Number Density Ratio Research Articles

Nonlinear Ion Acoustic Waves in Multicomponent Plasmas with Nonthermal Electrons-positron and Bipolar Ions

Abstract This paper studied the propagating characteristics of (2+1) dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons, positrons and bipolar ions. The dispersion relations are initially explored by using the small amplitude wave's dispersion relation. Then, the Sagdeev potential method is employed to study large amplitude ion acoustic waves. The analysis involves examining the system's phase diagram, Sagdeev potential function, and solitary wave solutions through numerical solution of an analytical process in order to investigate the propagation properties of nonlinear ion acoustic waves under various parameters. It is found that the propagation of nonlinear ion acoustic waves is subject to the influence of various physical parameters, including the ratio of number densities between the unperturbed positrons, electrons to positive ions, nonthermal parameters, the masses ratio of positive ions to negative ions, and the charge numbers ratio of negative ions to positive ions, the ratio of the electrons’ temperature to positrons’ temperature. In addition, the multicomponent plasma system has a compressive solitary waves with amplitude greater than zero or a rarefactive solitary waves with amplitude less than zero, in the meantime, compressive and rarefactive ion acoustic wave characteristics depend on the charge numbers ratio of negative ions to positive ions.

Soliton interaction in a two-temperature electron plasma with trapping and superthermality effects

Head-on collision of the two small-amplitude electron-acoustic (EA) solitons is studied in an unmagnetized collisionless plasma in the presence of superthermal (hot) trapped electrons. For this purpose, using a well-known extended Poincare–Lighthill–Kuo (PLK) method, a pair of the trapped Korteweg–de Vries (tKdV) equations is derived to investigate the soliton trajectories and phase shifts. The latter are found dependent on amplitudes of the interacting solitons, effectively altering with hot-electron superthermality and plasma parameters. Typical parameters for the electron diffusion region (EDR) and day-side auroral zone have been selected to examine the impact of hot-electron superthermality, trapping parameter, hot-to-cold electron number density ratio, and cold-to-hot electron temperature ratio on the profiles of potential excitations and phase shifts of interacting solitons. It is found that phase speed of the EA waves becomes altered by varying the κ–parameter, strongly modifying the nonlinearity and dispersive coefficients in a superthermal trapped plasma. However, particle trapping phenomenon does not affect the linear phase speed but introduces a fractional nonlinearity in the tKdV equations of two interacting solitons. The impact of the adiabatic and isothermal pressures is also highlighted to show new modifications in the propagation characteristics of two interacting solitons.

Dust particle surface potential in an argon-helium plasma using the (r,q)-distribution function

Abstract In this paper, the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law r , q -distribution function. Recent studies have reported the argon-helium plasma and conducted a brief theoretical and experimental survey. To deepen our understanding further, this study aims to analyze the argon-helium plasma comprehensively using the same pattern but with the r , q -distribution function. For this purpose, the current balance equations are derived for electron, helium and argon ions, when these charge species attain the quasineutrality condition. We numerically examined the currents of plasma species for a broad range of effective distribution function parameters r and q . It is revealed that the surface potential of dust particles is significantly affected by the parameters r and q , helium ion-to-electron temperature ratio, argon ion-to-electron temperature ratio, and helium ion to argon ion number density ratio. By incorporating the multi-ion (argon-helium) species, the significance of low-temperature non-Maxwellian dusty (complex) plasma is briefly examined.

Shear-induced phase behavior of bidisperse jammed suspensions of soft particles

Particle dynamics simulations are used to determine the shear-induced microstructure and rheology of jammed suspensions of soft particles. These suspensions, known as soft particle glasses (SPGs), have an amorphous structure at rest but transform into ordered phases in strong shear flow when the particle size distribution is relatively monodisperse. Here, a series of bidisperse SPGs with different particle radii and number density ratios are considered, and their shear-induced phase diagrams are correlated with the macroscopic rheology at different shear rates and volume fractions. These shear-induced phase diagrams reveal that a combination of these parameters can lead to the emergence of various microstructures such as amorphous, layered, crystals, and in some cases, coexistence of amorphous and ordered phases. The evolution of the shear stress is correlated with the change in the microstructure and is a shear-activated process. Stress shows pseudo-steady behavior during an induction period before the final microstructural change leading to the formation of ordered structures. The outcomes provide a promising method to control the phase behavior of soft suspensions and build new self-assembled microstructures.

