Positive and negative streamers in ambient air: measuring diameter, velocity and dissipated energy

Positive and negative streamers are studied in ambient air at 1 bar; they emerge from a needle electrode placed 40 mm above a planar electrode. The amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses have rise times of 30 ns or shorter. Diameters, velocities and energies of the streamers are measured. Two regimes are identified; a low voltage regime where only positive streamers appear and a high voltage regime where both positive and negative streamers exist. Below 5 kV, no streamers emerge. In the range from 5 to 40 kV, positive streamers form, while the negative discharges only form a glowing cloud at the electrode tip, but no streamers. For 5 to 20 kV, diameters and velocities of the positive streamers have the minimal values of d=0.2 mm and v \approx 10^5 m/s. For 20 to 40 kV, their diameters increase by a factor 6 while the voltage increases only by a factor 2. Above the transition value of 40 kV, streamers of both polarities form; they strongly resemble each other, though the positive ones propagate further; their diameters continue to increase with applied voltage. For 96 kV, positive streamers attain diameters of 3 mm and velocities of 4*10^6 m/s, negative streamers are about 20 % slower and thinner. An empirical fit formula for the relation between velocity v and diameter d is v=0.5 d^2/(mm ns) for both polarities. Streamers of both polarities dissipate energies of the order of several mJ per streamer while crossing the gap.Comment: 20 pages, 9 figures, accepted for J. Phys.

Inception and propagation of positive streamers in high-purity nitrogen: effects of the voltage rise-rate

Controlling streamer morphology is important for numerous applications. Up to now, the effect of the voltage rise rate was only studied across a wide range. Here we show that even slight variations in the voltage rise can have significant effects. We have studied positive streamer discharges in a 16 cm point-plane gap in high-purity nitrogen 6.0, created by 25 kV pulses with a duration of 130 ns. The voltage rise varies by a rise rate from 1.9 kV/ns to 2.7 kV/ns and by the first peak voltage of 22 to 28 kV. A structural link is found between smaller discharges with a larger inception cloud caused by a faster rising voltage. This relation is explained by the greater stability of the inception cloud due to a faster voltage rise, causing a delay in the destabilisation. Time-resolved measurements show that the inception cloud propagates slower than an earlier destabilised, more filamentary discharge. This explains that the discharge with a faster rising voltage pulse ends up to be shorter. Furthermore, the effect of remaining background ionisation in a pulse sequence has been studied, showing that channel thickness and branching rate are locally affected, depending on the covered volume of the previous discharge.Comment: 16 pages, 9 figure

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cram\'{e}r-Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model

Multiple-gap spark gap switch

A triggered multiple-gap spark gap switch has been developed and tested under atmosphere. By means of an LCR trigger circuit, the multiple-gap switch can be used very reliably. For the same switching voltage (35.5 kV), with increasing the number of gaps from 2 to 6, the switching current rise time is reduced from 13.5 to 6 ns, and the energy efficiency is increased from 87% to 92%. An eight-gap switch was also tested, and the switching current rise time is much smaller than the usable rise time of the current probe (3.5 ns). One interesting application of the multiple-gap switch is to improve the switching performance in the multiple-switch and transmission lines based pulsed power circuit. To verify this application, a six-gap switch was tested. In contrast to a single-gap switch, the output current rise time was improved from 21 to 11 ns by the six-gap switch

Spatial coupling of particle and fluid models for streamers: where nonlocality matters

Particle models for streamer ionization fronts contain correct electron energy distributions, runaway effects and single electron statistics. Conventional fluid models are computationally much more efficient for large particle numbers, but create too low ionization densities in high fields. To combine their respective advantages, we here show how to couple both models in space. We confirm that the discrepancies between particle and fluid fronts arise from the steep electron density gradients in the leading edge of the fronts. We find the optimal position for the interface between models that minimizes computational effort and reproduces the results of a pure particle model.Comment: 4 pages, 5 figure