Showing papers in "European Physical Journal D in 2014"

The density matrix renormalization group for ab initio quantum chemistry

Abstract: During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.

Coulomb heating behavior of fast light diclusters thorough the Si ⟨ 110 ⟩ direction: influence of the mean charge state

Abstract: In this work we report on the results for the Coulomb heating of H+ 2, B+ 2 and C+ 2 diclusters traveling in Si 〈 110 ⟩ direction covering an energy range from 200 keV/ion to 2400 keV/ion. Those results were obtained by combining the Rutherford backscattering spectrometry (RBS) and the particle induced X-ray emission (PIXE) techniques. By comparing the present results to those obtained previously for ions traveling in the narrower Si ⟨ 100 ⟩ channel, several common features are observed for the Coulomb heating values; especially, they follow a linear relationship as a function of the stored potential per ion. However, at variance with previous results, it is shown that the use of a Dirac-Hartree-Fock-Slater (DHFS) potential based on the ion mean charge states in amorphous targets leads to a considerable disagreement between the Coulomb heating values and the expected potential energies stored in the dicluster prior to the Coulomb explosion. In order to investigate this problem, a numerical procedure was developed in order to calculate the mean charge state values for ions traveling under channeling conditions. The use of the resulting charge states led to a linear relationship between the Coulomb heating values and the stored potential energy per ion of the diclusters. Moreover, the Coulomb heating/stored potential energy ratio amounts to about 2/3, which is in full agreement with those results obtained for the Si ⟨ 100 ⟩ direction.

Vacuum magnetic linear birefringence using pulsed fields: status of the BMV experiment

Abstract: We present the current status of the BMV experiment. Our apparatus is based on an up-to-date resonant optical cavity coupled to a transverse magnetic field. We detail our data acquisition and analysis procedure which takes into account the symmetry properties of the raw data with respect to the orientation of the magnetic field and the sign of the cavity birefringence. The measurement result of the vacuum magnetic linear birefringence k_\mathrm{CM}$ presented in this paper was obtained with about 200 magnetic pulses and a maximum field of 6.5\,T, giving a noise floor of about $8 \times 10^{-21}$\,T$^{-2}$ at $3\sigma$ confidence level.

Multiscale approach to the physics of radiation damage with ions

Abstract: The multiscale approach to the assessment of biodamage resulting upon irradiation of biological media with ions is reviewed, explained and compared to other approaches. The processes of ion propagation in the medium concurrent with ionization and excitation of molecules, transport of secondary products, dynamics of the medium, and biological damage take place on a number of different temporal, spatial and energy scales. The multiscale approach, a physical phenomenon-based analysis of the scenario that leads to radiation damage, has been designed to consider all relevant effects on a variety of scales and develop an approach to the quantitative assessment of biological damage as a result of irradiation with ions. Presently, physical and chemical effects are included in the scenario while the biological effects such as DNA repair are only mentioned. This paper explains the scenario of radiation damage with ions, overviews its major parts, and applies the multiscale approach to different experimental conditions. On the basis of this experience, the recipe for application of the multiscale approach is formulated. The recipe leads to the calculation of relative biological effectiveness.

Applied Bohmian mechanics

Abstract: Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics to address practical problems, rather than on its interpretation. Although the Bohmian and standard quantum theories have different formalisms, both give exactly the same predictions for all phenomena. Fifteen years ago, the quantum chemistry community began to study the practical usefulness of Bohmian mechanics. Since then, the scientific community has mainly applied it to study the (unitary) evolution of single-particle wave functions, either by developing efficient quantum trajectory algorithms or by providing a trajectory-based explanation of complicated quantum phenomena. Here we present a large list of examples showing how the Bohmian formalism provides a useful solution in different forefront research fields for this kind of problems (where the Bohmian and the quantum hydrodynamic formalisms coincide). In addition, this work also emphasizes that the Bohmian formalism can be a useful tool in other types of (nonunitary and nonlinear) quantum problems where the influence of the environment or the nonsimulated degrees of freedom are relevant. This review contains also examples on the use of the Bohmian formalism for the many-body problem, decoherence and measurement processes. The ability of the Bohmian formalism to analyze this last type of problems for (open) quantum systems remains mainly unexplored by the scientific community. The authors of this review are convinced that the final status of the Bohmian theory among the scientific community will be greatly influenced by its potential success in those types of problems that present nonunitary and/or nonlinear quantum evolutions. A brief introduction of the Bohmian formalism and some of its extensions are presented in the last part of this review.

