Positive Charge Region Research Articles

Effects of Charge Distribution in Thunderstorms on Lightning Propagation Paths in Darwin, Australia

Abstract The charge distributions in a thundercloud play an important role in the initiation and propagation of lightning discharges. To further understand the effects of charge distributions on lightning discharge, the authors conducted a very high-frequency (VHF) lightning observation campaign during the 2006/07 monsoon in Darwin, Australia, using a VHF broadband digital interferometer (DITF). A C-band polarimetric weather radar to estimate the precipitation profiles such as hydrometeor classification was operated by the Bureau of Meteorology (BOM) Research Centre. Cloud-to-ground (CG) and intracloud (IC) flashes were initiated from the outer and the inner parts of the upper side of the graupel regions, respectively. In the cases of CG flashes, the negative leaders travel first about 10 km horizontally through positive charge regions and then begin to bend toward the ground when they reach the edge of the positive charge regions where there is no graupel region underneath. In contrast, in the cases of the IC flashes the negatively charged graupel regions block the downward developments of negative leaders. It is noted that positive charge regions could facilitate the extension of the horizontal negative leader. These results may suggest that lightning flash types are closely dependent on their initiation locations and the surrounding charge distributions. The experimental results are consistent with other previous observation results and charge model simulations.

Characterization of the Interaction of the Dengue Virus Capsid Protein with Lipid Droplets

Dengue virus affects 100 million people yearly, but this number may grow since Aedes spp. mosquitoes, the disease vectors, are spreading to temperate climates, including in the USA. No effective vaccines are available. A poor understanding of the viral life cycle is to blame, especially regarding the viral assembly and encapsidation process, mediated by Dengue Virus Capsid Protein (DVCP). DVCP is a symmetric homodimmer α-helical protein that must interact with intracellular lipid droplets during viral encapsidation. DVCP charge distribution suggests that its α2-α2’ nonpolar region may interact with lipids and the α4-α4’ positive charged region could interact with viral RNA. By employing biophysical techniques combined with bioinformatics tools, we found this hypothesis correct. Nuclear magnetic resonance (NMR) shows a strong interaction with lipid droplets on the N-terminus and the α2-α2’ region of DVCP and points to a conformational change transmitted to the α4-α4’ region (C-terminus) via specific residues located in the α2-α2’ region. Aligning DVCP sequence with 16 Flavivirus spp. capsid proteins demonstrates that the residues identified by NMR as important for the lipid droplets interaction are conserved in the genus. Moreover, Dengue and West-Nile virus capsid protein structures super-impose in the α2, α3 and α4 helices, pointing to a fold conservation among Flavivirus spp. DVCP α4-helices superimpose with oligonucleotide binding motifs, being therefore likely to bind RNA. Upon interaction with DVCP, the zeta potential of lipid droplets progressively shifts from negative to positive values, suggesting the positive α4-helices exposure on the surface of the lipid droplet-DVCP conjugate. Concluding, DVCP specifically interacts with lipid droplets via its N-terminus and the α2-α2’ region, resulting in conformational changes in the α4-α4’ region and, finally, the DVCP-RNA binding. These regions could thus be targeted in future dengue drug development strategies.

Duration and extent of large electric fields in a thunderstorm anvil cloud after the last lightning

A series of balloon electric field (E) soundings and time‐correlated radar scans through the balloon locations are used to examine the evolution of charge and reflectivity inside a dissipating thunderstorm anvil. The soundings cover a 75 min period during and after the final lightning flash in distant convection. The first sounding measured large E magnitudes (maximum 65 kV m−1) and significant charge densities of both polarities (maximum +2.5 nC m−3) within and screening the anvil. Little change in the maximum E values occurred in the 30 min between the first and third soundings, although altitudes and densities of some charge regions decreased with time (maximum +0.6 nC m−3). Screening charge regions were observed in close coincidence with 12 dbZ radar reflectivity contours, and interior positive charge was found in the reflectivity maxima of both anvil decks. The fourth sounding ascended through visible but optically less dense cloud, and no enhanced E values were detected. Overall, the data indicate the interior positive charge region of the main anvil contained about 150 C and covered at least 250 km2 nearly 30 min after the last lightning flash. Potentially hazardous E values of 30–35 kV m−1 were measured at 9.9–10.2 km altitude, a common jet aircraft cruising altitude, more than 20 km away from and 32 min after the final lightning flash. About 50 min after the last flash, the main positive charge region contained an estimated 50 C, and potentially hazardous E values associated with the anvil extended over at least 220 km2.

