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A solution for the one-dimensional Poisson problem for a layer on the surface of a plasma ion emitter is obtained. The case of plasma with a directed ion velocity greater than the ionic sound one is considered. Moreover, the plasma surface is irradiated with an electron beam. As applied to the parameters of deuterium plasma flowing out of a gas dynamic open magnetic trap GDT, a physical model of a layer with boundary conditions on the plasma surface is formulated. It allows a two-dimensional numerical simulation of the source of an electron beam injected into a trap.

A diagnostic has been developed to study the focusing dynamics of a high-power electron beam on a target. The diagnostic uses a pinhole camera to observe bremsstrahlung from the converter target. A data acquisition system yields images of the beam focal spot with a frame duration of 20 ns and an almost unlimited recording duration. The focal spot dynamics of a linear induction accelerator with an energy of 1.5 MeV, a current of 1.2 kA and a pulse duration of 350 ns were studied. The focal spot was found to be disrupted within the first 100 ns of the pulse. Defocusing has a complex 3-D character. The feasibility of additional cleaning of the target using an accelerator pre-pulse was shown. Stable beam focusing for up to 200 ns was demonstrated.

The formation of electron beams and their transport in a mirror-type guiding magnetic field are modeled numerically for two types of an experimental electro-optical system in the accelerating diode of an electron source with a plasma low-pressure arc-discharge emitter. The observed behavior of currents is interpreted and the limiting values of currents transported in the system are obtained.

Numerical simulation of physical processes in the electron-optical system of a DUET accelerator was carried out using the ERA-DD code. The calculations were made on adaptive quasi-structured grids developed by the authors. A mathematical model for the emission plasma surface deformable when solving the problem is proposed. In this model, the problem is considered in a two-dimensional axisymmetric approximation and the front of the electron entrance to the computational domain is represented as a set of circular arcs connected by necks. In order to increase the accuracy of the calculations, it is proposed to divide the multi-scale extended domain into two subdomains and alternately solve self-consistent problems in the subdomains using the Schwarz alternating method. The beams are simulated by the method of current tubes, and the electric field potential is calculated by the finite volume method. The obtained characteristics of the beam are compared with experimental data. It is shown that for the operating parameters of the beam source, its losses on the accelerator components are minimal and can be caused primarily by the imperfect alignment of the holes in the mask and the support grid, as well as by deviations of electron beams generated by the structures located on the periphery of the emission electrode.

Influence of backstreaming ions from the target on spot size of focused 2 MeV electron beam was considered. The 2D version of the particle-in-cell code KARAT was used to study the formation of the ions stream and dynamics of the electron beam. It was shown that light species emitted from the target can disrupt the beam. The emission of low-ionized states of tantalum cannot disrupt the beam during about 30 ns or longer. A few non-invasive techniques of mitigation of the beam disruption were considered. Final magnetic lens with fast variation of magnetic field of several hundred Ampere-turns per nanosecond is capable to stabilize initial spot size of the compressed beam at the target.

In the Institute of Nuclear Physics, SB RAS, experiments are carried out on injection of electron beam into open magnetic trap GDT. The trap is a mirror cell with a large mirror ratio filled with deuterium plasma with subthermonuclear parameters. Two expanders are attached to both sides of the trap. There are volumes with a diverging magnetic field, used to reduce longitudinal losses from the trap. The source of the electron beam is located in the expander, in the region of a weak magnetic field and is exposed to a supersonic plasma ion stream emerging from the trap. The source of a diode-type operates with a thermionic cathode and a hollow metal anode. The plasma from the trap enters the diode through the anode liner and stops by the potential of the cathode, forming an anode electrode. Its surface and the metal surfaces of the electrodes determine the electron-optical characteristics of the diode and the beam formed in it. The paper presents the results of two-dimensional numerical simulation of the beam source and calculated electron beam angular characteristics. The numerical model uses the plasma flow parameters measured in the experiment and results of solving the one-dimensional Poisson equation for the Debye layer on the surface of the anode plasma.

