High-resolution, Flat-field, Plane-grating, F/10 Spectrograph with Off-axis Parabolic Mirrors

A high-resolution, flat-field, plane-grating, f/10 spectrometer based on the novel design proposed by Gil and Simon [Appl. Opt. 22, 152 (1983)] is demonstrated. The spectrometer design employs off-axis parabolic collimation and camera mirrors in a configuration that eliminates spherical aberrations and minimizes astigmatism, coma, and field curvature in the image plane. In accordance with theoretical analysis, the performance of this spectrometer achieves a high spatial resolution over the large detection area, which is shown to be limited only by the quality of its optics and their proper alignment within the spatial resolution of a 13 μm×13 μm pixelated CCD detector. With a 1500 lines/mm grating in first order, the measured spectral resolving power of λ/Δλ=2.5(±0.5)×104 allows the clear resolution of the violet Ar(I) doublet at 419.07 and 419.10  nm

Quadratic Reciprocity and the Group Orders of Particle States

The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena

Transversely observed Kr(L) spectrum and corresponding x-ray image of plasma channel morphology

<p><strong>Figure 5.</strong> Transversely observed Kr(L) spectrum and corresponding x-ray image of plasma channel morphology. These data represent file 677/18 May 2012. (a) Kr(L) transverse spectrum recorded at longitudinal coordinate <em>Z</em> = −0.9 mm as indicated in panel (b). The Kr²⁶⁺ 3s → 2p line at λ 7.504 Å exhibits a width δ_λ,l,t  4.5 eV. The Doppler width expected from a coulomb explosion of the Kr clusters is estimated to be ~4.4 eV; see text for discussion. The limiting spectral resolution of the instrument is estimated to be ~3 eV. (b) X-ray image of Kr(L) emission from the plasma channel recorded transversely with the x-ray pinhole camera. The (<em>y</em>, <em>z</em>) spatial resolution is estimated to be ~50 µm in both coordinates. The centre of the 2.65 mm diameter nozzle is located at <em>Z</em> 0.6 mm. The 248 nm pulse energy was 182 mJ, the plenum pressure was 141 psi, and the nozzle temperature was 262 K.</p> <p><strong>Abstract</strong></p> <p>Experimental evidence demonstrating amplification on the Kr²⁶⁺ 3s→2p transition at λ 7.5 Å (~1652 eV) generated from a (Kr)<em>_n</em> cluster medium in a self-trapped plasma channel produced with 248 nm femtosecond pulses is presented. The x-ray beam produced had a spectral width of ~3 eV and a corresponding beam diameter of ~150 µm, properties that were simultaneously determined by a two-dimensional x-ray spectral image formed with an axially placed von Hámos spectrometer and a matching Thomson image of the spatial electron density generated by the x-ray propagation.</p

Simultaneously recorded single-pulse images of (a) the Thomson scattered signal from the electron density and (b) the transverse Kr(L) ~ 1.7 keV x-ray emission zone (log scale) of a stable 248 nm channel produced in a Kr cluster target

