Calculation of the ion distribution function over transverse velocities under ICR heating conditions and separation parameters of a collector of heated ions

The ion distribution function over transverse velocities and the ion heating efficiency (which is defined as the fraction η of ions heated above a certain energy W_min) are calculated in the context of a plasma method for isotope separation on the basis of ion cyclotron resonance heating. The ion distribution function over longitudinal velocities is assumed to be linear in the range of low velocities. It is shown that, when the ions are heated to high energies, the averaged ion distribution function over transverse velocities becomes highly nonequilibrium and has two peaks. Results are presented from calculations of the ion heating efficiency η for W_min=40 eV and for different values of the parameter p that characterizes the ratio of the wavelength λ of the antenna electric field to the length L of the heating region. The relative roles of the time-of-flight and the Doppler broadening are analyzed, and the separation parameters of a collector of heated ions are estimated.     

Formation of a charge-exchange target for fast ions in the plasma of large-scale toroidal devices under NBI conditions

High-energy (E>0.2 MeV) charge-exchange diagnostics allow the determination of the distribution function of fast atoms produced via the neutralization of hydrogen isotope ions by target hydrogen-like impurity ions. To derive the distribution function from the experimental data requires knowledge of the composition and spatial distribution of the target ions in a tokamak plasma. A charge-exchange target forms as a result of the interaction between the main impurity nuclei and the heating neutral beams. In different devices, the heating beams are arranged in different ways with respect to the diagnostics; hence, in order to accurately estimate the contribution of the secondary ions to the detected signal, it is necessary to calculate their trajectories for every particular case. A model is proposed that takes into account elementary processes resulting in the ionization equilibrium of the ions of different impurities with allowance for ion motion in a specific tokamak configuration. As an example, the model is applied to the plasma of the JT-60U tokamak. Mechanisms for the formation of charge-exchange atomic flows in various energy ranges are considered. The relative contributions of different heating injectors to the charge-exchange flow are estimated. Based on the calculated results, a method is proposed for local measurements of the ion distribution function with the help of a stationary analyzer.     

Use of isotope effects to elucidate enzyme mechanisms

The chemical bond breaking steps are normally not rate limiting for enzymatic reactions. However, comparison of deuterium and tritium isotope effects on the same reaction, especially when coupled with 13C isotope effects for the same step measured with deuterated as well as unlabeled substrates, allows calculation of the intrinsic isotope effects on the bond breaking steps and thus a determination of the commitments to catalysis for the reactants. The variation in observed isotope effects as a function of reactant concentration can be used to determine kinetic mechanisms, while the pH variation of isotope effects can determine the stickiness of the reactants and which portions of the reactant mechanism are pH dependent. Finally the size of primary and secondary intrinsic isotope effects can be used to determine transition state structure.     

Analysis of the separation of gadolinium isotopes by the ICR method

The problem of separating gadolinium isotopes is discussed. The parameters of isotope separation in a plasma by the ICR method are estimated for a device with given operating parameters. The mean transverse energy 〈E_⊥〉 of the heated ions of the ¹⁵⁷Gd isotope and the heating efficiency η are calculated as functions of the frequency of the RF electric field in the plasma. The dependence of the heating efficiency η on the longitudinal temperature of the plasma flow is investigated. The issue of how the concentration of the target isotope ions at the collector plate depends on the longitudinal coordinate measured from the front edge of the plate is analyzed for different values of the frequency detuning parameter. The extraction coefficient Г for the target isotope is calculated as a function of the distance b between the collector plates for different frequency detunings.     

