Mathematical modeling of gas-dynamic and radiative processes in experiments with the use of laser and heavy-ion beams

Results are presented from theoretical and experimental studies of gas-dynamic and radiative processes in the plasma that is planned to be used in future experiments on the stopping of fast heavy-ion beams. These experiments are aimed at measuring the enhanced (as compared to cold substance) plasma stopping power. To reliably interpret the experimental results, it is necessary to create a hydrodynamically stable homogeneous plasma with a uniform temperature and a lifetime exceeding the transit time of the heavy-ion beam (3–5 ns). The method for calculating plasma gas-dynamic characteristics with allowance for radiative heat transfer is described. The specific features of the so-called ion model of plasma, which is used to calculate plasma radiative characteristics, are discussed. The emission spectrum formed as a result of conversion of laser radiation into X-rays and the subsequent passing through a triacetate cellulose (C₁₂H₁₆O₈) target is calculated. The simulated spectrum of transmitted radiation satisfactorily agrees with experimental data.     

Accelerated electrons and hard X-ray emission from X-pinches

The generation of accelerated electrons in the X-pinch minidiode is studied experimentally. It is well known that the explosion of an X-pinch consisting of two or more wires is accompanied by the formation of a minidiode, in which electrons are accelerated. The subsequent slowing down of electrons in the products of wire explosion causes the generation of hard X-ray (HXR) emission with photon energies higher than 10 keV. In this work, the spatial and temporal characteristics of X-pinch HXR emission are studied, the specific features of HXR generation are discussed, and the capability of applying this radiation to point-projection X-ray imaging of various plasma and biological objects is considered. The parameters of the electron beam produced in the X-pinch are measured using a Faraday cup and X-ray diagnostics. The experiments were performed with the XP generator (550 kA, 100 ns) at Cornell University (United States) and the BIN generator (270 kA, 150 ns) at the Lebedev Physical Institute (Russia).     

Symmetric multilayer megampere X-pinch

Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of ∼1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.     

Spatiotemporal behavior of X-ray emission above 20 keV from a Z-pinch produced by wire-array implosion

Results are presented from experimental studies of hard X-ray (HXR) emission in the photon energy range above 20 keV from dense radiating Z-pinch plasmas. The work is aimed at revealing the nature of fast-electron (electron beam) generation during the implosion of cylindrical and conical wire arrays in the Angara-5-1 facility at currents of up to 3 MA. It is found that the plasma implosion zippering caused by the inclination of wires affects the parameters of the HXR pulse emitted during the implosion of a conical array. It is shown that HXR emission correlates well with the decay of the plasma column near the cathode in the stagnation phase. HXR images of the pinch are produced by the bremsstrahlung of fast electrons generated during plasma column decay and interacting with plasma ions and the anode target. It is found that the use of conical arrays makes it possible to control the direction of plasma implosion zippering and the spatiotemporal and energy parameters of the pinch X-ray emission, in particular the X-ray yield. For wire array with diameters of 12 mm and linear masses of 200–400 μg/cm, the current of the fast electron beam is 20 kA and its energy is 60 J, which is about 1/500 of the energy of the main soft X-ray pulse.     

X-ray backlighting of the axial region of a multiwire liner plasma in the angara-5-1 facility

Results are presented from experiments on the X-ray backlighting of the axial region of an imploding high-current multiwire liner. Backlighting was performed with the use of an X-pinch serving as a source of soft X-ray emission, which was recorded by pin diodes. The use of several filters with different passbands in front of the pin diodes allowed the interpretation of the results of measurements in experiments with cascade composite liners. The sensitivity of the diagnostics was ≈125 µg/cm² for a plasma of high-Z elements (W) and ≈220 µg/cm² for a plasma of low-Z elements (C, O, N) at a photon energy of the probing radiation of 1.0–1.5 keV. An advantage of the method is its high time resolution (≈1 ns) and the possibility of the separation in time of the emission bursts from Z-and X-pinches on the liner axis. The method does not impose restrictions on the pulse duration of the backlighting radiation source.     

Laser radiation scattering from the wires and fibers of imploding arrays on the Angara-5-1 facility

A method is developed for measurements of laser radiation scattering by wires and fibers in different types of imploding arrays in the initial stage of plasma production at discharge currents per wire of up to 2 kA for aluminum arrays and up to 8 kA for tungsten arrays. The experiments were carried out on the Angara-5-1 facility at a current density in the wires of 10⁸ A/cm² and current growth rate of ～10¹³ A/s. It is found that the indicatrix of laser radiation reflected from the wires (fibers) in cylindrical and conical arrays is modified at currents of 0.1–10 kA per wire (fiber). The experimental data on the reflection and scattering of laser radiation from wires and fibers are compared with the results of numerical simulations of their electric explosion in vacuum. It is proposed that the change in the reflection indicatrix of laser radiation is caused by the onset of thermal instabilities. The typical size of density and temperature inhomogeneities on the wire surface is in a range of 10–20 μm, which probably results in a transition from specular to diffuse reflection of laser radiation. A simultaneous abrupt (over 2–3 ns) reduction in the reflection intensity from several wires of an array indicates a homogeneous distribution of the discharge current over the irradiated wires. This closes the issue of the quality of the contact between the wires and the electrodes. The obtained experimental information is of considerable importance for the development of numerical codes for simulations of the implosion of wire arrays and the refinement of the wire parameters in the initial stage of plasma production.     

