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DOE OSTI2014

SU-E-T-178: Experimental Study of Acceptable Movement Conditions for SBRT Lung Treatments

Purpose: To experimentally study the acceptable movement conditions for SBRT lung treatments we quantified with film dosimetry the change in dose distributions due to periodic movements of 5 different amplitudes and 4 respiratory gating duty cycles on a SBRT treatment plan. Methods: We planned a SBRT treatment plan for the QUASAR™ (Modus Medical) phantom equipped with the respiratory motion device. We placed a 3 mm water-equivalent sphere simulating a tumour inside the lung-equivalent insert. This sphere is divided in two hemispheres that allow placing films in between. We used radiochromic EBT2™ (Ashland) films. We oriented the lung insert in such a way that sagittal dose distributions could be measured. We applied a sinusoidal movement with 3 s period for 5 different amplitudes of 0(static), 5, 7, 10, 15 and 20 mm without gating. For the 20 mm amplitude we studied the gating technique with 4 duty cycles of 20, 40, 60 and 80% of the respiratory cycle. Each situation was irradiated in a Clinac 2100 linac (Varian) equipped with the RPM™ system. FilmQA Pro™ (Ashland) software together with an Expression 10000XL scanner (EPSON) were used to analyze and compare the measured dose distributions with those planned by the Eclipse™ TPS v. 8.9 (Varian) by means of gamma analysis with 6 criteria: 5%/3mm, 5%/2mm, 5%/1mm, 3%/3mm, 3%/2mm and 2%/2mm (threshold of 10%). Results: Movements with amplitude of less than 7mm do not significantly modified the dosimetry. Gating duty cycles of less than 40% yielded also acceptable results for a 2 cm amplitude movement. Conclusion: To safely perform daily accurate SBRT treatments, movements have to be restricted to 7 mm amplitude (±3.5 mm). Otherwise, a gating strategy should be considered.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

The scattering of spinning hadrons from lattice QCD

Hadron spectroscopy is predominantly the study of resonances that decay via the strong interaction into a multitude of stable hadrons, such as the pion. The vast majority of resonances decay via an intermediate hadron with non-zero intrinsic spin. In this thesis, I will present the results of scattering calculations featuring mesons with non-zero intrinsic spin. Before doing so, I will first give a brief introduction to QCD and review the framework necessary to perform lattice QCD calculations in Chapters 1 and 2. In Chapter 3, I present the first lattice calculation of ?? scattering in isospin-2. Here, ?? features in dynamically-coupled 3S1 and 3D1 partial-waves with JP=1+. No resonance enhancement is anticipated in the flavour exotic isospin-2 channel and as such it provides an ideal testing ground for this first calculation. I work at heavier than physical quark masses at the SU(3)F point where the up, down and strange quarks are mass degenerate. Finite-volume spectra are calculated and, utilising the relationship between the discrete energy spectrum and the infinite-volume scattering amplitudes, partial-wave amplitudes with J?3 and the degree of dynamical mixing between the coupled 3S1 and 3D1 channels are determined. In Chapter 4, I investigate ?? in isospin-1 where the a1 axial-vector resonance is expected to feature. Here, I present a discussion on G-parity and Bose-symmetry at the SU(3)F point. Working at heavier than physical quark masses, the resulting finite volume spectrum suggests that the a1 is a bound-state and that the 3S1- and 3D1-wave, ?? scattering amplitudes are similar to those in isospin-2. I present the first calculation of coupled ?? and ?? scattering in Chapter 5 where resonant enhancement is seen experimentally in the JP=1+ channel. Working at a somewhat lighter pion mass than in previous chapters, the finite-volume spectra are determined and the scattering amplitudes are calculated. Analytically continuing the amplitudes into the complex energy plane, a resonance pole is found, interpreted as the analogue of the b1 axial-vector, which couples dominantly to 3S1-wave ??, with a much-suppressed coupling to 3D1-wave ??, and a negligible coupling to ??. In Chapter 6, the exotic JPC=1?+ channel is studied. These quantum numbers are not allowed in the quark model but can be obtained, for example, through a gluonic excitation coupled to a quark-antiquark pair. In this exploratory calculation, performed at the SU(3)F point, the finite-volume spectra and coupled-channel scattering amplitudes are presented. A single resonance pole is found, interpreted as the exotic ?1, and couplings to meson-meson channels, including for example ??{1P1}, ???{1P1} and ??{3P1}, are calculated for the first time in lattice QCD. In order to minimally present the contents of a unitary n-channel scattering matrix, I introduce, in Chapter 7, an n-channel generalisation of the traditional two-channel Stapp parameterisation.

