Large Electric Field Strengths Research Articles

High-frequency irreversible electroporation ablation for the prostate in Beagle dogs.

Ablation procedures have garnered significant attention as a minimally invasive treatment of prostate diseases. However, the feasibility and safety of applying high-frequency irreversible electroporation (H-FIRE) to ablate the Beagle prostate for benign prostatic hyperplasia (BPH) treatment have not been thoroughly explored, the appropriate range of parameters has not been determined. In order to ensure the feasibility and safety of prostate ablation surgery, we conducted a study using Beagle dogs as subjects to investigate prostate tissue. We utilized a composite steep pulse therapy device to perform ablations on 26 lateral lobes of the prostate in 13 Beagles, employing various parameters for different needle distances. The effectiveness of this device was assessed through the observation of the ablation area, intraoperative muscle tremors, postoperative hematological examination, and gross inspection. The findings of our study revealed that 1,000 to 2,000 v/cm in electric field strength, combined with 5 µs pulse width and pulse number 100, is a safe parameter range for ablation of prostate tissue. At the same time, the large electric field strength (2,000 v/cm) has the best ablation effect with the biggest continuous and thorough ablation area. All parameters of H-FIRE were safe for Beagles. H-FIRE ablation for prostate is safe and effective in dogs, which has the potential to be a useful addition to the range of minimally invasive treatments available for the treatment of BPH against this backdrop of increasing surgical practice.

Electrochemical migration and dendrite growth between two electrodes: Experiments and Brownian dynamics simulations

Electrochemical migration (ECM) is a common cause of failure in printed circuit boards (PCB) due to dendrite growth between exposed metallic conductors under moisture especially in the presence of flux residues. Understanding this phenomenon, therefore, is of interest from technological and economical points of view. Here, we report experimental results of water drop tests on surfaces contaminated by various amount of flux residues, which are supplemented with Brownian dynamics (BD) results to gain molecular insight into ECM and dendrite growth. BD is a particle simulation method where the ions are modeled explicitly. We show dendrite growth curves (the length of the longest dendrite as a function of time) obtained from visual examination with digital video microscope and from BD simulations. Results for the time to failure are also shown for various values of the electric field strength and cation (Sn2+) concentration (dilution of contamination). We report a mapping of experimental and simulation results that is necessary due to the large concentrations and electric field strengths used in the BD simulations.

Giant permittivity response and enhanced nonlinear electrical properties in a novel perovskite-like ceramic with multiple elements

Copper calcium titanate (CaCu3Ti4O12, CCTO) ceramics are receiving a great deal of attention for advanced electronic and energy storage device applications owing to their giant permittivity response and good temperature stability. However, the development and real applications of CCTO ceramics are generally restricted by their large dielectric loss and low breakdown electric field strength. In the present study, a novel type of perovskite-like Na1/3(Ca1/2Sr1/2)1/3(Bi1/2Y1/2)1/3Cu3Ti4O12 (NCSBYCTO) ceramics were designed via multiple elements strategy based on the high-entropy concept. Consequently, all the NCSBYCTO ceramics present a giant permittivity response (103∼104), good stability of temperature and frequency, and remarkable relaxation characteristics, especially the NCSBYCTO ceramic sintered at 1050 °C exhibits a relative balance between the giant permittivity of about 7.0 × 103–9.5 × 103 and the lower dielectric loss of approximately 0.043–0.294 at a frequency range of 104–106 Hz under room temperature. Furthermore, all the NCSBYCTO ceramics present an obvious nonlinear characteristic. More encouragingly, a higher breakdown field strength of around 2552.56 V/cm accompanied by a larger nonlinear coefficient of about 6.48 is achieved in the NCSBYCTO ceramic sintered at 1070 °C. A significant electrical heterogeneity structure and electron defect structure induced by the existence of mixed-valence Cu+/Cu2+ and Ti3+/Ti4+ are also found in the NCSBYCTO ceramics. The giant permittivity response, low dielectric loss and improved nonlinear properties can be considered the synergistic effect of the defect mechanism and the internal barrier layer capacitor model. This finding offers a route for designing giant permittivity ceramics with brilliant dielectric properties and nonlinear behaviors, which is expected to benefit dual-functional device applications of capacitors and varistors.

