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.     

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.     

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.     

High-power electromagnetic wave in a magnetically insulated transmission line of the ANGARA-5-1 facility

Studies of physical phenomena in magnetically insulated transmission lines (MITLs) of high-power pulsed current generators, analysis of operation of existing megavolt generators, and designing of new high-current generators with a power of up to ∼10 TW require creating an efficient numerical code for modeling the propagation of a high-power electromagnetic pulse in an MITL. This paper presents basic theoretical concepts of MITL operation in the framework of telegraph equations with allowance for electron leakage and variations in the electrode emissivity and analyzes propagation of an electromagnetic wave in the MITLs of the ANGARA-5-1 eight-module facility toward a dynamic load installed in the central unit with a matrix inductance.     

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.     

Vortex electron dynamics in a high-current plasma lens

An analytic study is made of the following problems: the instability of a plasma against the excitation of vortex turbulence, the turbulence saturation amplitude, the types and spatial structures of the nascent vortices, and their nonlinear growth rates in an electrostatic plasma lens for focusing high-current ion beams.     

Small-size magnetically insulated plasma diodes for neutron generation

Results from experimental and theoretical studies of deuteron acceleration in small-size magnetically insulated plasma diodes are presented. The problems of creating accelerating tubes for neutron generation on the basis of magnetically insulated diodes are considered. The prospects of creating small-size neutron generators with neutron fluxes of 10¹⁰–10¹² neutrons/s into the full solid angle are estimated.     

Study of the contributions of the electrode materials to the plasma of a high-current vacuum spark

The contribution of the electrode material to the formation of the plasma of a low-inductive high-current vacuum spark and its influence on the process of discharge micropinching were studied using X-ray spectroscopy and laser diagnostics. Electrode system configurations are determined in which the contributions of the materials of both electrodes to the plasma emitting X-rays are comparable and in which the contribution of one electrode is dominating. It is found that discharge pinching occurs primarily in the vapor of the pointed electrode independently of its polarity. The experimental results indicate the formation of a suprathermal electron beam in the micropinch region.     

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.     

Study of the plasma parameters in a high-current pulsed magnetron sputtering system

Results are presented from experimental studies of the current-voltage characteristics and spatial and temporal parameters of the plasma in a high-current pulsed magnetron sputtering system with a 10-cm-diameter plane disk cathode. It is shown that the plasma density in such a system is three orders of magnitude higher than that in conventional dc magnetron discharges and reaches 10¹³ cm⁻³ at a distance of 250 mm from the cathode at a peak discharge current of 500 A. The plasma propagates from the cathode region at a velocity of 1 cm/μs in the axial direction and 0.25 cm/μs in the radial direction. Optical emission spectroscopy shows that the degree of plasma ionization increases severalfold with increasing discharge current, mainly at the expense of the sputtered material.     

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.     

Microwave amplification in a coaxial slow-wave plasma transmission line

Microwave generation by an electron beam in a coaxial transmission line in which the inner and outer conductors are both corrugated is studied theoretically. An annular electron beam propagates in a transport channel filled entirely with plasma. The eigenmodes of the plasma-filled coaxial line are studied, as well as how they are affected by the plasma density. It is shown that, in the presence of a plasma, the microwaves are amplified to a significantly greater extent and the spectrum of the generated microwaves is broader. The nonlinear amplification regime is analyzed. The maximum possible amplitude of the longitudinal electric field and the interaction efficiency are determined as functions of the plasma density. A comparison between the results obtained and the analogous parameters of a vacuum structure shows that plasma-filled hybrid structures are more promising than vacuum sources.     

Numerical simulations of a high-current plasma lens

The dynamic processes by which an electrostatic plasma lens with a wide-aperture ion beam and electrons produced from the secondary ion-electron emission relaxes to a steady state is investigated for the first time by the particle-in-cell method. The parameters of a two-dimensional mathematical model were chosen to correspond to those of actual plasma lenses used in experimental studies on the focusing of high-current heavy-ion beams at the Institute of Physics of the National Academy of Sciences of Ukraine (Kiev, Ukraine) and the Lawrence Berkeley National Laboratory (Berkeley, USA). It is revealed that the ion background plays a fundamental role in the formation of a high potential relief in the cross section of a plasma lens. It is established that, in the volume of the plasma lens, a stratified electron structure appears that is governed by the nonuniform distribution of the external potential over the fixing electrodes and the insulating magnetic field. The stratification is very pronounced because of the finite sizes of the cylindrical fixing electrodes of the lens. It is shown that the presence of such a structure limits the maximum compression ratio for an ion beam to values that agree with those observed experimentally.     