The paper reports on a comparative study of two different types of diode system for producing intense submillisecond electron beam in a source with low-pressure arc plasma emitter. The first is a planar multi-aperture diode comprising cathode and anode performed as molybdenum grids with 241 round openings of few millimeters in diameter. In the second system electrons are accelerated in a sheath between the grid-stabilized cathode plasma and the open boundary of beam-generated anode plasma. It was demonstrated in experiments that latter system should be advantageous in terms of maximally achievable beam current and total beam energy content, but there are drawbacks connected with slow anode plasma build-up that require further study.

Experiments on the detection of γ rays generated in the 13C(p, γ)14N reaction at the Novosibirsk vacuum-insulated tandem accelerator were carried out. Owing to the updated detection system, it was possible to measure the energy spread of beam protons and develop a method for long-term stabilization of the slow drift of the beam energy. The measured energy spread was 1.20 ± 0.15 keV, which was only 0.07% of the total beam energy. This makes the tandem accelerator developed by the vacuum-insulated Budker Institute of Nuclear Physics an attractive tool for solving various research and applied problems.

Emission of positively charged ions from a plasma emitter irradiated by a counterpropagating electron beam is studied theoretically. A bipolar diode with a plasma emitter in which the ion temperature is lower than the electron temperature and the counter electron flow is extracted from the ion collector is calculated in the one-dimensional model. An analog of Bohm’s criterion for ion emission in the presence of a counterpropagating electron beam is derived. The limiting density of the counterpropagating beam in a bipolar diode operating in the space-charge-limited-emission regime is calculated. The full set of boundary conditions on the plasma emitter surface that are required for operation of the high-current optics module in numerical codes used to simulate charged particle sources is formulated.

The generation of a 250-μs-wide electron beam in a plasma-emitter diode is studied experimentally. A plasma was produced by a pulsed arc discharge in hydrogen. The electron beam is extracted from a circular emission hole 3.8 mm in diameter under open plasma boundary conditions. The beam accelerated in the diode gap enters into a drift space in the absence of an external magnetic field through a hole 4.1 mm in diameter made in the anode. The influence of electron current deposition at the edge of the anode hole on the beam’s maximum attainable current, above which the diode gap breaks down, is studied for different accelerating voltages and diode gaps. The role of processes occurring on the surface of the electrodes is shown. For an accelerating voltage of 32 kV, a mean emission current density of 130 A/cm2 is achieved. The respective mean strength of the electric field in the acceleration gap is 140 kV/cm. Using the POISSON-2 software package, the numerical simulation of the diode performance is carried out and the shape of steady plasma emission boundaries in the cathode and anode holes is calculated. The influence of the density of the ion current from the anode plasma surface on the maximum attainable current of the electron beam is demonstrated.

Development of a new linear device for confinement of fusion plasmas is under way in the Budker Institute of Nuclear Physics, Novosibirsk. The new device combines features of existing GOL-3 and GDT...

Sub-THz radiation can be generated by conversion of plasma waves into electromagnetic (EM) radiation in a plasma with strong Langmuir (LT) turbulence produced via a two-stream instability of a high current relativistic electron beam (REB). Nonlinear plasmon-plasmon merging results in the generation of photons nearby the 2nd harmonic of the plasma frequency 2ω p (“2ω p -process”). For plasma densities of 1014 − 1015 cm−3, these frequencies are in the range of sub-THz waves at 370–570 GHz. The specific power density of sub-THz-wave emission from plasmas in the multi-mirror magnetic trap GOL-3 (at BINP) during injection of a 10-μs-REB with a current density of about 1 kA/cm2 at plasma densities n e ≈ 5∙1014 cm−3, electron temperatures T e ≈ 1.5 keV and magnetic induction B ≈ 4 T was measured to be approx. 1 kW/cm3 in the frequency band around 300 GHz. In the case of a weakly relativistic 100-μs-electron beam (90 keV) with 250 A/cm2 the corresponding results are 700 W/cm3 around 90 GHz with an efficiency of 1–2 % at n e ≈ 3∙1013 cm−3 (total power ≈ 30 kW). Theoretical investigations show that at a density of n e ≈ 3∙1015 cm−3 and a turbulence level of 5 % the generated sub-THz power can reach ≈ 1 MW/cm3.

