Lightning air terminals and method of design and application

Air terminals of two types having curved surface electrodes that act passively or dynamically to minimize or further reduce corona during the close approach of the down leader. In the first type, a fully grounded passive terminal, suitably located and comprising a conductive curved surface of a given radius on a grounded rod of given height, is located and suitably dimensioned in order to minimize corona discharges until the median field rises to a level sufficient to support streamer to leader conversion, as described below. In the second type, dynamic action is achieved by allowing the curved surface to float upwardly in voltage by use of capacitive coupling to the approaching leader. The raising of voltage being in the same polarity as the leader, acts to reduce the electric field immediately above, with consequent reduction in corona. When a flashover point is reached between the curved surface and the main earthed electrode there are provided free electrons in avalanche mode, and the curved surface is simultaneously grounded through the arc. This grounding causes an instant increase in the electric field immediately above the terminal. Streamer formation is enhanced by the liberation of free electrons, the photoionization created by the arc, and the instant increase in the electric field strength ahead of the streamer.

DISCLOSURE
 This invention relates generally to lightning protection, and more
 particularly to lightning air terminals and a method of design and
 application of such terminals.
 BACKGROUND OF THE DISCLOSURE
 In the field of practical lightning protection, there is a wide spectrum of
 technologies currently being used. To the left of this spectrum there are
 the air terminals claiming enhanced or more consistent performance.
 Whether these terminals enhance or retard corona development, or whether
 they are blunt or sharp, they have been broadly categorized under a
 generic term "ESE" meaning Early Streamer Emission.
 In the center of the spectrum there is the conventional practice widely
 specified in various Standards. This practice currently uses an
 electrogeometric model known as the "rolling sphere" which was adapted
 from the electric power transmission industry, and which is based on no
 electric field enhancement irrespective of air terminal location or
 configuration. The rolling sphere is notable for gaining credence from
 measurements taken on transmission lines. These lines are remarkable for
 their essentially two dimensional aspect and uniformity of height and
 conductor diameter. It was from this restricted base that the system was
 unilaterally adapted into the protection of three dimensional and complex
 geometrical structures.
 Within the Standards there is permitted a widely divergent practice. This
 may vary from clusters of, for example, six (6) meter high so called
 Franklin rods to much shorter terminals, sometimes called finials, spaced
 at closer intervals. There are also the systems with no vertical
 terminals, sometimes called the Faraday system, and which comprises
 conductors laid horizontally on exposed surfaces.
 To the right of the spectrum are the systems that claim absolutely to
 prevent lightning attachment by the use of arrays of sharp points designed
 to produce abundant corona. The corona is claimed to weaken the strength
 of the near electric field and cause the lightning to strike elsewhere.
 While none of the above techniques offer perfection, there is room to
 improve performance of air terminals and their location through better
 understanding of the attachment process.
 There are four phases in the attachment process of lightning to a ground
 point. The first is the quasi-static phase where electrical fields build
 below a storm cloud over some tens of minutes. These fields cause ground
 objects to be electrically stressed and, dependent on their height and
 geometric shape, they will emit corona. In the case of a negative cloud
 base, this corona is in the form of positive ions which create a space
 charge in the near field immediately above the object.
 In the longer term, these positive ions, which in reality are molecules of
 air, ascend with typical velocities of 1 ms.sup.-1 in the fields of 10
 kVm.sup.-1 and create non-linearity in the field to heights of several
 hundred meters. Thus, the electric field strength observed at ground
 becomes modified before any dynamic event occurs with typical values of 50
 kVm.sup.-1 having been recorded as reducing to values below 5 kVm.sup.-1
 near ground.
 The second phase relates to the approach of a down leader, a filament
 discharge with average velocity of 10.sup.5 ms.sup.-1 but with 20-50 .mu.s
 steps or pauses. The inter-pause velocities can exceed 10.sup.6 ms.sup.-1.
 This conveyance of charge toward ground causes a rapid increase in the
 field strength observed by ground points. There is very small initial
 change in the ground observed electric field strength when the leader is
 at high altitude, but with near approach, values will be escalating at a
 typical rate of 10.sup.9 Vm.sup.-1 s.sup.-1.