Woss, Antoni↗

DOE OSTI2016

η'-π production and search for exotic mesons at COMPASS and JLab12

In the exclusive production of $\eta\pi$ and $\eta'-\pi$ pairs with a 191 GeV/c pion beam at COMPASS resonance-like enhancement in the P-wave was observed. Such a resonance would carry exotic quantum numbers therefore, cannot be associated with the conventional quark-antiquark states. To examine the observed behavior we examine the properties of reaction amplitude using analyticity, unitarity and high-energy constraints. Following Regge prediction, for sufficiently large incident energy the five-particle amplitude for the reaction $p\pi->p\pi\eta$ is proportional to the reggeon-particle scattering amplitude $R\pi->\eta\pi$. In the resonance region, the reggeon-particle amplitudes are parametrized within N/D formalism supplemented by elastic unitarity constraints. At higher values of $\eta\pi$ invariant masse, the amplitude is reggeized similarly to normal four-particle amplitudes. Matching between the two parametrizations in the transition region is implemented via finite energy sum rules. To constrain the parameters of reggeon and decay vertices we employ the Regge factorization as well as SU(3) constraints and use data from other high-energy experiments. Finally, we consider the extension of the developed formalism for the photoproduction of $\eta\pi$ meson systems at GlueX.

Pauk, Vladiszlav↗

DOE OSTI2020

Lift Equivalence and Cancellation for Airfoil Surge–Pitch–Plunge Oscillations

A NACA 0018 airfoil in freestream velocity is oscillated in longitudinal, transverse, and angle-of-attack directions with respect to the freestream velocity, known as surge, plunge, and pitch. The lift-based equivalence method introduces phase shifts between these three motions to construct in-phase sinusoidal components for maximum lift, waveform construction. Lift cancellation is also determined with the exact negative pitch and plunge motion amplitudes found from the equivalence method to achieve out-of-phase wave destruction. Lift cancellation occurs when a combination of these motions is sought to obtain a constant lift magnitude throughout the oscillation cycle. To achieve both equivalence and cancellation of lift, a prescribed pure pitch amplitude through the Theodorsen theory equates the corresponding equivalent plunge amplitude and pitch–plunge phase shift. These Theodorsen, linear superposition findings of pitch–plunge are leveraged toward the Greenberg theory to determine a closed-form, surge–pitch–plunge solution through the addition of a surge–plunge phase shift and optimal surge amplitude for lift cancellation. The lift cancellation surge–pitch–plunge amplitudes define the equivalence amplitude investigated here and theoretically limit the experiment to combinations of the first lift harmonic of the Greenberg theory. The analytical results are then compared with experimental lift force measurements and dye visualization. Finally, the normalized lift differences due to unsteady wake and boundary-layer behavior are examined to explore the extents of the Greenberg theory for these cases of lift-based equivalence and cancellation.

