Changes between Version 7 and Version 8 of PolarizationMaps


Ignore:
Timestamp:
05/02/18 17:04:44 (7 years ago)
Author:
Jonathan
Comment:

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  • PolarizationMaps

    v7 v8  
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    52 Now $B_\perp$ is unchanged under rotations about the jet axis, however $B_x$ will be given by $B_\phi \cos \phi$
     52Now $B_\perp$ is unchanged under rotations about the jet axis, however $B_x$ will be given by $B_\phi \cos \phi$ or $B_x = B_\phi \frac{x_i}{\sqrt{x_i^2+(s \cos(\theta))^2}}$
     53
     54And finally we can change the path integral to an x integral under the substitution
     55
     56$x=\sqrt{x_i^2+s^2}$
     57
     58or
     59
     60$s = \sqrt{x^2-x_i^2}$
     61
     62and
     63
     64$ds/dx = \frac{x}{\sqrt{x^2-x_i^2}}$
     65
     66This gives
     67
     68
     69$\int_{x} { f(B'(x, y_i,0)) \frac{x^2}{x^2-x_i^2} dx}$
     70
     71and $B_x'(x,y_i,0)=B_\phi(x,y_i,0) \frac{x_i}{x}$
     72
     73