Amplitude Of Radial Oscillations Research Articles

Optimal Suppression of Oscillations in the Problem of a Spin-Up of a Two-Mass System

We consider a controlled mechanical system of many bodies, consisting of a load-bearing disk that rotates around its axis fixed in space, and a carried disk attached to it using weightless elastic elements. The presented bodies are in the same plane. The problem of minimizing the amplitude of radial oscillations is studied. To solve this problem over a sufficiently large interval, two numerical methods are used: the method of successive approximations in the control space and Newton’s method. The properties of the phase trajectories of the system are studied depending on the initial states of the disks. Various disk spin-up modes are detected. Using the smoothing procedure for optimal control, a continuous control is constructed that reduces the amplitude of radial oscillations.

Radial oscillation of intense relativistic electron beam in low-magnetic-field foil-less diode

The radial oscillation of an intense relativistic electron beam possesses two main features of the spatial period and the radial oscillation amplitude in a low-magnetic-field foil-less diode, and the large radial oscillation extremely limits the beam–wave conversion efficiency and stability of a high-power microwave device. Thus, the formation mechanism of the radial oscillation is analyzed in detail. The results show that the radial oscillation of an electron beam consists of a great number of electrons with different Larmor radii and guiding centers, and the large radial oscillation is mainly caused by the strong radial electric field and the directional difference between the electric field and the magnetic field in the anode–cathode gap. A low diode voltage or a proper large anode radius is beneficial to improve the beam quality. Considering that cathode plasmas have a dominant effect on the spatial distribution of electrons, the explosive emission model was improved with cathode plasmas, and the consistency between simulation and experimental results becomes better.

Experimental study of liquid-liquid interface oscillating in radial hele-shaw cell

The dynamics of the interface between two immiscible liquids with a high viscosity contrast is studied experimentally under steady displacement of interface and periodic variation of the flow rate of the pumped liquid in radial Hele-Shaw cell. Classic Saffman–Taylor instability, which develops when the viscous fluid is monotonously displaced by the inviscid one, is well known. In the present work, the excitation of Saffman–Taylor instability by means of oscillations of the liquid-liquid interface is demonstrated. The interphase boundary performs axisymmetric radial oscillations at small amplitude of oscillations and in the absence of an average pumping. With the growth of the amplitude of radial oscillations the interface instability is excited, which manifests itself in the development of an azimuthally periodic finger structure during a part of the period. “Finger-like” instability is determined by the relative amplitude of the oscillations of the interphase boundary and under the conditions of the performed experiments depends neither on the oscillation frequency nor on the radial size of the interface.

Effect of Local Electric Field on Radial Oscillation of Electron Beam in Low-Magnetic-Field Foilless Diode

The effect of the local electric field on the radial oscillation of the electron beam in the low-magnetic-field foilless diode is studied theoretically and experimentally. The results obtained with different methods show good coherence. The radial oscillation amplitude of the electron beam affected by the local electric field depends on the electric field intensity and the phases of electrons entering and leaving the local electric field region. It is found that the enhanced radial electric field near the drift tube head results in the change of the radial oscillation amplitude with the anode–cathode gap. Meanwhile, a method to effectively suppress the radial oscillation is proposed. Optimizing the anode–cathode gap and the tilt angle of the drift tube head can effectively adjust the matching state of the electron phase and the local electric field, and thus the transverse momentum of the electron beam can be greatly reduced due to the negative effect of the radial electric field.

Modulational Instability of Radial Oscillations of Coronal Loops

The radial modes of the coronal loops are used to interpret the observed microwave and hard x-ray pulsations during flares. The properties of radial oscillations are well studied in the approximation of linear magnetohydrodynamics, and their further study requires a nonlinear approach. Obviously, the first step in this path is the weakly nonlinear approximation, which is used in this work. The study uses cylindrical geometry with the previously obtained nonlinear Schrodinger equation for the amplitude of radial oscillations. The conditions under which modulation instability of radial modes takes place, leading to the appearance of quasiperiodic oscillations, are studied.

