Numerical investigation of the physical model of a high-power electromagnetic wave in a magnetically insulated transmission line

An efficient numerical code for simulating the propagation of a high-power electromagnetic pulse in a vacuum transmission line is required to study the physical phenomena occurring in such a line, to analyze the operation of present-day megavolt generators at an ∼10-TW power level, and to design such new devices. The main physical theoretical principles are presented, and the stability of flows in the near-threshold region at the boundary of the regime of magnetic self-insulation is investigated based on one-dimensional telegraph equations with electron losses. Numerical (difference) methods—specifically, a method of characteristics and a finite-difference scheme—are described and their properties and effectiveness are compared by analyzing the high-frequency modes.     

Comparison of the measured and calculated time profiles of the leakage current in the magnetically insulated transmission line of the angara-5-1 facility

One of the factors limiting the transmission of the electromagnetic pulse to the load in high-power electrophysical facilities is the current leakage in magnetically insulated transmission lines (MITLs). In this paper, the Angara-5-1 eight-module facility with an output power up to 6 TW is considered. The experimental and calculated time profiles of the leakage current for eight-module shots with a dynamic load (cylindrical arrays made of 40 tungsten wires) and single-module shots with a solid cylindrical metal load are compared. When interpreting the results, the contribution of vacuum electrons to the leakage current at the transition from the cylindrical to the conical section of the MITL is taken into account.     

Electron leakage mechanism in a plasma-filled magnetically insulated transmission line

It is shown that relativistic electron current can propagate across the magnetic field B ₀ over a distance d much larger than the electron gyroradius, r ₀ ? m _e v _z c/(eB ₀) ? d. This current is driven by the Hall electric field, which is generated on a spatial scale equal to the magnetic Debye radius r _B = B ₀/(4πen _e) and causes the electrons to drift in crossed electric and magnetic fields. For a plane equilibrium current configuration, analytic profiles of the electron velocity and electron density are calculated and the electric and magnetic fields are determined. The results obtained are used to explain electron leakages in magnetically insulated transmission lines filled with a plasma expanding from the electrodes. Equations describing an equilibrium configuration of the ions and electrons that drift simultaneously across a strong magnetic field are derived.     

Distribution of leakage currents in the cylindrical and conical sections of the magnetically insulated transmission line of the Angara-5-1 facility in experiments with wire arrays

Current leakages in the magnetically insulated transmission lines (MITL) impose restrictions on the transmission of electromagnetic pulses to the load in high-power electrophysical facilities. The multimodule Angara-5-1 facility with an output electric power of up to 6 TW is considered. In this work, the experimental and calculated profiles of leakage currents in two sections of the line are compared when the eight-module facility is loaded by a wire array. The azimuthal distribution of the current in the cylindrical section of the MITL is also considered.     

Study of the dynamics of the electrode plasma in a high-current magnetically insulated transmission line

A series of experiments was carried out in the S-300 facility (3 MA, 0.15 Θ, 100 ns) to study the behavior of a section of a magnetically insulated transmission line (MITL) at current densities of up to 500 MA/cm² and linear current densities of up to 6 MA/cm (i.e., at parameters close to those expected in a fast Z-pinch fusion reactor projected in Sandia National Laboratories). The surface explosion of the ohmically heated MITL electrode is accompanied by the formation of a plasma layer on its surface. This can deteriorate of the transmission properties of the line because the vacuum gap is short-circuited by the plasma produced. The parameters of the electrode plasma and its effect on the MITL transmission properties were investigated experimentally. Possible consequences of the above effects are evaluated, and MHD simulations of the electrode explosion and the subsequent spread of the plasma layer are performed. It is shown that the time during which an MITL segment preserves its transmission properties conforms to the requirements of the conceptual fusion reactor.     

Transportation properties of a high-current magnetically insulated transmission line and dynamics of the electrode plasma

Results are presented from experimental studies of a section of a magnetically insulated transmission line (MITL) with a current density of up to 500 MA/cm² and linear current density of up to 7 MA/cm (the parameters close to those in a fast-Z-pinch-driven fusion reactor projected at Sandia Laboratories). The experiments were performed in the S-300 facility (3 MA, 0.15 Ω, 100 ns). At high linear current densities, the surface of the ohmically heated MITL electrode can explode and a plasma layer can form near the electrode surface. As a result, the MITL can lose its transmission properties due to the shunting of the vacuum gap by the plasma produced. In this series of experiments, the dynamics of the electrode plasma and the dependence of the transmission properties of the MITL on the material and cleanness of the electrode surface were studied. It is shown experimentally that, when the current with a linear density of up to 7 MA/cm begins to flow along a model MITL, the input and output currents differ by less than 10% over a time interval of up to 230 ns for nickel electrodes and up to 350 ns for a line with a gold central electrode. No effect of the oil film present on the electrode surface on the loss of the transmission properties of the line was observed. It is also shown that electron losses insignificantly contribute to the total current balance. The experimental results are compared with calculations of the electrode explosion and the subsequent expansion of the plasma layer. A conclusion is made that the life-time of the model MITL satisfies the requirements imposed on the transmission lines intended for use in the projected thermonuclear reactor.     