 The third phase is when electric field strength observed by a ground point
 reaches the critical value to create avalanche breakdown. This commences
 with an initial corona burst in which streamers can develop, one of which
 may finally develop into a propagating leader. At this time, factors can
 be dimensioned such as electric field intensification arising from height
 and ground electrode curvature. Streamer development fields can also be
 determined in the laboratory, but up to now the laboratory experiments
 have not been able to readily model the field decay from the surface to
 "median" values in the first few meters above a terminal. The "median" or
 "ambient" field is defined as the unperturbed electric field, i.e., that
 which would exist in the absence of the object. There is a minimum value
 of the median field required to convert a streamer into a propagating up
 leader.
 The fourth phase is the continuing propagation of the up leader. Once the
 root of an up leader is formed, it requires the electric field strength
 ahead of it to exceed 300-500 kVm.sup.-1 to gain the necessary energy to
 continue propagation.
 Embedded within the above four phases is another spectrum based on the
 strength of electric field to cause breakdown of air, the electric field
 strength required to cause upward emission of filamentary streamer type
 discharges, and a value of electric field strength required to convert the
 filamentary discharge into an up leader. The former value is commonly
 quoted as having a nominal value of 3 MVm.sup.-1, while the latter value
 falls within the range 300-500 kVm.sup.-1. Of course, in nature these
 values will never be exact.
 There is a wide variation in geometric shape of ground points which range
 from sharp points to flat horizontal surfaces. At one end of the geometric
 shape spectrum is the so-called pointed Franklin rod. Should this rod
 produce a field intensification of 1000:1, then 3 MVm.sup.-1 at the tip is
 reached when the median field is only 3 kVm.sup.-1. No streamer
 development or propagation is possible in such low median fields but a
 continuing corona emission will provide an ascending space charge of
 ionoised air molecules in periods long before the initiation of a down
 leader.
 As the center of this spectrum is approached, the field intensification
 progressively reduces. The center is reached when, for example, a value of
 6:1 is achieved. This center of the spectrum would typically be a "blunt"
 rod which has a rounded upper surface of a given radius (such that the
 intensification is 6:1). In this case, the field strength at the tip of
 the rod reaches a corona emission level of 3 MVm.sup.-1 at the time when
 the median field reaches the leader propagation level of 500 kVm.sup.-1.
 At the other extreme of this spectrum is a flat surface with unity field
 intensification. Hence, the down leader needs to approach very close to
 produce 3 MVm.sup.-1 at the surface, but when breakdown with corona
 emission occurs, propagation would not only be absolutely assured, but
 would most likely be instantaneous.
 This spectrum leads to a number of conclusions, namely, that an elevated
 sharp point becomes unnecessarily active too early in the process, by
 producing field-reducing corona along with space charge. This blanket of
 charge particles lying above the grounded point will act as a shield and
 prevent the point observing the approach of the down leader. The result is
 that the down leader must approach much closer in order to force the
 creation of an up leader. It has been discovered that a rounded surface
 will provide a better performance by minimizing pre-discharge corona and,
 by suitable radius or diameter dimension, create streamers only when the
 near and median field can support their conversion to a leader.
 Hereafter, three different types of air terminals will be referred to,
 viz.: (I) A fully grounded conductor as specified in various Standards,
 i.e., a Franklin rod which is a long cylindrical conductor with a sharp,
 conical tip, the shorter finial version, or the rodless system of copper
 tapes commonly known as the Faraday system. Henceforth, these types of air
 terminal shall be referred to as "conventional passive". (II) A particular
 type of air terminal comprising a curved conductor, typically a sphere,
 placed on a conductive rod. The radius of curvature and overall height of
 this air terminal is dimensioned according to the method to be described.
 Hereafter, this type of air terminal shall be referred to as "RFI
 passive", RFI being the acronym for "reduced field intensification". (II)
 A particular type of curved surface air terminal comprising one or more
 insulated components which result in a triggering arc to enhance the
 initiation of the lightning attachment process; henceforth, this type of
 air terminal shall be referred to as "RFI triggering".
 The present invention and method then relate to: (i) significant
 improvements of Type I lightning air terminals, viz. the Type II
 terminals, (ii) certain improvements in the Type III system such as that
 shown in prior Gumley U.S. Pat. No. 4,760,213, and (iii) to a method of
 design and application of the Type II & III air terminals. Terminals of
 the type III seen in such patent are widely sold under the trademark
 DYNASPHERE.TM. by ERICO Lightning Technologies Pty. Ltd. of Hobart,
 Tasmania, Australia.