High energy storage density obtained by Bi(Ni0.5Hf0.5)O3-modified NBT-based ceramic at a low electric field

Na0.5Bi0.5TiO3 (NBT) ceramic is a potential dielectric material for the manufacture of high-performance dielectric ceramic capacitors due to its high polarization and environmentally friendly characteristics. In this work, (1–x)(0.70Na0.5Bi0.5TiO3–0.30SrTiO3)–xBi(Ni0.5Hf0.5)O3 (NBST–xBNH) ceramics have been prepared based on the strategy of refining grain size and inducing polar nano-regions (PNRs). As a result, the NBST–0.15BNH ceramic achieved large energy density and efficiency (Wrec = 4.11 J/cm3, η = 82.1%) at a low electric field of 240 kV/cm. This performance is outstanding compared to existing reports at similar breakdown electric fields. The introduction of Sr2+ enabled the NBST to have a high relaxation property, and the introduction of BNH induced PNRs, which ensured the high energy storage efficiency of the ceramics. BNH doping refined grain size, which contributed to the large breakdown electric field strength of the ceramics. In addition, stability tests showed that the NBST–0.15BNH ceramic had excellent thermal and frequency stability. The ceramic also demonstrated a fast discharge rate (t0.9 = 148 ns) in the charge-discharge test.

Improved Breakdown Strength and Restrained Leakage Current of Sandwich Structure Ferroelectric Polymers Utilizing Ultra-Thin Al2O3 Nanosheets.

Flexible capacity applications demand a large energy storage density and high breakdown electric field strength of flexible films. Here, P(VDF-HFP) with ultra-thin Al2O3 nanosheet composite films were designed and fabricated through an electrospinning process followed by hot-pressing into a sandwich structure. The results show that the insulating ultra-thin Al2O3 nanosheets and the sandwich structure can enhance the composites' breakdown strength (by 24.8%) and energy density (by 30.6%) compared to the P(VDF-HFP) polymer matrix. An energy storage density of 23.5 J/cm3 at the ultrahigh breakdown strength of 740 kV/mm can be therefore realized. The insulating test and phase-field simulation results reveal that ultra-thin nanosheets insulating buffer layers can reduce the leakage current in composites; thus, it affects the electric field spatial distribution to enhance breakdown strength. Our research provides a feasible method to increase the breakdown strength of ferroelectric polymers, which is comparable to those of non-ferroelectric polymers.

A novel method to measure small antennas using a wideband coaxial cone TEM cell

AbstractThis paper presents a novel method to measure physically small antennas using a coaxial cone transverse electromagnetic wave (TEM) cell. Due to the ultra‐wideband, large electric field strength, and high dynamic range characteristics, coaxial cone provides a reliable environment to measure parameters such as gain and antenna factor of small antennas. The frequency could cover 200 MHz–40 GHz. To investigate the suitability of the coaxial cone TEM cell to measure antenna, measurements for a wideband small antenna and a horn antenna are carried out. And the validity of this method is verified through comparison of the obtained results, the measurement uncertainty is evaluated. Compared to an anechoic chamber, the space, cost, and time requirements are reduced drastically. Accordingly, this method could be a more effective alternative way to conventional methods such as the three antennas method and the two antennas method using anechoic chambers.

The Precision Defect Engineering with Nonmetallic Element Refilling Strategy in g-C3 N4 for Enhanced Photocatalytic Hydrogen Production.

Traditional defect engineering and doping strategies are considered effective means for improving H2 evolution, but the uncontrollability of the modification process does not always lead to efficient activity. A defect-induced heteroatom refilling strategy is used here to synthesize heteroatoms introduced carbon nitride by precisely controlling the "introduction" sites on efficient N1 sites. Density functional theory calculations show that the refilling of B, P, and S sites have stronger H2 O adsorption and dissociation capacity than traditional doping, which makes it an optimal H2 production path. The large internal electric field strength of heteroatom-refilled catalysts leads to fast electron transfer and the hydrogen production of the best sample is up to 20.9mmolg-1 h-1 . This work provides a reliable and clear insight into controlled defect engineering of photocatalysts and a universal modification strategy for typical heteroatom and co-catalyst systems for H2 production.

