Breakdown of adiabatic invariance in spherical tokamaks

Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, above a threshold energy, the longitudinal invariant becomes non-adiabatic too, and confinement is lost as the motion becomes chaotic. We predict beam ions in present-day spherical tokamaks to be super-adiabatic but fusion alphas in proposed burning-plasma spherical tokamaks to be non-adiabatic.Comment: 6 pages, 8 figure

Variational calculations for resonance oscillations of inhomogeneous plasmas

The electrostatic resonance properties of an inhomogeneous plasma column are reported by application of the Rayleigh-Ritz method. A description of the rf equation of motion and pressure term that expresses the system of equations in Euler-Lagrange form is presented. The Rayleigh-Ritz procedure is applied to the corresponding Lagrangian to obtain approximate resonance frequencies and eigenfunctions. An appropriate set of trial coordinate functions is defined, which leads to frequency and eigenfunction estimates

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction

Attosecond Precision Multi-km Laser-Microwave Network

Synchronous laser-microwave networks delivering attosecond timing precision are highly desirable in many advanced applications, such as geodesy, very-long-baseline interferometry, high-precision navigation and multi-telescope arrays. In particular, rapidly expanding photon science facilities like X-ray free-electron lasers and intense laser beamlines require system-wide attosecond-level synchronization of dozens of optical and microwave signals up to kilometer distances. Once equipped with such precision, these facilities will initiate radically new science by shedding light on molecular and atomic processes happening on the attosecond timescale, such as intramolecular charge transfer, Auger processes and their impact on X-ray imaging. Here, we present for the first time a complete synchronous laser-microwave network with attosecond precision, which is achieved through new metrological devices and careful balancing of fiber nonlinearities and fundamental noise contributions. We demonstrate timing stabilization of a 4.7-km fiber network and remote optical-optical synchronization across a 3.5-km fiber link with an overall timing jitter of 580 and 680 attoseconds RMS, respectively, for over 40 hours. Ultimately we realize a complete laser-microwave network with 950-attosecond timing jitter for 18 hours. This work can enable next-generation attosecond photon-science facilities to revolutionize many research fields from structural biology to material science and chemistry to fundamental physics.Comment: 42 pages, 13 figure

On the Higher Order Edge-Connectivity of Complete Multipartite Graphs

Let G be a connected graph with p ≥ 2 vertices. For k = 1, 2, ..., P-1, the Kth order edge-connectivity of G, denoted by A(K} (e), is defined to be the smallest number of edges whose removal from e leaves a graph with k + 1 connected components. In this note we determine A(K} (e) for any complete multi partite graph G as a consequence, we give a necessary and sufficient condition for the graph Gn to be factored into spanning trees

Prospects and status of low-aspect-ratio tokamaks

The prospects for the low-aspect-ratio (A) tokamak to fulfill the requirements of viable fusion power plants are considered relative to the present status in data and modeling. Desirable physics and design features for an attractive Blanket Test Facility and power reactors are estimated for low-A tokamaks based on calculations improved with the latest data from small pioneering experiments. While these experiments have confirmed some of the recent predictions for low-A, they also identify the remaining issues that require verification before reliable projections can be made for these deuterium-tritium applications. The results show that the low-A regime of small size, modest field, and high current offers a path complementary to the standard and high A tokamaks in developing the full potential of fusion power

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Distorted HI Gas in the Widely Separated LIRG Arp 256

We present new interferometric HI and CO (1-0) observations of the luminous infrared source, Arp 256. Arp 256 consists of two spiral galaxies in an early stage of merging, with a projected nuclear separation of 29 kpc (54") and an infrared luminosity of 2.0E11 L_sun. Despite the large separation of the galaxies' nuclei and mildly disrupted stellar components, the HI disks are found to be strongly disrupted, and the southern galaxy in Arp 256 shows an elevated star formation efficiency, which is consistent with a nuclear starburst. Both of these results run contrary to expectations, posing interesting questions on the physical mechanisms involved in stimulating star formation during an interaction.Comment: 19 pages, 7 figures. Accepted for publication in AJ. Author added. Full resolution figures available at http://astro.uchicago.edu/home/web/jchen/arp25