Experimental investigation of steady state power balance in double null and single null H mode plasmas in MAST Upgrade
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The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance Δ d . Electron inertia ensures Δ d ≳ c/ω pe . The lines that lie within a magnetic flux tube of radius Δ d at the place where the field strength B is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where B = 0 vanishes, then distinguishable lines come no closer to the null than ≈ (a 2 c/ω pe ) 1/3 , where a is a characteristic spatial scale of the magnetic field. Here, the behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.
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A subaperture stitching interferometer system provides near-nulling of a subaperture wavefront reflected from an object of interest over a portion of a surface of the object. A variable optical element located in the radiation path adjustably provides near-nulling to facilitate stitching of subaperture interferograms, creating an interferogram representative of the entire surface of interest. This enables testing of aspheric surfaces without null optics customized for each surface prescription. The surface shapes of objects such as lenses and other precision components are often measured with interferometry. However, interferometers have a limited capture range, and thus the test wavefront cannot be too different from the reference or the interference cannot be analyzed. Furthermore, the performance of the interferometer is usually best when the test and reference wavefronts are nearly identical (referred to as a null condition). Thus, it is necessary when performing such measurements to correct for known variations in shape to ensure that unintended variations are within the capture range of the interferometer and accurately measured. This invention is a system for nearnulling within a subaperture stitching interferometer, although in principle, the concept can be employed by wavefront measuring gauges other than interferometers. The system employs a light source for providing coherent radiation of a subaperture extent. An object of interest is placed to modify the radiation (e.g., to reflect or pass the radiation), and a variable optical element is located to interact with, and nearly null, the affected radiation. A detector or imaging device is situated to obtain interference patterns in the modified radiation. Multiple subaperture interferograms are taken and are stitched, or joined, to provide an interferogram representative of the entire surface of the object of interest. The primary aspect of the invention is the use of adjustable corrective optics in the context of subaperture stitching near-nulling interferometry, wherein a complex surface is analyzed via multiple, separate, overlapping interferograms. For complex surfaces, the problem of managing the identification and placement of corrective optics becomes even more pronounced, to the extent that in most cases the null corrector optics are specific to the particular asphere prescription and no others (i.e. another asphere requires completely different null correction optics). In principle, the near-nulling technique does not require subaperture stitching at all. Building a near-null system that is practically useful relies on two key features: simplicity and universality. If the system is too complex, it will be difficult to calibrate and model its manufacturing errors, rendering it useless as a precision metrology tool and/or prohibitively expensive. If the system is not applicable to a wide range of test parts, then it does not provide significant value over conventional null-correction technology. Subaperture stitching enables simpler and more universal near-null systems to be effective, because a fraction of a surface is necessarily less complex than the whole surface (excepting the extreme case of a fractal surface description). The technique of near-nulling can significantly enhance aspheric subaperture stitching capability by allowing the interferometer to capture a wider range of aspheres. More over, subaperture stitching is essential to a truly effective near-nulling system, since looking at a fraction of the surface keeps the wavefront complexity within the capability of a relatively simple nearnull apparatus. Furthermore, by reducing the subaperture size, the complexity of the measured wavefront can be reduced until it is within the capability of the near-null design.
By the middle of 2006, the Interferometry Technology development program for NASA’s Terrestrial Planet Finder (TPF) Mission has the goal of demonstrating deep and stable interferometric nulling of broadband Mid-IR thermal radiation under conditions that are traceable to the expected on-orbit conditions. Specifically, the task is to demonstrate null levels of 10 to the negative 6 power, with a 50% BW centered at 10 um, with null stabilities of 10 to the negative 7 power all at cryogenic temperatures for observational periods of a couple of hours. The Achromatic Nulling activity at JPL addresses this concern in two testbeds: the warm nulling testbed and the cryonulling testbed. The warm nulling testbed will demonstrate the physics of nulling broadband thermal sources in an environment that is conducive to efficient research. We’ll explore nulling techniques, optical-mechanical alignment methods, motion control, and path-length metrology for a single beam interferometer, as well as preliminary planet detection techniques. Ultimate nulling capabilities under conditions that are more flight-like will be demonstrated in cryogenic nulling testbed. Knowledge gained from operation at room temperature will be applied to the cryongenic experiment where we face the additional challenges of extreme temperatures, cryongenic actuators, component survivability and fluxes that are within an order of magnitude of expected flux levels on orbit. Concurrently, we will develop a low flux mid-IR camera that will allow us to measure the nulls at these faint photon fluxes. This talk will review this development activity and will include recent nulling experimental results and plans for future work.
