Cyclotron Rotation Research Articles

Transformation of the Shape and Spectrum of an Ultrawideband Electromagnetic Pulse in a “Gigantic” Coaxial Line Filled with Magnetized Plasma

A propagation of ultrawideband electromagnetic pulses (UWB EMPs) through magnetized plasma has been experimentally studied using a “gigantic” coaxial line, which has been developed at IAP RAS for laboratory modeling of ionospheric effects. This coaxial line is 1.4 m in diameter and 10 m in length and is installed inside the chamber of the large-scale Krot plasma device. The line can be filled with rf inductively coupled plasma, magnetized or not. It allows one to explore the propagation of UWB EMPs in plasma along a long path without refraction and divergence and obtain a physical picture of EMP transformation. Under conditions where the duration of the UWB EMP is comparable to the period of electron plasma oscillations (fp−1), the period of cyclotron rotation of electrons (fc−1), or even significantly shorter, a complex of effects of transformation of the waveform and frequency spectrum of the pulse occurs. Without ambient magnetic field, a UWB EMP is distorted due to the effects of the cutoff and frequency dispersion. In dense magnetized plasma, i.e., when fp >> fc, the UWB EMP breaks into two wave packets, the high-frequency one (f > fp) and low-frequency one (f < fc). In rare magnetized plasma (fp << fc), the cyclotron absorption produces a long train of damped oscillations at a frequency close to the cyclotron frequency fc following the UWB EMP.

Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is, however, shown that the Landau and cyclotron resonance conditions which classically describe resonant energy–momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding centre rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave-driven radial current responsible for angular momentum absorption.

Electrically Tunable Gyrohelitrons with Crossed Fields

The generation frequency is ω ≈ k ω н in classical gyrotrons, where ω н = е B 0 / m is the electron cyclotron rotation frequency in a uniform longitudinal magnetic field with induction B 0 , e is the electron charge, m is the electron mass, k = 1, 2, 3… is the cyclotron frequency working harmonic number. Thus, the generation frequency ω being tuned is possible only by changing B 0 . This way is very inconvenient. It’s necessary a solenoid additional (control) winding. That difficulty can be eliminated in gyrotrons with crossed fields - electric 0 and magnetic 0 , here 0 ⊥ 0 . The frequency can be tuned by changing E 0 . This possibility can be realized at least two ways: a gyrotron based on a coaxial resonator with radial field E 0 ; a four-mirror gyrotron on traveling Т -waves with transverse in respect the traveling wave direction to uniform crossed fields – electric 0 and magnetic 0 . The single-screw electron flow has a rotation frequency , for the first gyrotron type, where , , Δ V is the potential difference between the inner (radius b 1 ) and outer (radius b 2 ) coaxial conductors, r 0 is the electron flow rotation radius. Thus, the generation frequency ω ≈ k ω н is determined by both B 0 and Δ V . Moreover, at Δ V = 0 the device becomes a classical high-orbit gyrotron, at B 0 = 0 a classical helitron. Therefore, at B 0 ≠ 0 and Δ V ≠ 0 it should be called a gyrohelitron, the generation frequency of which is tuned electrically - by changing Δ V . The article presents the design schemes of a gyrohelitron and a two-beam four-mirror gyrotron. In both cases, piezoelectric devices realize synchronous tuning of the frequency, just it allows the devices becoming fully electrically controllable. The following results were obtained for the gyrohelitron. Resonator field – H 211 , interaction on the second harmonic ω s ; a) narrow-band tuning 10 %: maximum efficiency – 55 %, minimum efficiency – 25 %; β 0 = v 0 / c = 0.27; q = v 0 ⊥ / v || = 2; b) broadband tuning 58 %: maximum efficiency – 18 %, minimum efficiency – 14 %; β 0 = v 0 / c = 0.2; q = v 0 ⊥ / v || = 2. The given results for the gyrohelitron indicate that it is promising to use electrical frequency tuning in a coaxial gyro-BWT and the amplification band in a gyro-TWT, since these devices do not require piezoelectric tuning of electrodynamic structures.

