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At least 271 records · Page 15

Study of Microphonic Effects on the C100 Cryomodule for High Energy Electron Beam Accelerators

The Continuous Electron Beam Accelerator Facility (CEBAF) at Thomas Jefferson National Laboratory (JLab) is a particle accelerator which can accelerate an electron beam to relativistic speeds and apply the beam onto target samples. The C100 superconducting radio frequency (SRF) cavity is the primary accelerating structure of the C100 cryomodule, one of the many cryomodules which compose the CEBAF linear accelerator. SRF cavities are particularly sensitive to internal and external vibrations that can result in a phenomenon called microphonics which degrade the operational stability of a cryomodule. The purpose of this thesis is to investigate the significance of mechanical disturbances on the electromagnetic resonant frequency of a C100 SRF cavity. Knowledge of the mechanical resonance of the cavities and cryomodule sheds light into how these disturbances are most easily realized as deformation which causes radio frequency (RF) detuning. Three studies were conducted: the development and hammer test calibration of a Finite Element Analysis (FEA) model of a C100 cavity, the development and hammer test calibration of an FEA model of a C100 cavity string, and the hammer test of the C100-10R cryomodule at the Cryomodule Test Facility (CMTF). The cavity FEA model was found to accurately predict two modes found in two real cavities in a simply supported configuration. The cavity string FEA model leveraged the calibrated cavity FEA model but was not found to accurately predict the modal behavior of a real cavity string. Even so, the modal behavior of the cavity string inside the C100-10R cryomodule was captured during a hammer test while it was partially assembled. Finally, the C100-10R cryomodule was placed in the CMTF to study RF detuning. The RF detuning spectra during hammer hits and background noise was captured. The results of the hammer testing indicate two strong peaks at low frequencies (9-10 Hz and 22-23 Hz). These two frequencies were found to be nearly coincident to four instances of mechanical resonance found during the hammer testing done on the partially-assembled C100-10R. Because of this, these two modes are believed to contribute to RF detuning of the cryomodule. This test event also included the testing of the effectiveness of a configuration of BNNT canisters designed to act as dampers. While these tests show promising results, the lurking variables render these tests somewhat inconclusive.

Hull, Caleb James↗

The effects of laser polarization and wavelength on injection dynamics of a laser wakefield accelerator

Here, we investigate the effects of laser polarization and wavelength on electron injection dynamics in a laser wakefield accelerator. During the ionization process, electrons gain residual momentum and kinetic energy via above threshold ionization, which has a strong dependence on laser polarization. A circularly polarized laser pulse results in a much higher residual momentum and kinetic energy gain for the ionized electrons compared with the linearly polarized case. This residual momentum results in particle injection because of the sensitivity of particle trapping to the initial conditions and enhanced the total injected beam charge in both experiments and particle-in-cell simulations. Due to the strong correlation of above threshold ionization with laser wavelength, in this work we extended the investigation to long wavelength (up to 20 μm) drive pulses using particle-in-cell simulations. Owing to the gain in kinetic energy, it may be expected that the charge trapped would consistently increase for circular polarization with increasing laser wavelength, but this was not observed. Instead, there are oscillations with wavelength in the relative trapped charge between linear and circular polarization cases, which arise because of ionization and heating effects on the plasma. Our studies highlight the complex interplay between several different physical effects, including injection regimes—above threshold ionization assisted injection, wave-breaking injection by carrier-envelope-phase effects and ionization injection—ionization gradient induced laser pulse evolution, and thermal modifications to the wake structure that need considering when extrapolating laser wakefield acceleration to different wavelength regimes.

Ma, Y. (ORCID:0000000239194856)↗

New generation bunch shape monitor for ion accelerators

Measuring longitudinal beam parameters is important for operation and development of high intensity linear accelerators, but it is notoriously difficult for proton and ion beams at non-relativistic energies. The Bunch Shape Monitor (BSM) is a device used for measuring the longitudinal bunch distribution in ion linacs. The existing BSM models have poor electron collection efficiency from the wire and are limited to one-dimensional measurements of the phase coordinate. In response to this problem, we have developed a new generation BSM with improved performance. The proposed design incorporates three major innovations: First, the collection efficiency was improved by adding a focusing field between the wire and the entrance slit, which will also allow measurements over a much wider dynamic range. Second, an improvement in the measurement speed was achieved by sampling longitudinal profiles of multiple energy slices simultaneously, where the BSM wire is placed at the exit of an ion spectrometer so that ions with different energies hit the wire at different horizontal coordinates along the wire. Finally, the design incorporates a motion system that can shift the wire and deflecting cavity together, enabling transverse profile measurements like a wire scanner. Here, in this paper, we will provide the design of the new BSM and report on its beam test results at the Spallation Neutron Source facility in Oak Ridge National Laboratory.

