF research presenting a possible scenario for PFI as well as the prospects for next generation ion sources.

The concept of a power plant for fast-ignition heavy ion fusion is developed. It is based on repetitive detonation of a cylindrical direct-drive target, producing 750 MJ of fusion yield in each microexplosion. A heavy-ion driver system providing consequent compression and ignition of the cylindrical DT target is described. Data on energy fluxes generated by the microexplosion are given. The design of the thin liquid wall reactor chamber is presented. The behaviour of the liquid film at the first wall and the blanket coolant and material under a pulsed energy flux loading is analysed. The energy conversion thermal scheme and power plant output parameters are presented. The state of the art at the ITEP-TWAC experimental accelerator is described.

The concept of a power plant for a fast ignition heavy ion fusion is briefly reviewed. The reactor chamber response to x-ray irradiation, ion debris and neutron flux is considered. Ablation of a thin liquid film at the first wall is simulated by means of a one-dimensional hydrodynamic code. Ion debris reheating of the vaporized coolant is evaluated. Vaporization and subsequent condensation of the coolant is computed with the use of a kinetic model of fast condensation. Heating of the blanket due to neutron deposition and corresponding generation of pressure and stress waves are simulated by means of the Monte Carlo (MCNP) code and by the strength media mechanics code, respectively.

This paper reports the results of a series of experiments on laser generated ions using the 100 TW laser at the ‘Laboratiore pour l’Utilisation des Lasers Intenses (LULI)’ at the Ecole Polythechnique in Palaiseau, France, and the 30 TW ‘Trident’ facility at Los Alamos National Laboratories in New Mexico, USA. It shows the importance of the ‘Target Normal Sheath Acceleration’ process (TNSA) for short pulse laser generated ion beams and its connection to the influence of target properties on the ion beam quality. It is shown that TNSA-generated protons form an ion beam with superior beam quality, following versatile spatial beam shaping approaches. These insights are set into perspective for a fast ignitor scenario based on short pulse laser generated protons.

The concept of power plant for a fast ignition heavy-ion fusion (FIHIF) is being developed. The characteristics of super-high-energy-ion driver are described. The scenario of 750 MJ fusion yield target compression and detonation is evaluated. The data on reactor chamber response to energy fluxes generated by microexplosion are given. The energy conversion thermal scheme and power plant output parameters are presented.

The features are studied of plasma production in the initial stage of implosion of hollow cylindrical wire arrays at electric-field growth rates of 1012 V/(cm s). The results are presented from the analysis of both UV emission from the wire plasma and the discharge parameters in the initial stage of the formation of a Z-pinch discharge. It is found that, a few nanoseconds after applying voltage to a tungsten wire array, a plasma shell arises on the wire surface and the array becomes a heterogeneous system consisting of metal wire cores and a plasma surrounding each wire (a plasma corona). As a result, the current switches from the wires to the plasma. A further heating and ionization of the wire material are due primarily to heat transfer from the plasma corona. A model describing the primary breakdown along the wires is created with allowance for the presence of low-Z impurities on the wire surface.

An overview of recent progress in the theory of inertial confinement fusion (ICF) targets is presented. Work on traditional target schemes, based on the hydrodynamic mode of ignition, is reviewed only briefly, while most of the attention is devoted to the fast ignition approach. The general advantages of fast ignition are illustrated with a simple model for characteristic assembled fuel configurations. Special attention is paid to a newly proposed concept of a cylindrical reactor-size target, compressed and ignited (in the fast ignition mode) by two separate beams of very energetic (Ei 0.5 GeV u−1) heavy ions.

A possibility is analyzed to use direct drive cylindrical targets in the fast ignition mode irradiated by beams of nearly relativistic heavy ions with long ranges in matter. The minimum beam energy required to compress the DT fuel in a 1-cm-long target to (ρR)DT = 0.5 g/cm2, ρDT = 100 g/cm3 is found to lie in the range 10–15 MJ. Ignition and axial burn propagation is achieved with a 0.2-ns, 0.4-MJ pulse of 100-GeV heavy ions. Thermonuclear energy gains in the range 50–150 appear to be possible.

