Ionization Energy Of Hydrogen Research Articles

A Mathematical Relationship between Hydrogenic Periodic Property and Nuclear Properties in Furtherance of Bohr’s Theory

Background: Atomic physics and nuclear matter physics are often exclusively studied. However, atomic properties are a direct function of nuclear properties. Establishing a mathematical relationship between nuclear and atomic properties could serve the interest of nuclear and atomic engineers. Nuclear - and atomic-based instrumentation engineering and nuclear medicine (and perhaps atomic medicine) applications could be the benefits.
 Objectives: The research is undertaken to 1) link nuclear property, the mass-radius of the nucleon, and ionization energy of hydrogen via the derivation of appropriate equation and 2) determine the mass-radii of the nucleons and some leptons.
 Methods: Theoretical and computational methods.
 Results and Discussion: As applicable to the previous results in the literature, the larger the mass of the elementary particles, the longer the radii. For the particles investigated, the order of the radius is muon (m-)<proton (p+)< neutron (n)< tauon (t-) corresponding to increasing mass, m-<p+< n<t-. The values of the mass radii were respectively » 0.1240, 1.1012, 1.1027, and 2.0855 fm.
 Conclusion: Nuclear properties such as the radius of any nucleon (ΓN) can be mathematically linked to atomic properties such as the ionization energy of hydrogen via equation which shows that ΓN is inversely proportional to the ionization energy of hydrogen and directly proportional to the rest-mass of the particle.

Can non-standard recombination resolve the Hubble tension?

The inconsistent Hubble constant values derived from cosmic microwave background (CMB) observations and from local distance-ladder measurements may suggest new physics beyond the standard $\Lambda$CDM paradigm. It has been found in earlier works that, at least phenomenologically, non-standard recombination histories can reduce the $\gtrsim 4\sigma$ Hubble tension to $\sim 2\sigma$. Following this path, we vary physical and phenomenological parameters in RECFAST, the standard code to compute ionization history of the universe, to explore possible physics beyond standard recombination. We find that the CMB constraint on the Hubble constant is sensitive to the Hydrogen ionization energy and $2s \rightarrow 1s$ two-photon decay rate, both of which are atomic constants, and is insensitive to other details of recombination. Thus, the Hubble tension is very robust against perturbations of recombination history, unless exotic physics modifies the atomic constants during the recombination epoch.

Phenylcyclopropane Energetics and Characterization of Its Conjugate Base: Phenyl Substituent Effects and the C-H Bond Dissociation Energy of Cyclopropane.

The α-C-H bond dissociation energy (BDE) of phenylcyclopropane (1) was experimentally determined using Hess' law. An equilibrium acidity determination of 1 afforded ΔH°acid = 389.1 ± 0.8 kcal mol-1, and isotopic labeling established that the α-position of the three-membered ring is the favored deprotonation site. Interestingly, the structure of the base proved to be a key factor in correctly determining the proper ionization site (i.e., secondary amide ions are needed, and primary ones and OH- lead to incorrect conclusions since they scramble the deuterium label). An experimental measurement of the electron affinity of 1-phenylcyclopropyl radical (EA = 17.5 ± 2.8 kcal mol-1) was combined with the ionization energy of hydrogen (313.6 kcal mol-1) to afford BDE = 93.0 ± 2.9 kcal mol-1. This enabled the effect of the phenyl substituent to be evaluated and compared to other situations where it is attached to an sp3- or sp2-hybridized carbon center. M06-2X, CCSD(T), G4, and W1BD computations were also carried out, and a revised C-H BDE for cyclopropane of 108.9 ± 1.0 kcal mol-1 is recommended.

Prediction and Derivation of the Higgs Boson from the Neutron and Properties of Hydrogen Demonstrating Relationships with Planck’s Time, the Down Quark, and the Fine Structure Constant