The paper summarizes recent advances in physics of multiple-mirror confinement. GOL-3 in Novosibirsk is the only existing large-scale device of this type. Achieved plasma parameters are: n ~ 1021 m...

The latest experimental campaign at the GOL-3 multiple-mirror trap was mainly aimed at features of heating and stability of the electron-beam-heated turbulent plasma. The discussed experiments feat...

A ribbon diode of a U-2 accelerator (800 kV, ∼30 kA) intended for generating a high-intensity electron beam for heating plasma in a GOL-3 multimirror magnetic trap (Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences) is described. The parameters of the beam characterized by a high brightness (∼7 kA/(cm2 sr)) in a magnetic field of ∼5 T resulting from a numerical simulation of the beam formation process are presented. The results of simulation of the beam transport and transformation of the profile of its cross section during movement of electrons in a curvilinear guiding magnetic field are presented. The calculated cross section is compared to the beam imprint on a target.

Experimental and theoretical investigations on simultaneous generation and transport of two microsecond E-beams with an electron energy of 0.8 MeV and beam currents of up to 3 kA at a high current density of ~1-1.5 kA/cm2 are described in this paper. Peculiarities of using such beams for a generation of millimeter and submillimeter radiation in a free-electron maser are discussed. Parameters of the beams that are suitable for these applications are experimentally demonstrated.

The geometry of the ribbon diode of the U-2 accelerator is optimized to increase both the current density and the total current of the relativistic electron beam for its subsequent injection into the plasma of a multimirror GOL-3 trap. Beam simulation in the diode was performed using the POISSON-2 applied software modified on the basis of the results obtained using the theory of a planar diode in an inclined magnetic field. As a result of the optimization, the diode geometry and the magnetic field configuration were found that should provide a factor of 1.5–2 increase in the current density in experiments with a small angular divergence of electron velocities.

The paper reviews recent experimental results from GOL-3. Currently efforts are focused on further development of a physical database for multiple-mirror confinement systems and also on an upgrade of plasma heating systems of GOL-3 device. In general, current GOL-3 parameters demonstrate good prospects of a multiple-mirror trap as a fusion reactor.

New operation regime with a high-mirror-ratio corrugation at first 2 meters of GOL-3 plasma was studied. Five corrugation periods of 44 cm length were created with mirror ratio R ≈ 2.7 by means of special configuration of a power feed of existing solenoid coils. First data on the plasma heating, confinement and features of neutron emission from the strongly corrugated plasma in the above conditions are presented.

First stage of neutral beam heating system was developed at the GOL-3 facility. Configuration of magnetic field and initial gas distribution were adopted for operation with NBI system. As a result the neutral beam with 0.5 MW power and 0.8 ms pulse duration was achieved and stable regimes suitable for beam injection experiments were found. The neutral beam system was used in first experiment as diagnostic tool for measuring the plasma density. Dynamics of plasma density and its radial distribution were studied in experiments.

Experiments involving irradiation of carbon targets with a hot electron plasma stream performed on the GOL-3 facility were aimed at the simulation of the effect of hot plasma of a thermonuclear reactor on plasma collectors in regimes close to those expected in the ITER. In these experiments, the emphasis was on the study of the surface-erosion processes exposed to the plasma stream. The graphite evaporation and chemical-erosion processes were studied with absolutely calibrated spectroscopic systems of the visible region. Spectroscopic experiments yielded data on the flow of carbon atoms from the surface of a plasma collector and on the contribution of chemical erosion to the surface-damage process. The obtained values are compared with the results of direct measurements of the erosion depth and the results of numerical calculations.

Performance of flash radiography units implies a high spatial resolution. Thus, focused electron beams are utilized to produce bremsstrahlung x-ray at the solid target. Strong heating of the target up to 1-10 eV temperature and formation of dense plasma can lead to beam disruption. In case of multi-pulse operation mode of radiography unit the plasma produced by the first pulse can strongly affect subsequent pulses. In present work we utilize the model of Zeldovich and Raizer to estimate the electron density in the target plasma. The typical parameters of radiography units based on linear induction accelerators is considered. It is shown that electron density in plasma expanding after first pulse is high enough to affect subsequent electron beams.

