Outer Electron Research Articles

Dynamic Responses of Outer Radiation Belt Electron Phase Space Densities to Geomagnetic Storms: A Statistical Analysis Based on Van Allen Probes Observations

AbstractUsing Van Allen Probes observations from September 2012 to June 2019, we statistically investigate responses of the Earth's outer radiation belt electron phase space densities (PSDs) in the adiabatic invariant coordinates to isolated geomagnetic storms. Electron PSDs for μ = 50–5,000 MeV/G, covering energy range of seed, relativistic and ultra‐relativistic electrons, are calculated to evaluate three types of storm‐time PSD responses (i.e., enhancement, depletion, and no change). In statistics, the seed PSD variations are dominated by enhancement‐type events, the percentages of which increase from >50% for small storms (−50 nT < SYM‐Hmin ≤ −30 nT) to >70% for large storms (SYM‐Hmin ≤ −50 nT). The relativistic and ultra‐relativistic PSDs exhibit the three response types with comparable occurrence rates for small storms but present predominantly enhancement‐type variations (>50%) for large storms. Enhanced storm activity increases the enhancement‐type responses for seed PSDs at all L* and for relativistic and ultra‐relativistic PSDs at L* > 3.5. It also results in the increased depletion‐type response occurrence for relativistic and ultra‐relativistic PSDs at lower L*. Our results further indicate that the depletion‐type responses manifest evident dependence on the level of solar and geomagnetic activity and the μ‐value, implying complex physics accounting for outer zone electron losses. Improved knowledge of the storm‐time dynamics of outer radiation belt electron PSDs is valuable to in‐depth comprehension of various mechanisms responsible for the electron acceleration and loss. It has important implications for future simulations and forecasts of radiation belt electron variability, in particular, during geomagnetically disturbed periods.

Insight into the synthesis of alkali metal modified Co-doped ZnFe2O4 with faveolate spinel structure and their enhanced selectivity of olefins during CO2 hydrogenation

Emission reduction of CO2 allows of no delay, and CO2 hydrogenation strategy reveals the great potential to achieve target of “Carbon Neutral”. Trapped with the low selectivity of olefins in our previous work of Co-doped ZnFe2O4, the alkali metal (Na, K) modified Co-doped ZnFe2O4 were synthesized, and their enhanced selectivity of olefins were present. The promotion caused by alkali metal modification revealed that more generation of metallic Fe and the additional generation of Fe5C2 species could be ascribed for the enhanced selectivity of C2-C4 olefins and C5+ products. The introduced alkali metal via the strong electronic interaction increased the outer electrons density around Fe atoms, which could promote the adsorption of CO2 and prohibited the secondary hydrogenation reaction of the formed olefins. Therefore, the enhanced selectivity of C2-C4 olefins over the alkali metal (Na, K) modified Co-doped ZnFe2O4 was emerged, while the CO2 conversion was suppressed (caused by the less generation of Fe3O4). Compared with Na-modified samples, the introduced K could make more generation of Fe5C2 to promote the carbon chain growth, due to its stronger alkalinity, thus leading to the highest selectivity of C5+ products over K-modified samples while the highest selectivity of C2-C4 olefins over Na-modified samples.

ALTERNATIVE EXPLANATION OF FILLING THE ELECTRONIC LAYERS OF ATOMS OF CHEMICAL ELEMENTS

The article provides a new approach to the formation of periods in Mendeleev's periodic system. Reconfiguration of the periods in the Mendeleev table using the newly proposed formula and the newly proposed quantum states for the outer electron shells of atoms of chemical elements is proposed. Purpose of work: Further development of the alternative theory of creation of electronic shells of atoms of chemical elements in D.I.Mendeleev's table. Results and discussions. The following order of formation of electron layers is proposed: principle quantum number (n), then the quantum state of the electrons forming the electronic configuration of the subperiods (first and second), and only then the remaining quantum orbitals (s, d, f and p). First and second new quantum states and a new formula for calculating the number of electrons in the outer electron shell of element periods and subperiods were proposed. The new level of electronic counting (II) and the new quantum number proposed by us allow to change the understanding of the internal structure of chemical elements without changing the general appearance and order of arrangement of chemical elements in D.I.Mendeleev's table itself, and therefore its contents. An important advantage of the proposed alternative model is that it takes into account and relies on already known, classical data for most of its main operational characteristics and is an extension of this important topic for classical chemistry theory. Therefore, the change in the number of periods, the introduction of a new quantum number in the form of D.I.Mendeleev's table, outwardly it does not differ much, but requires the necessary additional explanation. Concept. The proposed alternative approach to the structure and electronic structure of atomic shells of chemical elements in the periods and groups of D.I.Mendeleev's periodic system was recently developed by the authors and has good prospects for development primarily in the following directions: - identification of possible patterns of changes in the characteristics of chemical and physical properties of elements; - development of an accompanying model of the electronic structure of electronic shells of atoms of chemical elements of the proposed alternative model.