 The DYNASPHERE.TM. terminal utilizes a generally spherical or ellipsoidal
 curved surface electrode which is connected to the grounded central
 conductor by a high impedance current drain. An annular air gap is
 provided between the top of the generally spherical surface and the top of
 the central grounded conductor. Such lightning air terminals have a number
 of parameters such as the size and shape of the spherical surface, the
 size of the air gap, the shape of the tip of the central grounded
 conductor, the height of the terminal above the structure to be protected,
 and the location of the air terminal on the structure. One primary
 parameter is known as the "electric field intensification factor" which is
 derived from the height and curvature of the curved surface electrode.
 These factors have never before been defined in relation to practical
 lightning protection systems.
 There is accordingly a need for an improved, curved surface, RFI air
 terminal which will provide a more slowly decaying intensification across
 the near and median fields, and which creates a trigger or corona only
 when there is sufficient energy, particularly in the median field, to
 progress a streamer into a leader. In this way, the field reducing effect
 and non-linearities associated with corona and space charge are avoided.
 SUMMARY OF THE INVENTION
 In the first phase of the invention, a conductive sphere of a given radius
 is placed on a grounded rod of given height and dimensioned according to
 design algorithms to be presently discussed. In the next phase of the
 invention, an improved air terminal has a curved surface electrode
 supported by insulation on a grounded central rod with a blunt slightly
 domed tip. A concentric air gap is provided between the top of the central
 rod and a ring at the top of the curved surface. The surface is designed
 to have a natural capacitive coupling to an approaching down leader. In
 order to prevent early sparking or arcing across the air gap due to random
 ion collection in periods of quasi-static fields due to overhead storm
 presence, a high impedance/resistance connection is provided connecting
 the curved surface to ground. Interposed in the spark gap may be the
 concentric top of a non-conducting ring which projects just proud of the
 direct or shortest spark or arc line between the curved surface ring and
 the top of the central rod. This requires the arc to jump over the ring
 and, in doing so, enter a stronger electric field. In addition to the
 impedance/resistance connection, a trimming capacitor may also be
 connected between the curved surface and the central rod or ground to
 assist in optimizing the timing of the arc triggering.
 In another embodiment, the spark gap includes an additional concentric ring
 outside the non-conducting ring and connected by a series resistor to the
 curved surface. The combination of the capacitance between the curved
 surface and the central rod, supplemented by the trimming capacitor and
 the series resistor forms an RC discharge circuit which may be used to
 lengthen the duration of the arc triggering. The air terminals of the
 invention have a number of functional properties. They are positioned, and
 have a geometric shape, so that they do not produce corona emissions in
 the quasi-static electric fields before the approach of a down leader. The
 Type III triggering terminal senses the approach of a down leader and acts
 in a manner to further reduce the risk of corona generation. It recognizes
 when the median field has the strength to support up leader formation and
 its propagation. It then triggers a corona burst when such conditions are
 met and, simultaneously with the triggering, enhances the immediate
 electric field to produce streamer emission and streamer to leader
 conversion under optimum propagation conditions. The terminal also has no
 batteries, charging systems, radiation, or electronically active
 components. It is activated solely by energy from an approaching down
 leader.
 The invention includes a method of designing the parameters of the air
 terminals, some of which are their: (i) height, (ii) curvature of the
 rounded surfaces, (iii) position on a structure, (iv) size of the Type III
 floating surface and (v) spark gap length. Parameters (i), (ii) and (iii)
 are set by 2D or 3D finite element modeling of the electric fields around
 the air terminal, structure and lightning downleader, and taking into
 account the critical criteria for upleader initiation and propagation.
 Parametric computer modeling produces a set of general mathematical
 relationships, hereafter termed "algorithms", which enable the correct
 parameters to be selected for each specific lightning protection scenario
 without the need to perform an "online" analysis of each case. Also, the
 "attractive radius", "attractive area" or lightning capture volume of the
 parameter-set air terminal can be determined with respect to a given
 structure. Parameters (iv) and (v) are set, in conjunction with (ii)
 determined above, by using a laboratory arrangement which employs a high
 voltage generator capable of producing a voltage or electric field
 waveform that accurately simulates the rapidly escalating waveform found
 in natural conditions. The conventional Marx high volatge impulse
 generator used for decades for air terminal testing is totally unsuitable
 for this function.