Properties of hypermassive neutron stars formed in mergers of spinning binaries

We present numerical simulations of binary neutron star mergers, comparing irrotational binaries to binaries of NSs rotating aligned to the orbital angular momentum. For the first time, we study spinning BNSs employing nuclear physics equations of state, namely the ones of Lattimer and Swesty as well as Shen, Horowitz, and Teige. We study mainly equal mass systems leading to a hypermassive neutron star (HMNS), and analyze in detail its structure and dynamics. In order to exclude gauge artifacts, we introduce a novel coordinate system used for post-processing. The results for our equal mass models show that the strong radial oscillations of the HMNS modulate the instantaneous frequency of the gravitational wave (GW) signal to an extend that leads to separate peaks in the corresponding Fourier spectrum. In particular, the high frequency peaks which are often attributed to combination frequencies can also be caused by the modulation of the $m=2$ mode frequency in the merger phase. As a consequence for GW data analysis, the offset of the high frequency peak does not necessarily carry information about the radial oscillation frequency. Further, the low frequency peak in our simulations is dominated by the contribution of the plunge and the first 1--2 bounces. The amplitude of the radial oscillations depends on the initial NS spin, which therefore has a complicated influence on the spectrum. Another important result is that HMNSs can consist of a slowly rotating core with an extended, massive envelope rotating close to Keplerian velocity, contrary to the common notion that a rapidly rotating core is necessary to prevent a prompt collapse. Finally, our estimates on the amount of unbound matter show a dependency on the initial NS spin, explained by the influence of the latter on the amplitude of radial oscillations, which in turn cause shock waves.

The resonant mechanism of subdivision of a gas bubble in a fluid

Small nonlinear oscillations of a bubble in a fluid at the resonance of the frequencies of the radial mode and an arbitrary deformational mode 2 : 1 are considered. The deformational mode is determined by the associated Legendre polynomial with indices n = 2, 3, …, m = 0, 1, …, n. The energy transfer from the radial mode into the Legendre deformational mode is described by the method of invariant normalization. An analogy is established with oscillations of the material point on the string with the frequency ratio of the vertical mode to the horizontal one of 2. During the transfer, the amplitude of the Legendre mode with indices n, m exceeds the amplitude of radial oscillations by a factor of 3n at m = 0. As index m increases, the transfer time increases considerably and the maximal amplitude of the Legendre mode increases insignificantly in this case. From here, it is concluded that the deformational Legendre mode with indices n, m = n has the greatest probability to rise. The considered effect can serve as a mechanism of subdivision of gas bubbles under varying the external pressure in the fluid.

Vibration of a single microcapsule with a hard plastic shell in an acoustic standing wave field

Observation techniques for measuring the small vibration of a single microcapsule of tens of nanometers in an acoustic standing wave field are discussed. First, simultaneous optical observation of a microbubble vibration by two methods is investigated, using a high-speed video camera, which permits two-dimensional observation of the bubble vibration, and a laser Doppler vibrometer (LDV), which can observe small bubble vibration amplitudes at high frequency. Bubbles of tens of micrometers size were trapped at the antinode of an acoustic standing wave generated in an observational cell. Bubble vibration at 27 kHz could be observed and the experimental results for the two methods showed good agreement. The radial vibration of microcapsules with a hard plastic shell was observed using the LDV and the measurement of the capsule vibration with radial oscillation amplitude of tens of nanometers was successful. The acoustic radiation force acting on microcapsules in the acoustic standing wave was measured from the trapped position of the standing wave and the radial oscillation amplitude of the capsules was estimated from the theoretical equation of the acoustic radiation force, giving results in good agreement with the LDV measurements. The radial oscillation amplitude of a capsule was found to be proportional to the amplitude of the driving sound pressure. A larger expansion ratio was observed for capsules closer to the resonance condition under the same driving sound pressure and frequency.