We present the measurements and theoretical analysis of the deformation and fragmentation of spherical liquid–metal drops by picosecond and subpicosecond laser pulses. In the experiments, 60 μm droplets of Sn–In alloy were irradiated by Ti:Sa laser pulses with a peak energy fluence of ~100 J cm−2. The observed evolution of the droplet shape dramatically differs from that previously reported for nanosecond pulses. Invoking 2D hydrodynamic simulations, we explain how, due to the specifics of matter dynamics in the liquid–vapor phase coexistence region, a liquid droplet is transformed into a characteristic acorn-like expanding shell with two inner cavities. High sensitivity of the measured shell parameters to the details of the equation of state and metastable dynamics suggests that such experiments offer new possibilities in exploration of thermophysical properties of metals in the region of liquid–vapor phase transition.

Intense beams of heavy ions, envisaged for the near future at the Institute for Theoretical and Experimental Physics (Moscow) and Gesellschaft fur Schwerionenforschung (Darmstadt), will be well suited for conducting implosion experiments in cylindrical geometry. In such implosions, the initial pressure generated by the direct beam heating can be enhanced by more than a factor of 10. If, in addition, an external magnetic field is introduced, the effect of magnetothermal insulation may allow to reach kilovolt temperatures and significant thermonuclear neutron yields in magnetized implosions driven by the beam heating intensities as low as e≃1 TW/g. It is shown how the combined effect of the electrical resistivity and thermal conductivity sets a lower limit on the product UR (R is the radius, and U is the velocity of an imploding plasma volume) as a necessary condition for the regime of self-sustained magnetized implosion (SSMI). The optimal plasma parameters required for initiation of this regime are evalu...

In connection with fundamental issues relevant to magnetized target fusion, the distribution function of thermonuclear alpha particles produced in situ in a dense, hot, and strongly magnetized hydrogenic plasma considered fully ionized in a cylindrical geometry is investigated. The latter is assumed in local thermodynamic equilibrium with Maxwellian charged particles. The approach is based on the Fokker–Planck equation with isotropic source S and loss s terms, which may be taken arbitrarily under the proviso that they remain compatible with a steady state. A novel and general expression is then proposed for the isotropic and stationary distribution f(v). Its time-dependent extension is worked out numerically. The solutions are valid for any particle velocity v and plasma temperature T. Higher order magnetic and collisional corrections are also obtained for electron gyroradius larger than Debye length. f(v) moments provide particle diffusion coefficient and heat thermal conductivity. Their scaling on colli...

Ignition conditions in axially magnetized cylindrical targets are investigated by examining the thermal balance of assembled DT fuel configurations at stagnation. Special care is taken to adequately evaluate the energy fraction of 3.5 MeV alpha particles deposited in magnetized DT cylinders. A detailed analysis of the ignition boundaries in the ρR,T parametric plane is presented. It is shown that the fuel magnetization allows a significant reduction of the ρR ignition threshold only when the condition BR 6 × 105G cm is fulfilled (B is the magnetic field strength and R is the fuel radius).

We report on measurements of the equation-of-state of copper and gold in the multi-ten Megabar range, opacity measurements based on K-shell absorption in aluminium, and X-ray laser studies on a large number of neon-like ions applying the prepulse technique. For these investigations, the one-beam iodine laser facility ASTERIX emitting pulses with energies of up to 1000 J at 1315 nm and of up to 420 J at 438 nm was used. We also give a brief account of experimental and theoretical results referring to the propagation of an ultrashort pulse through underdense hydrogen or nitrogen plasmas and X-ray spectra from an optically field-ionized nitrogen plasma generated either by linearly or elliptically polarized light. For these investigations, 150-fs/200-mJ/800-nm pulses emitted from our titanium:sapphire laser ATLAS were employed.

Scaling of the ignition energy threshold Eig with the implosion velocity vim and isentrope parameter α of imploding spherical DT shells is investigated by performing one dimensional (1-D) hydrodynamic simulations of the implosion and hot spot formation dynamics. It is found that the a and b exponents in the power law approximation Eig ∝ αavim-b depend crucially on the subset of initial configurations chosen to establish the scaling law. When the initial states are generated in the same way as in the Livermore study (W.K. Levedahl, J.D. Lindl, Nucl. Fusion 37 (1997) 165), the same scaling, Eig ∝ α1.7 vim-5.5, is recovered. If, however, the initial states are generated by rescaling the parent configuration according to the hydrodynamic similarity laws, a different scaling is obtained, Eig ∝ α3.0 vim-9.1, which is very close to the α3vim-10 dependence predicted by the simple isobaric model for assembled fuel states. The latter is more favourable than the Livermore scaling when rescaling the fusion capsules to higher implosion velocities, but requires the peak drive pressure to be increased as P ∝ vim5.

