Lightning return stroke current from magnetic and radiation field measurements

Abstract

Expressions are derived that allow the current in a lightning return stroke to be calculated from a measurement of either the magnetic flux density or the radiation field (electric field intensity or magnetic flux density) of the discharge. Published magnetic field and radiation field data are of insufficient time resolution to allow an adequate current determination to be made.Most lightning current measurements have been made on strokes to tall buildings or towers and represent the current flowing at the lightning channel base . In an effort to determine the properties of lightning strokes not influenced by tall structures, Norinder and his co-workers [e.g., Norinder and Dahle, 1945] measured the magnetic fields from distant strokes to earth and from theory derived lightning currents. Urnan and McLain [1969], by assuming a range of channel currents and computing the resultant magnetic fields, have shown that the theory used by Norinder and coworkers is erroneous. As a result, the current rise times Norinder and his co-workers derived are invalid, whereas the peak currents they derived are probably within a factor of 2 of the actual peak currents.In this paper we derive expressions that allow the current in a lightning return stroke to be calculated from a measurement of either the magnetic flux density or the radiation field Copyright (•) 1970 by the American Geophysical Union.(electric field intensity or magnetic flux density) of the discharge. THEORY We assume that each point on the lightning channel is the same distance r from an observation point P on the earth's surface and that the earth is a perfectly conducting plane. Thus, we treat the channel as if it were composed of a circular arc above the earth's surface centered at P and its 'image' arc below the earth's surface. The 'arc' approximation to a vertical lightning channel is roughly valid for distances from the channel greater than about two or three times the return stroke height. For example, suppose one is solely interested in obtaining values for the rate of rise of current and the peak current. These occur in the first several microseconds of the return stroke so that the maximum return stroke height of interest is'a few hundred meters (corresponding to a typical initial return stroke velocity of about one-third the speed of light), and the theory can be aplied for measurements made at any distance 5143

Regularization of ill-posed return stroke current identification problem

“…But, in order to show a clear connection between the solution instability and the condition number, further on there have to be used relation (11), which establish a percentage relation between the maximum error of the solution, as related to any perturbations, that may occur in the effect, or in the problem structure -the kernel matrix. Thus the perturbation acts on the effect -vector as:…”

“…Some previous researches that were identified [9], [10], [11], [12], propose different versions of trial and error procedures for the reconstruction of the return current, using the measured field values, during lightning occurrence.…”

Evaluation of Lightning Return Stroke Current Using Measured Electromagnetic Fields

“…Therefore, the required equation system can be expressed by Equation (9) while Equations (6) to (8) are applied at the observation point for n max samples of electromagnetic fields where n max is the maximum number of time steps as follows:…”

“…On the other hand, indirect methods can evaluate the return stroke current using measured fields and they can cover a greater number of lightning occurrences compared to direct measurement [7]. Different methods are available to evaluate the current although some of these methods only consider the fields measured at a far distance from the lightning channel and ignore the electrostatic and induction components of the fields [7][8][9][10][11][12]. Furthermore, some methods evaluate the current by using measured fields that are recorded up to intermediate distances from the lightning channel [3,[13][14][15], although they can only determine the current values at only selected sample frequencies The current model is a basic assumption in these methods.…”

Evaluation of Lightning Current and Velocity Profiles Along Lightning Channel Using Measured Magnetic Flux Density

“…A number of inverse procedure algorithms only consider the radiation component of the electromagnetic fields in order to simplify the field expressions [9][10][11][12][13]. This means such algorithms can only be used at far distances from a lightning channel at which point the radiation component of the electromagnetic fields has more effect on the total field.…”