Subtle modification of isotope ratio proteomics; an integrated strategy for expression proteomics

Use of minor modification of isotope ratio to code samples for expression proteomics is being investigated. Alteration of (13)C abundance to approximately 2% yields a measurable effect on peptide isotopic distribution and inferred isotope ratio. Elevation of (13)C abundance to 4% leads to extension of isotopic distribution and background peaks across every unit of the mass range. Assessment of isotope ratio measurement variability suggests substantial contributions from natural measurement variability. A better understanding of this variable will allow assessment of the contribution of sequence dependence. Both variables must be understood before meaningful mixing experiments for relative expression proteomics are performed. Subtle modification of isotope ratio ( approximately 1-2% increase in (13)C) had no effect upon either the ability of data-dependent acquisition software or database searching software to trigger tandem mass spectrometry or match MSMS data to peptide sequences. More severe modification of isotope ratio caused a significant drop in performance of both functionalities. Development of software for deconvolution of isotope ratio concomitant with protein identification using LC-MSMS, or any other proteomics strategy, is underway (Isosolv). The identified peptide sequence is then be used to provide elemental composition for accurate isotope ratio decoding and the potential to control for specific amino acid biases should these prove significant. It is suggested that subtle modification of isotope ratio proteomics (SMIRP) offers a convenient approach to in vivo isotope coding of plants and might ultimately be extended to mammals including humans.     

Parameters of an ion beam and characteristic features of its slowing-down in a plasma during fast ignition of an inertial fusion target

The physics of the heating of an inertial fusion target by a high-energy ion beam under the conditions of fast ignition of fusion reactions is studied theoretically. The characteristic features of the formation of the spatial distribution of the energy transferred to the plasma from a beam of ions with different initial energies, masses, and charges under fast ignition conditions are determined. The notion of the Bragg peak is extended with respect to the spatial distribution of the temperature of the ion-beam-heated medium. The parameters of the ion beams are determined with which to initiate different regimes of fast ignition of a thermonuclear fuel precompressed to a density of 300–500 g/cm³—the edge regime, in which the ignition region is formed at the outer boundary of the target, and the internal regime, in which the ignition region is formed within the target and, in particular, in its central parts.     

Plasma outflow from a corrugated trap in the kinetic regime

The problem of stationary plasma outflow from an open corrugated trap in the kinetic regime is considered with allowance for pair collisions in the framework of a kinetic equation with the Landau collision integral. The distribution function is studied in the limit of small-scale corrugation and a large mirror ratio. In considering a single corrugation cell, a correction for the distribution function is calculated analytically. An equation describing variations of the distribution function along the system is derived and used to study the problem of plasma outflow into vacuum.     

A method to determine 18 O kinetic isotope effects in the hydrolysis of nucleotide triphosphates

A method to determine 18 O kinetic isotope effects (KIEs) in the hydrolysis of GTP that is generally applicable to reactions involving other nucleotide triphosphates is described. Internal competition, where the substrate of the reaction is a mixture of 18 O-labeled and unlabeled nucleotides, is employed, and the change in relative abundance of the two species in the course of the reaction is used to calculate KIE. The nucleotide labeled with 18 O at sites of mechanistic interest also contains 13C at all carbon positions, whereas the 16 O-labeled nucleotide is depleted of 13C. The relative abundance of the labeled and unlabeled substrates or products is reflected in the carbon isotope ratio (13C/12C) in GTP or GDP, which is determined by the use of a liquid chromatography-coupled isotope ratio mass spectrometer (LC-coupled IRMS). The LC is coupled to the IRMS by an Isolink interface. Carbon isotope ratios can be determined with accuracy and precision greater than 0.04% and are consistent over an order of magnitude in sample amount. KIE values for Ras/NF1(333)-catalyzed hydrolysis of [beta18 O3,13C]GTP were determined by change in the isotope ratio of GTP or GDP or the ratio of the isotope ratio of GDP to that of GTP. KIE values computed in the three ways agree within 0.1%, although the method using the ratio of isotope ratios of GDP and GTP gives superior precision (<0.1%). A single KIE measurement can be conducted in 25 min with less than 5 microg nucleotide reaction product.     