42 ENGINEERING↗

DOE OSTI2018

Transducer Installation Effects on Pressure Measurements in PGC Devices

Pressure gain devices such as rotating detonation engines present an extremely harsh environment, generally precluding the use of any intrusive probe measurement. The most widely used diagnostic is the measurement of high frequency pressure which can be used to determine the pressure amplitude, number of waves and their direction and the wave structure. The preferred approach for making pressure measurements is to install the sensing element flush with the combustion chamber wall, but is almost always inhibited by the extremely high heat fluxes that can damage the sensor. Alternately, recessed cavity or infinite probe installation is seldom used for high frequency pressure measurements. While amplitude attenuation and phase distortion of the pressure signal can be introduced by these installation types, its characterization in the presence of high amplitude steep fronted pressure waves encountered in PGC devices has not been previously performed. In the current work a highly modular calibration test-bed is designed to enable characterization of pressure transducers based on their installation in the presence of steep fronted high amplitude pressure waves. Two transducer types, piezoelectric PCB® 113B26 and water-cooled piezoresistive Kulite®WCT-312M were used and installed in the flush, recessed cavity and infinite tube probe configuration. The recessed cavity probe showed 5-26% amplitude attenuation and almost negligible time lag compared to the flush transducer, the infinite tube pressure (ITP) transducer showed a significantly higher delay and as much as 50% reduction in measured pressure amplitude. Secondary wave features from reflections within the test article, that were captured by the flush and recessed cavity transducer were damped by the infinite probe measurement.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2016

Simulations of the pairwise kinematic Sunyaev-Zel'dovich signal

The pairwise kinematic Sunyaev–Zel’dovich (kSZ) signal from galaxy clusters is a probe of their line of sight momenta, and thus a potentially valuable source of cosmological information. In addition to the momenta, the amplitude of the measured signal depends on the properties of the intracluster gas and observational limitations such as errors in determining cluster centers and redshifts. In this work, we simulate the pairwise kSZ signal of clusters at z<1, using the output from a cosmological N-body simulation and including the properties of the intracluster gas via a model that can be varied in post-processing. We find that modifications to the gas profile due to star formation and feedback reduce the pairwise kSZ amplitude of clusters by ∼50%, relative to the naive “gas traces mass” assumption. We demonstrate that miscentering can reduce the overall amplitude of the pairwise kSZ signal by up to 10%, while redshift errors can lead to an almost complete suppression of the signal at small separations. We confirm that a high-significance detection is expected from the combination of data from current generation, high-resolution cosmic microwave background experiments, such as the South Pole Telescope, and cluster samples from optical photometric surveys, such as the Dark Energy Survey. Furthermore, we forecast that future experiments such as Advanced ACTPol in conjunction with data from the Dark Energy Spectroscopic Instrument will yield detection significances of at least 20σ, and up to 57σ in an optimistic scenario. Our simulated maps are publicly available at http://www.hep.anl.gov/cosmology/ksz.html.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Spitzer Variability Properties of Low-gravity L Dwarfs

We present Spitzer Space Telescope variability monitoring observations of three low-gravity L dwarfs with previous detections of variability in the near-IR: 2MASS J0045+16, 2MASS J0501–00, and 2MASS J1425–36. We detect significant periodic variability in two of our targets, 2MASS J0045+16 and 2MASS J0501–00. We do not detect variability in 2MASS J1425–36. Combining our new rotation periods with rotational velocities, we calculate inclination angles of 22° ± 1°, 60{sub -8}{sup +13°}, and 52{sub -13}{sup +19°} for 2MASS J0045+16, 2MASS J0501–00, and 2MASS J1425–36, respectively. Our three new objects are consistent with the tentative relations between inclination, amplitude, and color anomaly previously reported. Objects with the highest variability amplitudes are inclined equator on, while the maximum observed amplitude decreases as the inclination angle decreases. We also find a correlation between the inclination angle and (J–K){sub 2MASS} color anomaly for the sample of objects with measured inclinations. Compiling the entire sample of brown dwarfs with Spitzer variability detections, we find no enhancement in amplitude for young, early-L dwarfs compared to the field dwarf population. We find a possible enhancement in amplitude of low-gravity late-L dwarfs at 4.5 μm. We do not find a correlation between amplitude ratio and spectral type for field dwarfs or for the young population. Finally, we compile the rotation periods of a large sample of brown dwarfs with ages 1 Myr–1 Gyr and compare the rotation rates predicted by evolutionary models assuming angular momentum conservation. We find that the rotation rates of the current sample of brown dwarfs fall within the expected range set by evolutionary models and breakup limits.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Fluctuation statistics in the scrape-off layer of Alcator C-Mod

