Jovan Cvetic

Calculation of lightning current parameters

The new expression of the lightning current at the striking point is analyzed. The basic four channel-base lightning current quantities are assumed to be known: current peak value, current rise-time, maximum of the current steepness and the charge transfer at the striking point. The algorithm for a fast calculation of the channel-base current parameters is proposed. The numerical example of the current parameters determination is given. The proposed algorithm can be successfully used for the lightning current modelling in power engineering as well as in the research of the radiated lightning electromagnetic pulse and its coupling with the overhead lines and other metallic structures.

An Improved Model for Prediction of the Dynamics of Lightning Channel Corona Sheath

We consider dynamics of the lightning-channel corona sheath that is implicitly specified by lumped-current-source lightning return-stroke models. Two slightly different corona models for prediction of charge motion in the corona sheath are proposed. Both models can be viewed as generalizations of the model proposed by Maslowski and Rakov (2006) [2] and are in agreement with measurements of the horizontal (radial) electric field component made in the immediate vicinity of triggered lightning channel.

Dynamics of a Lightning Channel Corona Sheath Using a Generalized Traveling-Current-Source Return Stroke Model—Theory and Calculations

Abstract-A generalized lightning traveling-current-source return stroke model (GTCS) and the measurements of Miki et al. [J. Geophys. Res., vol. 107, no. D16, pp. ACL2.1-ACL2.11, 2002], are used to calculate the dynamics of a lightning channel corona sheath surrounding a thin channel core during the return stroke stage. The channel corona sheath model that predicts the charge motion in the corona sheath is used to determine the corona sheath dynamics. This model can be viewed as the generalization of the corona sheath model proposed by Maslowski and Rakov [J. Geophys. Res., vol. 111, D14110, pp. 1-16, 2006]. According to this model, the corona sheath surrounding the thin channel core consists of two zones containing charge, zone 1 (inner zone containing net positive charge) and zone 2 (zone containing negative charge surrounding zone 1), respectively, and an outer zone 3 surrounding zone 2 without charge. Theoretical expressions for the corona sheath radii and the velocities of both zones are derived. Using a theoretical expression for the radial electric field in the immediate vicinity of the channel core derived for the GTCS model and the measured electric field waveforms of Miki et al. [J. Geophys. Res., vol. 107, no. D16, pp. ACL2.1-ACL2.11, 2002], the channel discharge function versus time is calculated. Based on this function and the measured channel-base current function, the corona sheath radii of both zones and their velocities versus time in the bottom portion of the channel are calculated. It is shown that the maximum radii of zones 1 and 2 at 2 m above ground are less than 1.5 and 6 cm, respectively. Corresponding maximum radial corona sheath velocities are less than 6 × 104 m/s. Small values of the maximum radii of zones 1 and 2 can be explained by the small value of the channel line charge density of 6.7 μC/m, due to vicinity of perfect ground. Using measured channel-base current and the calculated channel discharge function, the line charge distribution versus height is calculated. The current reflections from the striking point are considered. For the ground current reflection factor R = 1 (the reflection from the perfectly conducting ground) the peak value of the channel line charge density is 0.75 mC/m at the height of about 12 m above ground and for R = 0 (no current reflections) the peak value is 1.3 mC/m, at about 17 m above ground. The corresponding calculated values of the return stroke velocities in the channel bottom are 1.29 × 108 m/s (0.43c) and 1.68 × 108 m/s (0.56c), respectively. The corona sheath expansion velocity is about three orders of magnitude less than the calculated lightning return stroke velocity. The result concerning the channel line charge distribution is in the agreement with the measurements of Crawford et al. [J. Geophys. Res., vol. 106, pp. 14909-14917, 2001], whereas the calculated return stroke velocities are in a good agreement with the optical measurements of Willet et al. [J. Geophys. Res., vol. 93, pp. 3867-3878, 1988] and [J. Geophys. Res., vol. 94, pp. 1327513286,1989].

Synergetic effect in a mixture of noble gases around the Paschen minimum

DC and pulse breakdown in the He-Ar gas mixture are investigated for small pressures and inter-electrode gaps. Expressions for calculating the breakdown voltage of a gas mixture are derived, assuming that breakdown occurs by way of the Townsend breakdown mechanism and that Maxwell spectrum can be used for the free electron gas. The parameters considered in experiments have been chosen so as to be of interest in designing gas-filled surge arresters. The obtained results demonstrate that the derived breakdown voltage expressions are correct, and that a suitable choice of parameters can produce a positive synergetic effect with regard to gas-filled surge arrester design. The latter issue is especially interesting for lowering the dc breakdown voltage of unconditioned electrodes.

Extension of lightning corona sheath model during return stroke

A generalized lightning traveling current source return stroke model has been used to examine the characteristics of the lightning channel corona sheath. A model of lightning channel consisting of a charged corona sheath and a narrow, high conducting central core is assumed. The return stroke process is modeled with the positive charge coming from the channel core discharging the negative leader charge in the corona sheath. According to the corona sheath model proposed earlier by Maslowski and Rakov, it consists of three zones, zone 1 (inner zone containing net positive charge), zone 2 (surrounding zone 1 with negative charge and outer zone 3 without charge. We adopted the assumption of a constant electric field inside zone 1 of the corona sheath proved in the experimental research of the corona discharges in a coaxial geometry of Cooray. This assumption seems to be more realistic than the assumption of a uniform corona space charge density used previously in the study of Maslowski and Rakov, Marjanovic and Cvetic, and Tausanovic et al. Based on the measurements of the electric field performed by Miki et al, the conductivity of the channel sheath in zone 1 is calculated.