Electron acoustic solitary waves in relativistically quantum magnetoplasmas with electron exchange correlation effects

The propagating of electron acoustic solitary waves (EASWs) in relativistically magnetized quantum plasmas which consists inertial cold electrons, inertialess hot electrons and stationary background ions have been theoretically investigated. The modified Zakharov-Kuznetsov (ZK) equation is derived by adopting the standard reductive perturbation method to describe the nonlinear evolution of the EASWs. After discussing the effects of various parameter values on the solitary structures, it is shown that the solitary structures are very sensitive to the relativistic degeneracy effect, the cold to hot electrons number density ratio and the electron exchange correlation effects. The numerical analysis can be well described by the existing analytical theory. Our results may be useful in explaining the physics behind the formation of the EASWs in both astrophysical and laboratory plasmas.

Effect of Different Calcium and Magnesium Treatments on the Evolution of Nonmetallic Inclusions in AH36 Ship Plate Steel

Comprehensive thermodynamic calculations and high‐temperature experiments are performed to systematically evaluate the effect of calcium and magnesium additions on the modification and control of inclusions in AH36 ship plate steel. The results show that Al2O3 or MgAl2O4 inclusions are formed under the casting temperature conditions. Calcium treatment modifies the inclusions into calcium aluminate, of which components partially fall into the liquidus region, and the aspect ratio and number density of inclusions became smaller, avoiding nozzle clogging, but the inclusions are easy to gather and grow up, which would affect the steel properties. Magnesium treatment modifies the inclusions into dispersed magnesium‐aluminum spinel with small size. However, the number density and aspect ratio of inclusions increase, as well as the melting points of inclusions are high, which would easily cause nozzle clogging. When calcium–magnesium synergistic treatment, with the increase of magnesium proportion, the inclusions types increased, and the liquidus area of inclusions became narrower until it disappeared. Synergistic treatment with more calcium and less magnesium (Ca2Mg1) is optimal since the inclusions were fine and diffuse, and the corresponding liquidus area of inclusions is wider than the calcium treatment.

Nonthermal Acceleration of Electrons, Positrons, and Protons at a Nonrelativistic Quasi-parallel Collisionless Shock

Energetic positrons have been observed in the interstellar medium, and high-energy positrons with relativistic energies up to approximately 1 TeV have been detected in Galactic cosmic rays. We conducted a study on the acceleration of particles, specifically positrons, in a nonrelativistic quasi-parallel collisionless shock induced by a plasma consisting of protons, electrons, and positrons. The positron-to-proton number density ratio in the plasma is 0.1. We focused on a representative shock with a sonic Mach number of 17.1 and an Alfvénic Mach number of 16.8 in the rest frame of the shock. To investigate the acceleration mechanisms of particles including positrons in the shock, we utilized 1D particle-in-cell simulations. It was found that all three species of particles in the shock can be accelerated and exhibit power-law spectra. At the shock front, a significant portion of incoming upstream particles are reflected and undergo significant energy increases, and these reflected particles can be efficiently injected into the process of diffusive shock acceleration (DSA). Moveover, the reflected positrons can be further accelerated by an electric field parallel to the magnetic field when they move along the magnetic field upstream of the shock. As a result, positrons can be preferentially accelerated to be injected in the DSA process compared to electrons.

An overview of ion-acoustic solitary and shock waves in a magnetized nonthermal plasma: influence of trapped positrons and electrons

A magnetized nonthermal electron–positron-ion (e-p-i) plasma is considered to study the propagation properties of ion-acoustic solitary and shock waves in the presence of trapped positrons and electrons for the first time. The Schamel-κ (kappa) distribution function that describes plasma nonthermality and particle trapping is assumed to consider electrons and positrons. The diffusive effect of ion plasma fluid, which is responsible for shock dynamics, is taken into account. A nonlinear Schamel-Korteweg–de Vries-Burgers’ (SKdVB) equation is derived by employing the reductive perturbation approach, and the solitary and shock wave solutions of the SKdVB equation have also been derived for different limiting cases. It is found that only positive potential nonlinear structures (for both solitary and shock waves) are formed in the proposed plasma system. The condition for stable solitons in the absence of dissipation is analyzed, and the nature of arbitrary amplitude solitary waves (obtained via the Sagdeev potential approach) is discussed. It is found through theoretical and numerical investigation that different plasma compositional parameters (such as the trapping effect of electrons (β e ) and positrons (β p ), the obliquity effect (θ), electron-to-ion number density ratio (µ e ), the magnetic field effect (via Ω) and the viscous effect (via η)) have a significant influence on the dynamics of ion-acoustic solitary and shock waves. The theoretical and numerical investigations in this study may be helpful in describing the nature of localized structures in different plasma contexts, e.g. space and astrophysical plasmas and experimental plasmas where electron–positron-ion plasmas exist.