Molecular Characterization of a Class I P450 Electron Transfer System from Novosphingobium aromaticivorans DSM12444

Cytochrome P450 (CYP) enzymes of the CYP101 and CYP111 families from the oligotrophic bacterium Novosphingobium aromaticivorans DSM12444 are heme monooxygenases that receive electrons from NADH via Arx, a [2Fe-2S] ferredoxin, and ArR, a ferredoxin reductase. These systems show fast NADH turnovers (k(cat) = 39-91 s(-1)) that are efficiently coupled to product formation. The three-dimensional structures of ArR, Arx, and CYP101D1, which form a physiological class I P450 electron transfer chain, have been resolved by x-ray crystallography. The general structural features of these proteins are similar to their counterparts in other class I systems such as putidaredoxin reductase (PdR), putidaredoxin (Pdx), and CYP101A1 of the camphor hydroxylase system from Pseudomonas putida, and adrenodoxin (Adx) of the mitochondrial steroidogenic CYP11 and CYP24A1 systems. However, significant differences in the proposed protein-protein interaction surfaces of the ferredoxin reductase, ferredoxin, and P450 enzyme are found. There are regions of positive charge on the likely interaction face of ArR and CYP101D1 and a corresponding negatively charged area on the surface of Arx. The [2Fe-2S] cluster binding loop in Arx also has a neutral, hydrophobic patch on the surface. These surface characteristics are more in common with those of Adx than Pdx. The observed structural features are consistent with the ionic strength dependence of the activity.

A closer examination of terrestrial gamma‐ray flash‐related lightning processes

This paper presents detailed comparisons between terrestrial gamma‐ray flashes (TGFs) detected by the RHESSI satellite and the lightning processes observed by the Los Alamos Sferic Array (LASA). It was found that all RHESSI‐detected TGFs were related to normal intracloud flashes that transported electrons upward in the cloud. Detailed temporal comparisons suggest that TGFs are more likely related to small, rather than large, lightning pulses, mostly at the level of 10−1−100 V/m when the pulses are normalized to an observation distance of 100 km. The corresponding peak current was estimated to be 3–19 kA with most of them below 10 kA, if the discharges were assumed to be individual steps in a stepped‐leader process. If the discharges were considered to be directly associated with runaway breakdown processes with a current propagation speed of c, the peak current would be 0.4–3.2 kA. Analysis of events that were close to the LASA stations showed that TGFs were most likely to occur during the initial milliseconds of IC flashes while the discharge developed vertically upward from the negative to the positive charge regions in the cloud. The heights of the TGF‐related lightning pulses were estimated to be in the range of 10.5–14.1 km along the upward development. An intense NBE with a peak current of 80 kA and a height of 16.1 km was found 2.9 ms after one TGF, and is believed to not be directly associated with the TGF but may be preconditioned by the TGF‐related discharge process.

Using lightning locating system based on time-of-arrival technique to study three-dimensional lightning discharge processes

A time-of-arrival (TOA) system based on GPS technology for locating VHF radiation sources from lightning has been developed and used in observation sites in the northern Shandong Province, China. The 3D images of the lightning progression have been obtained successfully for the first time in China. The 3D-channel evolutions of typical negative CG, positive CG and IC lightning flashes have been discussed together with the data of fast electric field change. It was found that significant differences existed between the negative and positive CG lightning flashes in terms of the initiation and propagation of the radiation sources. The preliminary breakdown of a negative CG lightning flash propagated at a speed about 5.2×104 m/s. The stepped leader of negative CG lightning flashes was trigged by negative initial breakdown. Thereafter, it propagated downward at a speed of 1.3×105 m/s. The initial process of the positive CG lightning flashes was also a propagation process of negative streamer. These streamers propagated dominantly horizontally in the positive charge region and accumulated positive charges at the origin of the lightning, and as a consequence, initiated downward positive streamers. A new type of lightning discharge that was triggered by a narrow bipolar pulse (NBP) is discussed in this study. The NBP was originated at altitude of about 10.5 km in the upper positive charge region. As a distinct difference from normal IC flash, its channels extended horizontally all around and produced a lot of radiation sources. The source power of the NBP could approach 16.7 kW, which is much greater than that of normal lightning discharge ranging between 100 mW and 500 W. The 3D propagation of this new type of lightning discharge was observed and obtained for the first time in China. The possible initiation mechanism of this new type of lightning is discussed here.