Quantum Stirling heat engine and refrigerator with single and coupled spin systems

Abstract: We study the reversible quantum Stirling cycle with a single spin or two coupled spins as the working substance. With the single spin as the working substance, we find that under certain conditions the reversed cycle of a heat engine is NOT a refrigerator, this feature holds true for a Stirling heat engine with an ion trapped in a shallow potential as its working substance. The efficiency of quantum Stirling heat engine can be higher than the efficiency of the Carnot engine, but the performance coefficient of the quantum Stirling refrigerator is always lower than its classical counterpart. With two coupled spins as the working substance, we find that a heat engine can turn to a refrigerator due to the increasing of the coupling constant, this can be explained by the properties of the isothermal line in the magnetic field-entropy plane.

Bounds on quantum multiple-parameter estimation with Gaussian state

Abstract: We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state. Finally, we give some examples to show the utility of our analytical results.

Open quantum systems and Dicke superradiance

Abstract: We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system and also in a two-level system if the coupling W to the environment is complex and sufficiently large. Here nonlinearities occur. When W ij is imaginary, two singular (exceptional) points may exist. In the parameter range between these two points, width bifurcation occurs as function of a certain external parameter. A unitary representation of the S matrix allows to calculate the cross section for a two-level system, including at the exceptional point (double pole of the S matrix). The results obtained for the transition of level repulsion at small (real) W ij to width bifurcation at large (imaginary) W ij show qualitatively the same features that are observed experimentally in the transition from Autler-Townes splitting to electromagnetically induced transparency in optics. Fermi’s golden rule holds only below the dynamical phase transition while it passes into an anti-golden rule beyond this transition. The results are generic and can be applied to the response of a complex open quantum system to the action of an external field (environment). They may be considered as a guideline for engineering and manipulating quantum systems in such a way that they can be used for applications with special requirements.

Fluid simulations of ion scale plasmas with weakly distorted magnetic fields - FLR-Landau fluid simulations

Abstract: Three-dimensional simulations of turbulence in collisionless plasmas are presented, using a fluid model that extends the anisotropic MHD to scales of the order of the ion gyroradius and below in directions perpendicular to the ambient magnetic field. This model, which includes linear Landau damping and finite Larmor radius corrections to all the retained moments, provides an efficient tool to describe Alfvenic turbulence in the absence of cyclotron resonance. When sufficiently small scales are retained, no artificial damping nor collisional effects is required. Simulations with large-scale Alfvenic driving show the development of perpendicular power-law spectra (taken at zero parallel wavenumber) with an exponent close to -2.8 for the perpendicular magnetic field at scales smaller than the ion inertial length. The electric field spectrum displays a break at intermediate scales, consistent with Solar Wind observations. These spectra appear in a quasi-stationary state after early-formed sheet-like density and current structures have evolved into filaments. In the presence of temperature anisotropy, the nonlinear development of the mirror instability leads to pressure-balanced magnetic structures surrounded by significant ion velocity fields perpendicular to the ambient field. At later time, the system becomes turbulent, with the disruption of the magnetic structures into parallel filaments.

Laser selective spectromicroscopy of myriad single molecules: tool for far-field multicolour materials nanodiagnostics

Abstract: In this Colloquium, we discuss the main principles, achievements and perspectives in the field of highly parallel luminescence spectroscopy and imaging of single molecules (SM) in transparent solids. Special attention will be given to SM detection at low temperatures, where ultranarrow and bright zero-phonon lines (ZPL) of emitting centres are achievable for observation. Frequency of ZPL can be used as an additional property for separation of multiple SM images within diffraction limited volume, thus realising “multicolour” super-resolution microscopy. The extreme sensitivity of ZPL parameters to SM local environment allows application of SM spectromicroscopy for the study of structure and dynamics of doped solids on the nanometre scale. We show that the way to “bridge” the accidental rare events detected by SM probes to general material properties is a statistical analysis of spectral-spatial data obtained by a separated detection of all effectively fluorescing dye centres in a bulk sample. First experimental realisation of three-dimensional phononless luminescence SM spectromicroscopy with modification of SM point-spread function is demonstrated.