Landau damping effects on dust ion-acoustic solitary waves in a nonthermal pair-ion plasma

The Landau damping effects on the nonlinear propagation of dust ion-acoustic solitary waves (DIASWs) are studied in an electron-free unmagnetized collisionless dusty pair-ion plasma. The two species of nonthermal ions (positive and negative) are described by the kinetic Vlasov equations, whereas the massive charged dust grains form only the background plasma. Using the multi-scale reductive perturbation technique generalized for the applications to the Vlasov equation, we derive a modified Korteweg–de Vries (KdV) equation that governs the evolution of DIASWs with the effects of linear resonance, in particular, linear Landau damping. The properties of the phase velocity and the Landau damping rate of DIASWs are studied with the effects of positive and negative-ion nonthermality parameters ( α p , α n ), the ratios of the positive to negative ion masses (m) and temperatures (T) as well as the dust to negative-ion number density ratio (δ). It is found that, depend on the degree of positive to negative ion mass ratios (m), both of damped and growing oscillations occur in a collisionless dusty pair-ion plasma due to the resonance phenomena between the wave and the nonthermal particles of the system. The properties of the decay rates of the amplitude of the KdV soliton with a small effect of Landau damping are also studied with the above system of parameters. The results may be useful for understanding the localization of solitary pulses and associated resonance damping and/or growing oscillations of the wave in laboratory and space plasmas, in which the number density of free electrons is much smaller than that of ions and highly charged heavy, micron seized dust grains.

Multi-tracer power spectra and bispectra: formalism

The power spectrum and bispectrum of dark matter tracers are key and complementary probes of the Universe. Next-generation surveys will deliver good measurements of the bispectrum, opening the door to improved cosmological constraints and the breaking of parameter degeneracies, from the combination of the power spectrum and bispectrum. Multi-tracer power spectra have been used to suppress cosmic variance and mitigate the effects of nuisance parameters and systematics. We present a bispectrum multi-tracer formalism that can be applied to next-generation survey data. Then we perform a simple Fisher analysis to illustrate qualitatively the improved precision on primordial non-Gaussianity that is expected to come from the bispectrum multi-tracer. In addition, we investigate the parametric dependence of conditional errors from multi-tracer power spectra and multi-tracer bispectra, on the differences between the biases and the number densities of two tracers. Our results suggest that optimal constraints arise from maximising the ratio of number densities, the difference between the linear biases, the difference between the quadratic biases, and the difference between the products b 1 b Φ for each tracer, where b Φ is the bias for the primordial potential.

Radial Evolution of the Near-Sun Solar Wind: Parker Solar Probe Observations

Abstract A statistical study of the radial evolution of the solar wind within 0.3 au is shown in this Letter based on Parker Solar Probe observations. We show the radial distribution of the main solar wind parameters, including the solar wind speed V sw, magnetic field ∣B∣, the number density of electrons N e , protons N p , and α particles N α , and the temperature of protons T p and α particles T α . The power-law fitting results of these parameters in the near-Sun solar wind are compared with previous radial models. We also show the radial distribution of the angle between the magnetic field B , solar wind V sw, and radial vector R . In the solar wind within 0.3 au, θ BV sw , and θ BR mainly concentrate around 135°, and θ RV sw almost concentrates in the region less than 20°. Furthermore, we also present the radial distribution of the relative values between the solar wind parameters, including the electric neutrality estimation ((2 × N α + N p )/N e ≃ 1 within 0.2 au), relative number density ratio (N α /N p ≃ 0.02 in slow solar wind and N α /N p ≃ 0.04 in faster solar wind), relative temperature ratio (T α /T p decreases with the increase of heliocentric distance and its decay rate is larger in faster solar wind), and differential speed (both V α − V p and (V α − V p )/V A are larger in the faster solar wind and decrease as heliocentric distance increases).