Radial distribution of electrons rotation moment in hall effect and plasma-ion thrusters

The subject matter of the article is the radial distribution of electrons movement parameters inside electric propulsion thrusters with closed electrons drift. The radial magnetic field in Hall effect thrusters is the limits the axial flow of electrons because of interaction with azimuth electron current. In turn, this azimuth current exists as a result of rivalry between the attempt of the magnetic field to transform electrons current completely closed one and the loss of electrons rotation moment in collisions. Similar processes take place in the ionization chamber of plasma-ion thrusters with the radial magnetic field. The attempts to estimate electrons parameters through only collisions with ions and atoms inside volume have given the value of axial electrons current much lower than really being. This phenomenon is called anomalous electrons conductivity, which was tried to be explained as a consequence of various effects including "near-the-wall-conductivity", which was explained as a result of non-mirror reflection of electrons from the Langmuir layer near the walls of the thruster channel. The disadvantage of this name is the fact that the reflection of the electron occurs before reaching the surface from the potential barrier at the plasma boundary with any environment: the wall, but also with the environment vacuum. The potential distribution in the Langmuir layer is non-stationary and inhomogeneous due to the presence of so-called plasma oscillations. The definition of "conductivity" is just as unfortunate in this name, because the collisions are always not a factor of conductivity, but on the contrary – of resistance. The goal is to solve the task of electrons rotation moment distribution in the thruster channel. The methods used are the formulation of the kinetic equation for electrons distribution function over the velocities, radius, and projections of the coordinates of the instantaneous center of cyclotron rotation; solution of this equation and finding with its use the distribution of the gas-dynamic parameters of electrons along the cross-section of the channel. Conclusions. A mathematical model of electrons rotation moment dynamics is proposed, which allows using plasma-dynamics equations to analyze its distribution along the cross-section of thruster channel and to estimate the effect of "near-the-wall-conductivity" using appropriate boundary conditions.

Ab Initio molecular dynamics with screened Lorentz forces. II. Efficient propagators and rovibrational spectra in strong magnetic fields.

Strong magnetic fields have a large impact on the dynamics of molecules. In addition to the changes in the electronic structure, the nuclei are exposed to the Lorentz force with the magnetic field being screened by the electrons. In this work, we explore these effects using ab initio molecular dynamics simulations based on an effective Hamiltonian calculated at the Hartree-Fock level of theory. To correctly include these non-conservative forces in the dynamics, we have designed a series of novel propagators that show both good efficiency and stability in test cases. As a first application, we analyze simulations of He and H2 at two field strengths characteristic of magnetic white dwarfs (0.1 B0 = 2.35 × 104 T and B0 = 2.35 × 105 T). While the He simulations clearly demonstrate the importance of electron screening of the Lorentz force in the dynamics, the extracted rovibrational spectra of H2 reveal a number of fascinating features not observed in the field-free case: couplings of rotations/vibrations with the cyclotron rotation, overtones with unusual selection rules, and hindered rotations that transmute into librations with increasing field strength. We conclude that our presented framework is a powerful tool to investigate molecules in these extreme environments.

Strong surface magnetic field generation in relativistic short pulse laser–plasma interaction with an applied seed magnetic field

While plasma often behaves diamagnetically, we demonstrate that the laser irradiation of a thin opaque target with an embedded target-transverse seed magnetic field Bseed can trigger the generation of an order-of-magnitude stronger magnetic field with opposite sign at the target surface. Strong surface field generation occurs when the laser pulse is relativistically intense and results from the currents associated with the cyclotron rotation of laser-heated electrons transiting through the target and the compensating current of cold electrons. We derive a predictive scaling for this surface field generation, Bgen ∼ −2πBseedΔx/λ0 (in the large spot size limit), where Δx is the target thickness and λ0 is the laser wavelength, and conduct 1D and 2D particle-in-cell simulations to confirm its applicability over a wide range of conditions. We additionally demonstrate that both the seed and surface-generated magnetic fields can have a strong impact on application-relevant plasma dynamics, for example substantially altering the overall expansion and ion acceleration from a μm-thick laser-irradiated target with a kilotesla-level seed magnetic field.