Mass—luminosity relation and pulsational properties of Wolf—Rayet stars

The evolution of Population I stars with initial masses 70M ⊙ ≤ M ZAMS ≤ 130M ⊙ is considered. The computations were performed under various assumptions about the mass loss rate and were terminated at the phase of gravitational contraction after core helium exhaustion. The mass loss rate at the helium burning phase, Ṁ3α , is shown to be the main parameter that determines the coefficients of the mass—luminosity relation for Wolf—Rayet stars. Several more accurate mass—luminosity relations for mass loss rates Ṁ = f 3α Ṁ3α , where 0.5 ≤ f 3α ≤ 3, are suggested, along with the mass—luminosity relation that combines all of the evolutionary sequences considered. The results of the stellar evolution computations were used as initial conditions in solving the hydrodynamic equations describing the spherically symmetric motions of a self-gravitating gas. The outer layers of massive Population I stars are unstable against radial oscillations throughout the helium burning phase. The oscillation amplitude is largest at enhanced carbon and oxygen abundances in the outer stellar layers, i.e., at a lower initial stellar mass M ZAMS or a lower mass loss rate during the entire preceding evolution. In the course of evolution, the radial oscillation amplitude decreases and the small nonlinearity of the oscillations at M < 10M ⊙ allow the integral of mechanical work W done by an elementary spherical layer of gas in a closed thermodynamic cycle to be calculated with the necessary accuracy. The maximum of the radial dependence of W is shown to be located in layers with a gas temperature T ∼ 2 × 105 K, where the oscillations are excited by the iron Z-bump κ-mechanism. Comparison of the radial dependences of the integral of mechanical work W and the amplitude of the radiative flux variations suggests that the nonlinear radial oscillations of more massive Wolf—Rayet stars are also excited by the κ-mechanism.

Nonlinear behaviors of contrast agents relevant to diagnostic and therapeutic applications

The nonlinear properties of an encapsulated microbubble of a contrast agent were studied theoretically and experimentally. A modified nonlinear differential equation (Herring equation) was used to describe the radial oscillation of the microbubble and solved numerically. It was found that the nonlinear resonance frequency, at which the peak radial oscillation amplitude occurs, was a decreasing function of the acoustic amplitude of a driving ultrasonic pulse. Optical images of the contrast agent microbubbles under various ultrasonic exposure conditions: 1. sham exposure; 2. 2-MHz spatial peak acoustic pressure = 200 kPa, I SATA = 260 mW/cm 2, duty cycle = 7.5%, repetition period = 0.0266 ms; 3. 0.5-MHz spatial peak acoustic pressure = 200 kPa, I SATA = 130 mW/cm 2, duty cycle = 7.5%, repetition period = 0.1067 ms; have also shown that the lower-frequency ultrasound (US) excitation (0.5 MHz) is more effective in disruption of the microbubbles due to acoustic inertial cavitation than the higher frequency US (2 MHz). (E-mail: jwu@zoo.uvm.edu)

He I 1083 nm OSCILLATIONS AND DOWNFLOWS NEAR THE NORTH SOLAR POLE

Imaging spectroscopic data of the Sii 1082.7 nm (photospheric) and Hei 1083.0 nm (chromospheric) spectral lines were taken starting 22:05 UT on 23 July, 1996 with the NASA/NSO Spectromagnetograph at the NSO/Kitt Peak Vacuum Telescope. Observations were made near the north solar pole, with a field of view of 100 by 400 arc sec and with a temporal cadence of 53 s for 2 hr. Simple fitting to the line profiles measured the line position, depth, and spectral full-width at half-maximum. Power spectra of the velocity oscillations in each line were computed, and the oscillation power in the 2 to 6 mHz frequency band versus view angle was measured to search for horizontal oscillations. Horizontal waves are not detected to limiting amplitudes (1σ) of 22 m s-1 in the chromosphere and 9 m s-1 in the photosphere. These values are used to estimate limits for the energy flux into the corona. The amplitude of radial oscillations in the chromosphere is twice that of the photosphere. No statistically meaningful oscillation power is measured in the spectral parameters of the Hei line in the emission shell seen above the continuum limb. Finally, rapidly evolving red-shift events are observed in the Hei 1083 nm line on the disk; these events are some sort of coronal rain, and there are about 40 of these events on the solar disk at any moment.

Study of Beam Parameters of 240-CM Isochronous Cyclotron

For two years beam parameter investigations have been carried out at the Kiev cyclotron for the extraction process and the beam transport system. The data obtained show that high quality beam is obtained with 0.1% accelerating voltage stabilization and shape selection of the isochronous magnetic field which limits phase shift to ±5°. The system for radial beam phase selection provides control of bunch phase duration within 5°-25°. In this case the radial oscillation amplitude does not exceed 2-3 mm and extraction efficiency from the cyclotron is about 70%. The measured beam emittance at the accelerator output is 20 mm-mrad. for vertical motion and 28 mm-mrad. for horizontal motion. Energy spread in the extracted beam is less than the energy gain per turn and is about 0.3%. The complete beam transport system is in use and provides beam without losses to any of six experimental rooms.