Specific features of the structure of the Z-pinch emitting region formed during the implosion of a foam-wire load at the ANGARA-5-1 facility

Results are presented from experimental studies of the structure of the compressed plasma of a Z-pinch produced during the implosion of a foam-wire load at the current of up to 3 MA. The foam-wire load consisted of two nested cylindrical cascades, one of which was a solid or hollow cylinder made of low-density agar-agar foam, while the other was a wire array. The wall thickness of a hollow foam cylinder was 100–200 μm. The images of the pinch and its spectrum obtained with the help of multiframe X-ray cameras and a grazing incidence spectrograph with a spatial resolution were analyzed. Data on the spatial structure of the emitting regions and the soft X-ray (SXR) spectrum of the Z-pinch in the final stage of compression of a foam-wire load were obtained. The implosion modes characterized by the formation of hot regions during implosion of such loads were revealed. The characteristic scale lengths of the hot regions were determined. It is shown that the energy distribution of SXR photons in the energy range from 80 eV to 1 keV forms the spatial structure of Z-pinch images recorded during the implosion of foam-wire loads. It is revealed that the spectral density of SXR emission in the photon energy range of 300–600 eV from hot Z-pinch regions exceeds the spectral density of radiation from the neighboring Z-pinch regions by more than one order of magnitude. Groups of lines related to the absorption and emission of radiation by atoms and multicharged ions of carbon and oxygen in the outer foam cascade of a foam-wire load were recorded for the first time by analyzing the spatial distribution of the SXR spectra of multicharged ions of the Z-pinch. The groups of absorption lines of ions (C III, O III, O IV, and O VI) corresponding to absorption of SXR photons in the Z-pinch of a tungsten wire array, which served as the inner cascade of a foam-wire load, were identified. The plasma electron temperature measured from the charge composition of carbon and oxygen ions in the outer agar-agar foam cascade was 10–40 eV. During the implosion of foam-wire loads at currents of up to 3 MA, SXR pulses (hν > 100 eV) with a duration of 10 ns and peak power of 3 TW were detected. It is shown that the temporal profile of single-peak and double-peak SXR pulses can be controlled by varying the parameters of the outer and inner cascades of the foam-wire load.     

Transportation of an electromagnetic pulse to the load in the Angara-5-1 facility

One of the main problems in Z-pinch experiments is to transport power and energy from the generator to the load. As the pulse produced in a double forming line propagates to the load along a water-vacuum insulator, its power and energy decrease due to current leakage in the plasma shortening the gap and during the establishment of magnetic self-insulation in regions with a zero magnetic field. Only a fraction of the delivered energy is spent on the load implosion, whereas the rest of the energy goes on creating the magnetic field around the load. In this work, an analysis is made of what is the fraction of the generator energy that reaches the liner, what fraction is radiated, and what are losses of energy and current in different stages of transporting the electromagnetic pulse to the load of the Angara-5-1 facility.     

Measurements of the parameters of a condensed deuterated Z-pinch on the angara-5-1 facility

Results are presented from measurements of the parameters of high-temperature plasma in the Z-pinch neck formed when a current of up to 3.5 MA flows through a low-density polymer load. To enhance the effect of energy concentration, a deuterated microporous polyethylene neck with a mass density of 100 mg/cm³ and diameter of 1–1.3 mm was placed in the central part of the load. During the discharge current pulse, short-lived local hot plasma spots with typical dimensions of about 200–300 μm formed in the neck region. Their formation was accompanied by the generation of soft X-ray pulses with photon energies of E > 0.8 keV and durations of 3–4 ns. The plasma electron temperature in the vicinity of the hot spot was measured from the vacuum UV emission spectra of the iron diagnostic admixture and was found to be about 200–400 eV. The appearance of hot plasma spots was also accompanied by neutron emission with the maximum yield of 3 × 10¹⁰ neutrons/shot. The neutron energy spectra were studied by means of the time-of-flight method and were found to be anisotropic with respect to the direction of the discharge current.     

