Halo current rotation scaling in post-disruption plasmas

Halo current (HC) rotation during disruptions can be potentially dangerous if resonant with the structures surrounding a tokamak plasma. We propose a drift-frequency-based scaling law for the rotation frequency of the asymmetric component of the HC as a function of toroidal field strength and plasma minor radius (frot ∝ 1/BT a2 ). This scaling law is consistent with results reported for many tokamaks and is motivated by the faster HC rotation observed in the HBT-EP tokamak. Projection of the rotation frequency to ITER and SPARC parameters suggest the asymmetric HC rotation will be on the order of 10 Hz and 60 Hz, respectively.

Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

Distribution of Earth's radiation belts' protons over the drift frequency of particles

Using data on the proton fluxes of the Earth's radiation belts (ERBs) with energy ranging from 0.2 to 100 MeV on the drift L shells ranging from 1 to 8, the quasi-stationary distributions over the drift frequency fd of protons around the Earth are constructed. For this purpose, direct measurements of proton fluxes of the ERBs during the period from 1961 to 2017 near the geomagnetic equator were employed. The main physical processes in the ERB manifested more clearly in these distributions, and for protons with fd>0.5 mHz at L>3, their distributions in the {fd,L} space have a more regular shape than in the {E,L} space. It has also been found that the quantity of the ERB protons with fd ∼ 1–10 mHz at L∼2 does not decrease, as it does for protons with E > 10–20 MeV (with fd>10 mHz), but increases with an increase in solar activity. This means that the balance of radial transport and loss of ERB low-energy protons at L∼2 is disrupted in favor of transport of these protons: the effect of an increase in the radial diffusion rates with increasing solar activity overpowers the effect of an increase in the density of the dissipative medium.

Seismic Response Mitigation of a Long-Span Tower Bridge with Two Types of Constraint System

The stress of the main tower of a cable-stayed bridge depends on the connection type between the tower and deck. In order to study the most suitable longitudinal damping mode for a long-span cable-stayed bridge. In this article, a nonlinear finite element model is established based on a large span concrete cable-stayed bridge with a main span of 680 m. Without considering the influence of the transverse constraint, the damping effect of the elastic connection device and the viscous damper is simulated when the longitudinal seismic load is input. The results show that the stiffness of the main beam is increased by installing the elastic connection device, so the longitudinal drift frequency of the main beam is increased, but the stiffness of the structure is not changed by installing the viscous damper. Both viscous dampers and elastic connection structures can reduce the longitudinal displacement of the beam end, but viscous dampers are more favorable for the stress of the main tower. In terms of damping effect, viscous dampers are more suitable for long-span cable-stayed bridges, but, in terms of economy and parameter control, elastic connection devices have more advantages.

Distribution of the Earth's radiation belts protons over the drift frequency of particles

On the base of generalized data on the proton fluxes of the Earth's radiation belts (ERB) with energy from E ~ 0.2 MeV to 100 MeV at drift shells L from ~ 1 to 8, constructed stationary distributions of the ERB protons over the drift frequency fd of protons around the Earth. For this, direct measurements of proton fluxes of the ERB in the period 1961–2017 near the plane of the geomagnetic equator were used. The main physical processes in the ERB manifested more clearly in these distributions, and for protons with fd > 0.5 mHz at L > 3 distributions of the ERB protons in the space {fd, L} have a more orderly form than in the space {E, L}. It has been found also that the quantity of the ERB protons with fd ~ 1–10 mHz at L ~ 2 does not decrease, as for protons with E > 10–20 MeV (with fd > 10 mHz), but increases with an increase in solar activity. This means that the balance of radial transport and losses of the ERB low-energy protons at L ~ 2 is disrupt in advantage of transport: for these protons, the effect of an increase in the radial diffusion rates with increasing in solar activity overpowers the effect of an increase in the density of the dissipative medium.

Roles of magnetospheric convection on nonlinear drift resonance between electrons and ULF waves

<p>In the Earth's inner magnetosphere, charged particles can be accelerated and transported by ultralow frequency (ULF) waves via drift resonance. We investigate the effects of magnetospheric convection on the nonlinear drift resonance process, which provides an inhomogeneity factor S to externally drive the pendulum equation that describes the particle motion in the ULF wave  field. The S factor, defined as the ratio of the driving amplitude to the square of the pendulum trapping frequency, is found to vary with magnetic local time and as a consequence, oscillates quasi-periodically at the particle drift frequency. To better understand the particle behavior governed by the driven pendulum equation, we carry out simulations to obtain the evolution of electron distribution functions in energy and L-shell phase space. We find that resonant electrons can remain trapped by the low-m ULF waves under strong convection electric  field, whereas for high-m ULF waves, the electrons trajectories can be significantly modified. More interestingly, the electron drift frequency is close to the nonlinear trapping frequency for intermediate-m ULF waves, which corresponds to chaotic motion of resonant electrons. These  findings shed new light on the nature of particle coherent and diffusive transport in the inner magnetosphere.</p>

