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Frequency spirals

We study the dynamics of coupled phase oscillators on a two-dimensional Kuramoto lattice with periodic boundary conditions. For coupling strengths just below the transition to global phase-locking, we find localized spatiotemporal patterns that we call “frequency spirals.” These patterns cannot be seen under time averaging; they become visible only when we examine the spatial variation of the oscillators' instantaneous frequencies, where they manifest themselves as two-armed rotating spirals. In the more familiar phase representation, they appear as wobbly periodic patterns surrounding a phase vortex. Unlike the stationary phase vortices seen in magnetic spin systems, or the rotating spiral waves seen in reaction-diffusion systems, frequency spirals librate: the phases of the oscillators surrounding the central vortex move forward and then backward, executing a periodic motion with zero winding number. We construct the simplest frequency spiral and characterize its properties using analytical and numerical methods. Simulations show that frequency spirals in large lattices behave much like this simple prototype.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetoplasmonic RF mixing and nonlinear frequency generation

We present the design of a magnetoplasmonic Mach-Zehnder interferometer (MZI) modulator facilitating radio-frequency (RF) mixing and nonlinear frequency generation. This is achieved by forming the MZI arms from long-range dielectric-loaded plasmonic waveguides containing bismuth-substituted yttrium iron garnet (Bi:YIG). The magnetization of the Bi:YIG can be driven in the nonlinear regime by RF magnetic fields produced around adjacent transmission lines. Correspondingly, the nonlinear temporal dynamics of the transverse magnetization component are mapped onto the nonreciprocal phase shift in the MZI arms, and onto the output optical intensity signal. We show that this tunable mechanism can generate harmonics, frequency splitting, and frequency down-conversion with a single RF excitation, as well as RF mixing when driven by two RF signals. This magnetoplasmonic component can reduce the number of electrical sources required to generate distinct optical modulation frequencies and is anticipated to satisfy important applications in integrated optics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

High quality factor manganese-doped aluminum lumped-element kinetic inductance detectors sensitive to frequencies below 100 GHz

Aluminum lumped-element kinetic inductance detectors (LEKIDs) sensitive to millimeter-wave photons have been shown to exhibit high quality factors, making them highly sensitive and multiplexable. The superconducting gap of aluminum limits aluminum LEKIDs to photon frequencies above 100 GHz. Manganese-doped aluminum (Al-Mn) has a tunable critical temperature and could therefore be an attractive material for LEKIDs sensitive to frequencies below 100 GHz if the internal quality factor remains sufficiently high when manganese is added to the film. To investigate, we measured some of the key properties of Al-Mn LEKIDs. A prototype eight-element LEKID array was fabricated using a 40 nm thick film of Al-Mn deposited on a 500 μm thick high-resistivity, float-zone silicon substrate. The manganese content was 900 ppm, the measured T c = 694 ± 1mK, and the resonance frequencies were near 150 MHz. Using measurements of the forward scattering parameter S 21 at various bath temperatures between 65 and 250 mK, we determined that the Al-Mn LEKIDs we fabricated have internal quality factors greater than 2 × 10 5 , which is high enough for millimeter-wave astrophysical observations. In the dark conditions under which these devices were measured, the fractional frequency noise spectrum shows a shallow slope that depends on bath temperature and probe tone amplitude, which could be two-level system noise. In conclusion, the anticipated white photon noise should dominate this level of low-frequency noise when the detectors are illuminated with millimeter-waves in future measurements. The LEKIDs responded to light pulses from a 1550 nm light-emitting diode, and we used these light pulses to determine that the quasiparticle lifetime is 60 μs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Ionization instability induced striations in low frequency and pulsed He/H 2 O atmospheric pressure plasmas