Implosion dynamics of condensed Z-pinch at the Angara-5-1 facility

The implosion dynamics of a condensed Z-pinch at load currents of up to 3.5 MA and a current rise time of 100 ns was studied experimentally at the Angara-5-1 facility. To increase the energy density, 1- to 3-mm-diameter cylinders made of a deuterated polyethylene?agar-agar mixture or microporous deuterated polyethylene with a mass density of 0.03–0.5 g/cm³ were installed in the central region of the loads. The plasma spatiotemporal characteristics were studied using the diagnostic complex of the Angara-5-1 facility, including electron-optical streak and frame imaging, time-integrated X-ray imaging, soft X-ray (SXR) measurements, and vacuum UV spectroscopy. Most information on the plasma dynamics was obtained using a ten-frame X-ray camera (Е > 100 eV) with an exposure of 4 ns. SXR pulses were recorded using photoemissive vacuum X-ray detectors. The energy characteristics of neutron emission were measured using the time-offlight method with the help of scintillation detectors arranged along and across the pinch axis. The neutron yield was measured by activation detectors. The experimental results indicate that the plasma dynamics depends weakly on the load density. As a rule, two stages of plasma implosion were observed. The formation of hot plasma spots in the initial stage of plasma expansion from the pinch axis was accompanied by short pulses of SXR and neutron emission. The neutron yield reached (0.4–3) × 10¹⁰ neutrons/shot and was almost independent of the load density due to specific features of Z-pinch dynamics.     

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.     

Study of the implosion of foam-wire loads at the Angara-5-1 facility

Results are presented from experiments on studying the compactness of compression of imploding nested foam-wire loads at currents of up to 4 MA at the Angara-5-1 facility. The degree of pinch compression was estimated from the dynamics of the spatial distribution of the current (magnetic field) and the shape of the soft X-ray pulse. The load consisted of nested cascades, one of which being a wire array and the other being a hollow or solid low-density cylinder made of agar-agar foam with a wall thickness of 100?C200 ??m. In some experiments, one of the cascades was made of C₂₀H₁₇O₆ solid-state organic acid foam. The radial distribution of the magnetic field inside the nested cascades of the imploding foam-wire load (both between the cascades and inside the inner cascade) was measured using tiny magnetic probes. The measured radial distributions of the magnetic field are compared with the magnetic field configuration calculated using a one-dimensional MHD code simulating the implosion of a nested foam-wire load. It is shown that the spatial structure of the current and magnetic field during the implosion of such a load is determined by the development of supersonic and subsonic magnetized plasma flows in its cascades. The specific features of pinch formation and methods for the compensation of the nonsimultaneous pinch compression between the anode and the cathode (the zipper effect) during the implosion of a nested foam-wire load are analyzed.     

Studies of the implosion of cylindrical fiber arrays on the Angara-5-1 facility

Results are presented from experimental studies of the implosion of cylindrical kapron fiber arrays with addition of high- and medium-Z metal wires (tungsten, aluminum). The experiments were carried out on the Angara-5-1 facility at currents of 3–4 MA. The ablation rate in kapron fiber arrays is estimated and compared with that in tungsten wire arrays.     

An annular high-current electron beam with an energy spread in a coaxial magnetically insulated diode

An elementary theory of an annular high-current electron beam in a uniform transport channel and a coaxial magnetically insulated diode is generalized to the case of counterpropagating electron beams with a spread over kinetic energies. Expressions for the sum of the absolute values of the forward and backward currents in a uniform transport channel and for the flux of the longitudinal component of the generalized momentum in a coaxial magnetically insulated diode as functions of the maximum electron kinetic energy are derived for different values of the relative width of the energy distribution function. It is shown that, in a diode with an expanding transport channel and a virtual cathode limiting the extracted current, counterpropagating particle flows are established between the cathode and the virtual cathode within a certain time interval after the beginning of electron emission. The accumulation of electrons in these flows is accompanied by an increase in their spread over kinetic energies and the simultaneous decrease in the maximum kinetic energy. The developed model agrees with the results of particle-in-cell simulations performed using the KARAT and OOPIC-Pro codes.     

