Cyclotron Orbit Research Articles

Dipole Moment ofPH+and the Atomic Masses ofSi28,P31by Comparing Cyclotron Frequencies of Two Ions Simultaneously Trapped in a Penning Trap

By trapping pairs of ions in a Penning trap, alternating each ion between large and small cyclotron orbits, we have measured the cyclotron frequency ratios 12C2H4+/28Si+, 13C2H2+/28Si+, 28SiH3+/31P+, and 16O2+/31PH+, all to <30 ppt precision. The 16O2+/31PH+ data exhibit a bimodal distribution due to the polarizability of the Lambda-doubling components of the PH+ ground state, from which we obtain the electric dipole moment of 31PH+, 0.331(8) ea0. Combined with other atomic mass measurements we also obtain improved values for m(28Si), 27.976 926 535 0(6) u, and m(31P), 30.973 761 998 9(9) u.

Thermoelectric studies of the non-thermal equilibrium dynamics in chiral metals

The conventional pyroelectric effect is intimately connected to the symmetry, or rather lack of center of symmetry, of the material. Although the experiments we discuss involve studies of low symmetry materials, the pyroelectric currents observed are of an entirely new origin. Systems with broken-translational-symmetry phases that incorporate orbital quantization can exhibit significant departures from thermodynamic equilibrium due to a change in magnetic induction. For example, orbitally quantized field-induced spin- or charge density wave systems, in which the competition between the elastic forces of the density wave and pinning leads to a critical state analogous to the vortex phase of type II superconductors. This metastable state consists of a balance between the density-wave pinning force and the Lorentz force on the extended currents due to the drift of cyclotron orbits. This results in the establishment of a three-dimensional chiral metal that can extend deep into the bulk of the crystal. In this way the density wave pinning potential plays a similar role to the edge potential in a two-dimensional electron gas, leading to a large Hall angle and quantization of the Hall resistance. A thermal perturbation that reduces the pinning potential returns the system toward thermal equilibrium, which can only be achieved by current flow orthogonal to the surface. The observation of this new form of pyroelectric effect in the high magnetic field phase ( B > 30 T ) of the organic charge transfer salt α - ( BEDT - TTF ) 2 KHg ( SCN ) 4 is conclusive proof of the existence of a three-dimensional chiral metal.

Tendency of MHD Forces to Create Localized, Collimated Plasma-filled Flux Tubes &amp; Ion Orbit Instability in a Flux Tube

Electrostatic helicity injection involves the injection of new azimuthal magnetic flux to link the existing axial flux of an open magnetic field. Since magnetic flux is frozen into plasma, this injection of new flux requires the injection of new plasma as well. This associated plasma injection means that helicity injection involves an increase of the density in the flux tube comprised by the initial open magnetic field lines. The injection of plasma and its embedded magnetic flux results in a collimation of the open flux tube when the embedded magnetic flux becomes compressed due to flow stagnation. Plasma injection occurs in the form of jets originating from biased electrodes having plasma sources. These jets can originate from both cathodes and anodes. An ion orbit instability may occur for cathode-originating jets. In cathode-originating jets the ions move opposite to the direction of the conventional current and so experience an anti-pinch force which can be strong enough to overwhelm the usual magnetic force responsible for cyclotron orbit motion.

Stochastic ion heating in a field-reversed configuration geometry by rotating magnetic fields

Ion heating by application of rotating magnetic fields (RMFs) to a prolate field-reversed configuration (FRC) is explored by analytical and numerical techniques. For odd-parity RMFs (RMFo), perturbation analysis shows ions in figure-8 orbits gain energy at resonances of the RMFo frequency ωR, with the figure-8 orbital frequency ω. Since figure-8 orbits tend to gain the most energy from the RMF and are unlikely to escape in the cusp region (where most losses occur), they are optimal candidates for rapid stochastic heating, as compared to cyclotron and betatron orbits. Comparisons are made between heating caused by even- and odd-parity RMFs and between heating in currently operating and in reactor-scale FRC devices.