43 PARTICLE ACCELERATORS↗

Plasma heating and acceleration due to Landau damping of hydromagnetic waves.

We analyze energy and momentum exchange associated with Landau damping of hydromagnetic waves, from a macroscopic viewpoint, and compare the conclusions with those of the resonant quasi-linear theory. It is found that the heating of protons and electrons is correctly given by the resonant theory, but that the momentum exchange is not correctly described by the resonant theory.

Barnes, A.↗

GPU acceleration of hybrid functional calculations in the SPARC electronic structure code

We present a Graphics Processing Unit (GPU)-accelerated version of the real-space SPARC electronic structure code for performing hybrid functional calculations in generalized Kohn–Sham density functional theory. In particular, we develop a batch variant of the recently formulated Kronecker product-based linear solver for the simultaneous solution of multiple linear systems. We then develop a modular, math kernel based implementation for hybrid functionals on NVIDIA architectures, where computationally intensive operations are offloaded to the GPUs, while the remaining workload is handled by the central processing units (CPUs). Considering bulk and slab examples, we demonstrate that GPUs enable up to 8× speedup in node-hours and 80× in core-hours compared to CPU-only execution, reducing the time to solution on V100 GPUs to around 300 s for a metallic system with over 6000 electrons, and significantly reducing the computational resources required for a given wall time.

Kohn-Sham density functional theory↗

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Hizanidis, Kyriakos↗

Fermi, Wind, and SOHO Observations of Sustained Gamma-Ray Emission from the Sun

We report on the linear relationship between the durations of two types of electromagnetic emissions associated with shocks driven by coronal mass ejections: sustained gamma-ray emission (SGRE) and interplanetary type II radio bursts. The relationship implies that shocks accelerate approximately 10 kiloelectronvolts electrons (for type II bursts) and more than 300 megaelectronvolts protons (for SGRE) roughly over the same duration. The SGRE events are from the Large Area Telescope (LAT) on board the Fermi satellite, while the type II bursts are from the Radio and Plasma Wave Experiment (WAVES) on board the Wind spacecraft. Here we consider five SGRE events that were not included in a previous study of events with longer duration (more than 5 hours). The five events are selected by relaxing the minimum duration to 3 hours. We found that some SGRE events had a tail that seems to last until the end of the associated type II burst. We pay special attention to the 2011 June 2 SGRE event that did not have a large solar energetic particle event at Earth or at the STEREO spacecraft that was well connected to the eruption. We suggest that the preceding CME (Coronal Mass Ejection) acted as a magnetic barrier that mirrored protons back to Sun.

Gopalswamy, N.↗

Fast and scalable quantum Monte Carlo simulations of electron-phonon models

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly-bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. Here, these methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

McMillan electron lens in a system with space charge

Space charge (SC) forces of a circulating beam in a ring have both linear (defocusing) and nonlinear components, due to a nonuniform beam distribution. The linear component of SC forces produces a betatron tune shift, which is the largest for a zero-amplitude particle, while the nonlinear component produces an amplitude-dependent betatron tune spread. These SC effects are responsible for several undesirable phenomena in accelerators: emittance growth, particle losses, beam halo, etc. In this paper, we investigate the possibility to mitigate the distributed SC forces by a thin McMillan lens, providing an axially-symmetric kick, which is qualitatively opposite to the accumulated effect of beam's own SC. Experimentally, the proposed concept can be tested in Fermilab's IOTA ring. A thin McMillan lens can be implemented by a short (70) insertion of an electron beam with a specifically chosen density distribution in transverse directions. In this article, to test if McMillan lenses can reduce the tune spread induced by SC, we make several simulations with a 6-D particle tracking code, Synergia. We choose such beam and lattice parameters that the SC tune spread is roughly 0.5 and the emittance growth due to the half-integer resonance is clearly observed without the SC compensation. Then, we focus on reducing the emittance growth by adjusting the bare betatron tunes using the ring quadrupoles, and reducing the tune spread by the McMillan lenses. The results of reducing a large tune spread (≈ 0.5), reported here, are not perfect, but substantial. There is still room for further investigation. The simulations performed so far in this work indicate that McMillan lenses can cope with an SC tune spread of ≈ 0.1 per lens.