Evaluation of the Solid-Electrolyte Interphase Formation in a Bis(fluorosulfonyl)amide Based Ionic Liquid in the Presence Lithium Ion Using Different Redox Probes

The SEI formation in 0.5 M LiFSA/BMPFSA was investigated using different redox probes. The redox reaction of a metallocene and organic compound on a Pt electrode were investigated by cyclic voltammetry in BMPFSA and 0.5 M LiFSA/BMPFSA. Cyclic voltammograms were taken after holding the electrode at different potentials for 1 h. The cyclic voltammograms were unchanged in BMPFSA, indicating that BMPFSA was stable in the measured potential range and that the redox reaction was not affected by a change in the electric double layer structure. On the other hand, peak shifts were observed in the presence of Li+ at potentials more negative than –1.1 V vs. Ag|Ag(I), attributed to a decrease in the electron transfer rates and indicating that the SEI formation promoted by the interaction between Li+ and FSA– affects the redox reactions not only of metallocene but also of organic compounds that undergo outer sphere electron transfer reactions.

Outer Zone Relativistic Electron Response to Mesoscale Periodic Density Structures in the Solar Wind: Van Allen Probes Measurements

AbstractWe investigate the relativistic and the ultra‐relativistic outer radiation belt electron response to the Periodic Density Structures (PDS) in the solar wind. We have studied four intervals between 0000 UT and 1500 UT during 17 January 2013 interplanetary coronal mass ejection (ICME) sheath event following the passage of an interplanetary shock (IP) on 16 January, at 2240 UT. Earlier studies limited to geosynchronous orbit have shown that PDS induce Ultra‐Low‐Frequency (ULF) oscillations in the magnetosphere and modulate energetic electron intensities. Our study shows for the first time, using pitch angle resolved electron intensity measurements, that PDS modulate relativistic and ultra‐relativistic electron intensities in the heart of the radiation belts (L ≈ 4). We find that the modulation of electron intensities occur at frequencies close to those of interplanetary PDS. Furthermore, electron intensity modulations occur over a wide range of energy (≈200 keV to 4 MeV) and pitch angles (≈20–120°). This event study suggests that relativistic and ultra‐relativistic electron intensity modulations driven by PDS may be largely energy and pitch angle independent.

Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach.

Barium monofluoride (BaF) is a polar molecule of interest in measurements of the electron electric dipole moment. For this purpose, efforts are underway to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne. For a theoretical understanding of the electronic structure of such an embedded molecule, the need arises for efficient methods which are accurate but also able to handle a number of atoms which surround the molecule. The calculation for gas-phase BaF can be reduced to involve only outer electrons by representing the inner core of Ba with a pseudopotential, while carrying out a non-relativistic calculation with an appropriate basis set. Thus, the method is effectively at a scalar-relativistic level. In this work, we demonstrate to which extent this can be achieved using coupled-cluster methods to deal with electron correlation. As a test case, the SrF(X2Σ+→B2Σ+) transition is investigated, and excellent accuracy is obtained with the EOM-CC3 method. For the BaF(X2Σ+→A'2Δ, X2Σ+→A2Π, X2Σ+→B2Σ+) transitions, various coupled-cluster approaches are compared with very good agreement for EOM-CC3 with experimentally derived spectroscopic parameters, at the level of tens of cm-1. An exception is the excitation to the A'2Δ state, for which the energy is overestimated by 230cm-1. The poor convergence behavior for this particular state is demonstrated by providing results from calculations with basis sets of n = 3, 4, 5)-zeta quality. The calculated excitation energy for the B2Σ+ state agrees better with a deperturbation analysis than with the effective spectroscopic value, with a difference of 120cm-1.

Ti-Substituted O3-NaNi0.5Mn0.3Ti0.2O2 Material with a Disordered Transition Metal Layer and a Stable Structure.