Adiabaticity parameters for the categorization of light-matter interaction: From weak to strong driving

We investigate theoretically and numerically the light-matter interaction in a two-band system (TBS) as a model system for excitation in a solid-state band structure. We identify five clearly distinct excitation regimes, categorized with well-known adiabaticity parameters: (1) the perturbative multiphoton absorption regime for small driving field strengths, and four light-field-driven regimes, where intraband motion becomes important (2) the impulsive Landau-Zener (LZ) regime, (3) the nonimpulsive LZ regime, (4) the adiabatic regime, and (5) the adiabatic-impulsive regime for large electric field strengths. This categorization is tremendously helpful to understand the highly complex excitation dynamics in solids, in particular, when the driving field strength varies, and this categorization naturally connects Rabi physics with Landau-Zener physics. In addition, we find an insightful analytical expression for the photon orders connecting the perturbative multiphoton regime with the light-field-driven regimes. Moreover, in the adiabatic-impulsive regime, adiabatic motion and impulsive LZ transitions are equally important, leading to a broken symmetry of the TBS and a residual current when applying few-cycle laser pulses of broken temporal symmetry. This categorization allows a deep understanding of strong-field excitation in solids, including current and high-harmonic generation in a large variety of settings, and will help to find optimal driving parameters for a given purpose.

Ground and excited state dipole moments of 1-methylindole from thermochromic shifts in absorption and emission spectra

The permanent dipole moments of 1-methylindole in its ground and lowest excited singlet ππ*-state have been determined using the method of thermochromic shifts of the absorption and fluorescence spectra and compared to ab initio calculated dipole moments. While ab initio theory predicts an excited state dipole moment, which nearly equals that of the ground state, the thermochromic shifts give an excited state dipole moment, which is about 2 Debye larger than that of the ground state. Perturbation of the excited state through the large electric field strength of the solvent cavity leads to strong mixing with the next excited singlet state, which has a considerably larger dipole moment. This perturbation is analyzed using the method described by Lombardi [John R. Lombardi J. Phys. Chem. A 1998, 102, 2817–2823]. The perturbing state could be identified as 1La-state, which is the second adiabatic state in the gas phase, but the lowest state in a polar surrounding.

Dielectric SrTiO3 mesocrystal derived from a H2Ti4O9·H2O single crystal

Strontium titanate (SrTiO3, ST) is a typical paraelectric material that has been widely used in many fields as a dielectric material and an energy-storage material, especially in the electronics industry, due to its excellent dielectric properties. Herein, we report the preparation of pure ST polycrystal powder with uniform granules by the solvothermal treatment of layered titanate H2Ti4O9·H2O (HT) and Sr(OH)2·8H2O as the raw materials. The effects of specimen morphology and electric field strength on the electrical properties of ST ceramics were investigated by studying their responses to heat treatment at various temperatures. The results show that pure ST mesocrystals, nanoparticles, and ceramics were successfully prepared. The ST ceramics show a rare bimodal phenomenon and strong dielectric response, which is due to the specimens containing two forms of ST crystal structure, namely the traditional ST polycrystal and a rare ST mesocrystal. When sintered at 900 °C, the ST ceramic exhibited good electrical-response performance due to the uniform particle morphology of the specimen and a large electric field strength at 2 kV. This study demonstrates the influence of particle morphology and electric field strength on the electrical properties of ceramics and lays the foundation for the development of multifunctional oxide ceramics with excellent electrical properties.

Sauter–Schwinger effect with a quantum gas

The creation of particle–antiparticle pairs from vacuum by a large electric field is at the core of quantum electrodynamics. Despite the wide acceptance that this phenomenon occurs naturally when electric field strengths exceed Ec ≈ 1018 V m−1, it has yet to be experimentally observed due to the limitations imposed by producing electric fields at this scale. The high degree of experimental control present in ultracold atomic systems allow experimentalists to create laboratory analogs to high-field phenomena. Here we emulated massive relativistic particles subject to large electric field strengths, thereby quantum-simulated particle–antiparticle pair creation, and experimentally explored particle creation from ‘the Dirac vacuum’. Data collected from our analog system spans the full parameter regime from low applied field (negligible pair creation) below the Sauter–Schwinger limit, to high field (maximum rate of pair creation) far in excess of the Sauter–Schwinger limit. In our experiment, we perform direct measurements on an analog atomic system and show that this high-field phenomenon is well-characterized by Landau–Zener tunneling, well known in the atomic physics context, and we find full quantitative agreement with theory with no adjustable parameters.