Mechanism of resonant enhancement of electron drift in nanometer semiconductor superlattices subjected to electric and inclined magnetic fields

We address the increase of electron drift velocity that arises in semiconductor superlattices (SLs) subjected to constant electric and magnetic fields. It occurs if the magnetic field possesses nonzero components both along and perpendicular to the SL axis and the Bloch oscillations along the SL axis become resonant with cyclotron rotation in the transverse plane. It is a phenomenon of considerable interest, so that it is important to understand the underlying mechanism. In an earlier Letter (Phys. Rev. Lett. 114, 166802 (2015)) we showed that, contrary to a general belief that drift enhancement occurs through chaotic diffusion along a stochastic web (SW) within semiclassical collisionless dynamics, the phenomenon actually arises through a non-chaotic mechanism. In fact, any chaos that occurs tends to reduce the drift. We now provide fuller details, elucidating the mechanism in physical terms, and extending the investigation. In particular, we: (i) demonstrate that pronounced drift enhancement can still occur even in the complete absence of an SW; (ii) show that, where an SW does exist and its characteristic slow dynamics comes into play, it suppresses the drift enhancement even before strong chaos is manifested; (iii) generalize our theory for non-small temperature, showing that heating does not affect the enhancement mechanism and accounting for some earlier numerical observations; (iv) demonstrate that certain analytic results reported previously are incorrect; (v) provide an extended critical review of the subject and closely related issues; and (vi) discuss some challenging problems for the future.

Surfatron acceleration of weakly relativistic electrons by electromagnetic wave packet in space plasma

Resonant interactions between an electromagnetic wave packet and charged particles based on numerical calculations are investigated. The strong surfatron acceleration of weakly relativistic electrons by an electromagnetic wave packet in space plasma is studied. In the central area of the wave packet, the electric field amplitude is above a threshold value and this makes it possible to capture particles in the surfing mode. The work is carried out by exact solving of second order nonlinear, nonstationary equations for the wave packet phase on the particle's trajectory at the carrying frequency. Numerical modeling shows that the trapping of weakly relativistic electrons in strong acceleration mode occurs immediately for a wide enough range of favorable initial wave phase values (80% and more). Furthermore it has been demonstrated that the combination of ranges of the particle's initial parameters corresponding to the capturing in surfatron acceleration is large enough. Temporal dynamics of velocity components for accelerated particles and the particularities of their trajectory, taking into account cyclotron rotation at the initial stage and phase plane structure for numerically solved nonlinear equations, are considered. Simulation results allow us to draw conclusions about the possibility of surfatron acceleration of weakly relativistic charged particles in space plasma by an electromagnetic wave packet.

Discrete mathematical model of a sheet electron beam in a decaying magnetic field

A discrete model of a sheet electron beam is developed in a weakly relativistic approximation. A 3D simulation of the sheet electron beam with cyclotron rotation in an axially symmetric static magnetic field under time-periodic conditions of entry is performed. The velocity spread in the beam and the efficiency of converting the energy stored in the beam into DC power depending on the beam perveance are calculated.

Peculiar rotation of electron vortex beams

Standard electron optics predicts Larmor image rotation in the magnetic lens field of a TEM. Introducing the possibility to produce electron vortex beams with quantized orbital angular momentum brought up the question of their rotational dynamics in the presence of a magnetic field. Recently, it has been shown that electron vortex beams can be prepared as free electron Landau states showing peculiar rotational dynamics, including no and cyclotron (double-Larmor) rotation. Additionally very fast Gouy rotation of electron vortex beams has been observed. In this work a model is developed which reveals that the rotational dynamics of electron vortices are a combination of slow Larmor and fast Gouy rotations and that the Landau states naturally occur in the transition region in between the two regimes. This more general picture is confirmed by experimental data showing an extended set of peculiar rotations, including no, cyclotron, Larmor and rapid Gouy rotations all present in one single convergent electron vortex beam.