A high accuracy Higgs boson, H0, is an important physical constant. The Higgs boson is associated with the property of mass related to broken symmetry in the Standard Model. The H0 mass cannot be derived by the Standard Model. The goal of this work is to derive and predict the mass of H0 from the subatomic data of the frequency equivalents of the neutron, electron, Bohr radius, and the ionization energy of hydrogen. H0’s close relationships to the fine structure constant, α, the down quark, and Planck time, tP are demonstrated. The methods of the harmonic neutron hypothesis introduced in 2009 were utilized. It assumes that the fundamental constants as frequency equivalents represent a classic unified harmonic system where each physical constant is associated with a classic harmonic integer fraction. It has been demonstrated that the sum exponent of a harmonic integer fraction, and a small derived linear δ value of the annhilation frequency of the neutron, vn, 2.2718591 × 1023 Hz, (vns) as a dimensionless coupling constant represent many physical constants as frequency equivalents. This is a natural unit system. The harmonic integer fraction series is 1/±n, and 1 ± 1/n for n equals 1 to ∞. The H0 is empirically and logically is associated with harmonic fractions, 1/11 and 1 + 1/11. α-1 is associated with 11. α-1 is a free space scaling constant for the electromagnetic force so it is logical that 11 should also have a pair, but for a free space mass constant. Also there should be a harmonic faction pair for the down quark, 1 - 1/11, just as there is pairing of the up quark, 1 - 1/10, and top quark, 1 + 1/10. The harmonic neutron hypothesis has published a method deriving a high accuracy Planck time, tP from the same limited subatomic data. The δ line for H0 should be closely associated with tP since they both are related to mass. The preferred derived value related to tP2 is 125.596808 GeV/c2. A less attractive derived value is 125.120961 GeV/c2 from the weak force factors only. The experimental CMS and Atlas value ranges are 125.03+0.26+0.13-0.27-0.15 and 125.36±0.37±0.18 GeV/c2. Empirically the H0 δ line is closely related to the same factors of the tP δ line, but with inverse sign of the slope. The H0 completes the paring of a free space constant for mass, the down quark, and an inverse sign δ line factors with tP. It is possible to accurately derive the mass of H0 from subatomic physical data. The model demonstrates that H0 is closely associated with α, the down quark, and tP. This prediction can be scrutinized in the future to see if it is accurate. The model has already published accurate predictions of the masses of the quarks.

The Harmonic Neutron Hypothesis: Derivation of the Mass Equivalents of the Quarks from the Frequency Equivalents of the Ionization Energy of Hydrogen and the Annihilation Energy of the Neutron

ABSTR ACT: The harmonic neutron hypothesis states that all of the fundamental constants, when expressed as frequency equivalent coupling constant ratios, are related to the annihilation frequency of the neutron, vn 2.271859 × 1023 Hz. The constants are interrelated by classic standing wave, harmonic number properties, and have classic quantum spectral characteristics. If vns is raised by the exponents of a consecutive integer quantum fraction (qf ) series ([n ± 1]/n) for the principal quantum numbers, then n = 1 to ∞, representing many of the degenerate exponent values of the fundamental constants, including the quarks. The qf values have been shown to be symmetrically split by sign when plotted on an ln ln plane, similar to imaginary numbers. The hypothesis also states that, when plotted, the associated entities should align in linear patterns, and their principal quantum numbers should simultaneously be products of smaller harmonic numbers for higher hierarchical particle generations. The slopes and intercepts of the lines are derived solely from the properties of hydrogen, and the neutron have been published and used to derive other constants. It has been previously predicted that the quarks are associated with the slope, defined by the line connecting the points for Planck’s constant (−1, 0) and (−1/3, known exponent of the ionization energy of hydrogen −2/3), which is referred to as the electromagnetic line, or em line, whose principal quantum number is 3. Assuming that the quarks fall on integer slope multiples of the line connect (1, 0), the inverse slope of the em line, the quark values can be derived and compared to the known values. The quarks, sign, principal quantum numbers, quantum fractions, and known and predicted eV values include: up (−10, 9/10, 1.7–3.1 MeV, 2.3 MeV); down (−11, 10/11, 4.1–5.7 MeV, 4.7 MeV); strange (−30, 29/30, 100; +30 or −20 MeV, 106.6 MeV); charm (109, 110/109, 1,290; +50 or –110 MeV, 1,280 MeV); bottom (32, 33/32, 4190 +180 or −60 MeV, 4,214 MeV); and top (10, 11/10, 172.9 ± 1.5 GeV, and 172.2 GeV). The three harmonic numbers associated with the quarks are 3, 10, and 11. The strange quark is related to the product of 3 and 10, the bottom quark 3 and 11, and the charm quark 10 and 11. The paper explains the origin and rationale for the mass equivalents of the quarks and makes predictions of more accurate values than are known.

