Digital camera sensors aren't usually effected by magnetic fields. However, since large Tesla Coils can generate a significantly high number of volts I suspect that the digital camera sensors are affected.

When the E-M field is affected by the person interacting with it, the field and magnetic values will change.

I liked the video! I suggest using a longer lens to get further away and maybe some better lighting for the next one.
Source(s):
http://cat.inist.fr/?aModele=afficheN&cpsidt=17451997
http://sirius.ucsc.edu/demoweb/cgi-bin/?e_m-electmag-tesla

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It could be the lens, are you using a filter? This one is kind of out there but it worked for me. Wrap the camera in aluminum foil. When taking a video of a weapon firing that emitted Electro Magnetic field the only way to do it without having a screen full of white snow was to wrap the camera in Aluminum foil. Try that out. If that doesn't do the trick I would try another lens. Finally you may have to fix the problem in post production.
Source(s):
http://www.pentaxforums.com/forums/pentax-camera-accessories/36555-lens-fil...
http://www.trustedreviews.com/digital-cameras/review/2008/10/13/Digital-Pho...
http://www.michaelalmond.com/Articles/noise.htm
http://www.digital-rapids.com/Resources/Preprocessing/Preprocessing2.aspx

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Vertical Smear

Vertical smear refers to a common CCD-related issue that most video professionals are familiar with. Since the entire image is being captured at once on a CCD sensor, shots of bright lights can often have a vertical haloing effect, causing one column of pixels to appear brighter than the rest. The problem looks something like a lens-flare.
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I'm having trouble finding a good source for this, but what I think you're seeing is internal reflection within the lens elements of the camera. The light from the arc is very bright in contrast with the environment (almost totally dark).

This creates a condition where a tiny bit of the very bright arc gets reflected off of the surface of one of the lenses, which then gets reflected back toward the sensor. Repeat this for the number of elements in the lens.

If you look very carefully at the video, you can see that the patterns of the distortion follow that of a portion of the arc, which further bolsters my belief that this is the cause.

Remedying this could be difficult, because even the most expensive Anti-Reflective coatings can never completely eliminate internal reflection, particularly in extremely high-contrast situations like this. You may, as has been suggested, end up having to resort to post-processing to fix it.

Once I find a good source (that's not wikipedia), I'll add it in here.
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