We study long time series of the ion saturation current and oating potential, sampled by Langmuir probes dwelled in the outboard mid-plane scrape-off layer and embedded in the lower divertor baffle of Alcator C-Mod. A series of ohmically heated L-mode plasma discharges is investigated with line-averaged plasma density ranging from ne/nG = 0.15 to 0.42, where nG is the Greenwald density. All ion saturation current time series that are sampled in the far scrape-off layer are characterized by large-amplitude burst events. Coefficients of skewness and excess kurtosis of the time series obey a quadratic relationship and their histograms coincide partially upon proper normalization. Histograms of the ion saturation current time series are found to agree well with a prediction of a stochastic model for the particle density fluctuations in scrape-off layer plasmas. The distribution of the waiting times between successive large-amplitude burst events and of the burst amplitudes are approximately described by exponential distributions. The average waiting time and burst amplitude are found to vary weakly with the line-averaged plasma density. Conditional averaging reveals that the radial blob velocity, estimated from floating potential measurements, increases with the normalized burst amplitude in the outboard mid- plane scrape-off layer. For low density discharges, the conditionally averaged waveform of the floating potential associated with large amplitude bursts at the divertor probes has a dipolar shape. In detached divertor conditions the average waveform is random, indicating electrical disconnection of blobs from the sheaths at the divertor targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

Further studies of stall flutter and nonlinear divergence of two-dimensional wings

An experimental investigation is made of the purely torsional stall flutter of a two-dimensional wing pivoted about the midchord, and also of the bending-torsion stall flutter of a two-dimensional wing pivoted about the quarterchord. For the purely torsional flutter case, large amplitude limit cycles ranging from + or - 11 to + or - 160 degrees were observed. Nondimensional harmonic coefficients were extracted from the free transient vibration tests for amplitudes up to 80 degrees. Reasonable nondimensional correlation was obtained for several wing configurations. For the bending-torsion flutter case, large amplitude coupled limit cycles were observed with torsional amplitudes as large as + or - 40 degrees. The torsion amplitudes first increased, then decreased with increasing velocity. Additionally, a small amplitude, predominantly torsional flutter was observed when the static equilibrium angle was near the stall angle.

Dugundji, J.↗

NASA NTRS1987

The impact damped harmonic oscillator in free decay

The impact-damped oscillator in free decay is studied by using time history solutions. A large range of oscillator amplitude is covered. The amount of damping is correlated with the behavior of the impacting mass. There are three behavior regimes: (1) a low amplitude range with less than one impact per cycle and very low damping, (2) a useful middle amplitude range with a finite number of impacts per cycle, and (3) a high amplitude range with an infinite number of impacts per cycle and progressively decreasing damping. For light damping the impact damping in the middle range is: (1) proportional to impactor mass, (2) additive to proportional damping, (3) a unique function of vibration amplitude, (4) proportional to 1-epsilon, where epsilon is the coefficient of restitution, and (5) very roughly inversely proportional to amplitude. The system exhibits jump phenomena and period doublings. An impactor with 2 percent of the oscillator's mass can produce a loss factor near 0.1.

Brown, G. V.↗

NASA NTRS1986

Electric and magnetic observations of the structure of standing waves in the magnetosphere

Electric and magnetic field instruments on the DE 1 spacecraft provided observations of toroidal standing wave oscillations of magnetic shells in 1981 and 1982. The amplitude and nodal structure of these waves, as a function of increasing magnetic latitude, was studied and compared with model calculations of these waves. Eight pulsation events were selected for study. The pulsations in these events ranged in period from 20 to 300 s. They were observed at L values between 2.8 and 9.7 and at magnetic latitudes from the equator to 48 deg. The duration of these pulsation events was 20 to 30 min, and they usually consisted of a 5- to 10-min growth in amplitude, a 5- to 10-min interval of fluctuating amplitude, and a 5- to 20-min interval of decreasing amplitude. The relative E and B amplitudes and the phase relations between the E and B waves could be qualitatively explained by the nodal structure of the waves predicted by model calculations. Detailed quantitative comparisons of E and B amplitudes were in agreement with more recent model calculations. In a few cases, electron densities were also available as derived from plasma frequency observations; in these cases the standing wave periods calculated were reasonably close to, but somewhat less than, the observed periods.