NUMERICAL SIMULATIONS OF SPICULE ACCELERATION

Observations in the Hα line of hydrogen and the H and K lines of singly ionized calcium on the solar limb reveal the existence of structures with jet-like behavior, usually designated as spicules. The driving mechanism for such structures remains poorly understood. Sterling et al. shed some light on the problem mimicking reconnection events in the chromosphere with a one-dimensional code by injecting energy with different spatial and temporal distributions and tracing the thermodynamic evolution of the upper chromospheric plasma. They found three different classes of jets resulting from these injections. We follow their approach but improve the physical description by including non-LTE cooling in strong spectral lines and non-equilibrium hydrogen ionization. Increased cooling and conversion of injected energy into hydrogen ionization energy instead of thermal energy both lead to weaker jets and smaller final extent of the spicules compared with Sterling et al. In our simulations we find different behavior depending on the timescale for hydrogen ionization/recombination. Radiation-driven ionization fronts also form.

Ratio Relationships between π, the Fine Structure Constant and the Frequency Equivalents of an Electron, the Bohr Radius, the Ionization Energy of Hydrogen, and the Classical Electron Radius

This paper demonstrates and analyzes the multiple and complicated ratio inter-relationships among pi, π; the fine structure constant, α; the frequency equivalents of an electron, ve; the Bohr radius, va0; the ionization energy of hydrogen or the Rydberg constant, R; vR; and the classical electron radius, vre. These relationships are partially known, but many are not yet fully recognized. This paper presents all of them as a unified system, demonstrating an unexpected inter-relationship among the quantum properties of hydrogen that can be used to calculate and understand relationships between fundamental constants. These ratios are of logical origin, but are quite complicated and not intuitive. These relationships stem from geometry and the nature of the components of hydrogen: for example, they relate a transition of a mass/energy to a circumference distance. α is related to six different frequency equivalent ratios: the product of 4π and vR, divided by va0; the square root of 2 times vR divided by ve; va0 divided by the product of 2π times ve; the product of 2π and ve divided by vre; the square root of the ratio of va0 divided by vre; and the cube root of 4π times vR divided by vre. π is also related to multiple ratios of α and the hydrogen frequency equivalents from the previous relationships. 8π2 is equal to the ratio of va0 squared divided by the product of vR and ve. The combination products of α, 2, and 2π are the scaling ratios of the transformations between a mass/energy and a distance for all of the four hydrogen constants. If any three of the six constants are known, then the other three can be derived, demonstrating the intricate relationship of these constants. These relationships also must hold for effective α (running α) as well. In part, they explain its origin and why α must change in certain settings. Therefore these relationships extend to high energy physics, as well as adding new insights to effective α.

The Harmonic Neutron Hypothesis: Derivation of Planck Time and the Newtonian Constant of Gravity from the Subatomic Properties of a Neutron and Hydrogen

Planck time (t P ) is derived from subatomic physical constants: frequency equivalents of the neutron, the electron, the Bohr radius, and the ionization energy of hydrogen. t P squared represents a proportionality constant where the product with the frequency equivalents of two masses and the frequency equivalent distance equals the gravitational energy in Hz. This method is based on the harmonic neutron hypothesis explained herein: the fundamental constants represent a unified exponential consecutive integer (forces) or integer quantum fraction (1 ± 1/n) (particles, bosons, distances) system where the annihilation frequency of the neutron (v n s) is the base. All of the fundamental constants are associated with simple linear relationships of their components when plotted on a ln ln plane using the slopes and intercepts of two ln ln plotted lines associated with hydrogen, weak kinetic, wk, and electromagnetic, em. The degenerate, approximate value of t P 2 can be derived utilizing the quantum fraction values for the proton, 1, gravitational binding energy of electron, −1, the electron, 6/7, and the Bohr radius, 4/5. The approximate degenerate value yielded of t P is the square root of v n raised to the exponent −1−1−6/7−4/5 divided by 4π is 5.51548 × 10 −44 s, and the known value is 5.39124 × 10 −44 s. The predicted degener- ate value of Newton's gravitation constant G is 6.9854466 × 10 −11 m 3 kg −1 s −2 , whereas its known value is 6.67428 × 10 −11 m 3 kg −1 s −2 . Using the hydrogen line values a more precise prediction can be made beyond what can be measured. Two points define the t P 2 line, (0, −b wk −b em ) and (−1, −a wk ). The intercept of this line at the sum of the quantum fractions (−128/35 −1) representing t P 2 is used to derive t P. The hydrogen line derived t P value is 5.391141 × 10 −44 s. The hydrogen line derived G value is 6.6740402 × 10 −11 m 3 kg −1 s −2 . These derived values are within the known uncertainties. This method bridges from subatomic properties of hydrogen to gravity unifying these two systems and multiple forces.