Influence of the current growth rate on the polarity effect in a wire array in the Angara-5-1 facility

It is shown that, at a sufficiently high current growth rate, the initial stage of implosion of a wire array is significantly affected by the radial electric fields. Due to the specific electrode configuration of wire arrays, the magnitude of the oppositely directed radial electric fields in different wire segments can reach 5 MV/cm. It is found that the process of plasma formation proceeds in different ways in segments with oppositely directed initial radial electric fields. The influence of this effect (the so-called “polarity effect”) on the implosion of cylindrical tungsten wire arrays in the Angara-5-1 facility becomes significant when the load voltage grows at a sufficiently high rate.     

Interferometric measurements of the plasma density at the Z-pinch periphery in the angara-5-1 facility

Knowledge of spatial mass distribution is important for understanding the physics of implosion of megaampere-current wire arrays. The paper presents results from studying the electron density distribution at the periphery of a tungsten wire array near the instant of maximum compression by using laser interferometry at λ=0.69 µm. It is found that, at the instant of maximum compression (～100 ns after the beginning of the discharge), the estimated maximum local electron density inside the wire array reaches ～10¹⁸ cm^?3 at a distance of 0.3–3 mm from the initial wire positions. Assuming the average tungsten ion charge to be 10, the local linear mass density in this region turns out to be 3 µg/cm, which amounts to about 10% of the total linear mass density of the liner. A fraction of the generator current flows through this plasma. The duration of the soft X-ray pulse is 5–8 ns, which indicates the achievement of a fairly high compression ratio.     

X-ray backlighting of the periphery of an imploding multiwire array in the Angara-5-1 facility

Backlighting diagnostics for studying the peripheral region of an imploding liner in the Angara-5-1 facility by using X-ray emission from an X-pinch is described. The spatial resolution of the diagnostics was no worse than 4 µm. The X-pinch emission passed through the plasma was recorded with a photofilm. The plasma density was reconstructed from the photofilm blackening density with the help of a step attenuator made of the same material as the liner. Results are presented from experiments on X-ray backlighting of the peripheral region of a multiwire liner at the 70th ns after the beginning of the discharge. It was found that, by this time, the wire cores were depleted to different extent, their masses totalled 70% of the original wire mass, and their diameters had increased approximately threefold. The plasma ejected from the wire cores was found to be axially stratified with a spatial period of 200 µm. Sometimes the axial nonuniformity of the core material with a characteristic scale length of 20 µm was observed.     

Measurements of the azimuthal magnetic field within imploding multiwire arrays in the Angara-5-1 facility

Results are presented from measurements of the azimuthal magnetic fields within imploding multiwire tungsten arrays in the Angara-5-1 facility at currents of 2.5–4 MA. It is shown that the penetration of the magnetic field into the axial region of the wire array lags behind the discharge current pulse. The current of a precursor produced at the array axis prior to the implosion of the bulk array mass is measured. It is found that the magnetic field in the initial stage of implosion is azimuthally nonuniform. The mass distribution inside the array is calculated from the measured magnetic field.     

Studies of penetration of the magnetic field into electrically imploded loads in the Angara-5-1 facility

Results are presented from measurements of the distributions of the azimuthal magnetic field in aluminum, copper, molybdenum, tungsten and other wire arrays electrically imploded at currents of up to 3 MA in the Angara-5-1 facility. It is shown that the time during which the magnetic field of the current pulse reaches the array axis depends on the material of the wires or wire coating. The current of the precursor formed on the array axis before the implosion of the main load mass is measured. It is shown that the penetration of the load material with the frozen-in magnetic field into a polymer (agar-agar) foam liner is drastically different from that in the case of a wire array. It is found that the rate of current transfer to the array axis is maximum for tungsten wire arrays. The rates of plasma production during implosion of loads made of different materials are compared.     

Experimental study of the ion flux parameters and anode plasma dynamics in the Angara-5-1 facility

Results are presented from experimental studies of the anode plasma dynamics and measurements of the ion flux ejected along the axis of a high-current Z-pinch. Pinch discharges were formed by the implosion of tungsten wire arrays in the Angara-5-1 facility. It is shown that the ion energy spectrum depends on the mass and configuration of wire arrays, as well as on the diameter of the anode aperture. The shape of the ion spectrum indicates that the plasma propagates in the form of a compact plasmoid. Shadow and X-ray images of the plasma show that the axial velocity of the plasma outflowing through the anode aperture is comparable with the velocity of radial plasma compression and, for tungsten ions, can reach a value corresponding to an energy of 100 keV. The experimental data indicate that the ion energy spectrum mainly forms due to the electrodynamical acceleration of the plasma and cumulative jets. A possible mechanism for the production of compact plasma formations in the course of electrodynamic plasma acceleration is discussed.