Measurements of electric charge separated during the formation of rime by the accretion of supercooled droplets

Abstract. In these experiments, the electric charge carried by single particles ejected from the surface of a graupel particle growing by riming was measured. Simulated graupel pellets were grown by accretion of supercooled water drops, at temperatures ranging from −2 to −10 °C in a wind tunnel at air velocities between 5 and 10 m s−1, with the goal of studying the charging of graupel pellets under conditions of secondary ice crystal production (Hallett-Mossop mechanism). The graupel, and induction rings upstream and downstream of the graupel, were connected to electrometers and analyzing circuits of sufficient sensitivity and speed to measure, correlate and display individual charging events. The results suggest that fewer than 1% of the ejected particles carry a measurable electric charge (>2 fC). Further, it was observed that the graupel pellets acquire a positive charge and the average charge of a single splinter ejected is −14 fC. This mechanism of ejection of charged particles seems adequate to account for a positive charge of around 1 pC that individual precipitation particles of mm-size could acquire in the lower part of the cloud, which in turn could contribute to the lower positive charge region of thunderstorms.

Lightning Channels of Cloud-to-Ground Flashes Neutralizing Multiple Charge Regions Inside Winter Thunderclouds

Lightning Research Group of Osaka University (LRG-OU) has been developing and improving the VHF broadband digital interferometer (DITF) for thunderstorm observations. It enables us to locate the impulsive VHF radiation sources caused by lightning discharges with extremely high resolutions. As a result of the VHF observations during the 2007-2008 winter season in the Japan Sea coastal area, cloud-to-ground (CG) flashes that neutralize multiple charge regions inside thunderclouds are visualized by the VHF broadband DITF. The first flash is the positive CG flash that neutralizes multiple positive charge regions in a flash. The second flash is the bipolar lightning flash that neutralizes both positive and negative charge inside thunderclouds. In the case of bipolar lightning flashes, some tens millisecond after the return strokes, the subsequent negative breakdowns initiate from the proximities of the initiation points of the preceding negative stepped leaders. It was also found that the altitudes of negative charge regions are lower than 2km. The bipolar lightning flashes observed in this campaign neutralize positive charge after lowering the negative charge to the ground.

Simulated Electrification of a Small Thunderstorm with Two-Moment Bulk Microphysics

Abstract Electrification and lightning are simulated for a small continental multicell storm. The results are consistent with observations and thus provide additional understanding of the charging processes and evolution of this storm. The first six observed lightning flashes were all negative cloud-to-ground (CG) flashes, after which intracloud (IC) flashes also occurred between middle and upper levels of the storm. The model simulation reproduces the basic evolution of lightning from low and middle levels to upper levels. The observed lightning indicated an initial charge structure of at least an inverted dipole (negative charge above positive). The simulations show that noninductive charge separation higher in the storm can enhance the main negative charge sufficiently to produce negative CG flashes before upper-level IC flashes commence. The result is a “bottom-heavy” tripole charge structure with midlevel negative charge and a lower positive charge region that is more significant than the upper positive region, in contrast to the traditional tripole structure that has a less significant lower positive charge region. Additionally, the occurrence of cloud-to-ground lightning is not necessarily a result of excess net charge carried by the storm, but it is primarily caused by the local potential imbalance between the lowest charge regions. The two-moment microphysics scheme used for this study predicted mass mixing ratio and number concentration of cloud droplets, rain, ice crystals, snow, and graupel. Bulk particle density of graupel was also predicted, which allows a single category to represent a greater range of particle characteristics. (An additional hail category is available but was not needed for the present study.) The prediction of hydrometeor number concentration is particularly critical for charge separation at higher temperatures (−5° < T < −20°C) in the mixed phase region, where ice crystals are produced by rime fracturing (Hallett–Mossop process) and by splintering of freezing drops. Cloud droplet concentration prediction also affected the rates of inductive charge separation between graupel and droplets.