The Neutron Hypothesis: Derivation of the Mass of the Proton From the Frequency Equivalents of a Neutron, Electron, Bohr Radius, and Ionization Energy of Hydrogen

The mass of a proton is an important fundamental constant, but a logical rational for its mass is unknown. This paper demonstrates a method to accurately and logically derive the frequency equivalent of the mass of a proton, v p , from frequency equivalents of the masses of a neutron and electron, the Bohr radius, and the ionization energy of hydrogen. The hypothesis is that the fundamental constants are all related to annihilation frequency of the neutron (v n ) which is the fundamental frequency. The hypothesis states that the fundamental constants must be related to simple linear relationships on the ln ln planes based solely on the slopes and intercepts of two lines related to hydrogen, the weak kinetic line (electron, and Bohr radius), and the electromagnetic line (Planck constant, and ionization energy of hydrogen). The mass of the proton can be derived by subtracting the components lost in the beta decay process from v n . Each n is a principal quantum number and associated with at least one fundamental constant including the primes: 7, electron, 5, Bohr radius, 3, ionization energy, and 2, neutrino. The total kinetic energy lost in the beta decay process is related to the other principal quantum numbers which are not primes including 4, 6, and 8. There is a 2nd factor related to the principal quantum number 5 utilizing all of the slopes and intercepts of the two hydrogen lines. v n minus the sum of these lost frequency equivalents is 2.26873187 × 10 23 Hz. v p is 2.26873183 × 10 23 Hz. The relative error is 2 × 10 −8 . The derived mass equivalent of a proton is 1.67262166 × 10 −27 kg. The relative error is 2 × 10 −8 . The known proton mass is 1.6726216 × 10 −27 kg. The known relative error is 5 × 10 −8 kg.

Massive Stars and the Energy Balance of the Interstellar Medium. II. The 35M⊙Star and a Solution to the “Missing Wind Problem”

We continue our numerical analysis of the morphological and energetic influence of massive stars on their ambient interstellar medium for a 35 M☉ star that evolves from the main-sequence through red supergiant and Wolf-Rayet phases, until it ultimately explodes as a supernova. We find that structure formation in the circumstellar gas during the early main-sequence evolution occurs as in the 60 M☉ case but is much less pronounced because of the lower mechanical wind luminosity of the star. On the other hand, since the shell-like structure of the H II region is largely preserved, effects that rely on this symmetry become more important. At the end of the stellar lifetime 1% of the energy released as Lyman continuum radiation and stellar wind has been transferred to the circumstellar gas. From this fraction 10% is kinetic energy of bulk motion, 36% is thermal energy, and the remaining 54% is ionization energy of hydrogen. The sweeping up of the slow red supergiant wind by the fast Wolf-Rayet wind produces remarkable morphological structures and emission signatures, which are compared with existing observations of the Wolf-Rayet bubble S308, whose central star has probably evolved in a manner very similar to our model star. Our model reproduces the correct order of magnitude of observed X-ray luminosity, the temperature of the emitting plasma, and the limb brightening of the intensity profile. This is remarkable, because current analytical and numerical models of Wolf-Rayet bubbles fail to consistently explain these features. A key result is that almost the entire X-ray emission in this stage comes from the shell of red supergiant wind swept up by the shocked Wolf-Rayet wind rather than from the shocked Wolf-Rayet wind itself as hitherto assumed and modeled. This offers a possible solution to what is called the missing wind problem of Wolf-Rayet bubbles.

