Frequency Components of a Lightning Strike

[dreens]

Hi there,

I recently attended a physics demonstration (Lightning show at Boston Museum of Science, my favorite exhibit obviously), where the educator argued that the reason she could safely sit in a Faraday Cage while lightning was striking said cage was the skin effect.

As I understand it, the skin effect describes the tendency of alternating currents to flow close to the surface of conducting wires, whereas the reason one is kept safe in a Faraday cage is more a static, DC effect where charges rearrange on the surface of a conductor so as to cancel the field within.

Of course, a cage being struck by lightning is certainly not a time independent phenomenon. It could be that static charge rearrangement and the skin effect both play a role- the former before the bolt while the field is building up, and the latter while the bolt is ramping up creating a large time-varying B-field.

In order to decide which effect is dominant, or whether both are important, I would like to know the frequency spectrum of the current waveform describing a lightning bolt. In other words, if you plotted current over time, you would find an initially small, corona based current caused by slow electron transfer to air near the surface of the faraday charge and the voltage source (van-de-graff generator in this case). Then, during the bolt, the current would be large. At some point, enough current has flowed that the voltage no longer sustains the plasma, and the current drops down to zero.

So the current waveform should look roughly like a square-wave. What I want to know is what frequency (or time constant) characterizes how sharp the rising and falling edges of the square wave are, how wide the square wave is, how square-like it is, etc.

As for width of the square wave, maybe someone knows how long a lightning bolt usually lasts? Maybe 100ms or so?

As for the rise time, maybe someone knows how quickly lightning travels? I think I've seen slow motion video of lightning bolts "moving" from ground to cloud, if I knew how quickly they move it should roughly answer the question of how quickly the current ramps up.

Thanks,
Dave

 

[tech99]

Hi there,

I recently attended a physics demonstration (Lightning show at Boston Museum of Science, my favorite exhibit obviously), where the educator argued that the reason she could safely sit in a Faraday Cage while lightning was striking said cage was the skin effect.

As I understand it, the skin effect describes the tendency of alternating currents to flow close to the surface of conducting wires, whereas the reason one is kept safe in a Faraday cage is more a static, DC effect where charges rearrange on the surface of a conductor so as to cancel the field within.

Of course, a cage being struck by lightning is certainly not a time independent phenomenon. It could be that static charge rearrangement and the skin effect both play a role- the former before the bolt while the field is building up, and the latter while the bolt is ramping up creating a large time-varying B-field.

In order to decide which effect is dominant, or whether both are important, I would like to know the frequency spectrum of the current waveform describing a lightning bolt. In other words, if you plotted current over time, you would find an initially small, corona based current caused by slow electron transfer to air near the surface of the faraday charge and the voltage source (van-de-graff generator in this case). Then, during the bolt, the current would be large. At some point, enough current has flowed that the voltage no longer sustains the plasma, and the current drops down to zero.

So the current waveform should look roughly like a square-wave. What I want to know is what frequency (or time constant) characterizes how sharp the rising and falling edges of the square wave are, how wide the square wave is, how square-like it is, etc.

As for width of the square wave, maybe someone knows how long a lightning bolt usually lasts? Maybe 100ms or so?

As for the rise time, maybe someone knows how quickly lightning travels? I think I've seen slow motion video of lightning bolts "moving" from ground to cloud, if I knew how quickly they move it should roughly answer the question of how quickly the current ramps up.

Thanks,
Dave

I believe the lightning has a fast rise time of 25 microseconds or so, corresponding to about 10 kHz, and then a slow decay over a fraction of a second. Sometimes there are multiple discharges over a second or two.
Regarding the speed of propagation, witnesses say things such as "the lighting hit the pole and then traveled down it, and then jumped to the tree". So one actually wonders if the discharge grows along the path fairly slowly - an ionisation process occurring - and the big current surge then follows, as you describe.
The skin effect seems important as the discharge has an AC component, so a minimum depth of conductor is needed. With very low frequencies, there is a problem obtaining magnetic shielding by using a conducting cage (similar to the problem of sending video over coaxial cable).
I experienced a small spark from my umbrella shaft to my hand when crossing London Bridge, caused by a strike to the next bridge about 500m away. I estimated the voltage and then calculated the "antenna current" in the lightning, and it came out to 10kA, which is quite plausible!

 

[dreens]

Hey, thanks tech. That's a really neat experience with the umbrella giving you a shock!

I guess with a 10kHz component the skin depth would be half a millimeter or so, and the Faraday cage at the museum had ~cm thick bars, definitely enough so that the skin effect is protective at that frequency.

In fact, now that I think about it the bolts in the museum seemed much less long lived than those in actual cloud to ground lightning, suggesting that the skin effect may be more important than the DC faraday cage effect in that situation.