The build-up of radial oscillations induced by first harmonic field errors in a cyclotron

A formula is derived for the amplitude of radial oscillations in a cyclotron induced by first harmonic errors in the magnetic field, allowing for the variation of free oscillation frequency and harmonic amplitude with radius. Although this is in general tedious to evaluate, the effect of various machine parameters can be seen, and order of magnitude calculations can be made.

Invited Paper-Extraction Studies in an AVF Cyclotron

For the extraction of the beam in an AVF cyclotron a regenerative system or an electrostatic channel can be used. Some factors of importance for the beam will be discussed. Extraction with an electrostatic channel can give very high external beam quality and extraction efficiency. For such a system it is of importance whether the beam is extracted before or after the νR= <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> resonance. The beam can even pass the νR=2νZ resonance without blowing up vertically if attention is being paid to the radial oscillation amplitude and some machine parameters. The general orbit theory can be used for an analytical study of a regenerative system in an A.V.F. cyclotron.

Design and operation of the U.C.L.A. 50 MeV spiral-ridge cyclotron

The design and operation of the U.C.L.A. 50 Mev cyclotron is described. The magnetic field is presented in a series of graphs and orbit calculations on beam stability are given. The results of experimental observations and measurements on the internal beam include beam intensity graphs and photographs, piots of / nu /sub z/ and nu /sub r/ from r.f. knockout measurements, beam intensity as a function of dee voltage, and radial oscillation amplitude of the beam. Because of iack of shielding, the beam has been restricted to 2 mu a of 50 Mev protons by use of a 5% duty cycle. An increased intensity is expected when a puller electrode is used at the source. The tuning up of the beam by means of the eight circular coils for trimming the magnetic field has been found to be quite simple in practice. Efforts to get an external beam are now proceeding in the permanent shielding vault. (auth)

The Energy Spectrum of the 350 MeV Neutron Beam from the Liverpool Synchrocyclotron

A knowledge of the energy spectrum of the neutron beam from the 156-inch cyclotron was required for cross section measurements. The spectrum of the recoil protons produced in n-p collisions was measured with a counter telescope containing a copper absorber of variable thickness. A calibration run was made in the external proton beam to measure the transmission of the absorber as a function of proton energy. It was found that the shape of the spectrum was consistent with the assumption that the neutrons are produced in `elastic' proton-neutron collisions in the beryllium target. The shape is then determined by the amplitude of radial oscillations in the cyclotron and the energy lost by the protons in their multiple traversals of the target.

The Regenerative Deflector for Synchro-cyclotrons

Tuck and Teng have proposed to extract the beam from a synchrocyclotron by modifying the normal magnetic field in such a way as to build up the amplitude of radial oscillations until protons can escape from the magnet In the present paper the method is studied analytically and formulae are derived which express the performance in terms of the magnetic field perturbations. these formulae have been evaluated numerically in sufficient detail to guide practical design.

On Deflection at n = 1 in the Synchrocyclotron

This paper discusses the theory of a possible method of synchrocyclotron beam deflection in which the orbits expand until the point of maximum Hr(n=1) is reached, after which the ions escape and spiral outward. These spirals should have a uniform starting radius and a small pitch in order to give deflection efficiency of the order of 100 percent; it is shown that this requires a flat maximum of Hr at n=1, and small amplitude of radial oscillation. The radial and vertical oscillations of the beam and the couplings thereof are discussed in detail. It appears that the only field inhomogeneities which must be carefully minimized are those at n=1 and n=0. Limits on radial and vertical oscillations in the immediate vicinity of the ion source are set but the origins thereof in phenomena other than field inhomogeneity are not discussed.

Theory of the Capture Process in a Betatron-Injected Synchrotron

The investigation of electrons of all possible initial phases and phase velocities at transition between betatron and synchrotron phases of an electron synchrotron has been undertaken with a view toward determining the effect of different ways of applying the r-f. It has been found that for an average accelerator there is an advantage in a moderately slow increase of the voltage from zero to its final value, while for the extreme case where particles enter the transition region with large phase velocity, an asymptotic final radial oscillation amplitude is reached which is independent of the manner in which the voltage is applied, provided only that it is applied adiabatically.