 In combination, the above methods permit the electric field intensification
 to be determined jointly by height above a grounded surface and the size
 and curvature of curved surface conductive electrode. The method
 determines the electric field over and around the structure and provides a
 height and location for the air terminal so that no (or minimal) corona is
 formed during the quasi-static period of a thunder storm. The RFI
 triggering terminal inhibits corona formation even during the early stages
 of down leader progression, and will trigger the corona and streamers only
 when the median electric field, which is reached at distances typically
 ranging from 0.5 meters to about 10 meters beyond the air terminal, is of
 sufficient strength, typically 300-500 kV/m, to convert astreamer into a
 propagating leader. The potential on the curved surface and, hence, time
 at which the triggering takes place is controlled by the size of the spark
 gap. Because of the rapid escalation in field following the first trigger,
 repeat triggers occur at rapidly decreasing intervals.
 To the accomplishment of the foregoing and related ends, the invention then
 comprises the features hereinafter fully described and particularly
 pointed out in the claims, the following description and the annexed
 drawings setting forth in detail certain illustrative embodiments of the
 invention, these being indicative, however, of but a few of the various
 ways in which the principles of the invention may be employed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
 In the first phase of the invention, a conductive curved surface as seen in
 FIG. 1, typically a sphere 18, of a given radius is placed on a grounded
 rod 19 of given height and dimensioned according to design algorithms to
 be presently discussed. The passive, spherical air terminal so designed
 and placed may optimize the minimization of corona until the median field
 rises to a level sufficient to cause a surface discharge in the form of a
 corona burst. The embedded streamers are subsequently encouraged to
 develop into propagating leaders in the absence of space charge in the
 immediate vicinity. This is an improvement on the corona-producing sharp
 rods in current practice. The invention shows that simple replacement of
 sharp rods by blunt rods cannot achieve optimum performance and that the
 algorithms to be discussed are needed to determine the physical parameters
 according to location on a structure.
 Referring now to FIGS. 2-4, there is illustrated a further improvement by
 way of a triggering air terminal in accordance with the present invention
 which is activated by energy from an approaching down leader. The air
 terminal is shown generally at 20 and comprises a central conductive earth
 rod 21 for lightning attachment and conveyance of the discharge current to
 ground as indicated at 22. Surrounding the rod is a curved conductive
 surface 24 which is supported at its widest point by an installation
 spider 25 extending from insulation sleeve 26. The top of the curved
 surface is provided with a ring 28 which has an undercut inner edge 29
 forming a relatively sharp edge 30 at the top, seen in FIG. 3, which edge
 is concentric with the central conductor rod 21. The ring 28 forms an
 annular concentric air gap at the top of the air terminal shown generally
 at 32.
 The top of the conductive rod is at approximately the same elevation and
 has a blunt configuration formed into a slightly convex, shallow dome, or
 rounded conical top 34 provided with a relatively sharp horizontally
 projecting lip 35.
 Surrounding the top of the conductive rod is a non-conducting ring or
 sleeve 36 which is adjustably mounted on the central conducting earth rod
 as seen at 37. The very tip of the ring indicated at 38 is positioned just
 proud of the shortest spark track between the top of the central conductor
 and the ring 28. The tip of the annular non-conducting ring will project
 preferably from about 1 millimeters to about 2 millimeters above the
 shortest line of the spark or arc so that the spark must literally jump
 over the ring tip 38 as indicated at 39 and enter a stronger electric
 field.
 As seen in FIG. 2, there is provided an impedance/resistance unit 42
 connecting the outer curved surface electrode 24 to ground through the
 central rod 21. The purpose of this impedance/resistance unit is to
 prevent early arcing due to random ion collection in the period of a
 quasi-static field due to overhead storm presence. Also connecting the
 outer curved surface electrode to ground through the central rod is a
 trimming capacitor 43 to assist in optimizing the triggering point.
 Although a variety of shapes may be employed, the illustrated shape of the
 curved surface electrode 24 is similar to an oblate/prolate spheroid with
 the portion below the insulation spider at the widest point being oblate
 and the portion above being prolate. The size including the diameter or
 radius may be substantial as hereinafter noted with the diameter being
 typically from 50 mm to &gt;1 meter (for very tall structures, there may
 be a need for diameters &gt;1 meter in order to meet the corona
 criterion).
 Referring no to FIGS. 5 and 6, there is illustrated a modified form of air
 terminal which includes the grounded central conducting rod 21 having the
 blunt top 34 and the annular lip 35. The curved surface electrode 24 is
 provided with the annular ring 28 providing a somewhat larger air gap seen
 generally at 44. In addition to the non-conducting ring with the
 projecting tip 38, the spark gap is provided with a second annular
 conductive ring shown generally at 45. The ring 45 is supported on
 insulation bracket 46 from the central rod 21 but is electrically
 connected to the curved surface through a series resistor 47. The ring 45
 then becomes an arc time extension ring, and the combination of the
 capacitance between the surface 24 and the rod 21, supplemented by the
 capacitance 43 and the series resister 47, will form an RC discharge
 circuit to maintain the triggering arc for a longer duration.