The results of experiments and numerical simulation of compression of an intense electron beam in increasing field of magnetic mirror and its transmission through a linear magnetic system are presented. This system is used as a test module for a section of the GOL-3 magnetic trap. The study was carried out for the beam with a spread in initial electron pitch angles and a non-uniform radial current distribution. An analytical estimate of the vacuum beam-current limit was obtained taking into account the initial pitch angles of electrons and the beam compression in the magnetic field. The simulation results are compared with the results of experiments; in both cases similar phenomena of beam reflection and diode breakdown are observed.

A model of dynamics and heating of a plasma cloud in a magnetic field is considered in a two-temperature approximation. Based on a predictor-corrector-type implicit difference scheme, spreading of a plasma cloud in an external magnetic field is numerically simulated, and the influence of this field on spread dynamics is evaluated.

Terahertz emission from plasma with strong Langmuir turbulence excited by high current relativistic electron beam (REB) is experimentally studied at the GOL-3 facility (BINP)1. The typical parameters of the beam used in the experiments, were the following: 0.6÷0.8 MeV/20 kA/10 μs. In recent experiments the beam current density was about 1÷2 kA/cm2 in a plasma column with the density ∼ 2·1014 cm−3 that allowed us to get sub THz-emission with a power of a few kW/cm3 in the frequency range 100÷400 GHz.

An efficient algorithm is proposed enabling numerical simulations of plasma dynamics in a nonuniform magnetic field. The present numerical data are in good agreement with experimental data obtained in a GOL-3 setup and with previous simulations. The experimentally observed effect of fast transfer of energy to ions is confirmed.

Main results of researches on plasma heating and confinement of dense plasma in the multimirror trap GOL-3 are presented.Recently magnetic system of the facility was converted into completely multimirror one. This results in further improvement of energy confinement time of plasma with ion temperature {approx}1 keV. Collective plasma heating by {approx}120 kJ ({approx}8 {omega}s) relativistic electron beam results in T{sub e} {approx} 2 keV at {approx}10{sup 21} m{sup -3} density. High T{sub e} exists for {approx}10 {mu}s. To this time T{sub i} reaches {approx}2 keV. Ion temperature keeps at the high level during {approx}1 ms. The energy confinement time sufficiently increases and a value of n{tau}{sub E} = (1.5-3).10{sup 18} m{sup -3}s.

Study of a dense ({approx}10{sup 21} m{sup -3}) plasma heating by a relativistic electron beam and confinement of the plasma in multimirror magnetic field is carried out at the GOL-3 facility. The high-resolution spectral system in the visible region is used for investigation of plasma parameters.The analysis of the shape of D{sub {alpha}} spectral line shows that wings of this line are determined by the Doppler broadening from atoms being in the hot plasma core at high-temperature operation regime. A survey spectrometer with spatial and time resolution was used in addition to high-resolution spectrometer for detail study of this regime. Results of radial distribution measurements of D{sub {alpha}} line radiation show the presence of neutral deuterium in the hot plasma core. Ion temperature of the hot plasma achieves 2 keV.The evolution of radial distribution of D{sub {alpha}} line radiation, diagnostics features and results on ion temperature dynamics in the hot plasma core are presented in the paper.

Dense plasma heating by a relativistic electron beam and its confinement are studied in the multiple mirror trap GOL-3. Axial currents, which exist in the system, cause helical structure of the magnetic field. The safety factor q is shown to be below unity on the axis. Experimental data on the distribution and evolution of currents, structure of the magnetic field, and their influence on confinement and on MHD activity are discussed.

A novel high-power (10 MW) sub-millisecond electron beam is developed for injection into the open (linear) plasma devices. The beam is produced by extraction of electrons from a plasma of pulsed ar...