Molecular Dynamics Simulation of the Aggregation of Titanium Dioxide Nanocrystals: Preferential Alignment

We use classical molecular-dynamics simulations to study the aggregation of various titanium dioxide (anatase) nanocrystals in vacuum. In all cases, we observe a strong tendency for the nanocrystals to aggregate with certain preferred orientations in a "hinge" mechanism. Although some of the nanocrystals possess significant dipole moments, dipole-dipole interactions do not direct aggregation, implying that higher-order multipole moments are the driving force for preferential alignment. These high-order multipole moments originate from under-coordinated O and Ti surface atoms on the edges between nanocrystal facets, which create localized regions of positive and negative charge. The observed mechanism for preferential alignment may be a driving force for oriented attachment and the growth of anisotropic structures during crystallization.

Particle-in-cell modeling of magnetized argon plasma flow through small mechanical apertures

Motivated by observations of supersonic argon-ion flow generated by linear helicon-heated plasma devices, a three-dimensional particle-in-cell (PIC) code is used to study whether stationary electrostatic layers form near mechanical apertures intersecting the flow of magnetized plasma. By self-consistently evaluating the temporal evolution of the plasma in the vicinity of the aperture, the PIC simulations characterize the roles of the imposed aperture and applied magnetic field on ion acceleration. The PIC model includes ionization of a background neutral-argon population by thermal and superthermal electrons, the latter found upstream of the aperture. Near the aperture, a transition from a collisional to a collisionless regime occurs. Perturbations of density and potential, with millimeter wavelengths and consistent with ion acoustic waves, propagate axially. An ion acceleration region of length ∼200λD,e–300λD,e forms at the location of the aperture and is found to be an electrostatic double layer, with axially separated regions of net positive and negative charge. Reducing the aperture diameter or increasing its length increases the double layer strength.

Monte Carlo Simulation of Surface-Charging Phenomena on Insulators Prior to Flashover in Vacuum

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Before flashover across an insulator under high electric field in vacuum, there are charging phenomena occurring on the insulator surface, which significantly affect the developing process of flashover. Based on the secondary-electron-emission-avalanche model and by using the Monte Carlo method, a 2-D analysis of surface charge density on cylindrical and conical insulators prior to flashover in vacuum has been performed under unipolar voltage. Different materials are employed, i.e., alumina ceramic, PTFE, PMMA, and PI. The influences of materials, voltage amplitudes, and coning angles on charge distribution are investigated. The results reveal that negative charges exist in a small surface region near the cathode, while the surface charges positive in a larger region away from the cathode. With increasing applied voltage, both the negative charge density and region decrease, and even vanish, whereas both the positive charge density and region increase, and the peaks of both regions move toward the cathode. For the conical insulator with a negative angle, the positive charge density is greater than that with a positive angle, and the simulation describes well experimental data relating the coning angle, the surface charge, and the flashover voltage. </para>

Some inferences on the role of lower positive charge region in facilitating different types of lightning

It is generally thought that the lower positive charge region serves to enhance the electric field at the bottom of the main negative charge region and thereby facilitate the launching of a negatively‐charged leader toward ground. On the other hand, the presence of excessive lower positive charge region may prevent the occurrence of negative cloud‐to‐ground discharges by “blocking” the progression of descending negative leader from reaching ground and thus “converting” the potential cloud‐to‐ground flash to an intracloud (or cloud‐to‐air) one. Assuming that the preliminary breakdown pulse train is a manifestation of interaction of a downward‐extending negative leader channel with the lower positive charge region, we qualitatively examine the inferred dependence of lightning type on the magnitude of this charge region.

Intracloud discharge and the correlated basic charge structure of a thunderstorm in Zhongchuan, a Chinese Inland Plateau region

The intracloud (IC) discharge is closely related to the charge structure of thunderstorms. The location, charge moment and polarity of intracloud discharges have been analyzed by using the electric field changes from a 7-site network of slow antennas synchronized by GPS with 1 μs time resolution in the area of Zhongchuan in the Chinese Inland Plateau. Ten IC flashes, from a storm on August 20, 2004, have been fitted by using the non-linear least-square solution. The results show that five IC flashes occurred between the main negative charge region and the lower positive charge region and other five between the main negative charge region and the upper positive charge region during the mature stage of the thunderstorm. The centers of discharge were 3.2–5.6 km and 6.8–7.7 km above sea level. The neutralized moments were about 4.56–61.0 C km and 1.06–15.9 C km. It suggests that the charge structure related to the lightning discharge can be represented by a tripole but with a strong positive charge region in the lower part of the thunderstorm, with the lower positive charge region taking an active role in the discharge.