Dynamics of Lightning Discharge During Return Stroke

A new generalized lightning traveling current source return stroke model (GTCS) has been developed. The GTCS eliminates completely all shortcomings of the “engineering” lightning return stroke models concerning the current discontinuities and the discontinuities of the current derivative at the place of the return stroke wave-front. As a result of the suitable adopted channel charge distribution function the dynamics of the internal channel processes can be partially examined during the return stroke. Using two-layer cylindrical model of the lightning channel it is possible to derive a simple connection between the channel time-discharge constant and the channel discharge function. An example of the possible charge distribution along the channel-base is given enabling the calculation of the channel discharge function and the time-discharge constant. The expression connecting the permittivity and the conductivity of the channel sheath is figured out. Given results enable better understanding of the dynamics of the internal channel plasma processes during the return stroke. Besides, the examination of the channel dynamics is enabled based on the remote measurements of the radiated lightning electromagnetic pulse as well as on the measured optical signal during the return stroke.

Light intensity emitted from the lightning channel: comparison of different return stroke models

The intensity of the light pulse emitted from the lightning channel during the return stroke process is analysed. For the most frequently accepted value of the real lightning return stroke velocity, the time dependence of the apparent height and the apparent velocity are calculated by the causality consideration. The experimentally observed decrease of the apparent return stroke velocity along the channel of more than 25% is partly explained. Five return stroke models are considered and compared: Bruce-Golde (BG), transmission line, modified transmission line (MTL), travelling current source (TCS) and Diendorfer-Uman (DU) models. The expression for the total emitted light intensity, its rise-time and the peak light intensity along the channel are carried out. At close distances the BG, the TCS and the DU models give approximately the same shape of total light intensity as the channel-base current. The substantially longer rise-time of the emitted light signal at medium distances is explained by the relatively slow geometrical growth of the lightning channel. All models except the TL model propose the exponential decrease of the peak light intensity with the channel height which is in agreement with the experimental data. Simple expressions connecting the channel decay constant of the light intensity, return stroke velocity and the current-decay constant at the channel base in the case of the BG, the TCS and the DU models are derived. None of the models can adequately describe the increase of the light intensity rise-time along the channel observed at heights above 1 km. It is concluded that simultaneous measurements of the channel decay constant and the parameters of the channel-base current are necessary to prove the validity of any particular model as well as to calculate the return stroke velocity.

Pulse reflection from a lossy Lorentz medium half-space (TM polarization)

A closed form solution for transient reflection from a lossy Lorentz medium half-space has been expressed as an infinite series of Bessel functions of the first kind and fractional order. The delta pulse plane wave excitation in the case of TM polarization has been considered. The variation of a reflected waveform with the angle of incidence, normalized collision frequency and normalized characteristic binding frequency of a lossy Lorentz medium are presented in several computer plots. The time domain Brewster angle is noted in the early time response. It is shown how the obtained transient response might be used for diagnosing the main characteristic parameters of the Lorentz medium.

Highly charged ion beam diagnostics at the mVINIS Ion Source

In order to determine position, dimensions and intensities of multiply charged ion beams at the mVINIS Ion Source, a novel method was developed based on a fluorescent screen and a commercial digital TV camera. The spatial characteristics of multiply charged ion beams (for example the ionization states of Ar2+ to Ar10+) have been precisely measured and analyzed at the TESLA Accelerator Installation for the first time. In this work, we discuss in details the characteristics of Ar8+ion beams. The obtained ion beam characteristics were compared with the results of previously applied conventional methods of ion beam diagnostics.

Generalized traveling current source return stroke model with current reflections and attenuation along the channel

The generalized traveling current source return stroke model (GTCS), Cvetic and Stanic [1995] is extended to take into account current reflections occurring at ground and at the upper end of the lightning channel, as well as current attenuation along the channel. The ground reflection factor and the top reflection factor of the current pulses are taken from the extended TCS model, Heidler [2007]. Current sources are placed along the activated length of the lightning channel, represented by the channel discharge function introduced in the GTCS model. Multiple reflections give rise to current waves moving up and down along the lightning channel. The total current is composed of the source current according to the original GTCS model and the reflected currents. The current along the channel can be represented as a sum of integrals of current sources along the channel. The traveling-current-source-type of “engineering” return stroke models can be regarded as special cases of the extended GTCS model. Moreover, for a convenient set of input parameters, the transmission-line-type of return stroke models can be also derived from the extended GTCS model. Simultaneously, the existence of the current source at the channel base, inherently built in all transmission-line-type of models is explained. This result is purely theoretical, since these two classes of “engineering” models are based on different physical pictures that describe processes in the lightning channel during the return stroke.