O3-type NaNi0.5Mn0.5O2 (NNM) is very competitive for sodium-ion batteries (SIBs) due to its high capacity and easy production. Nevertheless, the intricate phase transitions during the charging-discharging significantly impede its practical application. This paper proposes a strategy for successfully synthesizing NaNi0.5Mn0.3Ti0.2O2 (NNMT) by combining coprecipitation and a high-temperature solid-state method. This method introduces Ti elements while retaining the electrochemically active Ni2+ content, thus, the NNMT has a high initial specific capacity of 151.4 mAh g-1 at 1 C. It is demonstrated that introducing Ti4+ leads to the transition metal layers becoming disordered by ex situ XRD, thus mitigating the irreversible phase transition of the material. In addition, Ti4+ does not have an outer electron, which can reduce electron delocalization in the transition metal layer and improve the material's cyclic stability. The NNMT possesses a capacity retention rate of 60.66% after 150 cycles, much higher than the initial NNM's 18.96%. It also exhibits an excellent discharge capacity of 86.8 mAh g-1 at 5 C. In conclusion, the cycling and rate performance of the Ti-substituted NNMT are greatly improved without capacity loss, which offers innovative concepts for the modification means of the SIBs layered oxide cathode materials.

Characterization of metal-binding behavior of DOM component structure in biochar: Analysis of binding sites, binding sequences and impact pathways

The binding of biochar-derived dissolved organic matter (BDOM) to heavy metals is a complex and dynamic process, with potentially different impact pathways. The outer electrons of various heavy metals can also affect their binding ability. This study comprehensively investigated the binding sites, sequences, constants, and influencing pathways of each component structure in BDOM through modern spectroscopic methods and multidimensional chemometrics. Here, the dominance of carboxyl and phenolic groups in the interaction of chromogenic dissolved organic matter (CDOM) with metal ions, which complex with BDOM, leads to an increase in the size of the BDOM molecule. In addition, Cu and Zn primarily bound to humic acids fluorophore, while Pb and Ni preferentially bound to protein-like fluorophore, likely due to the varying affinities of nitrogen- and carbon-based functional groups for different metals. Significant differences were observed in the interactions between different metal ions and fluorophores, involving both direct and indirect effects. Molecular perspectives and pathways suggested that the binding of BDOM to Zn was notably intricate, involving multiple conformational changes and impact pathways. These findings offer a crucial scientific foundation for a comprehensive comprehension of the interaction mechanisms between various metal ions and BDOM components.

Influence of Catalyst Surface Structure on the Electrochemical Hydrogenation of Cis,Cis-Muconic Acid

Adipic acid (AA) production from petroleum-based cyclohexane is one of the largest chemical processes in terms of annual volumetric turnover accounting for 3 million tons as of 2022. The current commercial approach to synthesize AA is through the oxidation of petroleum-derived cyclohexane using nitric acid. The release of N2O in stoichiometric amounts makes it one of the most significant greenhouse gas (GhG) emitting processes. The abundance of biomass in the Midwestern United States has driven significant research efforts to synthesize bio-derived and sustainable commodity products and lower the chemical industry’s carbon footprint.1 cis,cis-Muconic acid (ccMA), a biobased C6 diunsaturated diacid platform molecule can be transformed to commodity chemicals like caprolactam, adipic acid, and terephthalic acid, with AA being of particular interest for the synthesis of nylon 6,6.2 For the first time in literature, we demonstrate appreciable production of AA (conversion: 91%, selectivity: >95%) through electrochemical hydrogenation (ECH) of ccMA on PGM catalysts. Carbon-supported palladium (Pd/C) and platinum (Pt/C) selectively produced AA while bulk Pd and Pt yielded the monounsaturated trans-3-hexenedioic acid (t3HDA) intermediate and H2 under all tested conditions. Such an influence of surface structure on the electrochemistry of organics is not unprecedented. Koper et. al3 studied Pt single crystals for the electrochemical hydrogenation of acetone and showed how activity, selectivity, and extent of catalytic poisoning are highly sensitive to the Pt surface structure. Similarly, we used density functional calculations to elucidate the structure-sensitive nature of ccMA ECH and its intermediates by identifying thermodynamically preferred reaction pathways as a function of surface geometry (terrace vs steps). The energetics coupled with experimental observations suggest that the reduction of ccMA to t3HDA occurs through an outer sphere proton-coupled electron transfer mechanism, while the reduction of HDA to AA preferentially occurs on Pd and Pt (111), the most abundant facet in Pd/C and Pt/C. Our calculations also explain the exceptional performance of Pd/C compared to Pt/C by the weaker binding of Pd terrace sites compared to Pt. Overall, combining renewable electricity, in-situ hydrogen generation from water, and a biologically-produced intermediate enabled us to open a sustainable route for bio-adipic acid production. This allows us to further design and optimize the catalyst for the selective production of biobased AA.