A linear parameters study of ion cyclotron emission using drift ring beam distribution

Ion Cyclotron Emission (ICE) holds great potential as a diagnostic tool for fast ions in fusion devices. The theory of Magnetoacoustic Cyclotron Instability (MCI), as an emission mechanism for ICE, states that MCI is driven by a velocity distribution of fast ions that approximates to a drift ring beam. In this study, the influence of key parameters (velocity spread of the fast ions, number density ratio, and instability propagation angle) on the linear MCI is systematically investigated using the linear kinetic dispersion relation solver BO (Xie 2019 Comput. Phys. Commun. 244 343). The computational spectra region considered extends up to 40 times the ion cyclotron frequency. By examining the influence of these key parameters on MCI, several novel results have been obtained. In the case of MCI excited by super-Alfvénic fast ions (where the unique perpendicular speed of fast ion is greater than the perpendicular phase velocity of the fast Alfvén waves), the parallel velocity spread significantly affects the bandwidth of harmonics and the continuous spectrum, while the perpendicular velocity spread has a decisive effect on the MCI growth rate. As the velocity spread increases, the linear relationship between the MCI growth rate and the square root of the number density ratio transitions to a linear relationship between the MCI growth rate and the number density ratio. This finding provides a linear perspective explanation for the observed linear relation between fast ion number density and ICE intensity in JET. Furthermore, high harmonics are more sensitive to changes in propagation angle than low harmonics because a decrease in the propagation angle alters the dispersion relation of the fast Alfvén wave. In the case of MCI excited by sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is less than the perpendicular phase velocity of the fast Alfvén waves), a significant growth rate increase occurs at high harmonics due to the transition of sub-Alfvénic fast ions to super-Alfvénic fast ions. Similarly, for MCI excited by greatly sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is far less than the perpendicular phase velocity of the fast Alfvén waves), the growth rate at high harmonics also experiences a drastic increase compared to the low harmonic, thereby expanding the parameter range of the velocity spread.

How much large dust could be present in hot exozodiacal dust systems?

Context. An infrared excess over the stellar photospheric emission of main-sequence stars has been found in interferometric surveys, commonly attributed to the presence of hot exozodiacal dust (HEZD). While submicrometer-sized grains in close vicinity to their host star have been inferred to be responsible for the found near-infrared excesses, the presence and amount of larger grains as part of the dust distributions are weakly constrained. Aims. We quantify how many larger grains (above-micrometer-sized) could be present in addition to submicrometer-sized grains, while being consistent with observational constraints. This is important in order to distinguish between various scenarios for the origin of HEZD and to better estimate its observational appearance when observed with future instruments. Methods. We extended a model suitable to reproduce current observations of HEZD to investigate a bimodal size distribution. By deriving the characteristics of dust distributions whose observables are consistent with observational limits from interferometric measurements in the K and N bands we constrained the radii of sub- and above-micrometer-sized grains as well as their mass, number, and flux density ratios. Results. In the most extreme cases of some of the investigated systems, large grains ≳10 µm might dominate the mass budget of HEZD while contributing up to 25 % of the total flux density originating from the dust at a wavelength of 2.13 µm and up to 50 % at a wavelength of 4.1 µm; at a wavelength of 11.1 µm their emission might clearly dominate over the emission of small grains. While it is not possible to detect such hot-dust distributions using ALMA, the ngVLA might allow us to detect HEZD at millimeter wavelengths. Conclusions. Large dust grains (above-micrometer-sized) might have a more important impact on the observational appearance of HEZD than previously assumed, especially at longer wavelengths.