Fine-resolution simulation of cloud-to-ground lightning and thundercloud charge transfer

2-D 12.5 m-resolution simulations of cloud-to-ground (CG) lightning discharge processes have been performed using an improved stochastic lightning model for different types of cloud charge distributions, such as dipole, tripole, bi-dipole and multi-layer charge structures produced from the numerical simulation of thundercloud electrification. The modelling produced the fine branched channel structure of CG lightning and the results illustrate the relations between CG lightning channel propagation and cloud charge distribution. The simulated features of CG lightning are associated with the observed results. The simulation studies are essential in our understanding of complex charge transfer processes caused by CG lightning discharges in thunderclouds. The induced charges of opposite polarity are deposited or embedded in the local volumes where the bidirectional leaders passed during a CG lightning discharge. Although the embedding affects charge structure only in a pair of significant positive and negative charge regions closest to the ground, the electric field strength acutely weakens and electrostatic energy in thunderclouds is significantly consumed when the discharge terminates. In addition to simulating the upward and downward breakdown of the initial leader to ground and the ensuing return stroke (RS), the simulation assumes that current continues to flow in the channel to ground and determines the upward breakdown until the end of the discharge. For the subsequent discharge sub-process, the upward leader channel tends to transfer the charges with the same polarity as the RS, while the downward leader channel favors transfer of opposite charge to ground. In the sub-processes of a few CG flash simulations, the magnitude of the opposite charges from the downward leader exceeds that of charges with the same polarity from the upward leader so that the net charges transferred to the ground have a reversed polarity to the RS. The simulation presents similar features of CG lightning as those observed in realistic bipolar CG lightning.

Enhancement of water permeation across nanochannels by partial charges mimicked from biological channels

In biological water channel aquaporins (AQPs), it is believed that the bipolar orientation of the single-file water molecules inside the channel blocks proton permeation but not water transport. In this paper, the water permeation and particularly the water-selective behaviour across a single-walled carbon nanotube (SWNT) with two partial charges adjacent to the wall of the SWNT are studied by molecular dynamics simulations, in which the distance between the two partial charges is varied from 0.14 nm to 0.5 nm and the charges each have a quantity of 0.5 e. The two partial charges are used to mimic the charge distribution of the conserved non-pseudoautosomal (NPA) (asparagine/proline/alanine) regions in AQPs. Compared with across the nanochannel in a system with one +1 e charge, the water permeation across the nanochannel is greatly enhanced in a system with two +0.5 e charges when charges are close to the nanotube, i.e. the two partial charges permit more rapid water diffusion and maintain better bipolar order along the water file when the distance between the two charges and the wall of SWNT is smaller than about 0.05 nm. The bipolar orientation of the single-file water molecules is crucial for the exclusion of proton transfer. These findings may serve as guidelines for the future nanodevices by using charges to transport water and have biological implications because membrane water channels share a similar single-file water chain and positive charged region at centre and provide an insight into why two residues are necessitated in the central region of water channel protein.

Evolving Complex Electrical Structures of the STEPS 25 June 2000 Multicell Storm

Abstract Data from a three-dimensional lightning mapping array (LMA) and from two soundings by balloon-borne electric field meters (EFMs) were used to analyze the electrical structures of a multicell storm observed on 25 June 2000 during the Severe Thunderstorm Electrification and Precipitation Study (STEPS). This storm had a complex, multicell structure with four sections, each of whose electrical structure differed from that of the others during all or part of the analyzed period. The number of vertically stacked charge regions in any given section of the storm ranged from two to six. The most complex charge and lightning structures occurred in regions with the highest reflectivity values and the deepest reflectivity cores. Intracloud flashes tended to concentrate in areas with large radar reflectivity values, though some propagated across more than one core of high reflectivity or into the low-reflectivity anvil. Intracloud lightning flash rates decreased as the vertical extent and maximum value of reflectivity cores decreased. Cloud-to-ground flash rates increased as cores of high reflectivity descended to low altitudes. Most cloud-to-ground flashes were positive. All observed positive ground flashes initiated between the lowest-altitude negative charge region and a positive charge region just above it. The storm’s complexity makes it hard to classify the vertical polarity of its overall charge structure, but most of the storm had a different vertical polarity than what is typically observed outside the Great Plains. The electrical structure can vary considerably from storm to storm, or even within the same storm, as in the present case.