Formation and dynamics of plasma layers formed on the foil surface under the action of a high-current pulse

Results are presented from studies of the possibility of using a thin metal foil for recyclable vacuum transmission lines with magnetic insulation in a conceptual fusion reactor based on high-voltage high-current electromagnetic generators. Numerical simulations and experiments in the Angara-5-1 facility were carried out to determine both the threshold for the explosion of a foil heated by a current pulse and the parameters of the plasma layer formed at the foil surface. It was found experimentally that an additional plasma current channel forms on the surface of a 120-μm stainless-steel foil at a linear current density of 0.25–0.5 MA/cm, which corresponds to a magnetic field of 0.3–0.6 MG. For the same conditions, one-dimensional computer simulations of the foil heating were performed in an MHD model by using a wide-range semiempirical equation of state for stainless steel. The calculated threshold for plasma generation on the foil surface is compared with the experimental data. The main parameters of the plasma layer are also calculated at linear current densities of 2–10 MA/cm, which far exceed the threshold current density. The plasma layer parameters as functions of the linear current density are determined for the case of an iron foil.     

Long-lived Ar-Hg plasma in the afterglow of a high-current pulsed discharge

High-density (n > 10¹² cm^?3) argon-mercury plasma produced by a short (t ～ 20 μs) high-power pulsed discharge in argon with an admixture of mercury vapor at a discharge current of ～50 A, an argon pressure of ～4 mm Hg, and a mercury vapor pressure of ～10^?3 mm Hg was studied using optical spectroscopy and radio physics methods. It is found that the lifetime of this plasma after the end of the discharge pulse is up to 10^?2 s. It is shown that such an abnormally long lifetime of such an afterglow plasma, as compared to the plasma of an argon discharge without an admixture of mercury vapor, is related to the long residence time of atoms and ions of both argon and mercury in highly excited states due to chemi-ionization processes involving long-lived metastable argon ions. It is suggested that dissociative recombination of highly excited molecular ions of argon play an important role in the transfer of excitation to argon atoms and ions that are close to autoionization states.     

Peculiarities of the spatial structure and dynamics of the plasma of a fast Z-pinch produced in the high-Z medium of a high-current vacuum spark

The spatial structure and dynamics of the plasma of a high-current vacuum spark is investigated using pulsed shadowgraphy. Anisotropy of the plasma outflow from a micropinch region has been revealed. The existence of cavities in the sausage-type instability in the final stage of pinching has been recorded. The formation of a filamentary plasma structure at the discharge periphery is revealed.     

Self-consistent electron and ion motion in a high-current plasma channel

The problem of self-consistent motion of charged particles in a high-current plasma channel is solved using the kinetic model of a plasma with electron and ion beams whose motion is governed by the resulting electromagnetic field. It is shown that, in a high-density plasma, the ion motion makes the contribution of electrons to the current in the channel negative, in which case the ion current is higher than the net current and the plasma moves at a high speed as an electrically neutral axial stream whose direction coincides with the direction of the current in the channel.     

Optical studies of plasma inhomogeneities in a high-current pulsed magnetron discharge

Results are presented for experimental studies of the plasma glow in a high-current pulsed magnetron discharge by using a high-speed optical frame camera. It is found that the discharge plasma is inhomogeneous in the azimuthal direction. The plasma bunches rotate with a linear velocity of ∼1 cm/μs in the direction of electron Hall drift, and their number is proportional to the discharge current. Plasma inhomogeneities in the form of plasma jets propagate in the form of plasma jets from the cathode region toward the anode. It is shown analytically that the formation of inhomogeneities is caused by the necessity to transfer high-density electron current across the magnetic field.     

Focusing of heavy ion beams by a high-current plasma lens

Results are presented from studies of the focusing of wide-aperture low-energy (100–400 eV) and moderate-energy (5–25 keV) beams of heavy-metal ions by a high-current electrostatic plasma lens. It is found experimentally that, because of the significant electron losses, the efficient focusing of such beams can be achieved only if the external potentials at the plasma-lens electrodes are maintained constant. Static and dynamic characteristics of the lens are studied under these conditions. It is shown that, as the beam current and the electrode voltage increase, the maximum electrostatic field in the lens tends to a certain limiting value because of the increase in the spatial potential near the lens axis. The role of spherical and moment aberrations in the focusing of wide-aperture low-divergence ion beams is revealed. It is shown that, even when spherical aberrations are minimized, unremovable moment aberrations decrease the maximum compression ratio of a low-energy heavy-ion beam because of the charge separation of multiply charged ions in the focal region. At the same time, as the ion energy increases, the role of the moment aberrations decreases and the focusing of high-current heavy-ion beams by a plasma lens becomes more efficient than the focusing of light-ion (hydrogen) beams. This opens up the possibility of using electrostatic plasma lenses to control ion beams in high-dose ion implanters and high-current accelerators of heavy ions.     

The use of a high-current electron beam in plasma relativistic microwave oscillators

Relativistic microwave electronics faces the problem of using high currents of relativistic electron beams; i.e., it is possible to use beams the current of which is lower than that of actually existing high-current accelerators. We show the possibility of increasing the power of radiation generated in a plasma relativistic microwave oscillator (PRMO) due to an increase in the absolute value of current. For the beam currents close to the value of limiting vacuum current, the efficiency of microwave generation decreases; therefore, we study PRMO schemes with a high value of limiting vacuum current, i.e., schemes with a small gap between a hollow relativistic electron beam and the waveguide wall. The results of the experiment and numerical simulation are discussed.