An overview of current activities on Heavy-Ion Fusion at ITEP is presented. A project called TWAC (TeraWatt Accumulator) is in progress now, aiming at the production of TeraWatt power level (100 kJ/100 ns) of intense heavy-ion beams, concentrated on experimental targets [1] . The project is based on the use of the existing accelerator chain at ITEP: A 2 MV/2.7 MHz heavy-ion injector I-3, a 13 Tm booster ring UK, a 34 Tm synchrotron U-10, a system of beam transfer lines and a laser ion source of He-like medium mass ions. Volume energy deposition of the heavy-ion beam in a target is expected to generate hot, strongly compressed matter with extremely high energy density (>1 MJ/g) in dense plasmas. The scientific program includes a number of challenging issues on accelerator physics, the physics of high energy density in matter and relativistic nuclear physics. The results of numerical simulations relevant to the suggested high energy density in matter experiments with TWAC beams are discussed. A survey of current experiments on beam–plasma interaction using the ITEP 3 MeV proton linac is given here.

We report the first simultaneous measurement of the reflectivity and optical emission of a strong (4\char21{}8 Mbar) shock front emerging at a free surface of a solid. Planar shock waves were driven by thermal x rays from a laser-heated cavity. The inferred model-independent brightness temperature of the shock front in silicon turns out to be significantly below the expected Hugoniot temperature. We find that our data cannot be explained within the two-temperature model which assumes instantaneous metallization of silicon in the density jump.

Coulomb energy losses by 3-MeV protons in a capillary discharge channel are used as a diagnostics tool to measure the plasma density. By combining the proton energy loss data with the electron temperature measurements,we have been able to diagnose the free electron density ${n}_{\mathrm{fe}}=6.4\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ in a 3.3-eV ${\mathrm{CH}}_{2}$ plasma to an accuracy of $\ifmmode\pm\else\textpm\fi{}17%$. A considerably better accuracy can be expected for higher values of the electron temperature.

A self-similar solution of the gas dynamics equations with heat conduction, which describes homologous contraction and expansion of gaseous masses with a free external boundary, is investigated in detail. As a primary application, implosion of deuterium–tritium (DT) fuel in inertial confinement fusion targets is considered. For strongly non-adiabatic implosions the self-similar solution predicts that the flow pattern should approach an asymptotical regime in which it ceases to depend on the initial entropy. For DT masses relevant to inertial confinement fusion (ICF) this regime begins to dominate at αUim≳6×108 cm/s, where α=p/pdeg is the fuel isentrope parameter, and Uim is its implosion velocity. The solution has also a branch which describes an asymptotical regime of explosive expansion after an ultra-fast initial heating to a strongly radiating state.

Optical signals from shock waves emerging at a free surface of metals are expected to yield information about the equation of state and the transport and relaxation properties of hot dense plasmas. We present the results of optical measurements on planar shock waves (velocity {approx_equal}22km/s, pressure {approx_equal}8Mbar) in solid aluminum which were generated by exposing a miniature sample to intense thermal x rays from a laser-heated cavity. The reflectivity of the free surface of the sample for the light from a probe laser ({lambda}=532nm) and the absolute value of its optical emission were simultaneously registered with a 7-ps temporal resolution. For interpretation we used a two-temperature hydrodynamic code which includes the electron heat conduction and electron-ion relaxation and accounts for the nonequilibrium shock structure. The underlying self-consistent model for the equation of state and the transport coefficients of a metal over the relevant range of thermodynamic parameters are described in some detail. The reflectivity decay signal, which yields direct information on the effective collision frequency in the unloading material, and the emission peak, which is sensitive to the heat conductivity and dielectric permittivity of the hot and dense plasma behind the shock front, are well reproduced by the simulations. Themore » emission signals are, however, longer than predicted, possibly due to the residual surface roughness in the experiment. On a longer time scale of 1{endash}2 ns, the emission signal is well described by a simple radiation transport model with the Kramers-Uns{umlt o}ld opacity. {copyright} {ital 1997} {ital The American Physical Society}« less