Regular rather than chaotic origin of the resonant transport in superlattices.

We address the enhancement of electron transport in semiconductor superlattices that occurs in combined electric and magnetic fields when cyclotron rotation becomes resonant with Bloch oscillations. We show that the phenomenon is regular in origin, contrary to the widespread belief that it arises through chaotic diffusion. The theory verified by simulations provides an accurate description of earlier numerical results and suggests new ways of controlling resonant transport.

Imaging the dynamics of free-electron Landau states.

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.

40 years of Fourier transform ion cyclotron resonance mass spectrometry

This article reviews the development of Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) in several respects: (a) a strong static magnetic field serves to convert ion mass-to-charge ratio into cyclotron frequency. Because frequency is the most accurately measurable property, ICR MS inherently offers higher mass resolution and mass accuracy than any other mass analyzer. (b) Coherent excitation followed by induced charge detection yields a time-domain signal whose discrete Fourier transform produces a mass spectrum of ions spanning a wide m/z range simultaneously. By simple analogy to weighing objects with a mechanical balance, that “multiplex” advantage can be shown to be equivalent to “multichannel” detection by an array of individual single-channel detectors. (c) FT-ICR MS performance benefits from near-elimination of magnetic field inhomogeneity by inherent ion cyclotron rotation and ion axial oscillation; inherent nearly quadrupolar electrostatic trapping potential and nearly uniform rf electric field homogeneity near the center of the ICR ion trap (both improved even further by recent ICR cell designs); and theoretically optimal excitation and mass selection produced by stored-waveform inverse Fourier transformation (SWIFT). (d) External ion accumulation allows efficient coupling of atmospheric pressure continuous ionization sources (notably electrospray ionization) with pulsed high-vacuum FT-ICR MS excitation/detection, and injection of externally trapped ions through the “magnetic mirror” into the ICR ion trap has been optimized based on ion trajectory simulations. (e) MS/MS can be performed either inside (e.g., electron capture dissociation, infrared multiphoton dissociation) or outside (e.g., collision-induced dissociation, electron transfer dissociation) the ICR ion trap. (f) Finally, FT-ICR MS instrumentation and experimental event sequences have benefited from striking parallels to prior nuclear magnetic resonance spectroscopy developments. Similarly, non-ICR FT MS development (notably the orbitrap) has benefited from FT-ICR precedents.

Dynamics of a ribbon electron beam in the plane-symmetric reverse of a magnetic field

The dynamics of a charged particle in the model of a ribbon beam is studied in a plane-symmetric reversing magnetic field by means of numerical simulation. It is shown that the efficiency of converting the particle’s cyclotron rotation into the energy of its longitudinal motion depends on the initial phase of the particle’s entry. Increasing the length of the reverse field reduces the effect of the initial entry conditions.

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc2) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initial particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.

Alfvén Ion-Cyclotron Instability in a Mirror Trap with Highly Anisotropic Plasma

The Alfvén ion cyclotron instability is studied for mirror-confined bi-Maxwellian highly anisotropic plasmas. In such plasmas the wave length of unstable modes is of the order of the plasma scale length. Another specific feature is that a typical ion can execute several bounce oscillations along the strongly non-uniform plasma during the time of the phase divergence between the wave and cyclotron rotation. Traditional approaches such as WKB method and local dispersion relation fail under these conditions.An integral equation for the modes is derived. The spatial distribution of the eigenmodes as well as the marginal stability conditions are found by numerical solution of this equation. The asymptotics of these results in the limit of infinitely large anisotropy are obtained analytically. It is found that the mirror-confined highly anisotropic plasma can be much more stable than it follows from the traditionally used scaling.