Distribution of the lithium deposition on the collector during separation of lithium isotopes by the plasma ICR method

Results of experiments on isotope separation by the ion cyclotron resonance (ICR) method in plasma are presented. The deposition of hot lithium ions on a plane collector was studied. The density distribution and isotope composition of lithium deposited on the surface of the plane collector were measured. It is found that, without applying a positive potential to the collector plate, the deposition density is nonuniform in the direction perpendicular to the external magnetic field, whereas in the presence of a retarding potential (+20 V), the deposited layer becomes almost uniform. It is shown that the asymmetry of deposition is not caused by the rotating RF field selectively heating ions of the extracted isotope. Possible reasons for the nonuniform deposition of lithium on the collector are discussed.     

Nuclear forward scattering of synchrotron radiation by deoxymyoglobin

Nuclear forward scattering of synchrotron radiation is used to determine the quadrupole splitting and the mean square displacement of the iron atom in deoxymyoglobin in the temperature range between 50 K and 243 K. Above 200 K an abnormally fast decay of the forward scattered intensity at short times after the synchrotron flash is observed, which is caused by protein-specific motions. The results strongly support the picture that protein dynamics seen at the position of the iron can be understood by harmonic motions in the low temperature regime while in the physiological regime diffusive motions in limited space are present. The shape of the resonance broadening function is investigated. An inhomogeneous broadening with a Lorentzian distribution indicating dipole interactions results in a better agreement with the experimental data than the common Gaussian distribution. Received: 30 August 1999 / Revised version: 22 October 1999 / Accepted: 6 December 1999     

Determination of protein synthesis in vivo using labeling from deuterated water and analysis of MALDI-TOF spectrum.

This paper describes a method of determining protein synthesis and turnover using in vivo labeling of protein with deuterated water and analysis of matrix-assisted laser desorption time-of-flight mass spectrometer (MALDI-TOF) spectrum. Protein synthesis is calculated using mass isotopomer distribution analysis instead of precursor to product amino acid enrichment ratio. During protein synthesis, the incorporation of deuterium from water changes the mass isotopomer distribution (isotope envelop) according to the number of deuterium atoms (0, 1, 2, 3, etc.) incorporated, and the distribution of the protein with 0, 1, 2, 3,... atoms of deuterium follows a binomial distribution. A mathematical algorithm by which the distribution of deuterium isotopomers can be extracted from the observed MALDI-TOF spectrum is presented. Since deuterium isotopomers are unique to newly synthesized proteins, the quantitation of their distribution provides a method for the quantitation of newly synthesized proteins. The combined use of postsource decay sequence identification and mass isotopomer distribution analysis makes the use of in vivo labeling with deuterated water a precise method to determine specific protein synthesis.     

A new procedure for the statistical analysis of double-isotope incorporation data

A new method for analyzing the data of double-label incorporation experiments is presented. A quantity termed the fractional difference is used as the basis for assessing differences in the distribution of the two isotopes, as opposed to the usual isotope ratio. As part of the analysis, differences in distribution are evaluated in terms of the calculated system error limits. Those which fall outside these limits are selected as statistically significant and are subjected to complete quantitation.     

Quasilinear modification of the spectra of cyclotron emission from a toroidal plasma near the ECRH frequency

A study is made of the modification of the spectra of electron cyclotron emission from an ECR heated plasma in a toroidal magnetic confinement system into which the heating radiation is launched from the low-field side. It is shown that, at frequencies close to the heating frequency, cyclotron emission can become more intense because of the deformation of the distribution function of the resonant electrons. This effect can be used to diagnose the slightly pronounced quasilinear perturbations of the electron distribution in the thermal energy range, which are typical of experiments on ECR plasma heating. Results of a qualitative analysis carried out for model electron distribution functions are presented, and examples of three-dimensional numerical simulations of a circular tokamak are described.     