 The preferred air terminals illustrated in FIGS. 2-6 have properties so
 that they can be positioned and have geometric shapes such that they
 produce no corona emissions in the quasi-static electric fields before
 approach of a down leader. The air terminals also sense the approach of
 the down leader and act in a manner to reduce further the risk of corona
 generation. The terminals recognize when the median field has sufficient
 strength to support up leader formation and its propagation and trigger
 the emission of a streamer discharge when such conditions are met. The air
 terminals enhance the immediate electric field in conjunction with
 streamer emission in order to ensure optimum propagation conditions. They
 require no batteries, charging systems, radiation or electronically active
 components.
 The process of the present invention involves the determination of electric
 field concentration such as shown in FIG. 7 in a half section for
 computing simplicity. FIG. 7 illustrates the electric field shown
 generally by the equipotential lines 50 surrounding an air terminal shown
 generally at 51. The curved or rounded surface at the top of the terminal
 is shown at 52, while the central earthed rod is shown at 53. As is
 apparent, the electric field concentration around the air terminal and
 about the rounded surface decays in intensity with distance as the field
 returns to the median or unperturbed value.
 FIG. 8A illustrates the importance of this electric field decay with
 distance from the air terminals with very different field intensification
 factors. The line 55 represents the decay for a sharp rod such as a
 Franklin rod, which has a diameter of 6 mm and an overall height of 3
 meters. The line 56 represents the decay for a blunt air terminal such as
 disclosed in FIGS. 1-6, which has a spherical upper surface of radius 0.5
 m and an overall height of 2.5 meters. The respective field
 intensification factors are approximately 600 and 6.
 It should be noted that the decay distance to the ambient or median field
 is not a simple function of the intensification factor. It has a positive
 dependence on the height and radius of curvature but in different
 proportions, the height being the dominant factor. However, for a given
 height above ground, the electric field strength ahead of the terminal
 with the highest intensification (smallest radius) more quickly decays to
 the ambient field. Thus, any early formed streamer will find a rapidly
 decreasing field strength as it emerges from the air terminal tip. Such a
 streamer would not find sufficient energy in the field to progress into a
 leader (the amount of energy stored per unit volume in an electric field
 is in proportion to the square of the field strength). Thus, the streamer
 would collapse, and continually re-emerge until the down leader approached
 much more closely to give the required energy for streamer-to-leader
 conversion. However, a blunt configuration, whether passive or triggering,
 with the lower field intensification produces a much more linear decay as
 seen by the curve 56, with field strength remaining above the ambient
 value out to a much greater distance. This illustrates that a blunt
 configuration launching a streamer has a greater probability of converting
 that streamer into a stable, propagating leader, provided it meets the
 design algorithms to be presently discussed.
 With further reference to FIG. 8A, the sharp rod, with an intensification
 factor of about 600 to 1, will generate corona at a field strength of
 3,000/600 kVm.sup.-1, i.e. in an ambient field of only 5 kVm.sup.1. Thus,
 a space charge is being formed in those electric fields which exist before
 any down leader is initiated. As seen in FIG. 8B, the presence of positive
 ions 57 above a terminal 58 will act to reduce the strength of the normal
 negative field present below the thunder cloud shown. The effect of space
 charge in a large terminal-plane gap containing a uniform charge density
 of .about.0.5 .mu.C/m.sup.3, is shown in FIG. 8C. The electric field
 indicated by the curve 59 is almost completely neutralised at a distance
 of 4 meters from the terminal. Hence, streamers would never be able to
 propagate beyond this point. On the other hand, for the blunt rod, which
 has a 6:1 intensification, the median field of 500 kVm.sup.-1 needed to
 sustain leader propagation has been obtained at the moment the surface
 field at the terminal has reached 3 MVm.sup.-1. Corona will not only form
 when the electron avalanche is required to produce a streamer, but
 additionally will occur when the near field is strong enough to support
 streamer-to-leader conversion.