Surface conductivity of the diamond: A novel transfer doping mechanism

A novel doping mechanism is presented for the case of diamond that does not rely on the incorporation of dopant atoms into the crystal lattice as in conventional doping. Instead, adsorbates provide the acceptor level into which electrons are transferred, leading to a two-dimensional subsurface hole accumulation layer with an areal concentration of up to 10 13 cm −2. Two acceptor systems are discussed. One is based on the charge exchange between diamond and solvated H + ions in a water layer that forms spontaneously on all surfaces in air. The other relies on the high electron affinity of fullerenes and fluorinated fullerenes that act as efficient acceptors when physisorbed at the surface. In either case, the extremely low ionization energy of hydrogen terminated diamond that is matched by no other semiconductor is a necessary requirement for transfer doping.

Line radiation of multiply charged ions with a Fermi-Dirac level distribution of electrons at high temperatures

The line radiation of multiply charged ions with a Fermi–Dirac level distribution of electrons is investigated in the plasma temperature range where the motion of electrons may be treated as quasi-classical, and the potential in which they move, as Coulomb, which is valid under the conditions ZEH ≪ max(T, ℏω I ) ≪ Z 2EH, where EH = 13.6 eV is the ionization energy of hydrogen, Z is the atomic number of the ion being treated, and ω I is the frequency of electron reversal in the Coulomb field at an energy equal to the ionization energy. The spectrum and intensity of radiation of ions are calculated. In the limit of high plasma densities, the intensity of radiation per ion turns out to be independent of density and proportional to T 2 .

Development of an ion source for the low energy ion implantation

A mass-selected ion source has been developed for low energy ion implantation. The use of high current and low energy ion beam causes the target charge-up and space charge problem in the beam transport line. We have used the large area ion source without mass separation. The ionization energy of hydrogen is higher than that of diborane. If we can control the energy of electrons in the plasma, we can design a hydrogen-free ion source. In order to make clear the relationships between the energy of electrons and r.f. discharge parameters, we measured the r.f. discharge parameters with a Langmuir probe while changing the radio frequency, r.f. power and so on. The proportion of the hydrogen ions to total ions generated in the plasma could then be less than 1%.

Deducing the Shell Model from Ionization Energies and the Use of Models in Introductory Chemistry

A major objection of Rioux and DeKock (1) is the statement in our earlier paper (2) that electron repulsion is responsible for the relative ionization energies of H and He. Their work clearly shows that a quantum mechanical treatment of this problem reveals that kinetic energy considerations play a crucial role in these values. However, although their criticism is appropriate in the context of this more sophisticated QM treatment, it does not in any way invalidate our original paper, the goal of which was to provide a model, namely the shell model, for the electronic structure of atoms that is consistent with experimental ionization energies. For this purpose it is not even necessary to discuss the difference in the ionization energies of H and He because it is only the large decrease in the first ionization energy from He to Li, indicating that the third electron in Li is at a much larger distance from the nucleus than are the electrons in He, that is relevant to deducing the shell model. Still, students often ask "Why is the ionization energy of He not twice that of H?" Within this simple shell model, it would only be twice that of He if the electrons were the same distance from the nucleus as the single electron in H and if there were no repulsion between the two electrons. Repulsion between the two electrons in He would reduce the ionization energy of He to less than twice that of H. This is what was intended by the last sentence of the paragraph quoted by Rioux and DeKock: "The ionization energy of helium is slightly less than twice the ionization energy of hydrogen because of the repulsion between the two electrons in helium" (2).

Prominence Thread Models Including Ambipolar Diffusion

view Abstract Citations (37) References (36) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Prominence Thread Models Including Ambipolar Diffusion Fontenla, J. M. ; Rovira, M. ; Vial, J. -C. ; Gouttebroze, P. Abstract We present a study of the modeling of prominence slabs. Our models consider a collection of threads in energy balance with the surrounding corona and submitted to illumination from the underlying chromospheric layers. The models are isobaric, but temperature variations within the slab occur as a result of the energy balance constraint. We compute the non-LTE radiative transfer for a hydrogen model atom with five bound levels. The ionization is treated consistently with non-LTE radiative transfer and ambipolar diffusion (AD). The AD also affects the energy balance because of the transport of hydrogen ionization energy. We compute the emitted Lyman and Balmer spectra of our models and compare them with the observations. We find that the consideration of ambipolar diffusion increases the emission in Lyβ (and higher members of the Lyman series) as compared with the other lines. This contrasts with isothermal models that yield Lyβ emission that is too low. However, the AD models give excessive Lyβ emission, viz., too small a Lyα/Lyβ ratio compared with observations. We also compute models that include a cold core in which mechanical energy is dissipated. These models increase the Hα/Lβ ratio to values similar to the observed values for a moderate number of threads along the line of sight. However, these models still give too low a Lyα/Lyβ ratio. We conclude that the prominence observations in Lyβ show intensities that are not compatible with a steady state, field-aligned interface between the cold prominence and the hot coronal material. Also, the observations are not consistent with an isothermal slab isolated from the corona. Consequently, we suggest that at the prominence-corona interface, there is a substantial angle between the temperature gradient and the field, although this angle is significantly smaller than 90°. Publication: The Astrophysical Journal Pub Date: July 1996 DOI: 10.1086/177527 Bibcode: 1996ApJ...466..496F Keywords: DIFFUSION; SUN: CORONA; SUN: PROMINENCES; SUN: UV RADIATION full text sources ADS |