43 PARTICLE ACCELERATORS↗

Mechanism of parallel electric fields inferred from observations

Data from various experiments of the Atmosphere Explorer satellites are analyzed to test their consistency with the model of single-particle linear acceleration through a static parallel potential drop. Theoretical current/voltage and energy flux/voltage relations are applied to the data to predict the densities of source current carriers above the acceleration region for upward Birkeland currents. Comparison of these model predictions with simultaneous electron data indicates that the observed field-aligned potential drops are consistent with direct acceleration in the absence of anomalous resistivity.

Yeh, H.-C.↗

Changes in ribbon synapses and rough endoplasmic reticulum of rat utricular macular hair cells in weightlessness

This study combined ultrastructural and statistical methods to learn the effects of weightlessness on rat utricular maculae. A principle aim was to determine whether weightlessness chiefly affects ribbon synapses of type II cells, since the cells communicate predominantly with branches of primary vestibular afferent endings. Maculae were microdissected from flight and ground control rat inner ears collected on day 13 of a 14-day spaceflight (F13), landing day (R0) and day 14 postflight (R14) and were prepared for ultrastructural study. Ribbon synapses were counted in hair cells examined in a Zeiss 902 transmission electron microscope. Significance of synaptic mean differences was determined for all hair cells contained within 100 section series, and for a subset of complete hair cells, using SuperANOVA software. The synaptic mean for all type II hair cells of F13 flight rats increased by 100%, and that for complete cells by 200%. Type I cells were less affected, with synaptic mean differences statistically insignificant in complete cells. Synapse deletion began within 8 h upon return to Earth. Additionally, hair cell laminated rough endoplasmic reticulum of flight rats was reversibly disorganized on R0. Results support the thesis that synapses in type II hair cells are uniquely affected by altered gravity. Type II hair cells may be chiefly sensors of gravitational and type I cells of translational linear accelerations.

short duration↗

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Chemistry↗

Design and Principles of Linear Accelerators and Colliders." in Particle Physics Reference Library, pp. 295-336. Springer, Cham, 2020.

Linear accelerators (linacs) use alternating radiofrequency (RF) electromagnetic fields to accelerate charged particles in a straight line. Linacs were invented about 95 years ago and have seen many significant technical innovations since. A wide range of particle beams have been accelerated with linacs including beams of electrons, positrons, protons, antiprotons, and heavy ions. Linac parameter possibilities include pulsed versus continuous wave, low and high beam powers, low and high repetition rates, low transverse emittance beams, short bunches with small energy spreads, and accelerated multiple bunches in a single pulse. The number of linacs around the world has grown tremendously with thousands of linacs in present use, many for medical therapy, in industry, and for research and development in a broad spectrum of scientific fields. Researchers have developed accelerators for scientific tools in their own right, being awarded several Nobel prizes. Moreover, linacs and particle accelerators in general have enabled many discovery level science experiments in related fields, resulting in many Nobel prizes as well.

Seeman, John↗

Degradation of Poly- and Perfluoroalkyl Substances (PFAS) in Water via High Power, Energy-Efficient Electron Beam Accelerator