Hybrid X-pinches

Results from experimental studies of a hybrid X-pinch with an initial configuration in the form of a high-current diode with conical tungsten electrodes spaced by 1?C2 mm and connected to one another with 20- to 100-??m-diameter wires are presented. The experiments were carried out at four facilities with a current amplitude from 200 to 1000 kA and front duration from 45 to 200 ns. It is shown that, in spite of their simpler configuration, hybrid X-pinches with a short rise time of the current pulse (50?C100 ns) are highly competitive with standard X-pinches in the generated soft X-ray power and the formation of a single hot spot in them is much more stable, while hard X-ray emission is almost absent. The possibility of using hybrid X-pinches as soft X-ray sources for point projection X-ray imaging of plasma objects is considered.     

Multichannel vacuum arc discharge used for Z-pinch formation

Results are presented from experimental studies of the implosion dynamics and radiative characteristics of an aluminum Z-pinch formed from a plasma shell (PS). The PS with an initial diameter of 4 cm was produced with the help of a multichannel vacuum arc discharge and formed due to the evaporation of the electrode material in ten parallel arc discharges. The PS composition depended on the electrode material in the arc discharge. The described experiments were performed with aluminum electrodes. The total arc current was 80 kA. The PS implosion was provided by an IMRI-5 high-current generator with a current amplitude of 450 kA and rise time of 500 ns. The PS implosion resulted in the formation of a 0.2-cm-diameter plasma column with an electron temperature of 700?C900 eV and average ion density of (5?C8) × 10¹⁷ cm^?3. The maximum radiation power per unit length in aluminum K-lines reached 300 MW/cm, the duration of the radiation pulse being 20 ns.     

Modeling of the composition of materials for soft X-ray sources used in research on inertial confinement fusion

A method for calculating and optimizing the composition of materials for soft X-ray sources used in research on inertial confinement fusion is described. For a target-converter, a material composition is determined with which the conversion of laser light into X radiation is highly efficient. A comparative analysis is carried out of the efficiencies of generation of soft X-ray emission in the plasmas of some composite materials of thin conductors (wires) used as loads in X-and Z-pinches. Numerical calculations of the optical plasma properties are reported whose results make it possible to judge the emissivity of plasmas of different materials. The results obtained are compared to the data from other studies.     

Study of the radiation spectra of fast Z-pinches formed during the implosion of wire arrays in the Angara-5-1 facility

Results are presented from measurements of the radiation spectra of the Z-pinch tungsten plasma produced during the implosion of cylindrical wire arrays with a linear mass of 200?C400 ??g/cm and an initial diameter of 12?C20 mm at a current of ??3 MA in the experiments performed at the Angara-5-1 facility. The radiation spectra in the photon energy range of 50?C900 eV were recorded on a UF-4 X-ray film by using a spectrograph with a transmission grating. The radiation spectrum in the photon energy range of 1?C3 keV was recorded using a crystalline panoramic spectrograph. A curtain shutter was used to protect the transmission grating from fast microparticles produced due to the erosion of high-voltage electrodes. The total radiation yield was measured with a thermocouple calorimeter. It is shown that most of the tungsten plasma radiation energy is emitted in the photon energy range of 80?C300 eV. Measurements of the spectral intensity of pinch radiation with a spatial resolution along the pinch radius showed that the effective transverse diameter of the pinch did not exceed 2 mm, which agrees with independent current measurements of the pinch size. The results of measurements of the spectral intensity of pinch radiation were compared with calculations per-formed under the assumption of a stationary homogeneous plasma.     

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.     

Optical characteristics and parameters of the plasma of a barrier discharge excited in a mixture of mercury dibromide vapor with nitrogen and helium

Results are presented from experimental and theoretical studies of the optical characteristics and parameters of the plasma of an atmospheric-pressure barrier discharge excited in a HgBr₂: N₂: He mixture, which was used as the working medium of a small-size (with a radiation area of 8 cm²) exciplex gas-discharge radiation source. The mean radiation power of 87 mW was achieved at the radiation wavelength λ_max = 502 nm. The electron energy distribution function, the transport characteristics, the specific energy lost in the processes involving electrons, the electron temperature and density, and the rate constants of elastic and inelastic electron scattering by the components of the working mixture were calculated as functions of the reduced field E/N. The plasma of a discharge excited in a HgBr₂: N₂: He mixture can be used as the working medium of a small-size blue-green radiation source. Such a source can find application in biotechnology, photonics, and medicine and can also be used to manufacture gas-discharge display panels.     