Sea ice export through the Fram Strait derived from a combined model and satellite data set

Sea ice volume export through the Fram Strait plays an important role on the Arctic freshwater and energy redistribution. The combined model and satellite thickness (CMST) data set assimilates CryoSat-2 and Soil Moisture and Ocean Salinity (SMOS) thickness products together with satellite sea ice concentration. The CMST data set closes the gap of stand-alone satellite-derived sea ice thickness in summer and therefore allows us to estimate sea ice volume export during the melt season. In this study, we first validate the CMST data set using field observations, and then estimate the continuous seasonal and interannual variations of Arctic sea ice volume flux through the Fram Strait from September 2010 to December 2016. The results show that seasonal and interannual sea ice volume export vary from −244 (±43) to −973 (±59) km3 and −1974 (±291) to −2491 (±280) km3, respectively. The sea ice volume export reaches its maximum in spring and the mean amount of the melt season ice volume export accounts about one third of the yearly total amount. The minimum monthly sea ice export is −11 km3 in August 2015 and the maximum (−442 km3) appears in March 2011. Seasonal variations of sea ice thickness and drift frequency distributions infer that the thicker ice accompanied with slower ice motion is easier to appear when there is sea ice exporting through the Fram Strait outlet in summer.

Geomagnetic activity and local time dependence of the distribution of ultra low-frequency wave power in azimuthal wavenumbers, <i>m</i>

The azimuthal wavenumber m of ultra low-frequency (ULF) waves in the magnetosphere is a required parameter in the calculations of the diffusion rates of energetic electrons and protons in the magnetosphere, as electrons and protons of drift frequency ωd have been shown to radially diffuse due to resonant interaction with ULF waves of frequency ω = mωd. However, there are difficulties in estimating m, due to lack of multipoint measurements. In this paper we use magnetic field measurements at geosynchronous orbit to calculate the cross-spectrogram power and phase differences between time series from magnetometer pairs. Subsequently, assuming that ULF waves of a certain frequency and m would be observed with a certain phase difference between two azimuthally aligned magnetometers, the fraction of the total power in each phase difference range is calculated. As part of the analysis, both quiet-time and storm-time distributions of power per m number are calculated, and it is shown that during active times, a smaller fraction of total power is confined to lower m than during quiet times. It is also shown that in the dayside region, power is distributed mostly to the lowest azimuthal wavenumbers m = 1 and 2, whereas on the nightside it is more equally distributed to all m that can be resolved by the azimuthal separation between two spacecraft.

Deduction of the rates of radial diffusion of protons from the structure of the Earth's radiation belts

From the data on the fluxes and energy spectra of protons with an equatorial pitch angle of α0 ≈ 90° during quiet and slightly disturbed (Kp ≤ 2) periods, I directly calculated the value DLL, which is a measure of the rate of radial transport (diffusion) of trapped particles. This is done by successively solving the systems (chains) of integrodifferential equations which describe the balance of radial transport/acceleration and ionization losses of low-energy protons of the stationary belt. This was done for the first time. For these calculations, I used data of International Sun–Earth Explorer 1 (ISEE-1) for protons with an energy of 24 to 2081 keV at L = 2–10 and data of Explorer-45 for protons with an energy of 78.6 to 872 keV at L = 2–5. Ionization losses of protons (Coulomb losses and charge exchange) were calculated on the basis of modern models of the plasmasphere and the exosphere. It is shown that for protons with μ from ∼ 0.7 to ∼ 7 keV nT−1 at L ≈ 4.5–10, the functions of DLL can be approximated by the following equivalent expressions: DLL ≈ 4.9 × 10−14μ−4.1L8.2 or DLL ≈ 1.3 × 105(EL)−4.1 or DLL ≈ 1.2 × 10−9fd−4.1, where fd is the drift frequency of the protons (in mHz), DLL is measured in s−1, E is measured in kiloelectronvolt and μ is measured in kiloelectronvolt per nanotesla. These results are consistent with the radial diffusion of particles under the action of the electric field fluctuations (pulsations) in the range of Pc6 and contradict the mechanism of the radial diffusion of particles under the action of sudden impulses (SIs) of the magnetic field and also under the action of substorm impulses of the electric field. During magnetic storms DLL increases, and the expressions for DLL obtained here can change completely.