In this work, we present the results of two-dimensional radiation-hydrodynamics simulations of a hohlraum target whose outgoing radiation is used to produce a homogeneously ionized carbon plasma for ion-beam stopping measurements. The cylindrical hohlraum with gold walls is heated by a frequency-doubled ($\lambda_l = 526.5$ $\mu m$) $1.4$ $ns$ long laser pulse with the total energy of $E_l = 180$ $J$. At the laser spot, the peak matter and radiation temperatures of, respectively, $T \approx 380$ $eV$ and $T_r \approx 120$ $eV$ are observed. X-rays from the hohlraum heat the attached carbon foam with a mean density of $\rho_C = 2$ $mg/cm^3$ to a temperature of $T \approx 25$ $eV$. The simulation shows that the carbon ionization degree ($Z \approx 3.75$) and its column density stay relatively stable (within variations of about $\pm7\%$) long enough to conduct the ion-stopping measurements. Also, it is found that a special attention should be paid to the shock wave, emerging from the X-ray heated copper support plate, which at later times may significantly distort the carbon column density traversed by the fast ions., Comment: 12 pages, 12 figures

A modified version of the view factor equations is proposed which improves the accuracy of the description of temporal effects in energy redistribution by thermal radiation in cavities driven by power pulses typical for inertial confinement fusion (ICF). The method is applied to analyze the process of radiative symmetrization in the simplest type of closed cylindrical hohlraums heated by two x‐ray rings on the sidewall of the hohlraum case. Such hohlraums may be used in certain types of ICF targets driven by ion beams.

The investigation of beam-plasma interaction processes requires the development of plasma parameter diagnostic methods with high temporal and spatial resolution. The basic plasma parameters to be controlled when measuring the ion energy losses in ionized gases are the areal density of free electrons, the degree of ionization and the heavy element impurities during the electrical discharge in hydrogen. We present the relevant experimental results obtained by means of time-resolved, two-wavelength Mach-Zehnder interferometry based on HeNe ( λ = 0.63 μ m) and HeCd ( λ = 0.44 μ m) lasers. Optical emission line spectroscopy allowed us to follow the behaviour of the impurity concentrations with a high temporal resolution. Both methods have been used for diagnostic tests of a hydrogen plasma target.

Theoretical investigation has been performed on the conversion efficiency (CE) into the 13.5-nm extreme ultraviolet (EUV) radiation in a scheme where spherical microspheres of tin (Sn) are simultaneously irradiated by two laser pulses with substantially different wavelengths. The low-intensity short-wavelength pulse is used to control the rate of mass ablation and the size of the EUV source, while the high-intensity long-wavelength pulse provides efficient generation of the EUV light at λ=13.5 nm. The problem of full optimization for maximizing the CE is formulated and solved numerically by performing two-dimensional radiation-hydrodynamics simulations with the RALEF-2D code under the conditions of steady-state laser illumination. It is shown that, within the implemented theoretical model, steady-state CE values approaching 9% are feasible; in a transient peak, the maximum instantaneous CE of 11.5% was calculated for the optimized laser-target configuration. The physical factors, bringing down the fully o...

We report on a new experimental setup for ion energy loss measurements in dense moderately coupled plasma which has recently been developed and tested at GSI Darmstadt. A partially ionized, moderately coupled carbon plasma (ne ≤ 0.8• 1022 cm-3, Te = 15 eV, z = 2.5, Γ = 0.5) is generated by volumetrical heating of two thin carbon foils with soft X-rays. This plasma is then probed by a bunched heavy ion beam. For that purpose, a special double gold hohlraum target of sub-millimeter size has been developed which efficiently converts intense laser light into thermal radiation and guarantees a gold-free interaction path for the ion beam traversing the carbon plasma. This setup allows to do precise energy loss measurements in non-ideal plasma at the level of 10 percent solid-state density.

A new gain model based on an adiabatic self-similar solution of the hydrodynamic equations is proposed for inertial confinement fusion (ICF) targets ignited by means of a thermonuclear spark at the fuel centre. The model is applied to analyse gain curves corresponding to fixed values of the implosion velocity Uim. It is shown that the adequate ignition criterion, allowing for the inertia of the cold fuel, implies ρsRsTs varies as Uim at the time of ignition, as contrasted to fixed values of the spark areal density, ρsRs, and the temperature, Ts, assumed in many of the earlier publications. The modified ignition condition leads to the scaling Emin varies as α3Uim-7 and Gf* varies as (E/α3)0.4 for the ignition energy threshold, Emin, and the limiting fuel gain, Gf*, of ICF capsules; α is the isentrope parameter of the cold fuel, E is the energy invested in the DT fuel. Stability and symmetry constraints do not affect this scaling when the initial aspect ratio of the fusion capsule A0 >> 1; in the opposite case of initially thick capsule shells, the scaling of Emin and Gf* with Um, and α becomes ill defined