In previous work [Kawamura et al., Plasma Sources Sci. Technol. 25, 054009 (2016)] and [Kawamura et al., J. Phys. D: Appl. Phys. 50, 145204 (2017)], 1D kinetic particle-in-cell (PIC) simulations of narrow gap (1 to 4 mm), high frequency (27 MHz) or dc-driven, He/2%H 2 O atmospheric pressure plasmas (APPs) showed an ionization instability resulting in standing striations (spatial oscillations) in the bulk plasma. We developed a steady-state striation theory which showed that the striations are due to non-local electron kinetics. In both the high frequency and dc-driven cases, the equilibrium electron density n 0 in the plasma bulk was stationary. In this work, we first conduct 1D PIC simulations of a 1 mm gap He/2%H 2 O APP, driven by a sinusoidal current at a low frequency of f = 50 kHz such that ω = 2 πf is well below the ionization frequency ν iz . In this case, n 0 varies with time, and we observe a time-varying instability which quasistatically depends on n 0 ( t ). At each phase of the rf cycle, the discharge resembles a dc discharge at the same n 0 . At higher frequencies (200 kHz–1 MHz), ω approaches ν iz , and quasistatic equilibrium at each phase breaks down. The discharge is also driven with a 200 kHz, 50% duty cycle square wave pulse with a short rise and fall time of 0.1 μs in an attempt to directly measure the striation growth rate s during the on-cycle before it saturated. However, the spike in current during the rise time leads to a spike in electron temperature T e and hence ν iz and s at the beginning of the rise which saturated during the beginning of the on-cycle. To predict the instability growth rate and saturation during and after the current spike, we extend our striation theory to include time-varying n 0 , T e , ν iz , as well as terms for the nonlinear saturation and noise floor of the striation amplitude. Furthermore, the time-varying global model predictions are compared to the PIC simulations, showing reasonable agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Frequency Dependence of Trapped Flux Sensitivity in SRF Cavities

In this letter, we present the frequency dependence of the vortex surface resistance of bulk niobium accelerating cavities as a function of different state-of-the-art surface treatments. Higher flux surface resistance per amount of trapped magnetic field—sensitivity—is observed for higher frequencies, in agreement with our theoretical model. Higher sensitivity is observed for N-doped cavities, which possess an intermediate value of the electron mean-free-path, compared to 120 °C and EP/BCP cavities. Experimental results from our study showed that the sensitivity has a non-monotonic trend as a function of the mean-free-path, including frequencies other than 1.3 GHz, and that the vortex response to the rf field can be tuned from the pinning regime to flux-flow regime by manipulating the frequency and/or the mean-free-path of the resonator, as reported in our previous studies. The frequency dependence of the trapped flux sensitivity to the amplitude of the accelerating gradient is also highlighted.

43 PARTICLE ACCELERATORS↗

Frequency-tunable high- Q superconducting resonators via wireless control of nonlinear kinetic inductance

Frequency-tunable microwave resonators are in great demand especially in hybrid systems where precise frequency alignment of resonances is required. Here, we present frequency-tunable high- Q superconducting resonators fabricated from thin niobium nitride and niobium titanium nitride films. The resonant frequency is tuned by applying a magnetic field perpendicular to the hole structures in the resonator's inductor wire, whose kinetic inductance is modified by wirelessly induced DC supercurrents. A continuous in situ frequency tuning of over 300 MHz is achieved for a 10 GHz resonator with a moderate magnetic field of 1.2 mT. The planar resonator design and the noncontact tuning scheme greatly ease the fabrication complexity and can be widely applied in many hybrid systems for coupling microwave modes with other forms of excitations such as optical photons, phonons, magnons, and spins.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Propagating molecular rotational coherences through single-frequency pulses in the strong field regime