<p><strong>Figure 4.</strong> Simultaneously recorded single-pulse images of (a) the Thomson scattered signal from the electron density and (b) the transverse Kr(L) ~ 1.7 keV x-ray emission zone (log scale) of a stable 248 nm channel produced in a Kr cluster target. The channel was produced at a height of 1.60 mm above the opening of the nozzle. The x-ray camera utilized a pinhole with a diameter of 50 µm and had a spatial resolution estimated to be 75–100 µm. The Kr cluster target was produced by a cooled high-pressure pulsed-valve fitted with a circular nozzle having a diameter of 2.65 mm. These data correspond to pulse 519 (14 June 2012). The direction of propagation is left to right and the position of the nozzle is the same as shown in figure <a href="http://iopscience.iop.org/0953-4075/46/18/185601/article#jpb469036f2" target="_blank">2</a>(a); the coordinates (<em>Y</em>, <em>Z</em>) = (0, 0) correspond to the centre of the nozzle. The matching locations of corresponding features in these images are indicated by the vertical connection lines. The abrupt expansion of the signal in panel (a) at <em>Z</em> 0 mm signals the termination of the confined propagation. A weak halo surrounding the bright zone indicating peripheral ionization is visible. The channel termination at <em>Z</em> 0 mm in panel (b) that coincides with the Thomson image in panel (a) is manifest.</p> <p><strong>Abstract</strong></p> <p>Comparative single-pulse studies of self-trapped plasma channel formation in Xe and Kr cluster targets produced with 1–2 TW femtosecond 248 nm pulses reveal energy efficient channel formation (>90%) and highly robust stability for the channeled propagation in both materials. Images of the channel morphology produced by Thomson scattering from the electron density and direct visualization of the Xe(M) and Kr(L) x-ray emission from radiating ions illustrate the (1) channel formation, (2) the narrow region of confined trapped propagation, (3) the abrupt termination of the channel that occurs at the point the power falls below the critical power <em>P</em>_cr, and, in the case of Xe channels, (4) the presence of saturated absorption of Xe(M) radiation that generates an extended peripheral zone of ionization. The measured rates for energy deposition per unit length are ~ 1.46 J cm⁻¹ and ~ 0.82 J cm⁻¹ for Xe and Kr targets, respectively, and the single pulse Xe(M) energy yield is estimated to be > 50 mJ, a value indicating an efficiency >20% for ~ 1 keV x-ray production from the incident 248 nm pulse.</p

Details of Thomson images shown in panels (a) and (b) of figure 9

<p><strong>Figure 10.</strong> Details of Thomson images shown in panels (a) and (b) of figure <a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344f9" target="_blank">9</a>. These data correspond to file 520/14 June 2012. (a) Isometric view of Thomson image showing extension into the dark x-ray zone <em>Z</em> ≥ 0.5 mm illustrated in figure <a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344f9" target="_blank">9</a>(c). The arrow at <em>Z</em> = <em>Z</em>₁  1.8 mm specifies the location of the endpoint of the visible Thomson signal that indicates the presence of ionized material. (b) Axial line-out of the Thomson data pictured in panel (a). A discernable extension of the ionization is visible out to <em>Z</em> = <em>Z</em>₁  1.8 mm, a distance that represents a penetration of ~1.3 mm into the x-ray dark region shown in figure <a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344f9" target="_blank">9</a>(c) and is estimated to be comparable to the linear absorption length of the Kr cluster medium. This observation agrees with an earlier estimate [<a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344bib13" target="_blank">13</a>] of the ability to reach saturation of the absorption in Kr by Kr(L) emission; the clear conclusion was that, with a saturation parameter <em>ħ</em>ω/σ 400 J cm⁻², linear absorption would necessarily govern.</p> <p><strong>Abstract</strong></p> <p>Experimental evidence demonstrating amplification on the Kr²⁶⁺ 3s→2p transition at λ 7.5 Å (~1652 eV) generated from a (Kr)<em>_n</em> cluster medium in a self-trapped plasma channel produced with 248 nm femtosecond pulses is presented. The x-ray beam produced had a spectral width of ~3 eV and a corresponding beam diameter of ~150 µm, properties that were simultaneously determined by a two-dimensional x-ray spectral image formed with an axially placed von Hámos spectrometer and a matching Thomson image of the spatial electron density generated by the x-ray propagation.</p

Comparative Kr(L) spectra obtained under three different modalities of excitation are shown

<p><strong>Figure 12.</strong> Comparative Kr(L) spectra obtained under three different modalities of excitation are shown. (a) Axially recorded Kr(L) spectrum produced with self-trapped 248 nm channel (this work, file 677/18 May 2012). The principal feature is the ¹P₁ → ¹S₀ Kr²⁶⁺ 3s → 2p transition at λ 7.504 Å. (b) Kr(L) emission spectrum recorded with 248 nm excitation without channelled propagation. The emission profile is dominated by a broad feature involving several transitions in the 6.8–7.2 Å range. For details, see [<a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344bib1" target="_blank">1</a>]. (c) Kr(L) spectrum obtained with excitation at ~1 µm without channelled propagation. See [<a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344bib16" target="_blank">16</a>] for additional details.</p> <p><strong>Abstract</strong></p> <p>Experimental evidence demonstrating amplification on the Kr²⁶⁺ 3s→2p transition at λ 7.5 Å (~1652 eV) generated from a (Kr)<em>_n</em> cluster medium in a self-trapped plasma channel produced with 248 nm femtosecond pulses is presented. The x-ray beam produced had a spectral width of ~3 eV and a corresponding beam diameter of ~150 µm, properties that were simultaneously determined by a two-dimensional x-ray spectral image formed with an axially placed von Hámos spectrometer and a matching Thomson image of the spatial electron density generated by the x-ray propagation.</p