Statistics and Models of the Electron Plasma Density From the Van Allen Probes

AbstractWe use the full NASA Van Allen Probes mission (2012–2019) to extract the electron plasma density from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) and Electric Field and Waves (EFW) instruments and discuss the evolution of the plasmasphere. We generate new statistics including mean and standard deviations of the plasma density with respect to L‐shell, magnetic local time (MLT), and various geomagnetic indices. These statistics are generated to be applied in radiation belt physics and space weather codes (with fits provided). The mean plasmasphere is circular around Earth with respect to MLT for Kp < 1. The mean 100 cm−3 level line is above L = 5 and mean 10 cm−3 level expands above the Van Allen Probes apogee for Kp < 1. The outer electron belt lies within the plasmasphere for 60% of all times. As activity increases (Kp > 2), a gradual MLT asymmetry forms with higher mean density in the afternoon sector due to plumes expanding outward. Conversely, the mean density decreases on the dawn and night sectors. The mean density is between ∼500 and ∼50 cm−3 between L ∼ 4 and L ∼ 6 during quiet and moderately active times (Kp < 3), representing ∼80% of all times. Statistics in regions of high density below L = 2 are underdefined for intense activity. The highest standard deviation of density represents a factor 2.5 to 3 times the mean above L = 5 and for active times. We find the percent difference between the EFW and EMFISIS densities is bounded by ±20% for quiet and moderate activity (Kp < 5) and goes up to ±100% for extreme activity.

Degradation of pyrene at high concentrations in sediment and the implications for the microbiome in microbial electrochemical systems

The polycyclic aromatic hydrocarbons (PAHs) frequently accumulate in sediments, particularly those near industrial sites. The efficacy of microbial electrochemical systems (MESs) in electricity generation and PAHs degradation is intricately linked to the microbiome’s response to high contaminant levels. Metabolomics and metagenomics were applied to elucidate the impact of a high pyrene concentration on the functional structure and metabolic dynamics of sediment microbiomes within MES. In sediment with a high pyrene concentration, both the electrical output of MES and efficiency of their microbiomes in degrading organic substrates and pyrene were markedly reduced. These conditions were associated with the enrichment of PAH-degrading microorganisms, such as Hydrogenophaga and Flavobacterium. Analyses of metabolites and genetic profiles revealed that metabolic pathways were primarily influenced in MES exposed to low pyrene concentrations whereas fewer metabolic pathways were activated in MES exposed to high concentrations; instead, pathways representing functions critical for microbial survival and communication were activated as well. According to enzymatic analyses, low pyrene levels promoted carbohydrate metabolism by sediment microorganisms, whereas high levels had an inhibitory effect. An examination of electron transport enzymes revealed that intracellular electron transfer was facilitated by both low and high concentrations. However, high levels impeded enzymes associated with outer membrane electron transfer, hindering electron movement from intracellular to extracellular electron acceptors and thus negatively affecting the electrical output of MES. Our study provides crucial theoretical insight and mechanistic understanding for addressing the challenges that may be encountered when MES are used to treat pyrene-contaminated sediment near industrial sites.

The promotion of rare earth on Pt-SiO2-Al2O3 catalyst for NO oxidation in diesel exhaust

The effective oxidation of NO is the key to the catalytic treatment of diesel vehicle exhaust. Improving the NO oxidation ability is mainly to optimize the chemical state of the active site (Pt), followed by increasing the number of active centers. Considering that the atoms with electronegativity weaker than Pt can provide electrons to change the chemical state of Pt, rare earth elements with weak electronegativity are selected as additives to obtain Pt/M-SiO2-Al2O3 (M = Sc, Y, La, Ce, Pr, Nd, Sm, Eu) catalysts by co-impregnation method. Among them, the Pt/La-SiO2-Al2O3 catalyst has the best NO oxidation performance, compared with the Pt-SiO2-Al2O3, the NO conversion rate increased by 28 %. Due to the special outer electron arrangement of La, its electronegativity is the smallest in rare earth, which makes its outer electrons easy to transfer to Pt atoms, and has the strongest electron interaction. Thus, the highest content of Pt0 was detected in CO diffuse reflectance infrared Fourier transform spectroscopy (CO-DRIFTS) and X-ray photoelectron spectroscopy (XPS). In addition, CO chemisorption and transmission electron microscopy (TEM) confirmed that the introduction of La in the catalyst can significantly improve the dispersion of precious metals. Notably, this simple approach of affecting electron interaction by introducing weakly electronegative elements provides a reference for the design of noble metal catalysts with different valence states to solve complex problems.