In the weak-field limit in which microwave spectroscopy is typically carried out, an application of a single-frequency pulse that is resonant with a molecular transition will create a coherence between the pair of states involved in the rotational transition, producing a free-induction decay (FID) that, after Fourier transform, produces a molecular signal at that same resonance frequency. With the advent of chirped-pulse Fourier transform microwave methods, the high-powered amplifiers needed to produce broadband microwave spectra also open up other experiments that probe the molecular response in the high-field regime. This paper describes a series of experiments involving resonant frequency pulses interrogating jet-cooled molecules under conditions of sufficient power to Rabi oscillate the two-state system through many Rabi cycles. The Fourier-transformed FID shows coherent signal not only at the applied resonant frequency but also at a series of transitions initially connected to the original one by sharing an upper or lower level with it. As the duration of the single-frequency excitation is increased from 250 to 1500 ns, the number of observed off-resonant, but dipole-allowed, molecular coherences grow. The phenomenon is quite general, having been demonstrated in Z-phenylvinylnitrile, E-phenylvinylnitrile (E-PVN), benzonitrile, guaiacol, and 4-pentynenitrile. In E-PVN, the highest power/longest pulse duration, coherent signal is also present at energetically nearby but not directly connected transitions. Even in molecular samples containing more than one independent species, only transitions due to the single species responsible for the original resonant transition are present. Here, we develop a time-dependent model of the molecular/photon system and use it in conjunction with the experiment to test possible sources of the phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental observation of the geodesic acoustic frequency limit for the NBI-driven Alfvén eigenmodes in TJ-II

We study Alfvén Eigenmodes (AEs) in the TJ-II heliac in hydrogen plasmas heated by hydrogen cofield NBI. Taking advantage of the unique TJ-II flexibility in varying plasma current, we have observed strong variation of the AE frequency from f AE ~ 30 to ~ 220 kHz for selected modes. An advanced heavy ion beam probe diagnostic determines the spatial location and internal amplitudes of the modes. The modes satisfy a local AE dispersion relation including the geodesic acoustic frequency that represents the lowest frequency of the mode. Linear MHD-modeling with STELLGAP and FAR3D codes shows that the calculated temporal evolution of the mode frequency reproduces the observed maxima and minima at the same time intervals with a similar frequency range and the radial profile peaks near the outer edge of the observed one.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetic resonance force microscopy with matching frequencies of cantilever and spin

We have studied theoretically magnetic resonance force microscopy with a high-frequency nanomechanical cantilever when the cantilever frequency matches the resonant frequency of a single electron spin. Our analysis shows that in this situation, there is a small probability that the cantilever will oscillate with a large frequency shift. In conclusion, this can open new experimental opportunities for increasing the sensitivity in the detection of a single electron spin or even a single nuclear spin by using a high-frequency cantilever.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Kinetic simulation of a 50 mTorr capacitively coupled argon discharge over a range of frequencies and comparison to experiments

The effect of driving frequency in the range of 13.56–73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct “temperatures” for low-, mid-, and high-energy electrons at all the studied driving frequencies. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2–10 eV). Discrepancies due to limitations in experimental energy resolution outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, and the predicted effective electron temperature is within 25% of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model, and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which on temporal averaging would be zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Voltage waveform tailoring for high aspect ratio plasma etching of SiO 2 using Ar/CF 4 /O 2 mixtures: Consequences of low fundamental frequency biases

The use of non-sinusoidal waveforms in low pressure capacitively coupled plasmas intended for microelectronics fabrication has the goal of customizing ion and electron energy and angular distributions to the wafer. One such non-sinusoidal waveform uses the sum of consecutive harmonics of a fundamental sinusoidal frequency, f 0 , having a variable phase offset between the fundamental and even harmonics. In this paper, we discuss results from a computational investigation of the relation between ion energy and DC self-bias when varying the fundamental frequency f 0 for capacitively coupled plasmas sustained in Ar/CF 4 /O 2 and how those trends translate to a high aspect ratio etching of trenches in SiO 2 . The fundamental frequency, f 0 , was varied from 1 to 10 MHz and the relative phase from 0° to 180°. Two distinct regimes were identified. Average ion energy onto the wafer is strongly correlated with the DC self-bias at high f 0 , with there being a maximum at φ = 0° and minimum at φ = 180°. In the low frequency regime, this correlation is weak. Average ion energy onto the wafer is instead dominated by dynamic transients in the applied voltage waveforms, with a maximum at φ = 180° and minimum at φ = 0°. The trends in ion energy translate to etch properties. In both, the high and low frequency regimes, higher ion energies translate to higher etch rates and generally preferable final features, though behaving differently with phase angle.

