Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution.(adsbygoogle = window.adsbygoogle || []).push({});

Now initially i thought we would just use the standard LT,

x=x'

y=y'

s'=/gamma (s-βct).

Now someone suggested to me that infact the transform will be non trivial when a longitudinal dependent radial field is perpendicular to the boost axis.

Can someone suggest some literature that would point me in the right direction?

Just for reference the field follows as,

B_{\theta}=Const \times r^(-1/2)e^{-r^{2}/2*sigma_{r}^{2}} e^{-s^{2}/2\sigma_{s}^{2}}

Sorry i am not sure how to make it latex

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# Lorentz Transform of a radial & longitudinal dependent magnetic field

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