Yang Dai

Ultrabright multikilovolt coherent tunable x-ray source at λ ∼ 2.71–2.93 Å

Detailed molecular structural information of the living state is of enormous significance to the medical and biological communities. Since hydrated biologically active structures are small delicate complex three-dimensional (3D) entities, it is essential to have molecular scale spatial resolution, high contrast, distortionless, direct 3D modalities of visualization of naturally functioning specimens in order to faithfully reveal their full molecular architectures. An x-ray holographic microscope equipped with an x-ray laser as the illuminator would be uniquely capable of providing these images. A quantitative interlocking concordance of physical evidence, that includes (a) the observation of strong enhancement of selected spectral components of several Xeq+ hollow-atom transition arrays (q = 31, 32, 34, 35, 36, 37) radiated axially from confined plasma channels, (b) the measurement of line narrowing that is spectrally correlated with the amplified transitions, (c) evidence for spectral hole-burning in the spontaneous emission, a manifestation of saturated amplification, that corresponds spectrally with the amplified lines, and (d) the detection of an intense narrow (δθx ~ 0.2xa0mrad) directed beam of radiation, (1) experimentally demonstrates in the λ ~ = 2.71–2.93xa0A range (ωx ~ = 4230–4570xa0eV) the operation of a new concept capable of producing the ideal conditions for amplification of multikilovolt x-rays and (2) proves the feasibility of a compact x-ray illuminator that can cost-effectively achieve the mission of biological x-ray microholography. The measurements also (α) establish the property of tunability in the quantum energy over a substantial fraction of the spectral region exhibiting amplification (Δωx ~ 345xa0eV) and (β) demonstrate the coherence of the x-ray output through the observation of a canonical spatial mode pattern. An analysis of the physical scaling revealed by these results indicates that the capability of the x-ray source potentially includes single-molecule microimaging, the key for the in situ structural analysis of membrane proteins, a cardinal class of drug targets. An estimate of the peak brightness achieved in these initial experiments gives a value of ~1031–1032xa0photonsxa0s−1xa0mm−2xa0mrad−2/(0.1%xa0bandwidth), a magnitude that is ~107–108-fold higher than presently available synchrotron technology.

Saturated multikilovolt x-ray amplification with Xe clusters: single-pulse observation of Xe(L) spectral hole burning

Single-pulse measurements of spectral hole burning of Xe(L)xa03d → 2p hollow atom transition arrays observed from a self-trapped plasma channel provide new information on the dynamics of saturated amplification in the λ ~ 2.8–2.9 A region. The spectral hole burning on transitions in the Xe34+ and Xe35+ arrays reaches full suppression of the spontaneous emission and presents a corresponding width Δωx ~ = 60 eV, a value adequate for efficient amplification of multikilovolt x-ray pulses down to a limiting length τx ~ 30 as. The depth of the suppression at 2.86 A indicates that the gain-to-loss ratio is ≥10. An independent determination of the x-ray pulse energy from damage produced on the surface of a Ti foil in the far field of the source gives a pulse energy of 20–30xa0µJ, a range that correlates well with the observation of the spectral hole burning and indicates an overall extraction efficiency of ~10%.

Explosive supersaturated amplification on 3d→2p Xe(L) hollow atom transitions at λ ∼ 2.7-2.9 Å

The Xe(L) system at ? ~ 2.9 ? uniformly exhibits all of the canonical attributes of a strongly saturated amplifier on the full ensemble of single-vacancy Xeq+ transition arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The key observables are (1) sharp spectral narrowing, (2) the detection of a narrow directed beam (??x200 ?rad), (3) an increase in the amplitude of the emission and the development of an intense output (?106 enhancement) and (4) the observation of deep spectral hole-burning on the inhomogeneously broadened spontaneous emission profile. Experimentally determined by two methods, (a) line narrowing and (b) signal enhancement, the observations for several single-vacancy 3d?2p transitions indicate a range of values for the effective small signal (linear) gain constant given by go25?100 cm?1. Quantitative analysis shows that this result stands in clear conflict with the corresponding upper bound go40?80 cm?1 that is based on available spectroscopic data and estimated with conventional theory. Overall, the observed values deviate substantially from expectations scaled to the spectral density of the measured Xe(L) spontaneous emission profile; they are systematically too high. The most extreme example is the heavily saturated Xe32+ transition at ? = 2.71 ?, a case that fails to reconcile the lower bound of the measured signal strength with the corresponding theoretically predicted maximal value; the former falls above the latter by a factor exceeding 400 giving an enormous gap. Moreover, although saturation is a prominent characteristic of the amplification at ?2.71 ?, as demonstrated by spectral hole-burning, the theoretical upper bound of go given for this transition is far too small for saturation to be reached. The Xe31+ transition at ?2.93 ? exhibits comparably pronounced anomalous behaviour. This double paradox is resolved with the Ansatz that the amplification is governed principally by the saturated gain gs, not the conventionally described small signal value go. This interpretation is further supported by the observation of deep spectral hole-burning, the signature of strong saturation, that occurs uniformly across the spectrum of the spontaneous emission profile. The effective amplification exhibits an anomalously weak dependence on the spectral density; saturation is the rule, not the exception. A lucid manifestation of the saturation is the recording of spectrally resolved x-ray yields on the Xe31+ array that are sufficiently high to produce gross structural damage to the material in the film plane of the spectrograph. The behaviour of the amplifier can be best described as an explosive supersaturated amplification. The source of this exceptionally strong amplification can be traced to the dynamically enhanced radiative response of the excited Xe hollow atom states located in the clusters that are mode coupled to the plasma waveguide forming the amplifying channel.