Cahill, L. J., Jr.↗

NASA NTRS1987

The impact damped harmonic oscillator in free decay

Brown, G. V.↗

NASA NTRS1987

Sensitivity of LFC techniques in the non-linear regime

For all the Laminar Flow Control (LFC) techniques examined, finite-amplitude effects are destabilizing, i.e., finite-amplitude 2-D Tollmien-Schlichting (TS) waves grow faster than predicted by linear theory. It was also found, in direct contrast to the results from linear theory for low-amplitude waves, that temperature fluctuations exert a further destabilizing influence on finite amplitude 2-D TS waves. The controlled boundary layers are, of course, subject to intense 3-D secondary instabilities. The instantaneous growth rates of both the fundamental and subharmonic instabilities are strongly tied to the amplitude of the primary 2-D wave. The principal finite-amplitude effects upon the 3-D secondary instabilities occur through the faster growth of the 2-D waves.

Bushnell, Dennis M.↗

NASA NTRS1992

Modified fast frequency acquisition via adaptive least squares algorithm

A method and the associated apparatus for estimating the amplitude, frequency, and phase of a signal of interest are presented. The method comprises the following steps: (1) inputting the signal of interest; (2) generating a reference signal with adjustable amplitude, frequency and phase at an output thereof; (3) mixing the signal of interest with the reference signal and a signal 90 deg out of phase with the reference signal to provide a pair of quadrature sample signals comprising respectively a difference between the signal of interest and the reference signal and a difference between the signal of interest and the signal 90 deg out of phase with the reference signal; (4) using the pair of quadrature sample signals to compute estimates of the amplitude, frequency, and phase of an error signal comprising the difference between the signal of interest and the reference signal employing a least squares estimation; (5) adjusting the amplitude, frequency, and phase of the reference signal from the numerically controlled oscillator in a manner which drives the error signal towards zero; and (6) outputting the estimates of the amplitude, frequency, and phase of the error signal in combination with the reference signal to produce a best estimate of the amplitude, frequency, and phase of the signal of interest. The preferred method includes the step of providing the error signal as a real time confidence measure as to the accuracy of the estimates wherein the closer the error signal is to zero, the higher the probability that the estimates are accurate. A matrix in the estimation algorithm provides an estimate of the variance of the estimation error.

Kumar, Rajendra↗

NASA NTRS1993

Observational evidence of preferred flow regimes in the Northern Hemisphere winter stratosphere

Ten years of stratospheric geopotential height data are analyzed in an attempt to determine whether there are preferred flow regimes in the Northern Hemisphere winter stratosphere. The data are taken from Stratospheric Sounding Units on board NOAA satellites. The probability density estimate of the amplitude of the wavenumber 1 10-mb height is found to be bimodal. The density distribution is composed of a dominant large-amplitude mode and a less frequent low-amplitude mode. When the wavenumber 1 10-mb height data are projected onto the phase plane defined by the 10-mb zonal-mean winds and wavenumber 1 100-mb heights, three preferred regimes are evident. The small-amplitude mode separates into a strong zonal wind-weak wave regime and a weak zonal wind-weak wave regime. The large-amplitude mode is an intermediate zonal wind-strong wave regime. Transitions between the large-amplitude regime and the weak zonal wind-weak wave regime are found to be associated with major stratospheric warmings. The clustering of the stratospheric data into the preferred flow regimes is interpreted in light of the bifurcation properties of the Holton and Mass model. The interannual variability of the Northern Hemisphere winter stratosphere is interpreted in terms of the relative frequency of the observed preferred regimes.