Ultrasensitive 3He magnetometer for measurements of high magnetic fields

Abstract: We describe a 3He magnetometer capable to measure high magnetic fields (B> 0.1 T) with a relative accuracy of better than 10-12. Our approach is based on the measurement of the free induction decay of gaseous, nuclear spin polarized 3He following a resonant radio frequency pulse excitation. The measurement sensitivity can be attributed to the long coherent spin precession time T2 ∗ being of order minutes which is achieved for spherical sample cells in the regime of “motional narrowing” where the disturbing influence of field inhomogeneities is strongly suppressed. The 3He gas is spin polarized in situ using a new, non-standard variant of the metastability exchange optical pumping. We show that miniaturization helps to increase T2 ∗ further and that the measurement sensitivity is not significantly affected by temporal field fluctuations of order 10-4.

Gas breakdown and secondary electron yields

Abstract: In this paper we present a systematic study of the gas breakdown potentials. An analysis of the key elementary processes in low-current low-pressure discharges is given, with an aim to illustrate how such discharges are used to determine swarm parameters and how such data may be applied to modeling discharges. Breakdown data obtained in simple parallel-plate geometry are presented for a number of atomic and molecular gases. Ionization coefficients, secondary electron yields and their influence on breakdown are analyzed, with special attention devoted to non-hydrodynamic conditions near cathode.

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

Abstract: The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.

Semiclassical Vlasov and fluid models for an electron gas with spin effects

Abstract: We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.

Electron swarm transport in THF and water mixtures

Abstract: The transport coefficients of electrons in mixtures of gaseous water and tetrahydrofuran (THF) are calculated using a multi-term solution of the Boltzmann equation. Electron transport coefficients at room temperature are presented over a range of reduced electric fields from 0.1–1000 Td, with significant differences between the behaviour in pure water and pure THF being found. The influence of the water to THF mixture ratio on the calculated transport coefficients is also presented.

Overview of recent advances in treatment planning for ion beam radiotherapy

Abstract: To achieve practical calculations of dose delivery in ion beam radiotherapy, the physical models of beam propagation need to be properly implemented and supplemented by models describing the complex mechanisms of radiation damage in the biological tissues. TRiP98 is the first and most advanced treatment planning system for particles, in which physical and biological models have been incorporated to develop a clinically applicable tool for dose optimization and delivery. We report our recent advances in TRiP98 code development, in particular towards hypoxia-driven and multi-modal dose optimization. We also discuss the present needs and possible extensions of our models for which input from nanoscale physics is required.

Analysis of intermittent heating in a multi-component turbulent plasma

Abstract: Kinetic effects and turbulence are two phenomena that characterize the solar wind, and, therefore, kinetic models represent the best tool of investigation for this collisionless plasma. In this work, hybrid Vlasov-Maxwell simulations are performed to investigate the intermittent heating of the solar wind, in a two-dimensional multi-ion plasma composed by protons, alpha particles and fluid electrons. The numerical results show that particle distribution functions depart from the typical Maxwellian configuration under the effect of the turbulence. Both ion species develop temperature anisotropy, with respect to the local magnetic field, that increases during the development of the turbulent cascade. During the nonlinear evolution of the system, coherent structures (vortices and current sheets) appear in physical space, related to the intermittent nature of the magnetic field. Conditioned ion temperature distributions suggest that enhancements of ion temperatures are associated with stronger coherent structures, in agreement with recent solar wind data analyses.

Time and spatial resolved optical and electrical characteristics of continuous and time modulated RF plasmas in contact with conductive and dielectric substrates

Abstract: Cold atmospheric pressure plasma jets are often used as a remote plasma source for substrate treatments. However, this substrate acts as an electrode and this additional electrode can induce effects on plasma parameters such as the dissipated power, gas temperature, etc. In this work the influence of substrates of different conductivity and permittivity in direct contact with three different operational modes of atmospheric pressure RF plasma jets is investigated. Two different electrode configurations (creating either a linear or a cross electric field) and, for the linear field configuration, two voltage modulations (continuous RF and kHz pulsed RF) have been studied. Electrical and optical diagnostic methods have been performed in order to get quantitative data of the change in plasma dissipated power and gas temperature, when the plasma is in direct contact with the substrate. In all three investigated cases the power dissipation and gas temperature, significantly increase when the plasma is in direct contact with a conductive substrate. The increase of power is attributed to a change of the equivalent electrical circuit, leading to a more favourable matching between the power input and the plasma source.