The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor T i j takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.
An adaptive-nulling method has been proposed to augment the nulling-optical- interferometry method of detection of Earth-like planets around distant stars. The method is intended to reduce the cost of building and aligning the highly precise optical components and assemblies needed for nulling. Typically, at the mid-infrared wavelengths used for detecting planets orbiting distant stars, a star is millions of times brighter than an Earth-sized planet. In order to directly detect the light from the planet, it is necessary to remove most of the light coming from the star. Nulling interferometry is one way to suppress the light from the star without appreciably suppressing the light from the planet. In nulling interferometry in its simplest form, one uses two nominally identical telescopes aimed in the same direction and separated laterally by a suitable distance. The light collected by the two telescopes is processed through optical trains and combined on a detector. The optical trains are designed such that the electric fields produced by an on-axis source (the star) are in anti-phase at the detector while the electric fields from the planet, which is slightly off-axis, combine in phase, so that the contrast ratio between the star and the planet is greatly decreased. If the electric fields from the star are exactly equal in amplitude and opposite in phase, then the star is effectively nulled out. Nulling is effective only if it is complete in the sense that it occurs simultaneously in both polarization states and at all wavelengths of interest. The need to ensure complete nulling translates to extremely tight demands upon the design and fabrication of the complex optical trains: The two telescopes must be highly symmetric, the reflectivities of the many mirrors in the telescopes and other optics must be carefully tailored, the optical coatings must be extremely uniform, sources of contamination must be minimized, optical surfaces must be nearly ideal, and alignments must be extremely precise. Satisfaction of all of these requirements entails substantial cost.
In measuring the figure error of an aspheric optic using a null lens, the wavefront contribution from the null lens must be independently and accurately characterized in order to isolate the optical performance of the aspheric optic alone. Various techniques can be used to characterize such a null lens, including interferometry, profilometry and image-based methods. Only image-based methods, such as phase retrieval, can measure the null-lens wavefront in situ - in single-pass, and at the same conjugates and in the same alignment state in which the null lens will ultimately be used - with no additional optical components. Due to the intended purpose of a Dull lens (e.g., to null a large aspheric wavefront with a near-equal-but-opposite spherical wavefront), characterizing a null-lens wavefront presents several challenges to image-based phase retrieval: Large wavefront slopes and high-dynamic-range data decrease the capture range of phase-retrieval algorithms, increase the requirements on the fidelity of the forward model of the optical system, and make it difficult to extract diagnostic information (e.g., the system F/#) from the image data. In this paper, we present a study of these effects on phase-retrieval algorithms in the context of a null lens used in component development for the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission. Approaches for mitigation are also discussed.
We report management of power exhaust will be a crucial task for tokamak fusion reactors. Reactor concepts are often proposed with double-null divertors, i.e. having two magnetic separatrices in an up-down symmetric configuration. This arrangement is potentially advantageous since the majority of the tokamak exhaust power tends to flow to the outer pair of divertor legs at large major radius, where the geometry is favorable for spreading the heat over a large surface area and there is more room for advanced divertor configurations. Despite the importance, there have been relatively few studies of divertor power sharing in near double null configurations and no studies at the poloidal magnetic fields and scrape-off layer power widths anticipated for a reactor. Motivated by this need we have undertaken a systematic study on Alcator C-Mod, examining the effect of magnetic flux balance on the power sharing among the four divertor legs in near double-null plasmas. Ohmic L-modes at three values of plasma current and ICRF-heated enhanced D-alpha (EDA) H-modes and I-modes at a single value of plasma current are explored, producing poloidal magnetic fields of 0.42, 0.62 and 0.85 Tesla. For Ohmic L-modes and ICRF-heated EDA H-modes, we find that the point of equal power sharing between upper and lower divertors occurs remarkably close to a balanced double null. Power sharing amongst the outer (upper versus lower) and inner (upper versus lower) pairs of divertors can be described in terms of a logistic function of magnetic flux balance, consistent with heat flux mapping along magnetic field lines to the outer midplane. Power sharing between inner and outer legs is found to follow a Gaussian-like function of magnetic flux balance with non-zero power to the inner divertors at double null. The overall behavior of H-modes operated near double null and for I-modes operating to within one heat flux e-folding of double null are found similar to Ohmic L-modes, with a significant reduction of power on the inner divertor legs. The results are encapsulated in terms of empirically-informed analytic functions of magnetic flux balance. When combined with magnetic equilibrium control system specifications, these relationships can be used to specify the power flux handling requirements for each of the four divertor target plates.