Fast electron energy deposition in a magnetized plasma: Kinetic theory and particle-in-cell simulation

The collisional dynamics of a relativistic electron jet in a magnetized plasma are investigated within the framework of kinetic theory. The relativistic Fokker–Planck equation describing slowing down, pitch angle scattering, and cyclotron rotation is derived and solved. Based on the solution of this Fokker–Planck equation, an analytical formula for the root mean square spot size transverse to the magnetic field is derived and this result predicts a reduction in radial transport. Some comparisons with particle-in-cell simulation are made and confirm striking agreement between the theory and the simulation. For fast electron with 1 MeV typical kinetic energy interacting with a solid density hydrogen plasma, the energy deposition density in the transverse direction increases by a factor 2 for magnetic field of the order of 1 T. Along the magnetic field, the energy deposition profile is unaltered compared with the field-free case.

Plasma-sheath instability in Hall thrusters due to periodic modulation of the energy of secondary electrons in cyclotron motion

Particle-in-cell simulation of Hall thruster plasmas reveals a plasma-sheath instability manifesting itself as a rearrangement of the plasma sheath near the thruster channel walls accompanied by a sudden change of many discharge parameters. The instability develops when the sheath current as a function of the sheath voltage is in the negative conductivity regime. The major part of the sheath current is produced by beams of secondary electrons counter-streaming between the walls. The negative conductivity is the result of nonlinear dependence of beam-induced secondary electron emission on the plasma potential. The intensity of such emission is defined by the beam energy. The energy of the beam in crossed axial electric and radial magnetic fields is a quasiperiodical function of the phase of cyclotron rotation, which depends on the radial profile of the potential and the thruster channel width. There is a discrete set of stability intervals determined by the final phase of the cyclotron rotation of secondary electrons. As a result, a small variation of the thruster channel width may result in abrupt changes of plasma parameters if the plasma state jumps from one stability interval to another.

Determination of bond dissociation energies using mass spectrometry

AbstractFourier transform ion cyclotron resonance mass spectrometry (FT‐ICR/MS) offers the opportunity for gas phase cluster formation reactions at very low pressures and at temperatures that are different from room temperature. Reactions take place with single positive‐charge metal ions that are normally +2, +3, +4, etc., charged in solution. The ions formed are detected by measuring the current induced by their cyclotron rotation, but they cannot be physically separated and collected. Collision‐induced dissociation (CID) is widely used for ion‐structure determination via the fragmentation of the excited ions. CID study aims to determine the relationship between the Vpp [peak‐to‐peak voltage of the radiofrequency (rf) pulse] and the mass‐to‐charge (m/z) ratio, which will be used for the calculation of the center‐of‐mass translational kinetic energy (Ekcm) of the excited ion under investigation. CID studies are restricted to stable ions with relatively high abundance. Nevertheless, with the evolution of computational chemistry, such problems can be overcome whereby CID calculations will be used to provide the substantial parameters for computer software, such as the Gaussian 03 program, for the structure determination of the less stable NixS anions. The latter constitutes the core for our current research. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Recuperation of Charged Particle Energy in Traps with Rotating Plasma

Physical principles of recuperation (return) of charged particle energy in traps with rotating plasma are discussed. A specificity of these systems is that normally ion injection occurs due to ionization of neutral atoms in a volume with crossed fields. As this takes place, ions are accelerated in these fields in such way that the speed of cyclotron rotation equals the speed of azimuth drift of the plasma as a whole. A particle moves in the laboratory reference system along a cycloid, the ion energy being zero at the top point of the cycloid. This specificity of ion movement is used for recuperation of its energy when it leaves the trap. A two-stage recuperation scheme is considered. These stages are the ion’s transition of the centrifugal barrier and collection of ions on the electrodes that form the radial electric field. The conditions for rather efficient realization of such recuperation are discussed.