On-Chip Dispersion Measurement of the Quadratic Electro-Optic Effect in Nonlinear Optical Polymers Using a Photonic Integrated Circuit Technology

A novel method to determine the dispersion of the quadratic electro-optic effect in nonlinear optical materials by using a silicon-on-insulator microring resonator is presented. The microring consists of a silicon slot waveguide enabling large dc electric field strength at low applied voltages. The dispersion of third-order hyperpolarizability of a linear conjugated dye is approximated by using a two-level model for the off-resonant spectral region. As an example, the dispersion of the resonance wavelength of the resonator filled with a dye doped polymer was measured in dependence of the applied dc voltage. The polymer was poly (methylmethacrylate) doped with $\text{5 wt}\%$ disperse red 1 (DR1), and the measurements have been carried out at the telecommunication wavelength band around $\text{1550 nm}$ (optical C -band). The described measurements represent a new technique to determine the dispersion of the third-order susceptibility and molecular hyperpolarizability of the material filled into the slot of the ring-resonator.

Second harmonic generation from complementary triangular Au metamaterials

Sub-wavelength square array of a triangular Au platelet and its complementary structure (i.e. that of a triangular hole in a square film of Au) are compared in terms of second harmonic generation efficiency for fundamental light in the near infrared and visible region of spectrum for normal incidence. Electric field strength around the convex corners of a triangular particle is at least 10 times larger than the one around the concave corners of triangular hole in the complementary structure. Nevertheless the SHG intensity at the respective resonant frequency is found to be comparable, which are numerically estimated by an overlap integral of nonlinear polarization and electric field at the SHG frequency in the nonlinear optical scattering theory originally proposed by Roke et al. (Phys. Rev. B 70, 115106 (2004)). The reason is due to the large electric field strength at the sides of the triangular hole at the resonance frequency, which compensates the suppressed electric field at the concave corners in the overlap integral.

First Map of Coherent Low‐Frequency Continuum Radiation in the Sky

AbstractLightning discharges and radio transmitters emit low‐frequency (∼3–300 kHz) electromagnetic waves with large electric field strengths and stable phases. This phase stability makes it possible to map the source locations of lightning and transmitters in the sky. Electromagnetic waves with smaller electric field strengths generally exhibit a reduced phase stability, caused by numerous simultaneous physical processes that blend into an underlying continuum radiation trapped inside the Earth‐ionosphere cavity. It is therefore currently not known whether the source locations of continuum radiation can be determined. Here we show the first map of coherent continuum radiation in the sky above an array of high‐precision radio receivers. The source locations of the coherent continuum radiation are found at elevation angles ∼30∘−60∘ above the horizon. The identified source locations are attributed to intermittent radio transmitters that emit electromagnetic waves with electric field strengths ∼2 orders of magnitude below the instrumental noise floor. The results demonstrate that it is possible to simultaneously map the signals from coherent continuum radiation, lightning discharges, and radio transmitters in the sky. This work thereby lays the foundation toward the discovery of many more coherent source locations of low‐frequency electromagnetic waves in the sky. It is expected that the identified source locations vary with time as a result of the impact of solar variability on the D‐region ionosphere. Future studies have therefore the potential to contribute to a novel remote sensing and an improved understanding of the D‐region ionosphere, influenced by the near‐Earth space environment.

Re-igniting the afterglow plasma column of an AC powered gliding arc discharge in atmospheric-pressure air

The stability and re-ignition characteristics of the plasma column of an alternating current (AC) powered gliding arc discharge operating in atmospheric-pressure air were investigated for better plasma-mode controlling and optimized applications. By modulating the AC power supply and the air flow field, the states of afterglow plasma column were varied. When pulsating the AC power supply sequence, re-ignitions of the afterglow columns were introduced and their characteristics were studied using simultaneous high-speed photography and electrical measurements. Two re-ignition types were observed in the afterglow column with different decay times (the temporal separation of two sequential pulsed AC power trains). For a short decay time (<200 μs at 10 l/min air flow), the afterglow column can be recovered mildly without current spikes, which is called a glow re-ignition event. If the decay time is so long that the electric field strength becomes larger than 120 kV/m, the re-ignition event occurs with current spikes and bright emissions, which is called a spark re-ignition event. A quasi-equilibrium model is proposed to estimate the chemical compositions in the plasma column and to explain the observed phenomena. It infers that the chemical dissociation and ionization processes enhanced by vibrationally excited nitrogen molecules are dominating in the afterglow plasmas and thereby the electrons can survive a long time to keep the conductivity of the afterglow column, forming a glow re-ignition event. Whereas under large electric field strength (>120 kV/m), the electron impact ionization becomes dominant to trigger the spark re-ignition event.