The goal of the 2-year workplan was to see if electron beam (EB) could be used to break down a sub-set of the larger chemical family of per and polyfluoroalkylated substances (PFAS) in an energy efficient and economical manner when compared to conventional water treatment technologies. Year one (Y1) work focused on sample EB treatment work in the Fermi National Accelerator Laboratory’s (FNALs) Accelerator Applications Demonstration and Development (A2D2) EB accelerator. While there are reportedly thousands of types of PFAS, for the point of most of the work herein, a small subset was examined, typically perfluorooctane sulfonate (PFOS) and perfluorooctanoate (PFOA). PFOA and PFOS are two of the most well studied PFAS and are studied for baseline evaluations and are considered most useful. The work from Y1 provided information about the optimal operating parameters and additives to use when treating PFOS and PFOA via EB. The data were then used to see where in a water treatment system an EB accelerator would be best suited to treat PFAS. A conventional water treatment technology, GAC, was then compared to e-beam treatment technology with respect to energy and costs for treatment. In year two (Y2), several conventional e-beam accelerator designs, and FNAL’s developmental compact SRF accelerator design, were evaluated for their suitability in PFAS treatment, from an energy efficiency and cost standpoint. Several EB parameters were evaluated and optimized for the removal of PFOA and PFOS from water at normal pressure and temperature, measured as total PFAS removal. Under the optimized test conditions both PFOA showed complete destruction to inorganic fluoride, and PFOS to inorganic fluoride and sulfate, with mass balance. The effect on PFAS removal relative to solution pH, total EB dose, EB dose rate, dissolved oxygen concentration (DO), temperature, and initial PFAS concentration were evaluated. In general, PFOA was easier to destroy than PFOS. Degradation products, typically observed under less-than-optimal EB conditions, provided insight to degradation mechanisms. Products were identified to rule out possible deleterious biproduct formation. The water radiolysis radical reaction kinetics with PFOS and PFOA were not dependent on the initial concentration over 5-orders of magnitude from 2 μg/L to 20 mg/L. This is thought to be because there was an overabundance of the reactive water radiolysis radicals relative to PFAS molecules and largely attributed to aqueous electrons. The reaction rates appeared to be diffusion limited. Testing at higher concentrations (100-200 mg/L) showed a decrease in removal efficiency, suggesting alternative kinetics, possibly second order rates, at higher concentrations. In all, we successfully defined a set of optimal EB parameters to treat PFOA and PFOS at concentrations of 20 mg/L in water with destruction efficiencies near 100%. We further tested the optimized EB parameters with other types of PFAS, including shorter and longer fluorocarbon chain homologs of PFOA and PFOS, and PFAS with alternative functional groups such as sulfonamides. Based on our results EB can be optimized as an effective destructive technology for removing PFAS from water. The conditions optimized for PFOA and PFOS were less effective with ultra-short fluorocarbon compounds like TFMS, PFES, PFPS and PFBS, and likely require re-optimization of parameters to them. In all, it was determined that from a cost and energy efficiency standpoint, EB would be best applied to waste streams with relatively high concentrations of PFOS and PFOA and is not as cost effective as GAC treatment for removing low concentrations of PFAS from water. Higher concentrations of PFAS can be found in the wastewater of conventional treatment processes such as RO and IE and therefore EB may be used to supplement such treatment technologies. Some real-world IE regeneration wash water and RO reject water containing higher concentrations of PFAS and obtained from pilot scale industrial wastewater treatment system at a fluorochemical manufacturing facility, showed that EB could remove PFAS from such types of wastewaters. The IE regenerant wash water appeared to be the most efficient of the two types of wastewaters tested. However, some further optimization of the EB parameters for the specific PFAS types present in those wastewaters may be required. Also, the effects of co-present TOC and mineral salts should be considered during such optimization efforts. From the experimental Y1 results it was seen that the aqueous electron drives degradation of the PFAS. In a hypothetical water treatment skid using EB for PFAS destruction the parameters of the system should be optimized to promote aqueous electron production. Before EB treatment, the PFAS should be preconcentrated when possible, the pH should be raised to pH 10 or higher to enhance aqueous electron production, and the water should be nitrogen purged to remove dissolved oxygen to minimize aqueous electron scavenging. An excel spreadsheet was created that calculates optimal conditions based on inlet PFAS concentration and desired outlet concentration, by optimizing the accelerator power, dose rate, water treatment rate, pH and dissolved oxygen levels to reach the desired endpoint. Given this information on accelerator operating conditions five different EB accelerator systems were compared. One EB system was a continuous-wave, linear superconducting accelerator being designed at Fermilab. Three other EB systems (IMPELA at 5% and 25% duty factor and the ILU-14) were normal conducting pulsed linear accelerators. The fifth system was an IBA Rhodotron which is a normal conducting, circular, continuous-wave accelerator. The accelerator efficiency (% of the incoming power that is used in water treatment) was the dominating factor in accelerator choice. The radio frequency (RF) power supply and the accelerator design (superconducting versus warm technology) drive the accelerator efficiency. The IBA Rhodotron was seen to be the most energy efficient commercially available technology with a wall-plug (total) power efficiency of 43% at 400 kW. The Fermilab design, with a prototype for a different application currently being fabricated, was the most energy efficient at 55% when driven by a Klystron RF power supply and as high as 77% when powered by a magnetron. As the Fermilab design was the most energy efficient by approximately 10-30%, further design work was done on the accelerator and beam delivery system specific to the destruction of PFAS in water. The Fermilab design is unique from industrial accelerators in that is superconducting. Superconducting technology allows for the acceleration of electrons without losses. The accelerator must be cooled to below the point where it is superconducting and is operated around 4 degrees Kelvin. The bulk of the design work for the accelerator is on making the accelerator as energy efficient as possible so that it does not require liquid helium and can be cooled with conduction cooling via cryocoolers. Final design work resulted in an EB accelerator that would operate at minimally 200 kW and 10 MeV. Prototype construction would cost $\$ $7.8 million dollars when driven by a Klystron power supply. A second version of the same accelerator would cost $\$ $5.5 million dollars when driven by a magnetron that is still under development. The commercially available 300 kW IBA Rhodotron cost was estimated at approximately $\$ $9 million. While it is hard to directly compare, an operational GAC system used by 3M for groundwater treatment capital cost (2022 dollars) was estimated to cost $\$ $3.3 million. While the capital expense of the EB accelerator systems was higher than GAC, the accelerator EB treatment would result in destruction of the PFAS and not just sequestration of PFAS to form a new waste stream that requires further treatment or disposal. The operating cost to destroy the PFAS via 400 kw EB system was less than $\$ $1000/kg of PFAS destroyed when treating at a 20 mg/L PFAS concentration, compared to GAC with operating costs that calculated at $\$ $27,530 per kg of PFAS sequestered when treating 100 μg/L PFOA and PFOS combined concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