The probability of escape of the products of charged particles resulting from thermonuclear fusion of advanced fuels in the hotspot

Establishing fuel ignition conditions depends on the stability of hotspot ignition. Excessive energy escape from the plasma leads to its cooling and shutdown. In this research, the escape probability of charged particles due to the p/11B fuel fusion has been investigated. First, the contribution of p/11B fuel plasma electrons in the Alpha particle energy loss based on the Krokhin and Rozanov (KR) model and then the auxiliary contribution of plasma ions in the Alpha particle energy loss produced in the hotspot of p/11B fuel, based on Li–Petrasso (LP) calculations were analyzed numerically. By calculating the escape fraction of Alpha particles, it has been shown that the contribution of the stopping power of the electrons of the plasma is dominant at both 70 and 170 keV temperatures, which are the starting temperature of the p/11B fuel reaction and the proper ignition temperature, respectively. By increasing the density of p/11B fuel from 300 to 400 g/cc, it can be seen that at a temperature of 70 keV, the penetration depth of Alpha particles decreases from 1200 to 900 μm based on the KR model. It has also been shown that by reducing the number density ratio of boron to protons from 0.3 to 0.2 and 0.1, due to the reduction of the coupling of electrons and ions, which leads to the reduction of collisions with Alpha particles, the stopping length of Alpha particles increases.

Large amplitude dust-acoustic solitary waves and double layers in nonthermal warm complex plasmas

Using a Sagdeev pseudo-potential approach, where the nonlinear structures are stationary in a comoving frame, the arbitrary or large amplitude dust-acoustic solitary waves and double layers have been studied in dusty plasmas containing warm positively charged dust and nonthermal distributed electrons and ions. Depending on the values of the critical Mach number, which varies with the plasma parameter, both supersonic and subsonic dust-acoustic solitary waves are found. It is found that our plasma system under consideration supports both positive and negative supersonic solitary waves and only positive subsonic solitary waves and negative double layers. The parametric regimes for the existence of subsonic and supersonic dust-acoustic waves and how the polarity of solitary waves changes with plasma parameters are shown. It is observed that the solitary wave and double layer solutions exist at the values of Mach number around its critical Mach number. The basic properties (amplitude, width, speed, etc.) of the solitary pulses and double layers are significantly modified by the plasma parameters (viz., ion to positive dust number density ratio, ion to electron temperature ratio, nonthermal parameter, and positive dust temperature to ion temperature ratio). The applications of our present work in space environments (viz., cometary tails, Earth’s mesosphere, and Jupiter’s magnetosphere) and laboratory devices, where nonthermal ion and electron species along with positively charged dust species have been observed, are briefly discussed.

Dissociative Recombination of Rotationally Cold OH+ and Its Implications for the Cosmic Ray Ionization Rate in Diffuse Clouds

Observations of OH+ are used to infer the interstellar cosmic ray ionization rate in diffuse atomic clouds, thereby constraining the propagation of cosmic rays through and the shielding by interstellar clouds, as well as the low energy cosmic ray spectrum. In regions where the H2-to-H number density ratio is low, dissociative recombination (DR) is the dominant destruction process for OH+ and the DR rate coefficient is important for predicting the OH+ abundance and inferring the cosmic ray ionization rate. We have experimentally studied DR of electronically and vibrationally relaxed OH+ in its lowest rotational levels, using an electron–ion merged-beams setup at the Cryogenic Storage Ring. From these measurements, we have derived a kinetic temperature rate coefficient applicable to diffuse cloud chemical models, i.e., for OH+ in its electronic, vibrational, and rotational ground level. At typical diffuse cloud temperatures, our kinetic temperature rate coefficient is a factor of ∼5 times larger than the previous experimentally derived value and a factor of ∼33 times larger than the value calculated by theory. Our combined experimental and modeling results point to a significant increase for the cosmic ray ionization rate inferred from observations of OH+ and H2O+, corresponding to a geometric mean of (6.6 ± 1.0) × 10−16 s−1, which is more than a factor of 2 larger than the previously inferred values of the cosmic ray ionization rate in diffuse atomic clouds. Combined with observations of diffuse and dense molecular clouds, these findings indicate a greater degree of cosmic ray shielding in interstellar clouds than has been previously inferred.

Near-Sun In Situ and Remote-sensing Observations of a Coronal Mass Ejection and its Effect on the Heliospheric Current Sheet