Results are presented from experiments on the injection of solid pellets into a plasma heated by an electron beam in the GOL-3 device. For this purpose, two pellet injectors were installed in the device. The target plasma with a density of ∼1015 cm−3 was produced in a solenoid with a field of 4.8 T and was heated by a highpower electron beam with an electron energy of ∼1 MeV, a duration of ∼7 s, and a total energy of 120–150 kJ. Before heating, the pellet was injected into the center of the plasma column transversely to the magnetic field. The injection point was located at a distance of 6.5 or 2 m from the input magnetic mirror. Polyethylene pellets with a mass of 0.1–1 mg and lithium-deuteride pellets with a mass of 0.02–0.5 mg were used. A few microseconds after the electron beam starts to be injected into the plasma, a dense plasma bunch is formed. In the initial stage of expansion, the plasma bunch remains spherically symmetric. The plasma at the periphery of the bunch is then heated and becomes magnetized. Next, the dense plasma expands along the magnetic field with a velocity on the order of 300 km/s. A comparison of the measured parameters with calculations by a hydrodynamic model shows that, in order to provide such a high expansion velocity, the total energy density deposited in the pellet must be ∼1 kJ/cm2. This value substantially exceeds the energy density yielded by the target plasma; i.e., the energy is concentrated across the magnetic field onto a dense plasma bunch produced from the evaporated particle.

The present investigation focuses on further development of the plasma based high-voltage modulator for plasma immersion ion implantation devices. The modulator produces high-voltage pulses using grid controlled extraction of electrons from the plasma, which is used for the ion implantation. The operation features of the modulator in connection with a radio-frequency plasma are described. The device is applied to nitrogen ion implantations of stainless steel. The results indicate considerable hardness improvement, which confirms the practical utility of the high-voltage modulator.

Theoretical and experimental problems in the realization of a concept of a multi-beam generator are studied for the case of a four-channel planar FEM oscillator at 75 GHz. Computer simulations and “cold” and “hot” experiments have demonstrated clear possibility for construction of this oscillator based on the ELMI-device.

The experimental results on a multiple-mirror trap GOL-3 with a short section of reduced magnetic field (“magnetic pit”) are presented. The reduced specific energy release from a relativistic electron beam in the pit brings about a region with a temperature several times lower than in the surrounding plasma. The existence of the low-temperature region directly demonstrates that the longitudinal electron heat conductivity is suppressed in the collective electron-beam interaction with plasma.

Experiments on plasma heating by a high power electron beam at the GOL-3 facility have shown, that ion temperature with a multiple mirror configuration of the magnetic field is much higher than for plasma heating in a simple solenoid. A new mechanism of fast collective heating of a plasma ions is suggested. The efficiency of the heating depends on local density of the beam electrons. In the corrugated magnetic field this creates a periodical longitudinal variation of plasma pressure during the beam injection. Then the pressure gradients result in plasma motion towards the midplane of each magnetic cell. Numerical simulations and special experiments demonstrate that fast thermalization of the energy of the directed plasma motion occurs. This mechanism requires about one ion-ion collision time that is much faster than usual electron-to-ion energy transfer time.

The problem of energy recuperator for a high current sheet electron beam used to drive a millimeter-waves generator is considered. There are two main obstacles to solving the problem. The first one is the presence of a magnetic field guiding beam electrons. The second obstacle is significant energy and angular spreads of the electrons in the waste beam. To overcome these obstacles, we suggest a novel scheme of a recuperator. The main idea of the proposed scheme is the use of a decelerating electrical field together with a guiding magnetic field that has longitudinal and spatial periodic transverse components. Resonance of a bounce electron motion with the cyclotron motion in this field gives a strong increase in the Larmour radius of electrons with the energy in a narrow interval. The decelerated electrons with the resonance energy fall away from the beam and are absorbed by a collector at a proper potential. It is shown that efficiency of this novel scheme can reach about 80% even if the sheet beam has a broad energy spectrum.

Recently high plasma parameters were reached in experiments on plasma heating in the multi-mirror open trap GOL-3. In these experiments deuterium plasma with density 10-10 cm in the 12-m trap with corrugated magnetic field of 4.8T/3.2T was heated by a relativistic electron beam of eU ≤ 0.8 MeV, I ≤ 20 kA, j ~ 1-2 kA/cm, pulse duration ~ 9 μs and angular spread θ ≤ 0.2 rad. The electron temperature Te ~ 1-4 keV and ion one to Ti ~ 1-2 keV were reached. After the beam pulse the electron temperature of the plasma quickly (~ 20 μs) decreased to ~100 eV. In turn, this leads to an increase in the rate of cooling of ions through the ion-electron collisions, which, together with particle losses determines the energy confinement time of plasma as 0.5-1 ms. To increase the plasma parameters a prolonged heating of the plasma by the electron beam is proposed. The paper considers basic physical phenomena in the beamplasma interaction and required parameters of the longpulse beam. A choice of long pulse beam parameters is based on the obtained experimental results and scalings. Then estimates of the expected plasma parameters under the influence of the new beam have been done.