E-Beam Irradiation Beamline at Jefferson Lab for Wastewater Treatment

Electron beam (e-beam) irradiation is an advanced method for removing the emerging organic contaminants in wastewater, such as 1,4-dioxane, and per- and polyfluoroalkyl sub?stances (PFAS), which have the potential to be regulated in the near future but are difficult to degrade by conventional treatment methods. This dissertation was based on a collabo?rating study between Jefferson Lab (Jlab) and Hampton Roads Sanitation District (HRSD) to evaluate the impacts of e-beam irradiation on the degradation of 1,4-dioxane and PFAS. It presents the detailed design of an e-beam irradiation beamline, the beamline simulation using general particle tracer (GPT), the installation, and the successful commissioning. The beamline is an extended section to the Upgraded Injector Test Facility (UITF) at Jlab, which is a continuous wave (CW), superconducting radio frequency (SRF) linear accelerator with an energy up to 10 MeV. To let the sample volume receive a significant and uniform dose distribution, the sample target was designed by investigating the dose distribution simulated with a Monte-Carlo code, FLUKA. The optimized beam energy was 8 MeV and the beam current for irradiation was ? 100 nA. With the use of a solenoid and a raster, the electron beam was expanded to the optimized size, 1? ? 15 mm, at the sample target. This dis?sertation also presents the irradiation experiments for 64 1,4-dioxane samples and 48 PFAS samples in different water matrices, including real wastewater, which were prepared and an?alyzed by HRSD. The absorbed doses of samples were obtained by designing a new method that combines the FLUKA simulation and dose mapping experiments. The irradiation re?sults showed that around 95% of 1,4-dioxane was removed at a low dose of ? 2 kGy, and PFAS was possibly removed at a lower dose compared to similar research. This work is a first implementation of SRF technology for wastewater irradiation. It pro?vides a valuable new research platform for wastewater remediation. This will be in support of future industrial applications of advanced SRF technologies and better understanding of the effect of e-beam irradiation on wastewater or water treatment.

Li, Xi↗

On the acceleration of the auroral plasma of the Earth due to conic instability

The role of electrostatic conic instability in the diffusion of spilled particles and the acceleration of the auroral plasma of the Earth are numerically investigated by means of quasi-linear equations. Linear increments to the conic instability under magnetospheric conditions are introduced. The quasi-linear equation is averaged along tubes of force taking into account the drift across the magnetic field lines. It is shown that the existence of a conic instability leads to small spills and isotropic distribution of particles, but is also accompanied by significant acceleration of electrons.

Churayev, R. S.↗