Inductively Coupled Plasma Etching and Electrically Active Damage of Bulk, Single-Crystal Ga2O3

Monoclinic β phase Ga2O3 is attracting great attention for high power electronics, military applications, and solar blind photodetectors for deep-UV detection, all because of its large direct bandgap (~4.9 eV) and theoretical critical electric field (EC) strength of 8 MV/cm. [1,2,3] There has been a tremendous achievement in both bulk and epitaxial growth of β-Ga2O3. The large bulk β-Ga2O3 is commercially available, and n-type epistructures are also coming onto the market in limited quantities.[4] Record high Vertical diode fabricated on β -Ga2O3 with a reverse breakdown voltage of 1600 V was demonstrated[5], and Ga2O3 based variety of electronic devices have also been reported including metal-semiconductor field-effect transistors, depletion-mode metal-oxide-semiconductor field-effect transistors, and finfets fabricated on either bulk or thin films.[6,7,8,9] It is quite clear that more organized study of etching is needed for intradevice isolation or for exposing layers in gate recess processing for subsequent Schottky gate formation. While numerous wet etchants have been reported for Ga2O3, including HNO3/HCl, H2SO4, H3PO4 and HF-based solutions,[10,11] not too much is known about its dry etching characteristics and the associated mechanisms and effects on the optical properties of the material. In this study, we will report the effect of dry etching conditions on etching rates and damage induced by the ion bombardment on vertical β-Ga2O3 rectifiers. A Plasma Therm 760 Inductively Coupled Plasma (ICP) system was employed for dry etching by varying the ICP power ranging from 100 to 800W, chuck power (15-400 W) with either Cl2/Ar or BCl3/Ar discharges. The highest etch rate achieved was ~130 nm/min using 800 W ICP source power and 200 W chuck power (13.56 MHz). The etched Ga2O3 surfaces become oxygen-deficient under strong ion-bombardment conditions, and the electrically active damage introduced during etching was quantified using Schottky barrier height and diode ideality factor measurements. For low etch rate conditions (~12 nm/min) at low powers (150 W ICP source power at 2 MHz and 15 W rf chuck power at 13.56 MHz). There was only a small decrease in reverse breakdown voltage (~6%) while the Schottky barrier height decreased from 1.2 eV to 1.01 eV and the ideality factor increased from 1.00 to 1.06. Under higher etch rate (~70 nm/min) and power (400 W ICP and 200 W rf power) conditions, the damage was more significant, with the reverse breakdown voltage decreasing by ~35%, the barrier height was reduced to 0.86 eV and the ideality factor increased to 1.2. By annealing the etched samples at 450°C, the Schottky barrier height, diode ideality factor and reverse breakdown voltage were restored as compared to the reference sample. I. Stepanov, V.I. Nikolaev, V. E. Bougrov and A.E. Romanov, Rev. Adv. Mater. Sci., 44, 63 (2016).Higashiwaki, K. Sasaki, H. Murakami, Y. Kumagai, A. Koukitu, A. Kuramata, T. Masui and S. Yamakosh, Semicond. Sci. Technol., 31, 034001 (2016).Higashiwaki, K. Sasaki, A. Kuramata, T. Masui and S. Yamakoshi, Appl. Phys. Lett., 100, 013504 (2012).Higashiwaki, K. Sasaki, H. Murakami, Y. Kumagai, A. Koukitu, A. Kuramata, T. Masui and S. Yamakosh, Semicond. Sci. Technol., 31, 034001 (2016).Yang, S. Ahn, F. Ren, S. J. Pearton, S. Jang, and A. Kuramata, IEEE Electron Device Lett,. 38(7), 906 (2017).H. Wong, K. Sasaki, A. Kuramata, S. Yamakoshi and M. Higashiwaki, IEEE Electr. Dev. Lett., 37, 212 (2016).Michele Baldini, Martin Albrecht, Andreas Fiedler, Klaus Irmscher, Robert Schewski, and Günter Wagner, ECS J. Solid State Sci. Technol. 6, Q3040 (2017).Higashiwaki, K. Sasaki, H. Murakami, Y. Kumagai, A. Koukitu, A. Kuramata, T. Masui and S. Yamakosh, Semicond. Sci. Technol., 31, 034001 (2016).Shihyun Ahn, Fan Ren, Janghyuk Kim, Sooyeoun Oh, Jihyun Kim, Michael A. Mastro and S. J. Pearton, Appl. Phys. Lett.109, 062102 (2016).Takayoshi Oshima, Takeya Okuno, Naoki Arai, Yasushi Kobayashi and Shizuo Fujita, Jpn. J. Appl. Phys. 48, 040208 (2009)Shigeo Ohira and Naoki Arai, Phys. Stat. Sol. (c) 5, No. 9, 3116-3118 (2008)