 In natural conditions, however, the attachment process is a competition
 between several upward leaders. These competing leaders are not fully
 independent. Mutual repulsion or quenching of a leader by earlier
 propagating leaders is observable and may be predicted from finite element
 modeling. Accordingly, in the design of the system it is important not to
 ignore other nearby potential cites for upward leader initiation as
 hereinafter described. With the process of this invention, it is possible
 to define optimum conditions for lightning attachment and to assess these
 conditions for all competing points such as building corners and parapets.
 Thus, one or more air terminals of correct proportion can be located to
 provide superior performance over any nearby competing point.
 Referring now to FIGS. 9, 10 and 11, FIG. 9 illustrates the equipotential
 lines 60 of the electric field distribution around the terminal 20 under
 the static conditions where all of the elements are effectively grounded.
 Referring now to FIG. 10, there is illustrated a typical electric field
 observed by a ground point below a descending down leader. The electric
 field lines of equipotential are shown at 62. Under natural conditions,
 when the median field reaches the order of 500 kVm.sup.-1, there is
 observed a field rising at typical rates of 10.sup.9 Vm.sup.-1 sec.sup.-1.
 The natural electric field increase due to the approaching down leader is
 illustrated in the graph of FIG. 11. The capacitive coupling between the
 floating surface 24 and the down leader charge, plus the restriction
 placed on the flow of displacement currents through the
 impedance/resistance 42 means that the surface of the curved surface
 electrode 24 will rise in voltage, or float upwardly in voltage. FIG. 10
 illustrates the equipotentials around an air terminal of the invention
 with a grounded rod and a floating curved surface electrode, elevated in
 potential due to the capacitive coupling to an approaching down leader.
 In comparing FIGS. 9 and 10, it should be seen that there is a reduction in
 field strength above the terminal at the point in time when the down
 leader is approaching. This reduction in field strength results in the
 preclusion of extensive surface corona from the terminal during the
 initial dynamic phase of the leader approach.
 In FIG. 11, there is illustrated the field reduction with distance for the
 grounded and floating conditions described in connection with FIGS. 10 and
 11. It is to be noted that within 100 millimeters there is a stronger
 field for the floating surface electrode illustrated at 64, but thereafter
 the field reduces to prevent any streamer growth. Conversely, the electric
 field at the surface 24 will always be lower in the floating state. The
 floating curve 64 crosses the grounded curve 66 at 67 which is within the
 first 100 millimeters from the tip. The field above the terminal is
 noticeably less than would be found in a grounded state under the same
 median field conditions. The raising of the potential of the curved
 surface therefore acts to reduce the chance of extensive corona formation
 during the down leader approach. When the surface 24 has reached some tens
 of kV, there will be a sparkover at the annular ring. The sparkover
 creates three key benefits, the first being to create free electrons at
 the point of highest electric field strength. Secondly it will assist
 electronic acceleration through the process of photo ionization, and
 finally the spark itself is a conductor, and in discharging the conductive
 surface 24, acts to ground that surface through to the central rod. This
 shifts the air terminal from one curve to the other as seen in FIG. 11,
 and results in an immediate increase in the near field. In this manner,
 the conditions are then ideal to initiate and propagate an up leader.
 The ideal parameters of the air terminal of the present invention are
 determined primarily through two means: (A) computer modelling of electric
 fields using 2D and 3D finite element analysis, and (B) laboratory tests
 using a monotonically increasing or "concave" field which simulates the
 natural lightning strike. Method (A) is used to determine the correct
 height and curvature of the floating conductive surface and method B is
 used to determine the correct area of the surface and the size of the
 triggering air gap. The objective of both methods, in combination, is to
 create a trigger at a time when both the rate of rise of electric field
 and the median electric field are simulating the ideal propagation
 conditions as would be found in nature.
 With respect to method (B), the concave curve 70 of the required electric
 field is seen in FIG. 12. The curve 70 is obtained by the generator shown
 schematically in FIG. 13 as hereinafter described. The generator
 illustrated is capable of precisely simulating the electric field due to a
 lightning down leader, even including the well known steps or pauses as
 the leader progresses toward its point of attachment near the ground. The
 steps or pauses, smoothed out, are illustrated by the points 71.
 Heretofore, a Marx generator has been used for laboratory studies, but for
 this purpose a Marx generator is unsuitable since the wave form is the
 antithesis of the natural wave form. The Marx generator produces a
 "convex" waveform with the highest dV/dt at t=0, and the air terminal
 under test will experience the highest capacitive coupling when the median
 field is virtually 0. In this manner, a trigger discharge can occur too
 early and leave a residual space charge to act against future streamer
 emission. Accordingly, a generator must be employed which in effect
 duplicates the monotonically increasing field which simulates nature as
 seen in FIG. 12. Such a generator is shown in FIG. 13.