MHD processes during the cascade development of the neck and hot spot in an X-pinch

Results are presented from two-dimensional MHD simulations of X-pinch implosion. The simulations were performed in the (r, z) and (x, y) geometries for homogeneous (dense plasma) and heterogeneous (core-corona) loads. The formation of a minidiode, the development of a neck and an X-radiating hot spot, and the influence of the plasma corona on the implosion dynamics of the dense X-pinch plasma were investigated. For through simulations, the conical neck model was used, whereas a detailed analysis of the X-ray burst was performed in the parabolic neck model. The MHD processes occurring during the implosion of oblique shock waves and the onset of instability of the plasma column were examined. It is found that, due to the quasi-periodic character of these processes, the neck compression proceeds in a cascade fashion. The plasma state in a hot spot just before the break of the neck is analyzed, and the possibility of generating fast particle beams is considered.     

Nonequilibrium radiative properties in fluctuating plasmas1

A general kinetic model was developed to simulate the radiative properties of nonstationary fluctuating plasmas and characterize the relationship between the nonstationary fluctuation time and the atomic relaxation times. The developed theory is applied to the radiative line emission in the case of instabilities in tokamaks. It is shown by exact time dependent simulations that involve explicitly LSJ-split excited states that the radiation emission in fluctuating plasma can be larger than in the corresponding stationary limits. For regular fluctuations like the sawtooth activity, also the startup phase of sawtooth activity can lead to higher emission compared to the time dependent regular phase. It is demonstrated that the sawtooth crash can be almost exactly followed by resonance line emission like H-like Lyman-alpha and He-like Helium-alpha of, e.g., argon impurity ions, whereas the effective charge state distribution lags seriously behind.     

The role of the conserved residues His-246, His-199, and Tyr-255 in the catalysis of catechol 2,3-dioxygenase from Pseudomonas stutzeri OX1

Catechol 2,3-dioxygenase (C2,3O) from Pseudomonas stutzeri OX1, which is able to grow on various aromatic substrates as the sole source of carbon and energy, has been expressed in Escherichia coli, purified, characterized, and found to be very similar to other dioxygenases from Pseudomonas species. Interestingly, the activity of the protein shows a rather unusual pH dependence when assayed on catechol. A model of the catalytic mechanism was developed that is able to reproduce the catalytic behavior of the protein as a function of the pH. The model includes multiple equilibria and four productive intermediates with different ionization states of the enzyme-substrate complex. The fitting of the theoretical curve to the experimental data suggests that a tyrosine and two histidine residues are involved in catalysis. Mutants (H246N)-, (H246A)-, (H199N)- and (Y255F)-C2,3O were produced to investigate the role of highly conserved His-199, His-246, and Tyr-255. The strongly reduced activity of the mutants suggests a primary catalytic role for each of these residues. Moreover, mutants at positions 199 and 246 display pH profiles different from that of the wild-type protein, thus indicating that residues His-246 and His-199 play a role in determining the unusual pH dependence of the enzyme. In addition, electron-withdrawing groups on catechol, which increase the acidity of the phenolic hydroxyl group, are able to counterbalance the effect of the mutation H246N in reducing catalytic activity but cause a further reduction of the activity of (H199N)-C2,3O. This finding suggests that His-246 is involved in the initial catechol deprotonation, whereas His-199 promotes the reaction between oxygen and the aromatic ring.     

Ion recombination and energy balance in lead and gallium laser erosion plasmas

The ion recombination times, the energy balance characteristics, and the time behavior of the radiation intensity of lead and gallium laser plasmas are determined by analyzing the trailing edges of the waveforms of various spectral lines. Reasons for different decay rates of the spectral lines are analyzed. Experiments on laser erosion of lead and gallium targets under the action of repetitive neodymium laser radiation with a pulse duration of 20 ns, wavelength of 1.06 μm, repetition rate of 12 Hz, and peak intensity on the target surface of 10⁸–10⁹ W/cm² were carried out at a residual air pressure of 3–12 Pa.     

A review of projection radiography of plasma and biological objects in X-Pinch radiation

A review of studies on the X-pinch as a radiation source for X-ray projection shadow radiography (XPSR) and X-ray absorption spectroscopy (XAS) is presented. The ultimate capabilities of the techniques and ways of their achievement are considered. XPSR has been successfully used to study high-energy-density plasma objects, in particular, exploding wires and wire arrays. Using XPSR, the internal structure and dynamics of a wire explosion and wire array implosion have been investigated for the first time, which has made it possible to develop an adequate consistent theory of the processes occurring in the wire loads of generators with currents from several units of kiloamperes to a few tens of megamperes. The use of XAS for diagnostics of wire loads has allowed one for the first time to measure the parameters of matter in the wire core and plasma corona of the load. X-ray images of various biological objects have obtained, including those with the use of the phase contrast method. This review is a logical continuation of the review “Х-Pinch” [Plasma Phys. Rep. 41, 319, 493 (2015)], in which the Х-pinch as a physical object was considered.     

Self-consistent electron and ion flows in a fast Z-pinch

Results are presented from experimental studies of fast Z-pinches produced in plasmas of high-Z elements. An analysis of a plasma structure emitting X radiation and time-resolved measurements of the electron emission showed that a self-consistent regime of electron and ion motion is established in the plasma channel of the discharge. It was found that, in this regime, the electron component makes a negative contribution to the net current and an electrically neutral supersonic plasma flow propagates along the discharge axis in the direction of the net current.