Tight binding analogue of cyclotron orbits

AbstractThe magnetic translation group describes the symmetry of the itinerant electron on two‐dimensional lattice with perpendicular magnetic field. For such a finite system, with periodic condition the properties of the irreducible representations of this group are responsible for the tight‐binding analogue of cyclotron orbits of the free electron case. The relation between the size of the planar lattice and the structure of the group and its irreducible representations is pointed out. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Evolution of charge carriers for transport in electron-doped cuprate superconductorLa1.89Ce0.11CuO4thin films

To reveal the evolution of charge carriers to the transport in ${\mathrm{La}}_{1.89}{\mathrm{Ce}}_{0.11}\mathrm{Cu}{\mathrm{O}}_{4}$, we carefully measured the temperature and magnetic-field dependences of the Hall resistivity $({\ensuremath{\rho}}_{xy})$ and longitudinal resistivity $({\ensuremath{\rho}}_{xx})$. Two sign reversals of the Hall resistivity are observed in the normal state. In addition, the ${\ensuremath{\rho}}_{xy}$ and ${\ensuremath{\rho}}_{xx}$ show ${B}^{2}$ dependence in the temperature region of $40--50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, similar to the behavior of the compensated metal; that is, the effective concentrations of electrons $({n}_{e}^{*})$ and holes $({n}_{h}^{*})$ are nearly equal. The possible origin of the sign reversal is attributed to the competition between ${n}_{e}^{*}∕{n}_{h}^{*}$ and ${\ensuremath{\tau}}_{e}∕{\ensuremath{\tau}}_{h}$ (the relaxation time ratio of electrons to holes), and the change of cyclotron orbits induced by the magnetic field is also considered.

Plasmon mechanism of resistance magnetooscillations in a two-dimensional electron system in strong electric fields

A multielectron approach is developed to explain the resistance magnetooscillations in two-dimensional electron systems that have recently been detected under the action of microwave pumping [1] or a strong dc electric field [23]. A qualitative change in the screened impurity potential in a strong electric field is taken into account for the first time. When considered in the rest frame of the center of the cyclotron orbit, the impurity potential becomes nonstationary and, thus, should be screened dynamically. This fact substantially changes the picture of impurity scattering in a “pure” two-dimensional system: a dissipative current is induced by the excitation of two-dimensional plasmons rather than by one-electron transitions between the Landau levels. In the case of microwave pumping, every period of resistance oscillation in a reciprocal magnetic field is formed by the excitation of the corresponding magnetoplasmon branch, and the fine structure of oscillations is formed by the singularities of the magnetoplasmon density of states. In a “dirty” two-dimensional system, the role of electron-electron interaction weakens, collective excitations cease to exist, and the results transform into the well-known results obtained in terms of a one-electron approach.

AlAs two-dimensional electrons in an antidot lattice: Electron pinball with elliptical Fermi contours

We report ballistic transport measurements in a two-dimensional electron system confined to an AlAs quantum well and patterned with square antidot lattices of period $a = $0.6, 0.8, 1.0 and 1.5 $\mu$m. In this system two in-plane conduction-band valleys with elliptical Fermi contours are occupied. The low-field magneto-resistance traces exhibit peaks corresponding to the commensurability of the cyclotron orbits and the antidot lattice. From the dependence of the position of the peak associated with the smallest commensurate orbit on electron density and $a$, we deduce the ratio of the longitudinal and transverse effective masses $m_l/m_t=5.2\pm 0.4$, a fundamental parameter for the anisotropic conduction bands in AlAs.

Reduction of ion magnetron motion and space charge using radial electric field modulation

Ions of the same m/ z must remain in phase with each other during the detection time period used for FTICR-MS signal acquisition for optimal performance. The loss of coherence of the ion cloud during detection leads to faster rates of signal decay which results in a decrease in the achievable resolution and mass measurement accuracy with FTICR-MS technology. As the ions spin on their excited cyclotron orbit, many factors contribute to de-phasing of ion motion, such as the presence of radial electric fields and the Coulombic interaction of ion clouds of different mass-to-charge ratios. With the application of Electron Promoted Ion Coherence or EPIC, signal duration can be increased. Since FTICR-MS achieves high performance through measurement of frequency, the ability to observe ions over a longer time period increases the performance of FTICR-MS. Radial electric fields are an unavoidable consequence of applied trapping potentials to confine ion motion parallel to the magnetic field in the ICR cell; however, the presence of radial electric fields also induces magnetron motion. With EPIC it is possible to control the shape of the radial electric fields that the ions experience by changing the number of electrons that are sent through the center of the ICR cell. Furthermore, the electric field shape produced with EPIC can be altered to decrease space charge contributions by increasing the length of the ion oscillation path along the axis of the ICR cell and decrease radial electric field effects, which alter detected ion cyclotron frequencies. Here we report theoretical and experimental results to evaluate and describe the impact of EPIC on the performance of FTICR-MS.