Geometric properties of the first singlet S-wave excited state of two-electron atoms near the critical nuclear charge

Abstract In this work the geometric structure parameters and radial density distribution of 1s2s 1 S excited state of the two-electron atomic system near the critical nuclear charge Z c were calculated in detail under tripled Hylleraas basis set. Contrary to the localized behavior observed in the ground and the doubly excited 2p 2 3 P e states, for this state our results identify that while the behavior of the inner electron increasingly resembles that of a hydrogen-like atomic system, the outer electron in the excited state exhibits diffused hydrogen-like character and becomes perpendicular to the inner electron as nuclear charge Z approaches Z c. This study provides insights into the electronic structure and stability of the two-electron system in the vicinity of the critical nuclear charge.

Theory for Outer Sphere Electron Transfer Coupled with Ion Transfer Kinetics on Atomically Stepped Metal

Theory for Outer Sphere Electron Transfer Coupled with Ion Transfer Kinetics on Atomically Stepped Metal

Determination of Outer Radiation Belt MeV Electron Energization Rates and Delayed Response Times to Solar Wind Driving During Geomagnetic Storms

Determination of Outer Radiation Belt MeV Electron Energization Rates and Delayed Response Times to Solar Wind Driving During Geomagnetic Storms

Upper Limit of Outer Belt Electron Acceleration and Their Controlling Geomagnetic Conditions: A Comparison of Storm and Non‐Storm Events

AbstractWe perform a comprehensive investigation of the statistical distribution of outer belt electron acceleration events over energies from 300 keV to ∼10 MeV regardless of storm activity using 6‐years of observations from Van Allen Probes. We find that the statistical properties of acceleration events are consistent with the characteristic energies of combined local acceleration by chorus waves and inward radial diffusion. While electron acceleration events frequently occur both at <2 MeV at L < 4.0 and at multi‐MeV at L > 4.5, significant acceleration events are confined to L > ∼4.0. By performing superposed epoch analysis of acceleration events during storm and non/weak storm events and comparing their geomagnetic conditions, we reveal the strong correlation (>0.8) between accumulated impacts of substorms as measured by time‐integrated AL (Int(AL)) and the upper flux limit of electron acceleration. While intense storms can provide favorable conditions for efficient acceleration, they are not necessarily required to produce large maximum fluxes.

Role of outer shell electron-nuclear distant of transition metal atoms (TMA) on band gap reduction and optical properties of TiO2 semiconductor

The reduction of the band gap of titanium dioxide (TiO2) via transition metal atoms (TMAs) is the focus of many research groups to increase its absorption to visible region of electromagnetic (EM) radiation. In this modeling it was shown that atoms having near outer electron shells affect strongly on the band gap of TiO2. The TiO2 has exceptional photoactivity, high stability, and cost-effectiveness. The results of the current study emphasized that adjustable TiO2 photocatalyst material can be produced through band gap reduction by Pt, Pd, and Ni dopants. The electronic configurations and optical properties of both undoped and (Ni, Pd and Pt)-doped TiO2 have been studied using first-principles calculations within the framework of Density Functional Theory (DFT) with the aid of the Vienna Ab initio Simulation Package (VASP). The role of electronegativity of TMAs on band gap drop was discussed for the first time. The band gap of clean TiO2 was found to be 3.2 eV using the band structure (BS) and Tauq model. The results indicate that Ni TMA with lowest electronegativity reduces the band gap of TiO2 to the lowest value (0.86 eV). The results of BS and density of state revealed the fact that small outer shell electron-nuclear distant TMA more affected the band gap of TiO2. The band gap determined from the imaginary part of the optical dielectric function closely aligns with those determined from the BS diagram. The increase in the refractive index (n) was observed with the increase of Ni, Pd, and Pt into the TiO2 structure, which indicates an increase in charge density within the TiO2 structure. The reflectance, absorbance, and transmittance results suggest that Pd and Pt-doped TiO2 are responsive to the visible region of electromagnetic radiation, whereas Ni-doped TiO2 exhibits responsiveness in the IR region. In its pure state; TiO2 was found almost transparent in the visible and IR regions of EM radiation.