Instabilities in Photoionized Interstellar Gas

We present a linear analysis of acoustic and thermo-reactive instabilities in a diffuse gas, photoionized and heated by a radiation field, cooled by collisional excitation of hydrogen and metal lines. The hydrogen recombination reaction has a stabilizing effect on the thermal mode found by Field (1965) since the condensation instability occurs in a narrower region of the parameter space and grows on longer time scales due to its oscillatory character. This effect is stronger when the mean photon energy is not much larger than the hydrogen ionization energy. Moreover, for fixed values of thermal pressure and photoionization rate, there are thermo- reactive unstable equilibria for which no transition to a stable phase is possible. By extending our analysis of the thermo-reactive modes to the nonlinear regime we show that when no phase transition is possible the medium evolves through a series of nonequilibrium states characterized by large amplitude, nonlinear periodic oscillations of temperature, density and hydrogen ionization fraction. We find also unstable acoustic waves which, for solar metal abundances, are the fastest growing modes in two temperature intervals: around $T\sim 100$~K and $T\sim 8000$~K (i.e. cold and warm phase, respectively), independent of the mean photon energy. Possible implications for the interstellar medium and intergalactic medium are briefly outlined.

General relation between refractive index and energy gap in semiconductors

A review is given of existing relations and rules of thumb between refractive index and energy gap in semiconductors. An error deviation was calculated on more than one hundred materials. With only one set of fitting parameters, our model n 2 = 1 + [ A/( E g + B )] 2, based on the classical oscillator theory, gives good fit except for IV–VI materials like PbS, PbSe, PbTe. The constant A was found to have the same value as the hydrogen ionization energy i.e. 13.6 eV and B = 3.4 eV.

Energy balance in the solar transition region. I - Hydrostatic thermal models with ambipolar diffusion

The energy balance in the lower transition region is analyzed by constructing theoretical models which satisfy the energy balance constraint. The energy balance is achieved by balancing the radiative losses and the energy flowing downward from the corona. This energy flow is mainly in two forms: conductive heat flow and hydrogen ionization energy flow due to ambipolar diffusion. Hydrostatic equilibrium is assumed, and, in a first calculation, local mechanical heating and Joule heating are ignored. In a second model, some mechanical heating compatible with chromospheric energy-balance calculations is introduced. The models are computed for a partial non-LTE approach in which radiation departs strongly from LTE but particles depart from Maxwellian distributions only to first order. The results, which apply to cases where the magnetic field is either absent, or uniform and vertical, are compared with the observed Lyman lines and continuum from the average quiet sun. The approximate agreement suggests that this type of model can roughly explain the observed intensities in a physically meaningful way, assuming only a few free parameters specified as chromospheric boundary conditions.

Ultraviolet absorption in cesium seeded hydrogen

The influence of cesium-seed fraction on the ultraviolet photoabsorption coefficient of a cesium-hydrogen plasma is determined over the pressure range from 0·1 to 100 atm. Plasma temperatures from 5000°K to 20 000°K, and cesium-hydrogen ratios of 10 -1, 10 -2, 10 -3 and zero are investigated, maintaining a constant electron density. The plasma photoabsorption coefficient is calculated in the ultraviolet region (4·0–25·0 eV). The most pronounced effect is due to the bound-free absorption of cesium at energies below the hydrogen ionization energy. This effect is important at low plasma temperatures.