36 MATERIALS SCIENCE↗

Development of a prototype compact fibre frequency synthesiser for mobile femtosecond optical clocks

A prototype compact fibre frequency synthesiser based on a femtosecond erbium fibre laser and an original hybrid highly nonlinear fibre is developed and preliminarily studied. This synthesiser will ensure an extremely low relative instability of synthesised frequencies (down to 10{sup -17}) with the use of a corresponding optical standard and will be used in mobile optical clocks. The realised frequency stabilisation principle makes the synthesiser universal and allows it to transfer the frequency stability of various types of optical standards to the synthesised radio- and optical frequencies. (extreme light fields and their applications)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the duration of continuous operation of an optical frequency standard based on strontium atoms

This paper examines methods for increasing the duration of autonomous continuous operation of optical frequency standards. We have realised the secondary cooling of strontium atoms without using phase stabilisation during the formation of cooling and intermixing light beams and proposed a clock laser frequency stabilisation algorithm that compensates for the acoustic noise-induced laser frequency instability. Experiments have been performed using two distinct algorithms for laser frequency stabilisation to the frequency of an atomic transition. The maximum duration of continuous autonomous operation of the system was 25 000 to 50 000 s with one stabilisation algorithm and 70 000 to 200 000 s with the other algorithm. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transcriptional burst frequency and burst size are equally modulated across the human genome

Gene expression occurs either as an episodic process, characterized by pulsatile bursts or as a constitutive, Poisson-like accumulation of gene products. It is not clear which mode of gene expression (constitutive versus bursty) predominates across a genome or how transcriptional dynamics are influenced by genomic position and promoter sequence. Here, we use time-lapse fluorescence microscopy, building off of theoretical studies that exploit the time-resolved structure of stochastic fluctuations in gene expression, to develop a three-dimensional method for mapping underlying gene-regulatory mechanisms. Over 8,000 individual human genomic loci were analyzed, and at virtually all loci, episodic bursting as opposed to constitutive expression was found to be the predominant mode of expression. Quantitative analysis of the expression dynamics at these 8,000 loci indicates that both frequency and size of transcriptional bursts vary equally across the human genome independent of promoter sequence. Strikingly, weaker expression loci modulate burst frequency to increase activity, while stronger expression loci modulate burst size to increase activity. Transcriptional activators, such as TNF, generate similar patterns of change in burst frequency and burst size. In summary, transcriptional bursting dominates across the human genome, both burst frequency and burst size vary by chromosomal location, and transcriptional activators alter burst frequency and burst size, depending on the expression level of the locus.

noise biology↗

THE DOUBLE PULSAR ECLIPSES. I. PHENOMENOLOGY AND MULTI-FREQUENCY ANALYSIS

The double pulsar PSR J0737-3039A/B displays short, 30 s eclipses that arise around conjunction when the radio waves emitted by pulsar A are absorbed as they propagate through the magnetosphere of its companion pulsar B. These eclipses offer a unique opportunity to directly probe the magnetospheric structure and the plasma properties of pulsar B. We have performed a comprehensive analysis of the eclipse phenomenology using multi-frequency radio observations obtained with the Green Bank Telescope. We have characterized the periodic flux modulations previously discovered at 820 MHz by McLaughlin et al. and investigated the radio frequency dependence of the duration and depth of the eclipses. Based on their weak radio frequency evolution, we conclude that the plasma in pulsar B's magnetosphere requires a large multiplicity factor ({approx}10{sup 5}). We also found that, as expected, flux modulations are present at all radio frequencies in which eclipses can be detected. Their complex behavior is consistent with the confinement of the absorbing plasma in the dipolar magnetic field of pulsar B as suggested by Lyutikov and Thompson and such a geometric connection explains that the observed periodicity is harmonically related to pulsar B's spin frequency. We observe that the eclipses require a sharp transition region beyond which the plasma density drops off abruptly. Such a region defines a plasmasphere that would be well inside the magnetospheric boundary of an undisturbed pulsar. It is also two times smaller than the expected standoff radius calculated using the balance of the wind pressure from pulsar A and the nominally estimated magnetic pressure of pulsar B.