During the thirteenth encounter of the Parker Solar Probe (PSP) mission, the spacecraft traveled through a topologically complex interplanetary coronal mass ejection (ICME) beginning on 2022 September 5. PSP traversed through the flank and wake of the ICME while observing the event for nearly two days. The Solar Probe ANalyzer and FIELDS instruments collected in situ measurements of the plasma particles and magnetic field at ∼13.3 R S from the Sun. We observe classical ICME signatures, such as a fast-forward shock, bidirectional electrons, low proton temperatures, low plasma β, and high alpha particle to proton number density ratios. In addition, PSP traveled through two magnetic inversion lines, a magnetic reconnection exhaust, and multiple sub-Alfvénic regions. We compare these in situ measurements to remote-sensing observations from the Wide-field Imager for Solar PRobe Plus instrument on board PSP and the Sun Earth Connection Coronal and Heliospheric Investigation on the Solar Terrestrial Relations Observatory. Based on white-light coronagraphs, two CMEs are forward modeled to best fit the extent of the event. Furthermore, Air Force Data Assimilative Flux Transport magnetograms modeled from Global Oscillation Network Group magnetograms and Potential Field Source Surface modeling portray a global reconfiguration of the heliospheric current sheet (HCS) after the CME event, suggesting that these eruptions play a significant role in the evolution of the HCS.

Separate and joint clustering characteristics of large-Stokes-number sprays subjected to turbulent co-flows

Separate and joint droplets, clusters, and voids characteristics of sprays injected in a turbulent co-flow are investigated experimentally. Simultaneous Mie scattering and interferometric laser imaging for droplet sizing along with separate hotwire anemometry are performed. The turbulent co-flow characteristics are adjusted using zero, one or two perforated plates. The Taylor-length-scale-based Reynolds number varies from 10 to 38, and the Stokes number estimated based on the Kolmogorov time scale varies from 3 to 25. The results show that the mean length scale of the clusters normalized by the Kolmogorov length scale varies linearly with the Stokes number. However, the mean void length scale is of the order of the integral length scale. It is shown that the number density of the droplets inside the clusters is approximately 7 times larger than that in the voids. The ratios of the droplets number densities in the clusters and voids to the total number density are independent of the test conditions and equal 5.5 and 0.8, respectively. The joint probability density function of the droplets diameter and clusters area shows that the droplets with the most probable diameter are found in the majority of the clusters. It is argued that intensifying the turbulence broadens the range of turbulent eddy size in the co-flow which allows for accommodating droplets with a broad range of diameters in the clusters. The results are of significance for engineering applications that aim to modify the clustering characteristics of large-Stokes-number droplets sprayed into turbulent co-flows.

Vertical Structure of the Milky Way Disk with Gaia DR3

Using a complete sample of about 330,000 dwarf stars, well measured by Gaia DR3, limited to the galactic north and south solid angles |b|<75° and up to a vertical distance of 2 kpc, we analyze the vertical structure of the Milky Way stellar disks, based on projected tangential velocities. From selected subsamples dominated by their corresponding population, we obtain the thin and thick disk scale heights as hZ=279.76±12.49 pc and HZ=797.23±12.34 pc, respectively. Then from the simultaneous fitting of the sum of two populations over the whole sample, assuming these scale heights, we estimate the thick-to-thin disk number density ratio at the galactic plane to be ρT/ρt=0.750±0.049, which is consistent with a previous result by the authors: in the galactic plane there is a significant number of thick disk stars, possibly as many as thin disk ones, which also points to the existence of more thick disk stars than generally thought. The overall fit does not closely follow the data for |Z|>700 pc and points to the presence of more stars beyond the thin disk that cannot be accounted for by the two-disk model.

A Constraint on the Amount of Hydrogen from the CO Chemistry in Debris Disks

The faint CO gases in debris disks are easily dissolved into C by UV irradiation, while CO can be reformed via reactions with hydrogen. The abundance ratio of C/CO could thus be a probe of the amount of hydrogen in the debris disks. We conduct radiative transfer calculations with chemical reactions for debris disks. For a typical dust-to-gas mass ratio of debris disks, CO formation proceeds without the involvement of H2 because a small amount of dust grains makes H2 formation inefficient. We find that the CO to C number density ratio depends on a combination of n H Z 0.4 χ −1.1, where n H is the hydrogen nucleus number density, Z is the metallicity, and χ is the far-UV flux normalized by the Habing flux. Using an analytic formula for the CO number density, we give constraints on the amount of hydrogen and metallicity for debris disks. CO formation is accelerated by excited H2 when either the dust-to-gas mass ratio is increased or the energy barrier of chemisorption of hydrogen on the dust surface is decreased. This acceleration of CO formation occurs only when the shielding effects of CO are insignificant. In shielded regions, the CO fractions are almost independent of the parameters of dust grains.