MHC-IIB Filament Assembly and Cellular Localization Are Governed by the Rod Net Charge

BackgroundActin-dependent myosin II molecular motors form an integral part of the cell cytoskeleton. Myosin II molecules contain a long coiled-coil rod that mediates filament assembly required for myosin II to exert its full activity. The exact mechanisms orchestrating filament assembly are not fully understood.Methodology/Principal FindingsHere we examine mechanisms controlling filament assembly of non-muscle myosin IIB heavy chain (MHC-IIB). We show that in vitro the entire C-terminus region of net positive charge, found in myosin II rods, is important for self-assembly of MHC-IIB fragments. In contrast, no particular sequences in the rod region with net negative charge were identified as important for self-assembly, yet a minimal area from this region is necessary. Proper paracrystal formation by MHC-IIB fragments requires the 196aa charge periodicity along the entire coiled-coil region. In vivo, in contrast to self-assembly in vitro, negatively-charged regions of the coiled-coil were found to play an important role by controlling the intracellular localization of native MHC-IIB. The entire positively-charged region is also important for intracellular localization of native MHC-IIB.Conclusions/SignificanceA correct distribution of positive and negative charges along myosin II rod is a necessary component in proper filament assembly and intracellular localization of MHC-IIB.

Radar and Lightning Observations of the 3 June 2000 Electrically Inverted Storm from STEPS

AbstractThis study addresses the kinematic, microphysical, and electrical evolution of an isolated convective storm observed on 3 June 2000 during the Severe Thunderstorm Electrification and Precipitation Study field campaign. Doppler-derived vertical velocities, radar reflectivity, hydrometeor classifications from polarimetric radar, and Lightning Mapping Array (LMA) charge structures are examined over a nearly 3-h period. This storm, characterized as a low-precipitation supercell, produced modest amounts of hail, determined by fuzzy-logic hydrometeor classification as mostly small (&amp;lt;2 cm) hail, with one surface report of large (≥2 cm) hail. Doppler-derived updraft speeds peaked between 20 and 25 m s−1, and reflectivity was never greater than 60 dBZ. The most striking feature of this storm was its total lack of cloud-to-ground (CG) lightning. Though this storm was electrically active, with maximum flash rates near 30 per minute, no CG flashes of either polarity were detected. The charge structure inferred from the LMA observations was consistent with an inverted dipole, defined as having a midlevel positive charge region below upper-level negative charge. Inverted charge structures have typically been considered conducive to producing positive CG lightning; however, the 3 June storm appeared to lack the lower negative charge layer below the inverted dipole that is thought to provide the downward electrical bias necessary for positive CG lightning.

Self-consistent ensemble Monte Carlo simulations show terahertz oscillations in single-walled carbon nanotubes

We investigate electrical transient and stationary transport properties of semiconducting single-walled zigzag carbon nanotubes (CNTs), using a transient ensemble Monte Carlo (MC) simulator that self-consistently solves the semiclassical transport and Poisson equations. We developed the ensemble MC simulator to obtain time and space dependencies of the CNT electron concentration, velocity, and current profiles self-consistently with electrical potential distribution on the tube. Our calculated MC results indicate that self-induced terahertz CNT current oscillations on the tube and at the contacts emerge under several direct current biases. We associate these terahertz CNT oscillations with intersubband scatterings that cause the transfer of electrons from the first subband to the second, intrasubband scatterings and the nonlinear dispersion curves of each subband. The slow-moving electrons in the second subband bunch together locally on the tube, whereas the fast-moving first subband electrons move beyond the bunch and leave a relatively positive charged region behind. Also, intrasubband scatterings and subband curves give rise to low and high density electron regions by creating dispersion. These relatively low and high density electron regions create a charge dipole that then perturbs the electrical potential, resulting in a propagating domain, and thus current oscillations at tens of terahertz. After we investigate the physics of these calculated terahertz oscillations, we propose methods to modulate and shift the main oscillation frequency by varying the applied bias, tube length, or the diameter.