From 2e- to 4e- pathway in the alkaline oxygen reduction reaction on Au(100): Kinetic circumvention of the volcano curve.

We report the free energy barriers for the elementary reactions in the 2e- and 4e- oxygen reduction reaction (ORR) steps on Au(100) in an alkaline solution. Due to the weak adsorption energy of O2 on Au(100), the barrier for the association channel is very low, and the 2e- pathway is clearly favored, while the barrier for the O-O dissociation channel is significantly higher at 0.5eV. Above 0.7V reversible hydrogen electrode (RHE), the association channel becomes thermodynamically unfavorable, which opens up the O-O dissociation channel, leading to the 4e- pathway. The low adsorption energy of oxygenated species on Au is now an advantage, and residue ORR current can be observed up to the 1.0-1.2V region (RHE). In contrast, the O-O dissociation barrier on Au(111) is significantly higher, at close to 0.9eV, due to coupling with surface reorganization, which explains the lower ORR activity on Au(111) than that on Au(100). In combination with the previously suggested outer sphere electron transfer to O2 for its initial adsorption, these results provide a consistent explanation for the features in the experimentally measured polarization curve for the alkaline ORR on Au(100) and demonstrate an ORR mechanism distinct from that on Pt(111). It also highlights the importance to consider the spin state of O2 in ORR and to understand the activation barriers, in addition to the adsorption energies, to account for the features observed in electrochemical measurements.

Super-X and conventional divertor configurations in MAST-U ohmic L-mode; a comparison facilitated by interpretative modelling

Measurements are presented, alongside corresponding interpretative SOLPS-ITER simulations, of the first MAST-U experiments comparing ohmically heated L-mode fuelling scans in Conventional divertor (CD) and Super-X divertor (SXD) configurations. In experiment, at comparable outer mid-plane separatrix electron density, ne,sep,OMP , the maximum lower outer target heat load was found to be a factor 16 ±7 lower in SXD compared to CD. In simulation, a factor 26.8 reduction was found (slightly higher than the experimental range), suggesting an additional reduction in SXD compared to the factor 9.3 expected from geometric considerations alone. According to the simulations, this additional reduction in the SXD is due to a net radial transport of the energy remaining downstream of the Te=5 eV location. This energy is carried out of the critical (highest heat load) flux tube by deuterium atoms, demonstrating the importance of a longer legged divertor which provides space for this to occur. Importantly, in both simulation and experiment, the SXD has minimal impact on the upstream ne and Te profiles. Spectral inferences of detachment front movement in SXD compare well between simulation and experiment. In regions of high magnetic field gradient, the parallel movement of the front towards the X-point becomes less sensitive to increasing ne,sep,OMP , in qualitative agreement with simplified models and previous predictive simulations. Additional aspects, regarding the target ion flux rollover, upstream separatrix temperature and drift effects, are also presented and discussed.

ULF Wave Transport of Relativistic Electrons in the Van Allen Belts: Criteria for Transition to Radial Diffusion

AbstractRelativistic electrons in the radiation belts can be transported as a result of wave‐particle interactions (WPI) with ultra‐low frequency (ULF) waves. Such WPI are often assumed to be diffusive, parametric models for the radial diffusion coefficient often being used to assess the rates of radial transport. However, these WPI transition from initially coherent interactions to the diffusive regime over a finite time, this time depending on the ULF wave power spectral density, and local resonance conditions. Further, in the real system on the timescales of a single storm, interactions with finite discrete modes may be more realistic. Here, we use a particle‐tracing model to simulate the dynamics of outer radiation belt electrons in the presence of a finite number of discrete frequency modes. We characterize the point of the onset of diffusion as a transition from separate discrete interactions in terms of wave parameters by using the “two‐thirds” overlap criterion (Lichtenberg & Lieberman, 1992, https://doi.org/10.1007/978‐1‐4757‐2184‐3), a comparison between the distance between, and the widths of, the electron's primary resonant islands in phase space. Further, we find the particle decorrelation time in our model system with typical parameters to be on the timescale of hours, which only afterward can the system be modeled by one‐dimensional radial diffusion. Direct comparison of particle transport rates in our model with previous analytic diffusion coefficient formulations show good agreement at times beyond the decorrelation time. These results are critical for determining the time periods and conditions under which ULF wave radial diffusion theory can be applied.