Isotope ratio determination in boron analysis

Traditionally, boron (B) isotope ratios have been determined using thermal ionization mass spectrometry (TIMS) and, to some extent, secondary ion mass spectrometry (SIMS). Both TIMS and SIMS use a high-resolution mass analyzer, but differ in analyte ionization methods. TIMS uses electrons from a hot filament, whereas SIMS employs an energetic primary ion beam of Ga+, Cs+, or O- for analyte ionization. TIMS can be used in negative or positive ion modes with high sensitivity and precision of B isotope ratio determination. However, isobaric interferences may be a problem, if the sample is not well purified and/or memory of the previous sample is not removed. Time-consuming sample preparation, analyte (B) purification, and sample determination processes limit the applications of TIMS for routine analyses. SIMS can determine B and its isotope ratio in intact solid samples without destroying them, but has poorer resolution and sensitivity than TIMS, and is difficult to standardize for biological samples. Development of plasma-source mass spectrometry (MS) enabled the determination of B concentration and isotope ratio without requiring sample purification. Commonly used plasma-source MS uses an Ar inductively coupled plasma (ICP) as an ionization device interfaced to a low-resolution quadrupole mass analyzer. The quadrupole ICP-MS is less precise than TIMS and SIMS, but is a popular method for B isotope ratio determination because of its speed and convenience. B determination by ICP-MS suffers no spectroscopic interferences. However, sample matrices, memory effects, and some instrument parameters may affect the accuracy and precision of B isotope ratio determination if adequate precautions are not taken. New generations of plasma-source MS instruments using high-resolution mass analyzers provide better sensitivity and precision than the currently used quadrupole ICP-MS. Because of the convenience and high sample throughput, the high-resolution ICP-MS is expected to be the method of choice for B isotope ratio determination. The current state of instrumental capabilities is adequate for B isotope determination. However, precision and accuracy are primarily limited by sample preparation, introduction, and analytical methodology, including 1. Analyte loss and isotope fractionation during sample preparation. 2. The precision of B isotope determination in small samples, especially those containing low concentrations. 3. Difficult matrices. 4. Memory effects. Sample preparation by alkali fusion allows rapid and complete decomposition of hard-to-digest samples, but high-salt environments of the fused materials require extensive sample purification for B ratio determination. The alternative wet-ashing sample decomposition with HF also results in B loss and isotopic fractionation owing to the high volatility of BF3. Open-vessel dry- or wet-ashing methods usually do not work well for animal samples, and are also prone to B loss and contamination. Closed-vessel microwave digestion overcomes these problems, but the digests of biological materials have high C contents, which cause spectral interference on 11B and affect 11B/10B ratios. Exchange separation/preconcentration of B using exchange (cation or anion exchange, B-specific resin, e.g., Amberlite IRA-743) tend to cause B isotope fractionation, and C eluting from these resin columns may interfere with B isotope ratio determination. Memory effects of B that occur during sample determination may cause serious errors in B isotope ratio determination, especially when samples varying in B concentrations and/or isotope composition are analyzed together. Although the utilization of high-resolution plasma-source MS will undoubtedly improve analytical precision, it is the sample preparation, sample introduction, and analytical methodology that represent the primary limitation to accurate and precise B isotope ratio determination.     