The basic advantage of single-mode fibers for deep nulling applications resides in their spatial filtering ability, and has now long been known. However, and as suggested more recently, a single-mode fiber can also be used for direct coherent recombination of spatially separated beams, i.e. in a 'multi-axial' nulling scheme. After the first successful demonstration of deep (<2e-6) visible LASER nulls using this technique (Haguenauer & Serabyn, Applied Optics 2006), we decided to work on an infrared extension for ground based astronomical observations, e.g. using two or more off-axis sub-apertures of a large ground based telescope. In preparation for such a system, we built and tested a laboratory infrared fiber nuller working in a wavelength regime where atmospheric turbulence can be efficiently corrected, over a pass band (approx.1.5 to 1.8 micron) broad enough to provide reasonable sensitivity. In addition, since no snapshot images are readily accessible with a (single) fiber nuller, we also tested baseline rotation as an approach to detect off-axis companions while keeping a central null. This modulation technique is identical to the baseline rotation envisioned for the TPF-I space mission. Within this context, we report here on early laboratory results showing deep stable broad-band dual polarization infrared nulls <5e-4 (currently limited by detector noise), and visible LASER nulls better than 3e-4 over a 360 degree rotation of the baseline. While further work will take place in the laboratory to achieve deeper stable broad-band nulls and test off-axis sources detection through rotation, the emphasis will be put on bringing such a system to a telescope as soon as possible. Detection capability at the 500:1 contrast ratio in the K band (~2.2 microns) seem readily accessible within 50-100 mas of the optical axis, even with a first generation system mounted on a >5m AO equipped telescope such as the Palomar Hale 200 inch, the Keck, Subaru or Gemini telescopes.
Management of power exhaust will be a crucial task for tokamak fusion reactors. Reactor concepts are often proposed with double-null divertors, i.e. having two magnetic separatrices in an up-down symmetric configuration. This arrangement is potentially advantageous since the majority of the tokamak exhaust power tends to flow to the outer pair of divertor legs at large major radius, where the geometry is favorable for spreading the heat over a large surface area and there is more room for advanced divertor configurations. Despite the importance, there have been relatively few studies of divertor power sharing in near double null configurations and no studies at the poloidal magnetic fields and scrape-off layer power widths anticipated for a reactor. Motivated by this need we have undertaken a systematic study on Alcator C-Mod, examining the effect of magnetic flux balance on the power sharing among the four divertor legs in near double-null plasmas. Ohmic L-modes at three values of plasma current and ICRF-heated enhanced D-alpha (EDA) H-modes and I-modes at a single value of plasma current are explored, producing poloidal magnetic fields of 0.42, 0.62 and 0.85 Tesla. For Ohmic L-modes and ICRF-heated EDA H-modes, we find that the point of equal power sharing between upper and lower divertors occurs remarkably close to a balanced double null. Power sharing amongst the outer (upper versus lower) and inner (upper versus lower) pairs of divertors can be described in terms of a logistic function of magnetic flux balance, consistent with heat flux mapping along magnetic field lines to the outer midplane. Power sharing between inner and outer legs is found to follow a Gaussian-like function of magnetic flux balance with non-zero power to the inner divertors at double null. The overall behavior of H-modes operated near double null and for I-modes operating to within one heat flux e-folding of double null are found similar to Ohmic L-modes, with a significant reduction of power on the inner divertor legs. The results are encapsulated in terms of empirically-informed analytic functions of magnetic flux balance. When combined with magnetic equilibrium control system specifications, these relationships can be used to specify the power flux handling requirements for each of the four divertor target plates.
Mammary epithelial cells from p53 null mice have been shown recently to exhibit an increased risk for tumor development. Hormonal stimulation markedly increased tumor development in p53 null mammary cells. Here we demonstrate that mammary tumors arising in p53 null mammary cells are highly aneuploid, with greater than 70% of the tumor cells containing altered chromosome number and a mean chromosome number of 56. Normal mammary cells of p53 null genotype and aged less than 14 wk do not exhibit aneuploidy in primary cell culture. Significantly, the hormone progesterone, but not estrogen, increases the incidence of aneuploidy in morphologically normal p53 null mammary epithelial cells. Such cells exhibited 40% aneuploidy and a mean chromosome number of 54. The increase in aneuploidy measured in p53 null tumor cells or hormonally stimulated normal p53 null cells was not accompanied by centrosome amplification. These results suggest that normal levels of progesterone can facilitate chromosomal instability in the absence of the tumor suppressor gene, p53. The results support the emerging hypothesis based both on human epidemiological and animal model studies that progesterone markedly enhances mammary tumorigenesis.