Pinning and transport of cyclotron (Landau) orbits by electromagnetic vortices

Electromagnetic waves with phase defects in the form of vortex lines combined with a constant magnetic field are shown to pin down cyclotron orbits (Landau orbits in the quantum mechanical setting) of charged particles at the location of the vortex. This effect manifests itself in classical theory as a trapping of trajectories and in quantum theory as a Gaussian shape of the localized wave functions. Analytic solutions of the Lorentz equation in the classical case and of the Schr\"odinger or Dirac equations in the quantum case are exhibited that give precise criteria for the localization of the orbits. There is a range of parameters where the localization is destroyed by the parametric resonance. Pinning of orbits allows for their controlled positioning -- they can be transported by the motion of the vortex lines.

Imaging electrons in a magnetic field

We present simulations of an imaging mechanism that reveals the trajectories of electrons in a two-dimensional electron gas (2DEG), as well as simulations of the electron flow in zero and small magnetic fields. The end goal of this work is to implement the proposed mechanism to image the flow of electrons inside a ballistic electron device from one specific point (A) to another (B) in a 2DEG, using a low-temperature scanning probe microscope with a charged tip. The tip changes the electron density in the 2DEG beneath it and deflects the electrons traveling nearby, thereby changing the conductance from point A to point B. The simulations presented here show that by measuring the transmission of electrons from A to B versus tip position, one can image the electron flow. This forward scattering mechanism is well suited for imaging in a magnetic field, in contrast to previous probes that depended on backscattering. One could use this technique to image cyclotron orbits in an electron-focusing geometry, in which electrons travel from point A to point B in semi-circular paths bouncing along a wall. Imaging the motion of electrons in magnetic fields is useful for the development of devices for spintronics and quantum information processing.

Current focusing in InSb heterostructures

We report transverse electron focusing in a symmetrically doped, InSb-based two-dimensional electron system. In a focusing device, the application of a perpendicular magnetic field steers the electron current from an injecting quantum point contact into a collector quantum point contact whenever the diameter of the cyclotron orbit corresponds to an integer fraction of the injector to collector spatial separation. In low-temperature measurements of in-plane gated devices, we observe peaks in the collector voltage at magnetic fields where focusing is expected. The first peak displays substructure which is preserved at temperatures as high as 10 K and under a variety of gating conditions. We speculate that this substructure originates from spatially distinct paths for electrons with different spin polarizations arising from the large Dresselhaus effect expected for InSb-based electron systems.

Geometric resonance of bragg-reflected cyclotron orbits in unidirectional lateral superlattices: The role of harmonics of the potential modulation

A new class of small amplitude low-field magnetoresistance oscillation observed in a unidirectional lateral superlattice (ULSL) attributable to the geometric resonance of Bragg-reflected cyclotron orbits (open orbits) reveals the presence of higher harmonics in the potential modulation. By contrast, the commensurability oscillation (CO) exhibited by the same ULSL sample appears to be explicable by a formula taking only the fundamental component into consideration. The apparent inconsistency is ascribed to the difference in the sensitivity to the higher harmonics of the two types of magnetoresistance oscillations. The amplitude of the new oscillation is discussed in terms of the probability of the magnetic breakdown and the ratio of the distance traveled by the electrons during one period of the open orbit to the mean free path.

Mass ratio of two ions in a Penning trap by alternating between the trap center and a large cyclotron orbit

We have implemented a technique for precision mass comparison of two ions trapped simultaneously in a Penning trap in which each ion is alternately positioned at the center of the trap – where the cyclotron frequency is measured – and in a large cyclotron “parking” orbit. Systematic shifts in the cyclotron frequency ratio have been studied by comparing 13C 2H 2 +/ 14N 2 + and 14N 2 +/ 28Si +. Using the method to compare 28SiH 3 +/ 31P + we have obtained a new atomic mass for 31P, M[ 31P] = 30.973 761 999 7 (61) u.