The geometry of the von Hámos spectrometer that recorded the axial Kr(L) spectrum is illustrated

<p><strong>Figure 3.</strong> The geometry of the von Hámos spectrometer that recorded the axial Kr(L) spectrum is illustrated. As described in the text, axial translation along the <em>Z</em>-axis controllably positions the focal point of the instrument so that the spectrum of the amplified Kr(L) beam can be faithfully recorded as a strong signal on the CCD in the plane of the instrument without significant interference from the two regions of isotropic emission that are associated with the formation and termination of the self-trapped plasma channel. (a) Focal point of spectrometer positioned within the isotropic emission zone at the exit of the plasma channel. (b) Focal point of spectrometer positioned outside of both isotropically radiating regions that are accordingly designated as off-axis, defocused zones. With this geometrical configuration, only the directed Kr(L) 7.5 Å beam can produce a strong signal on the plane of the detector, thereby selectively recording the spectrum of the amplified Kr(L) transition on the CCD.</p> <p><strong>Abstract</strong></p> <p>Experimental evidence demonstrating amplification on the Kr²⁶⁺ 3s→2p transition at λ 7.5 Å (~1652 eV) generated from a (Kr)<em>_n</em> cluster medium in a self-trapped plasma channel produced with 248 nm femtosecond pulses is presented. The x-ray beam produced had a spectral width of ~3 eV and a corresponding beam diameter of ~150 µm, properties that were simultaneously determined by a two-dimensional x-ray spectral image formed with an axially placed von Hámos spectrometer and a matching Thomson image of the spatial electron density generated by the x-ray propagation.</p

Spectral details of Kr(L) amplification are presented

<p><strong>Figure 7.</strong> Spectral details of Kr(L) amplification are presented. These data correspond to file 677/18 May 2012. (a) Composite spectra are shown illustrating the axial (red) and transverse (brown) spectra. The transverse Kr(L) spectrum corresponding to <em>Z</em> = 0.3 mm is practically null; the axial von Hámos spectrometer, with the focal plane located at <em>Z</em> = 0.3 mm, as shown in panel (b), reveals sharp spectral structure with a width δ_λ,l  3 eV that is particularly obvious on the dominant Kr²⁶⁺ 3s → 2p transition at λ 7.5 Å. The depth-of-field of the axial von Hámos spectrometer is estimated to be ≤ 300 µm, as indicated by the shaded zone centred at <em>Z</em> = 0.3 mm in panel (b). Compare these spectra to those presented in figure <a href="http://iopscience.iop.org/0953-4075/46/15/155601/article#jpb468344f6" target="_blank">6</a>(a). (b) Transverse x-ray camera image of Kr(L) emission profile with a spatial resolution estimated to be ~50 µm. The axial position <em>Z</em> = 0.3 mm corresponds to the location of the focal plane of the axial von Hámos spectrometer.</p> <p><strong>Abstract</strong></p> <p>Experimental evidence demonstrating amplification on the Kr²⁶⁺ 3s→2p transition at λ 7.5 Å (~1652 eV) generated from a (Kr)<em>_n</em> cluster medium in a self-trapped plasma channel produced with 248 nm femtosecond pulses is presented. The x-ray beam produced had a spectral width of ~3 eV and a corresponding beam diameter of ~150 µm, properties that were simultaneously determined by a two-dimensional x-ray spectral image formed with an axially placed von Hámos spectrometer and a matching Thomson image of the spatial electron density generated by the x-ray propagation.</p