Pierce, R. B.↗

NASA NTRS1994

Cosmic temperature fluctuations from two years of COBE differential microwave radiometers observations

The first two years of Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) observations of the cosmic microwave background (CMB) anisotropy are analyzed and compared with our previously published first year results. The results are consistent, but the addition of the second year of data increases the precision and accuracy detected CMB temperature fluctuations. The 2 yr 53 GHz data are characterized by rms temperature fluctuations of (delta-T)(sub rms) (7 deg) = 44 +/- 7 micro-K and (delta-T)(sub rms) (10 deg) = 30.5 +/- 2.7 micro-K at 7 deg and 10 deg angular resolution, respectively. The 53 x 90 GHz cross-correlation amplitude at zero lag is C(0)(sup 1/2) = 36 +/- 5 micro-K (68% CL) for the unsmoothed (7 deg resolution) DMR data. We perform a likelihood analysis of the cross-correlation function, with Monte Carlo simulations to infer biases of the method, for a power-law model of initial density fluctuations, P(k) proportional to R(exp n). The Monte Carlo simulations indicate that derived estimates of n are biased by +0.11 +/- 0.01, while the subset of simulations with a low quadrupole (as observed) indicate a bias of +0.31+/- 0.04. Derived values for 68% confidence intervals are given corrected (and not corrected) for our estimated biases. Including the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 14.3(sup + 5.2 sub -3.3) micro-K (12.8(sup + 5.2 sub -3.3) micro-K0 with a spectral index n = 1.42(sup + 0.49 sub -0.55)(n = 1.53(sup + 0.49 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.2 +/- 11.5 micro-K (17.4 +/- 1.5 micro-K). The marginal likelihood of n is 1.42 +/- 0.37 (1.53 +/- 0.37). Excluding the quadrupole anisotropy, the most likely quadrupole-normalized amplitude is Q(sub rms-PS) = 17.4(sup + 7.5 sub -5.2) micro-K (15.8(sup + 7.5 sub -5.2) micro-K) with a spectral index n = 1.11(sup + 0.60 sub -0.55) (n = 1.22(sup + 0.60 sub -0.55). With n fixed to 1.0 the most likely amplitude is 18.6 +/- 1.6 micro-K (18.2 +/- 1.6 micro-K). The marginal likelihood of n is 1.11 +/- 0.40 (1.22 +/- 0.40). Our best estimate of the dipole from the 2 yr DMR data is 3.363 +/- 0.024 mK toward Galactic coordinates (l, b) = (264.4 deg +/- 0.2 deg, 48.1 deg +/- 0.4 deg), and our best estimate of the rms quadrupole amplitude in our sky is 6 +/- 3 micro-K (68% CL).

Bennett, C. L.↗

NASA NTRS1995

The making of an Alfvenic fluctuation: The resolution of a second-order analysis

Ulysses observations of the high speed polar streams show that they are largely occupied by very large amplitude Alfvenic fluctuations accompanied by many rotational discontinuities. These fluctuations have a nearly constant magnetic intensity or amplitude, and the magnetic field direction per wave cycle sweeps only through a limited arc, much as a car wiperblade would do. Barnes and Hollweg (JGR, 79, 2302, 1974) suggested that this unusual waveform could arise from an obliquely propagating and linearly polarized Alfven wave of finite amplitude. From a second-order analysis, they showed that the existence of a particular solution with a constant amplitude but could not resolve the outcome of the homogeneous solution which consisted of fast waves. They suggested that Landau damping of these fast waves may be needed to get the observed waveform. We present a 1 1/2 D hybrid simulation which is fully nonlinear and correctly describes the ion kinetics for an initially monochromatic and linearly polarized Alfven wave propagating obliquely to the background magnetic field. The wave has a large amplitude and a wavelength so long that it can be considered dispersionless for simulation times. At early times, the second harmonic in density and in magnetic field transverse to the initial wave magnetic field are generated and have more power than other harmonics. Steepening is observed with a weak fast shock emerging, but no rotational discontinuity is left behind, and instead a constant amplitude and an arc-shaped waveform is made. The compressional component which develops after the shocks have dissipated is to zeroth order better described as a pure acoustic wave than as a fast wave. This might be explained by the relaxing of the Alfven wave to a state where its ponderomotive force vanishes so that the compressional component can travel almost independently of it.

Vasquez, Bernard J.↗

NASA NTRS1997

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.↗