79 ASTRONOMY AND ASTROPHYSICS↗

GLOBAL AND LOCAL CUTOFF FREQUENCIES FOR TRANSVERSE WAVES PROPAGATING ALONG SOLAR MAGNETIC FLUX TUBES

It is a well-established result that the propagation of linear transverse waves along a thin but isothermal magnetic flux tube is affected by the existence of the global cutoff frequency, which separates the propagating and non-propagating waves. In this paper, the wave propagation along a thin and non-isothermal flux tube is considered and a local cutoff frequency is derived. The effects of different temperature profiles on this local cutoff frequency are studied by considering different power-law temperature distributions, as well as the semi-empirical VAL C model of the solar atmosphere. The obtained results show that the conditions for wave propagation strongly depend on the temperature gradients. Moreover, the local cutoff frequency calculated for the VAL C model gives constraints on the range of wave frequencies that are propagating in different parts of the solar atmosphere. These theoretically predicted constraints are compared to observational data and are used to discuss the role played by transverse tube waves in the atmospheric heating and dynamics, and in the excitation of solar atmospheric oscillations.

79 ASTRONOMY AND ASTROPHYSICS↗

The density and mass of unshocked ejecta in Cassiopeia a through low frequency radio absorption

Characterizing the ejecta in young supernova remnants is a requisite step toward a better understanding of stellar evolution. In Cassiopeia A the density and total mass remaining in the unshocked ejecta are important parameters for modeling its explosion and subsequent evolution. Low frequency (<100 MHz) radio observations of sufficient angular resolution offer a unique probe of unshocked ejecta revealed via free-free absorption against the synchrotron emitting shell. We have used the Very Large Array plus Pie Town Link extension to probe this cool, ionized absorber at 9'' and 18.''5 resolution at 74 MHz. Together with higher frequency data we estimate an electron density of 4.2 cm{sup –3} and a total mass of 0.39 M {sub ☉} with uncertainties of a factor of ∼2. This is a significant improvement over the 100 cm{sup –3} upper limit offered by infrared [S III] line ratios from the Spitzer Space Telescope. Our estimates are sensitive to a number of factors including temperature and geometry. However using reasonable values for each, our unshocked mass estimate agrees with predictions from dynamical models. We also consider the presence, or absence, of cold iron- and carbon-rich ejecta and how these affect our calculations. Finally we reconcile the intrinsic absorption from unshocked ejecta with the turnover in Cas A's integrated spectrum documented decades ago at much lower frequencies. These and other recent observations below 100 MHz confirm that spatially resolved thermal absorption, when extended to lower frequencies and higher resolution, will offer a powerful new tool for low frequency astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

Application of simulations and theory of sub-cyclotron frequency modes to DIII-D

Theoretical and numerical study of Alfvén eigenmodes (AEs) in the sub-cyclotron frequency range explains the observed frequency scaling with beam parameters in experiments across different devices. Global Alfvén (GAEs) and compressional Alfvén eigenmodes (CAEs) are frequently excited during neutral beam injection (NBI) in the National Spherical Torus Experiment (NSTX/NSTX-U), as well as other beam-heated devices such as MAST and DIII-D. These modes are driven unstable through the Doppler shifted cyclotron resonance with the NBI ions and can be excited in ITER due to super-Alfvénic velocities and anisotropy of the fast ion distribution. Numerical models and theory for sub-cyclotron frequency modes, previously developed and used to study the excitation of GAEs/CAEs in the NSTX(-U), have been successfully applied to explain the DIII-D observations. Simulations for DIII-D demonstrate that the modes with ω/ω ci ≈ 0.6, previously mis-identified as compressional Alfvén eigenmodes, have shear polarization and should be identified as the GAEs. Simulation results match the observed frequencies and estimated toroidal mode numbers in DIII-D experiments. Good agreement is found between scaling of the experimentally observed GAE frequencies with NBI parameters for NSTX, NSTX-U and DIII-D and scaling predicted by the theory and simulations. Here, the DIII-D simulation results also demonstrate that GAEs can be excited for larger aspect-ratio devices and smaller (sub- Alfvénic) beam injection velocities, therefore they can be unstable in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