 Referring now to FIG. 13, there is illustrated a high voltage generator
 shown generally at 72. A computer 73 is installed with a high speed
 digital I/O card unit 74 which is used to output a 10-bit data word which
 is a pulse width modulated (PWM) representation of the rate of rise of a
 point on the desired wave form. Typically, the PWM frequency is 100 kHz
 and the data rate is 2 MHZ. This enables a PWM resolution of about 5%.
 Hence, it allows delays indicated at 75 to be inserted between each bit in
 the data stream in 5% steps in order to create a ripple effect increasing
 the slope between the points 71.
 Each delayed bit of output data is passed through opto-driver 76 to into
 one of ten opto-driven cables shown and then passed into an isolated
 switched-mode power supply (SMPS) with its own floating DC power supply,
 shown generally at 76. The fiber optic signals are converted back to
 electrical form inside each SMPS.
 The output stage of the generator uses transformers shown generally at 78
 configured in a flyback topology to eliminate the need for output
 inductors. When the transformer primary winding switches 79 are activated
 by the amplified SMPS outputs, the primary side of each transformer acts
 as an inductor due to the blocking action of the output diode 80. When the
 switches are deactivated, the voltage reverses, and the inductive energy
 stored in the primary is released through the secondary winding. The
 output diode 80 then acts so that a negative voltage appears on each
 output.
 Rise times greater than 1 kV/.mu.s are achievable with the illustrated
 system. The advantage of series stacking the modules comprising the
 generator is that each module only needs to be able to output a voltage of
 V.sub.out /n and, more importantly, output it at a rate of only 1/n of the
 required slew rate, where n is the number of modules. An additional
 benefit of increasing the number of modules is that the ripple affect from
 the interleaving is smoothed even further. It will thus be appreciated
 that only the two outside modules are illustrated in the schematic FIG.
 13, while the intermediate modules are not shown but otherwise the same.
 Other advantages of the generator are that the test waveform can be changed
 from concave, to linear, to convex in a relatively short period of time
 (on the order of minutes) so that empirical corrections for variations in
 temperature, pressure and humidity are not needed. With the computer, the
 wave shapes can be stored and recalled at any time to repeat a test. The
 air terminals are tested in laboratory rigs using an overhead screen and
 can accordingly simulate natural lightning strikes on air terminals from
 various elevations and azimuth with the near and median fields being
 determined.
 With the illustrated generator, a person skilled in the art may produce a
 field strength across the gap between the air terminal of the type
 illustrated and a test electrode which will be equal to the leader
 progression field, and simultaneously achieve a field rate of rise to
 match that of nature. The size of the annular spark gap 32 may then be set
 according to the surface area (capacitance) of the floating surface and
 the value of the surface to rod capacitance 42.
 With respect to method (A), computer modelling of the electric fields at
 the surface and around the air terminal in the invention, using the finite
 element method (or an equally applicable technique such as the charge
 simulation method), has resulted in a set of "non-linear scaling laws",
 "parametric models" or "mathematical algorithms" which can be applied to
 any particular lightning protection scenario such that the up leader
 criteria are met. This was achieved via a parametric study of the field
 intensification factor as a function of the: (i) air terminal height, (ii)
 air terminal surface curvature and size, and (iii) distance from the air
 terminal under static (grounded) and dynamic (floating) conditions. As an
 example, a parametric model for computing the field intensification factor
 K.sub.i of a spherical air terminal of a given height h and radius of
 curvature r is:
EQU K.sub.i =1.44(h/r).sup.0.866 +1
 The broadest application of the method of the present invention requires
 knowledge of the local site parameters which must include all structural
 elements deemed to be in competition with an optimized and ideally placed
 air terminal. This involves a much more extensive series of parametric
 studies, which give the field intensification factor as a function of each
 variable as well as combinations of variables. General algorithms have
 been derived and used to compute the correct air terminal parameters and
 the location on the structure to be protected. The algorithms cover a
 variety of physical principles relating to the field intensification
 factor. These include the: (i) variation of the field intensification
 factor with the height, width and distance in the x, y and z directions
 for rectangular and cylindrical structures as well as simple aggregate
 structures of this type; (ii) combined field intensification factor of air
 terminal plus structure, as a function of structure shape, height, width
 and distance in three dimensions; (iii) combined field intensification
 factor of any other projections on a structure (e.g., parapets, masts,
 communications antenna, etc), as a function of structure shape, height,
 width and distance in three dimensions; (iv) effect of the proximity of
 another object on the field intensification factors in (i), (ii) and
 (iii); and the electric field at different locations due to a down leader
 approaching from different directions, located at different heights and
 carrying different quantities of electric charge.