General approach to the quantum kicked particle in a magnetic field: Quantum-antiresonance transition

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for general values of the conserved coordinate x(c) of the cyclotron orbit center. The system exhibits spectral structures ["Hofstadter butterflies" (HBs)] and quantum diffusion depending sensitively on x(c). Most significant changes take place when x(c) approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially "doubles" and the quantum-diffusion coefficient D(x(c)) is strongly reduced. An explanation of these phenomena, including an approximate formula for D(x(c)) in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all x(c) is briefly considered.

Commensurability oscillations in the surface-acoustic-wave-induced acoustoelectric effect in a two-dimensional electron gas

We study the acoustoelectric effect generated by surface acoustic waves (SAW) in a high-mobility two-dimensional electron gas with isotropic and especially small-angle impurity scattering. In both cases the acoustoelectric effect exhibits Weiss oscillations periodic in ${B}^{\ensuremath{-}1}$ due to the commensurability of the SAW period with the size of the cyclotron orbit and resonances at the SAW frequency $\ensuremath{\omega}=k{\ensuremath{\omega}}_{c}$ multiple of the cyclotron frequency. We describe how oscillations in the acoustoelectric effect are damped in low fields where ${\ensuremath{\omega}}_{c}{\ensuremath{\tau}}_{*}\ensuremath{\lesssim}1$ (with the time scale ${\ensuremath{\tau}}_{*}$ dependent on the type of scattering) and find its nonoscillatory part, which remains finite to the lowest fields.

Nonadiabatic orbit features in ion distribution functions of fast flow magnetotail configurations

One of the major problems in space physics is the limitation of measurements. We present here one way to infer global characteristics of the magnetosphere from only a single satellite position. Several consistent orbit‐tracing (COT) models of fast flows in thin plasma sheets were constructed. The resulting ion distribution functions were examined to see if there are any features which can distinguish a uniform earthward flow of plasma from flows which are confined in a narrow channel in the dawn‐dusk direction. The model distribution functions during uniform flows had the appearance of an initially isotropic f(v) that had simply been shifted by the earthward flow speed. The model f(v) exhibited lima bean–shaped features when the flow was confined to a region comparable to the diameter of a cyclotron orbit based on Bz. Distribution functions observed by the Geotail satellite were examined for comparisons, and the measured distributions were found to exhibit features similar to those obtained in the COT model. We are able to demonstrate that the distributions measured by Geotail may only be reproduced in our technique if the convective electric field is confined in the dawn‐dusk direction.

Spin Separation in Cyclotron Motion

Charged carriers with different spin states are spatially separated in a two-dimensional hole gas. Because of strong spin-orbit interaction, holes at the Fermi energy in GaAs have different momenta for two possible spin states traveling in the same direction, and, correspondingly, different cyclotron orbits in a weak magnetic field. Two point contacts, acting as a monochromatic source of ballistic holes and a narrow detector arranged in the magnetic focusing geometry are demonstrated to work as a tunable spin filter.

The use of the X-ray photoelectron spectroscopy for studying inverse β-decay

In the paper, a brief substantiation of the application of a new method for studying the inverse β-decay is presented with the use of Auger- and photoelectron spectra for registering the electrons occurring during the interaction of low-energy (∼1 MeV and lower) electron anti-neutrino ( ν ̄ e − ) with a substance. The new method is an alternative to the existing method based on the use of high-energy ν ̄ e − (∼10 MeV) of the electrons which are formed during the interaction with a substance and have the energy sufficient for the appearance of Cerenkov effect. An electronic magnetic spectrometer with high sensitivity, double focusing by non-uniform magnetic field π√2 and the radius of the cyclotron orbit of 100 cm was chosen for realizing the method. The spectrometer was built, and the first X-ray electron spectra were obtained. The constant of the instrument was determined.

The use of the X-ray photoelectron spectroscopy for studying inverse $beta;-decay

In the paper, a brief substantiation of the application of a new method for studying the inverse β-decay is presented with the use of Auger- and photoelectron spectra for registering the electrons occurring during the interaction of low-energy (∼1 MeV and lower) electron anti-neutrino (ν̄e−) with a substance. The new method is an alternative to the existing method based on the use of high-energy ν̄e− (∼10 MeV) of the electrons which are formed during the interaction with a substance and have the energy sufficient for the appearance of Cerenkov effect. An electronic magnetic spectrometer with high sensitivity, double focusing by non-uniform magnetic field π√2 and the radius of the cyclotron orbit of 100 cm was chosen for realizing the method. The spectrometer was built, and the first X-ray electron spectra were obtained. The constant of the instrument was determined.