Plasmid DNA damage induced by helium atmospheric pressure plasma jet

Abstract: A helium atmospheric pressure plasma jet (APPJ) is applied to induce damage to aqueous plasmid DNA. The resulting fractions of the DNA conformers, which indicate intact molecules or DNA with single- or double-strand breaks, are determined using agarose gel electrophoresis. The DNA strand breaks increase with a decrease in the distance between the APPJ and DNA samples under two working conditions of the plasma source with different parameters of applied electric pulses. The damage level induced in the plasmid DNA is also enhanced with increased plasma irradiation time. The reactive species generated in the APPJ are characterized by optical emission spectra, and their roles in possible DNA damage processes occurring in an aqueous environment are also discussed.

Non-classical plasma sheaths: space-charge-limited and inverse regimes under strong emission from surfaces

Abstract: The collisionless plasma sheath represents an important example of Vlasov theory application. In this study, Particle-in-Cell/Monte Carlo Collision methodology has been used to study different examples of plasma sheaths under strong negative charge emission from surface. Secondary electrons emitted by primary electrons (acceleration region of Hall-effect discharge) and by photons (dusty plasma) are responsible for a complete inverse sheath: the potential monotonically increases toward a positively charged wall that is shielded by a single layer of negative charge. No ion-accelerating presheath exists in the bulk plasma region and the ion flux at the wall is zero. In the case of production of hydrogen negative ions by neutral conversion on the plasma grid in the extraction region of a negative ion source, a space-charge-limited regime occurs with the formation of a non-monotonic double layer in front of the grid.

Electron impact fragmentation of cytosine: partial ionization cross sections for positive fragments

Abstract: We have measured mass spectra for positive ions produced by low-energy electron impact on cytosine using a reflectron time-of-flight mass spectrometer. The electron impact energy has been varied from 0 to 100 eV in steps of 0.5 eV. Ion yield curves of most of the fragment ions have been determined by fitting groups of adjacent peaks in the mass spectra with sequences of normalized Gaussians. The ion yield curves have been normalized by comparing the sum of the ion yields to the average of calculated total ionization cross sections. Appearance energies of the fragment ions have been determined, showing that the fragments 68 u–84 u have appearance energies between 10 and 11 eV, whereas fragments of 55 u and lower mass all have appearance energies above 12 eV. Most of the ion yields of 55 u and smaller show multiple onsets. Several groups of fragments have ion yield curves with nearly the same shape, clearly indicating the relevance of tautomerization in the fragmentation of cytosine.

Maxwell solvers for the simulations of the laser-matter interaction

Abstract: With the advent of high intensity laser beams, solving the Maxwell equations with a free-dispersive algorithm is becoming essential. Several Maxwell solvers, implemented in Particle-In-Cell codes, have been proposed. We present here some of them by describing their computational stencil in two-dimensional geometry and defining their stability area as well as their numerical dispersion relation. Numerical simulations of Backward Raman amplification and laser wake-field are presented to compare these different solvers.

Dissociative electron attachment to titatinum tetrachloride and titanium tetraisopropoxide

Abstract: Here we present a dissociative electron attachment study of titanium tetrachloride and titanium tetraisopropoxide in the incident electron energy range from about 0–18 eV The results are compared to electron impact ionization and fragmentation of these compounds and discussed in relation to the role of secondary electrons in focused electron beam induced deposition We also use the opportunity and describe in detail a recently constructed crossed beam apparatus for the study of the energy dependency of ion formation in low energy electron interaction with gas phase molecules

Recent positron-atom cross section measurements and calculations

Abstract: We review recent cross section results for low-energy positron scattering from atomic targets. A comparison of the latest measurements and calculations for positron collisions with the noble gases and a brief update of the newest studies on other atoms is presented. In particular, we provide an overview of the cross sections for elastic scattering, positronium formation, direct and total ionisation, as well as total scattering, at energies typically between about 0.1 and a few hundred eV. We discuss the differences in the current experimental data sets and compare those results to the available theoretical models. Recommended data sets for the total cross section are also reported for each noble gas. A summary of the recent developments in the scattering from other atoms, such as atomic hydrogen, the alkali and alkaline-earth metals, and two-electron systems is finally provided.