Continuous-Flow Electrophoresis of DNA and Proteins in a Two-Dimensional Capillary-Well Sieve.

Continuous-flow electrophoresis of macromolecules is demonstrated using an integrated capillary-well sieve arranged into a two-dimensional anisotropic array on silicon. The periodic array features thousands of entropic barriers, each resulting from an abrupt interface between a 2 μm deep well (channel) and a 70 nm capillary. These entropic barriers owing to two-dimensional confinement within the capillaries are vastly steep in relation to those arising from slits featuring one-dimensional confinement. Thus, the sieving mechanisms can sustain relatively large electric field strengths over a relatively small array area. The sieve rapidly sorts anionic macromolecules, including DNA chains and proteins in native or denatured states, into distinct trajectories according to size or charge under electric field vectors orthogonally applied. The baseline separation is achieved in less than 1 min within a horizontal migration length of ∼1.5 mm. The capillaries are self-enclosed conduits in cylindrical profile featuring a uniform diameter and realized through an approach that avoids advanced patterning techniques. The approach exploits a thermal reflow of a layer of doped glass for shape transformation into cylindrical capillaries and for controllably shrinking the capillary diameter. Lastly, atomic layer deposition of alumina is introduced for the first time to fine-tune the capillary diameter as well as to neutralize the surface charge, thereby suppressing undesired electroosmotic flows.

Photocurrent microscopy of contact resistance and charge carrier traps in organic field-effect transistors

We use a pentacene transistor with asymmetric source drain contacts to test the sensitivity of scanning photocurrent microscopy (SPCM) for contact resistance and charge traps. The drain current of the device strongly depends on the choice of the drain electrode. In one case, more than 94% of the source drain voltage is lost due to contact resistance. Here, SPCM maps show an enhanced photocurrent signal at the hole-injecting contact. For the other bias condition, i.e., for ohmic contacts, the SPCM signal peaks heterogeneously along the channel. We argue from basic transport models that bright areas in SPCM maps indicate areas of large voltage gradients or high electric field strength caused by injection barriers or traps. Thus, SPCM allows us to identify and image the dominant voltage loss mechanism in organic field-effect transistors.

Excited atoms in argon gas discharge plasma

General principles are discussed for a gas discharge plasma involving excited atoms where electron-atom collision processes dominate. It is shown that an optimal kinetic model of this plasma at not large electric field strengths can be based on the rate constants of quenching excited atom states by electron impact. The self-consistent character of atom excitation in gas discharge plasma is important and results in the tail of the energy distribution function of electrons being affected by the excitation process, which in turn influences the excitation rate. These principles are applied to an argon gas discharge plasma where excitation and ionization processes have a stepwise character and proceed via formation of argon atom states with the electron shell 3p54s.

Enhanced translational diffusion of confined water under electric field

High resolution quasielastic neutron scattering measurements have been used to study the effects of applied electric field on the dynamics of water molecules confined in the pores of folded silica sheet material FSM-12 with an average pore diameter (apd) of 16 Å. In the absence of field, there is a significant slowing down of the water molecule diffusion as the temperature is lowered, in agreement with previous observations. The application of a moderate electric field of 2.5 kV/mm remarkably enhances the translational diffusion of water molecules. We interpret this as being due to a disruption of the hydrogen bonding by the electric field. This new observation suggests that existing theories valid at large electric field strengths may have to be corrected at moderate fields.