Double optimization of Xe(L) amplifier power scaling at λ ~ 2.9 Å

The spectral and spatial characteristics of the Xe(L) amplifier at ? ~ 2.9 ? determine an optimum for the scaling of the peak power with channel length. The Xe31+ and Xe32+ (3d ? 2p) transition arrays represent two identical spectral optima for amplification, a property stemming from the extremum of spectral components (3245) characteristic of their electron configurations. Adroit matching of the spatial distribution of the intensity characteristic of the propagating 248 nm pulse dynamically generating the self-trapped plasma channel with the intensity required to excite selectively and efficiently the Xe31+ and Xe32+ arrays can also simultaneously maximize the spatial volume of the excitation. The net outcome of this double maximization is an amplifying channel for the optimal transitions that possesses high gain (~100 cm?1), low losses (<10?1cm?1) and a diameter of 15?20 ?m, a size sufficient to produce an x-ray pulse energy of ~50?100 mJ from a channel having an average xenon density of ~1020 cm?3 and a length of 1 cm. Since previous studies have experimentally demonstrated the ability to produce a saturated bandwidth of ~60 eV, a magnitude sufficient to support a pulse duration of ~30 as, peak powers Px 1 PW are clearly within the scaling limits of the Xe(L) system. The corresponding peak brightness scaling limit is accordingly bounded from below by Px/?2 1030 W cm?2 sr?1.

Ultraviolet?infrared wavelength scalings for strong field induced L-shell emissions from Kr and Xe clusters

Comparison of Xe(L)/Kr(L) emission spectra generated from Xe and Kr clusters by ultraviolet (248 nm) and infrared (800/1060 nm) excitation reveals sharply different wavelength scalings. An interpretation of these contrasting scalings based on L-shell Auger widths explains this difference and supports the theoretical attribution of the strong hollow-atom Xe(L) emission produced with 248 nm irradiation to an ordered phase-dependent coupling. These results indicate that clusters of Yb, Ta and W may produce comparably strong hollow atom L-shell emission at ~8 keV with 248 nm excitation.

Computation with Inverse States in a Finite Field FP: The Muon Neutrino Mass, the Unified Strong-Electroweak Coupling Constant, and the Higgs Mass

The construction of inverse states in a finite field F{sub P{sub {alpha}}} enables the organization of the mass scale with fundamental octets in an eight-dimensional index space that identifies particle states with residue class designations. Conformance with both CPT invariance and the concept of supersymmetry follows as a direct consequence of this formulation. Based on two parameters (P{sub {alpha}} and g{sub {alpha}}) that are anchored on a concordance of physical data, this treatment leads to (1) a prospective mass for the muon neutrino of {approximately}27.68 meV, (2) a value of the unified strong-electroweak coupling constant {alpha}* = (34.26){sup {minus}1} that is physically defined by the ratio of the electron neutrino and muon neutrino masses, and (3) a see-saw congruence connecting the Higgs, the electron neutrino, and the muon neutrino masses. Specific evaluation of the masses of the corresponding supersymmetric Higgs pair reveals that both particles are superheavy (> 10{sup 18}GeV). No renormalization of the Higgs masses is introduced, since the calculational procedure yielding their magnitudes is intrinsically divergence-free. Further, the Higgs fulfills its conjectured role through the see-saw relation as the particle defining the origin of all particle masses, since the electron and muon neutrino systems, together with their supersymmetric partners, are the generators of the mass scale and establish the corresponding index space. Finally, since the computation of the Higgs masses is entirely determined by the modulus of the field P{sub {alpha}}, which is fully defined by the large-scale parameters of the universe through the value of the universal gravitational constant G and the requirement for perfect flatness ({Omega} = 1.0), the see-saw congruence fuses the concepts of mass and space and creates a new unified archetype.