The problem of interaction of a plasma flow with an inhomogeneous magnetic field is considered. The field is generated by magnetic coils. Field lines along the coil axis form a channel which is use...

A numerical simulation of decelerating, scattering, and trapping fast electrons by plasma in a magnetic trap is reported. Fast non-thermal electrons are generated via the interaction of the relativistic electron beam with the plasma. Their energy significantly exceeds the thermal energy of plasma particles. For real experimental conditions where the mean free path of electrons is larger than the length of a local magnetic pit, the kinetic equation for distribution function of electrons is numerically solved. The effect of electron scattering and trapping into the pit is calculated.

Experiments on fast plasma heating by the relativistic electron beam in the GOL-3 facility succeeds in the creation of a 10 15 cm -3 plasma with electron temperature of up to a few keV. The heating is produced due to two-stream instability of the beam that causes high level of plasma microturbulence. The experiments show some specific features of plasma behaviour during the beam injection. The beam-induced turbulence is the reason of non-classical transport processes in the plasma. Anomalies in longitudinal thermal conductivity, resistivity of the plasma and in lifetime of hot electrons are observed. Transition to classical transport coefficients occurs when the plasma turbulence disappears after the beam injection stops.

This paper presents the results of experiments on two-stage heating of a dense plasma by a relativistic electron beam in the GOL-3 facility. A dense plasma with a length of about a meter and a hydrogen density up to 1017 cm−3 was created in the main plasma, whose density was 1015 cm−3. In the process of interacting with the plasma, the electron beam (1 MeV, 40 kA, 4 μs) imparts its energy to the electrons of the main plasma through collective effects. The heated electrons, as they disperse along the magnetic field lines, in turn reach the region of dense plasma and impart their energy to it by pairwise collisions. Estimates based on experimental data are given for the parameters of the flux of hot plasma electrons, the energy released in the dense plasma, and the energy balance of the beam-plasma system. The paper discusses the dynamics of the plasma, which is inhomogeneous in density and temperature, including the appearance of pressure waves.

At the GOL-3 facility, experiments on the interaction of powerful hot electron streams with various materials have been performed. For energy densities of the hot electron stream above 10 MJ/m2 an explosive-like erosion was observed, which at energy densities of 30 MJ/m2 reaches 500 mu m for fine grain graphite and 200 mu m for tungsten. Under these conditions, the corona of the carbon vapour cloud has temperatures below 1.2 eV and densities up to 1017 cm-3. It propagates along the magnetic field lines with maximum velocities of 2.1*106 cm/s. The longitudinal and transverse (along and across magnetic field lines) vapour velocities of the colder bulk plasma are about 106 cm/s. A model for explosive-like erosion was developed and tested against the GOL-3 results. For graphite the destruction threshold is 10 kJ/g. This value is considerably lower than the vaporization enthalpy of 20.5 kJ/g for three atomic vaporization. The validated model was applied to a numerical analysis of the occurrence of explosive-like erosion for ITER disruptions and runaway electrons. If the energy density of the runaways remains below 30 MJ/m2, explosive-like erosion of graphite occurs for electron energies below 20 MeV. For the energetic tail of Maxwellian plasma electrons with temperatures up to 20 keV and power densities of 10 MW/cm2 without any angular spread, explosive-like erasion becomes comparable to erosion by vaporization

Investigation of mechanism of plasma ions heating in a multimirror magnetic trap became actual due to the essential progress in experiments on GOL-3 facility at Budker Institute of Nuclear Physics. The mechanism of fast (in comparison with the Coulomb one) acceleration and heating of ions in a multimirror trap with injection of a powerful relativistic electron beam is discussed.