The use of isotope effects to determine enzyme mechanisms

Isotope effects are one of the most powerful kinetic tools for determining enzyme mechanisms. There are three methods of measurement. First, one can compare reciprocal plots with labeled and unlabeled substrates. The ratio of the slopes is the isotope effect on V/K, and the ratio of the vertical intercepts is the isotope effect on V(max). This is the only way to determine V(max) isotope effects, but is limited to isotope effects of 5% or greater. The second method is internal competition, where the labeled and unlabeled substrates are present at the same time and the change in their ratio in residual substrate or in product is used to calculate an isotope effect, which is that on V/K of the labeled reactant. This is the method used for tritium or (14)C, or with the natural abundances of (13)C, (15)N, or (18)O. The third method involves perturbations from equilibrium when a labeled substrate and corresponding unlabeled product are present at chemical equilibrium. This also gives just an isotope effect on V/K for the labeled reactant. The chemistry is typically not fully rate limiting, so that the isotope effect on V/K is given by: (x)(V/K)=((x)k+c(f)+c(r)(x)K(eq))/(1+c(f)+c(r)) where x defines the isotope (D, T, 13, 15, 18 for deuterium, tritium, (13)C, (15)N, or (18)O), and (x)(V/K), (x)k, and (x)K(eq) are the observed isotope effect, the intrinsic one on the chemical step, and the isotope effect on the equilibrium constant, respectively. The constants c(f) and c(r) are commitments in forward and reverse directions, and are the ratio of the rate constant for the chemical reaction and the net rate constant for release from the enzyme of the varied substrate (direct comparison) or labeled substrate (internal competition and equilibrium perturbation) for c(f), or the first product released or the one involved in the perturbation for c(r). The intrinsic isotope effect, (x)k, can be estimated by comparing deuterium and tritium isotope effects on V/K, or by comparing the deuterium isotope effect with (13)C ones with deuterated and undeuterated substrates. Adding a secondary deuterium isotope effect and its effect on the (13)C one can give an exact solution for all intrinsic isotope effects and commitments. The effect of deuteration on a (13)C isotope effect allows one to tell if the two isotope effects are on the same or different steps. Applications of these methods to several enzyme systems will be presented.     

Influence of water flow on skeletal isotopic composition in the coral Pocillopora damicornis

Fragments of branching Pocillopora damicornis coral colonies were grown in experimental flumes under two water flow regimes. Colony size and buoyant weight increased most rapidly in the fast-flow regime. Branch tips from the upper and outer parts of the colonies showed the lowest and most consistent skeletal oxygen isotope ratios. Flow regime had little influence on the lowest oxygen isotope ratios, which were at least 3.5‰ lighter than the calculated oxygen isotopic equilibrium. These “kinetic” isotope effects are comparable to those observed in Porites corals. Relatively more branch tips showed extreme ¹⁸O depletions under low-flow conditions, and among small coral colonies. Isotopic variability was greater among branch tips from the lower and inner parts of the colonies and at high flow. Skeletal oxygen and carbon isotope ratios generally showed positive correlations. Despite the particularly large offsets from isotopic equilibrium, the isotopically lightest branches showed the greatest isotopic consistency and therefore would make the best isotopic thermometers. Isotopic variability within the colony may provide an indication of flow regime.     

Concerning the procedure of recovering the electron energy distribution function from the soft X-ray spectrum

In the course of experiments on electron-cyclotron resonance heating of plasma in the L-2M stellarator, it was found that, at high specific heating powers, the SXR spectrum was distorted in the entire photon energy range under study (from 1.5 to 15 keV). To determine the character of this distortion, a procedure was proposed for recovering the electron energy distribution function (EEDF) from soft X-ray (SXR) measurements. The SXR spectra were analyzed for different values of the specific heating power. Numerical calculations show that the edge plasma contributes insignificantly to the chord-averaged SXR spectrum. A conclusion is drawn on the applicability and accuracy of the procedure for recovering the EEDF at high specific heating powers.     

Quasi-stationary and ratio of expectations distributions: A comparative study

Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach ( [Darroch and Seneta, 1965] and [Darroch and Seneta, 1967]) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.     

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.     

Fast ignition of an inertial fusion target with a solid noncryogenic fuel by an ion beam

The burning efficiency of a preliminarily compressed inertial confinement fusion (ICF) target with a solid noncryogenic fuel (deuterium-tritium beryllium hydride) upon fast central ignition by a fast ion beam is studied. The main aim of the study was to determine the extent to which the spatial temperature distribution formed under the heating of an ICF target by ion beams with different particle energy spectra affects the thermonuclear gain. The study is based on a complex numerical modeling including computer simulations of (i) the heating of a compressed target with a spatially nonuniform density and temperature distributions by a fast ion beam and (ii) the burning of the target with the initial spatial density distribution formed at the instant of maximum compression of the target and the initial spatial temperature distribution formed as a result of heating of the compressed target by the ion beam. The threshold energy of the igniting ion beam and the dependence of the thermonuclear gain on the energy deposited in the target are determined.