Effects of rotation in the energy spectrum of C60

Abstract: In this paper, motivated by the experimental evidence of rapidly rotating C60 molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static C60 are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

Abstract: We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of N n “nuclei” and N e “electrons” We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view

Influence of water conductivity on particular electrospray modes with dc corona discharge — optical visualization approach

Abstract: The effect of water conductivity on electrospraying of water was studied in combination with positive DC corona discharge generated in air. We used a point-to-plane geometry of electrodes with a hollow syringe needle anode opposite to the metal mesh cathode. We employed total average current measurements and high-speed camera fast time-resolved imaging. We visualized the formation of a water jet (filament) and investigated corona discharge behavior for various water conductivities. Depending on the conductivity, various jet properties were observed: pointy, prolonged, and fast spreading water filaments for lower conductivity; in contrast to rounder, broader, and shorter quickly disintegrating filaments for higher conductivity. The large acceleration values (4060 m/s2 and 520 m/s2 for 2 μS/cm and 400 μS/cm, respectively) indicate that the process is mainly governed by the electrostatic force. In addition, with increasing conductivity, the breakdown voltage for corona-to-spark transition was decreasing.

Differential and integral electron scattering cross sections from tetrahydrofuran (THF) over a wide energy range: 1–10 000 eV

Abstract: Total, integral inelastic and integral and differential elastic cross sections have been calculated with the screening-corrected additivity rule (SCAR) method based on the independent atom model (IAM) for electron scattering from tetrahydrofuran (THF). Since the permanent dipole moment of THF enhances rotational excitation particularly at low energies and for small angles, an estimate of the rotational excitation cross section was also computed by assuming the interaction with a free electric dipole as an independent, additional process. Our theoretical results compare very favourably to the existing experimental data. Finally, a self-consistent set of integral and differential interaction CSs for the incident energy range 1 eV–10 keV is established for use in our low energy particle track simulation (LEPTS). All cross section data are supplied numerically in tabulated form.

Enhancing Bremsstrahlung production from ultraintense laser-solid interactions with front surface structures

Abstract: We report the results of a combined study of particle-in-cell and Monte Carlo modeling that investigates the production of Bremsstrahlung radiation produced when an ultraintense laser interacts with a tower-structured target. These targets are found to significantly narrow the electron angular distribution as well as produce significantly higher energies. These features combine to create a significant enhancement in directionality and energy of the Bremstrahlung radiation produced by a high-Z converter target. These studies employ short-pulse, high intensity laser pulses, and indicate that novel target design has potential to greatly enhance the yield and narrow the directionality of high energy electrons and γ-rays. We find that the peak γ-ray brightness for this source is 6.0 × 1019 s−1 mm−2 mrad−2 at 10 MeV and 1.4 × 1019 s−1 mm−2 mrad-2 at 100 MeV (0.1% bandwidth).

Temperature-and airflow-related effects of ozone production by surface dielectric barrier discharge in air

Abstract: Discharge ozone production depends on different quantities and the effect of one quantity on this process cannot be separated from the effects of other quantities. Thus the temperature influences the reaction rates of individual reactions involved in ozone generation and destruction, the thermodynamic properties, and the density of the feeding gas. The density of the feeding gas influences the reduced electric field, which affects ionization of the gas, production of electrons and consequently the electrical parameters of the discharge. Taking into account these considerations we investigated the effect of temperature and various arrangements of the input and output of the feeding gas to and from the discharge chamber together with related changes of electrical parameters of the surface dielectric barrier discharge on its ozone production for the temperatures in which commercial ozone generators function. We found that if the temperature of air at the output from the discharge chamber is increased from 15.0 ± 0.5 to 25.0 ± 0.5 °C, the discharge ozone production and peak discharge voltage decrease. Both the discharge ozone production and the peak discharge voltage are also affected by the way in which the feeding air is supplied to and leaves the discharge chamber. We also showed that for all ways in which the feeding air is supplied to and leaves the discharge chamber the discharge nitrogen dioxide production follows the same trends as discharge ozone production.