This system was one of the test methods considered for measuring the radius of curvature of one or more of the 18 segmented mirrors that form the 6.5 m diameter primary mirror (PM) of the James Webb Space Telescope (JWST). The assembled telescope will be tested at cryogenic temperatures in a 17-m diameter by 27-m high vacuum chamber at the Johnson Space Center. This system uses a Leica Absolute Distance Meter (ADM), at a wavelength of 780 nm, combined with beam-steering and beam-shaping optics to make a differential distance measurement between a ring mirror on the reflective null assembly and individual PM segments. The ADM is located inside the same Pressure-Tight Enclosure (PTE) that houses the test interferometer. The PTE maintains the ADM and interferometer at ambient temperature and pressure so that they are not directly exposed to the telescope s harsh cryogenic and vacuum environment. This system takes advantage of the existing achromatic objective and reflective null assembly used by the test interferometer to direct four ADM beamlets to four PM segments through an optical path that is coincident with the interferometer beam. A mask, positioned on a linear slide, contains an array of 1.25 mm diameter circular subapertures that map to each of the 18 PM segments as well as six positions around the ring mirror. A down-collimated 4 mm ADM beam simultaneously covers 4 adjacent PM segment beamlets and one ring mirror beamlet. The radius, or spacing, of all 18 segments can be measured with the addition of two orthogonally-oriented scanning pentaprisms used to steer the ADM beam to any one of six different sub-aperture configurations at the plane of the ring mirror. The interferometer beam, at a wavelength of 687 nm, and the ADM beamlets, at a wavelength of 780 nm, pass through the objective and null so that the rays are normally incident on the parabolic PM surface. After reflecting off the PM, both the ADM and interferometer beams return to their respective instruments on nearly the same path. A fifth beamlet, acting as a differential reference, reflects off a ring mirror attached to the objective and null and returns to the ADM. The spacings between the ring mirror, objective, and null are known through manufacturing tolerances as well as through an in situ null wavefront alignment of the interferometer test beam with a reflective hologram located near the caustic of the null. Since total path length between the ring mirror and PM segments is highly deterministic, any ADM-measured departures from the predicted path length can be attributed to either spacing error or radius error in the PM. It is estimated that the path length measurement between the ring mirror and a PM segment is accurate to better than 100 m. The unique features of this invention include the differential distance measuring capability and its integration into an existing cryogenic and vacuum compatible interferometric optical test.
A method of measuring aberrations in a null-lens including assembly and alignment aberrations. The null-lens may be used for measuring aberrations in an aspheric optic with the null-lens. Light propagates from the aspheric optic location through the null-lens, while sweeping a detector through the null-lens focal plane. Image data being is collected at locations about said focal plane. Light is simulated propagating to the collection locations for each collected image. Null-lens aberrations may extracted, e.g., applying image-based wavefront-sensing to collected images and simulation results. The null-lens aberrations improve accuracy in measuring aspheric optic aberrations.
The crux of visible exoplanet detection is overcoming significant star-planet contrast ratios on the order of 10(exp -7) to 10(exp -10)-at very small angular separations. We are developing an interferometric nulling coronagraph designed to achieve a 10(exp -6) contrast ratio at a working science bandpass of 20% visible light. Achieving large, broadband suppression requires a pseudo-achromatic phase flip, while maintaining a strict error budget. Recent results from our nulling interferometer testbed yield contrast ratios at the 1.05x10(exp -6) level, with a 15% visible bandpass. This result is at 65% of our final bandpass requirement, although limitations of our current configuration make major hardware changes essential to broadening the bandpass. We make the argument that broadening the bandpass should not necessarily adversely affect the null depth until beyond the 20% visible light level. Using the same setup we are able to reach monochromatic null depths of 1.11x10(exp -7) (?= 638 nm)averaged over three seconds. This paper will describe our experimental approach for achieving deep broadband nulls, as well as error considerations and limitations, and the most recent results for our nulling coronagraph testbed.