 A typical result is shown in FIG. 14 where an air terminal 82 is placed
 away from a competing parapet 83 on a rectangular structure 84. In this
 case, the median field may be the optimum for sustained leader
 propagation, such as 500 kV/m and the terminal height and radius adjusted
 to meet the ideal streamer launch parameters. Likewise, the near fields of
 the parapet 83 may be computed to find whether they exceed the optimum,
 and in which case, the terminal should be moved closer to the parapet to
 regain dominance. In FIG. 14, the illustrated plot of equipotentials
 around the structure 84 in the yz plane of the 3D model is for a
 vertically descending leader as indicated by the arrow 85. However, in
 FIG. 15, the plot of equipotentials around the structure is with the down
 leader approaching obliquely from the right as seen by the arrow 86.
 In FIG. 16, there is shown another method where the equipotentials of the
 electric field around a structure 84 are determined, and in addition to
 the air terminal 82 there is provided an air terminal 88 on the parapet
 83. The equipotentials are shown with an obliquely approaching down leader
 illustrated at 90. The air terminal is placed near a corner parapet with
 suitable height and radius to be an ideal attachment point for the
 obliquely approaching lightning down leader.
 Accordingly with the finite element modeling of the near and median field
 intensification with down leaders approaching from various directions and
 with different electrical charges, a suitable optimal system can be
 developed for the structure.
 For the ideal air terminal the height projecting above the structure may be
 from about 1 meter to 6 meters or even higher. Also the size or curvature
 of the curved surface electrode may vary from about 50 mm in diameter to
 in excess of 1.5 meters in diameter. A preferred range is from about 0.5
 meters to about 1 meter in diameter. The distance to the median field for
 these configurations is in the range 0.5 to 10 meters.
 In any event, an air terminal is provided with a curved surface electrode
 acting dynamically to minimize and further reduce corona during the close
 approach of a down leader. This is achieved by allowing the curved surface
 to float upwardly in voltage by use of a capacitive coupling to the
 approaching leader. The raising of the voltage in the same polarity as the
 leader acts to reduce, on average, the electric field in the vicinity of
 the air terminal. This acts to eliminate or substantially reduce corona in
 the dynamic phase of leader approach. When a flashover or spark point is
 achieved between the curved surface and the main central earthed
 electrode, there are provided free electrons in avalanche mode, and the
 curved surface is simultaneously grounded through the arc. The grounding
 causes an instant increase in the electric field above the terminal at a
 time when there is virtually no space charge effect. Streamer formation is
 enhanced by the liberation of free electrons, the photoionization created
 by the arc, and the instant increase in the electric fields ahead of the
 streamer. In the dynamic phase during the near approach of a down leader,
 the E field is intensified so as to have a field strength sufficient to
 cause a corona and on-going development into a streamer without the
 impediment of an intervening space charge.
 The air terminal is designed so that a streamer is only launched when both
 the near field and the median field strength, within a few meters of the
 terminal, are sufficiently strong to convert an initiating streamer into a
 propagating leader. The height and curvature of the terminal determines
 the E field intensification factor, and up leader conversion is assured,
 and the process is enhanced by propagation into an electric field devoid
 of distortions due to corona emissions in the form of space charges. The
 invention also includes a method to simulate natural lightning strike
 conditions and control not only the position of the lightning ground
 attachment, but also the ideal air terminal parameters to achieve the
 proper initiation of the streamer and up leader conversion. The system
 recognizes that there may be other structural points competing to be first
 launched leader and compares all points on approach of down leaders using
 a computer analysis involving three dimensional computer finite element
 modeling.
 The overall system differentiates from the industry generic term of "early
 streamer emission" in that such terminals become active far too early and
 produce space charge from failed attempts to launch streamers. This
 invention more properly relates to the term "controlled streamer emission"
 by holding off streamers until leader conversion and propagation
 conditions are optimized.
 To the accomplishment of the foregoing and related ends, the invention then
 comprises the features particularly pointed out in the claims, these being
 indicative, however, of but a few of the various ways in which the
 principles of the invention may be employed.