Determination of Supersymmetric Particle Masses and Attributes with Genetic Divisors

Arithmetic conditions relating particle masses can be defined on the basis of (1) the supersymmetric conservation of congruence and (2) the observed characteristics of particle reactions and stabilities. Stated in the form of common divisors, these relations can be interpreted as expressions of genetic elements that represent specific particle characteristics. In order to illustrate this concept, it is shown that the pion triplet ({pi}{sup {+-}}, {pi}{sup 0}) can be associated with the existence of a greatest common divisor d{sub 0{+-}} in a way that can account for both the highly similar physical properties of these particles and the observed {pi}{sup {+-}}/{pi}{sup 0} mass splitting. These results support the conclusion that a corresponding statement holds generally for all particle multiplets. Classification of the respective physical states is achieved by assignment of the common divisors to residue classes in a finite field F{sub P{sub {alpha}}} and the existence of the multiplicative group of units F{sub P{sub {alpha}}} enables the corresponding mass parameters to be associated with a rich subgroup structure. The existence of inverse states in F{sub P{sub {alpha}}} allows relationships connecting particle mass values to be conveniently expressed in a form in which the genetic divisor structure is prominent. An examplemorexa0» is given in which the masses of two neutral mesons (K{degree} {r_arrow} {pi}{degree}) are related to the properties of the electron (e), a charged lepton. Physically, since this relationship reflects the cascade decay K{degree} {r_arrow} {pi}{degree} + {pi}{degree}/{pi}{degree} {r_arrow} e{sup +} + e{sup {minus}}, in which a neutral kaon is converted into four charged leptons, it enables the genetic divisor concept, through the intrinsic algebraic structure of the field, to provide a theoretical basis for the conservation of both electric charge and lepton number. It is further shown that the fundamental source of supersymmetry can be expressed in terms of hierarchical relationships between odd and even order subgroups of F{sub P{sub {alpha}}}, an outcome that automatically reflects itself in the phenomenon of fermion/boson pairing of individual particle systems. Accordingly, supersymmetry is best represented as a group rather than a particle property. The status of the Higgs subgroup of order 4 is singular; it is isolated from the hierarchical pattern and communicates globally to the mass scale through the seesaw congruence by (1) fusing the concepts of mass and space and (2) specifying the generators of the physical masses.«xa0less

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.

Amplification at λ ~ 2.8 Å on {\rm Xe}({\rm L})\,(2{\rm \bar s}2{\rm \bar p}) double-vacancy states produced by 248 nm excitation of Xe clusters in plasma channels

double-vacancy states undergo strong amplification in relativistic self-trapped plasma channels on 3d → 2p transitions in the λ = 2.78–2.81 A region. The 2P3/2 → 2S1/2 component at λ 2.786 A exhibits saturated amplification demonstrated by both (1) the observation of spectral hole-burning in the spontaneous emission profile and (2) the correlated enhancement of 3p → 2s cascade transitions (2S1/2 → 2Pj; j = 1/2, 3/2) at λ = 2.558 A and λ = 2.600 A. The condition of saturation places a lower limit of ~1017 W cm−2 on the intensity of the x-ray beam produced by the amplification in the channel. The anomalous strength of the amplification signalled by the saturation mirrors the equivalently anomalous behaviour observed for all 3d → 2p transitions corresponding to single-vacancy Xeq+ arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The conspicuous absence of amplification involving states with double-vacancy configurations suggests the operation of a selective interaction that enhances the production of states. Overall, the generation of double-vacancy states of this genre demonstrates that an excitation rate approaching ~1 W/atom for ionic species is achievable in self-trapped plasma channels.

Amplification at λ ∼ 2.8 Å on double-vacancy states produced by 248 nm excitation of Xe clusters in plasma channels

double-vacancy states undergo strong amplification in relativistic self-trapped plasma channels on 3d → 2p transitions in the λ = 2.78–2.81 A region. The 2P3/2 → 2S1/2 component at λ 2.786 A exhibits saturated amplification demonstrated by both (1) the observation of spectral hole-burning in the spontaneous emission profile and (2) the correlated enhancement of 3p → 2s cascade transitions (2S1/2 → 2Pj; j = 1/2, 3/2) at λ = 2.558 A and λ = 2.600 A. The condition of saturation places a lower limit of ~1017 W cm−2 on the intensity of the x-ray beam produced by the amplification in the channel. The anomalous strength of the amplification signalled by the saturation mirrors the equivalently anomalous behaviour observed for all 3d → 2p transitions corresponding to single-vacancy Xeq+ arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The conspicuous absence of amplification involving states with double-vacancy configurations suggests the operation of a selective interaction that enhances the production of states. Overall, the generation of double-vacancy states of this genre demonstrates that an excitation rate approaching ~1 W/atom for ionic species is achievable in self-trapped plasma channels.