Difference between revisions of "Introduction to Synchrotron Radiation and Relativistic Beaming"

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These work to cancel themselves out to form \emph{mostly} linearly polarized emission. For an ensemble of particles following a power-law distribution in energy to the $-p$ degree, the intensity of radiation that is linearly polarized can be shown to be about 70 percent of the total intensity: $\Pi = (p+1)/(p+7/3)$. Knowing that in practice $p$ ranges from 2 to 3, we get back that the degree of polarization is roughly 70 percent (Rybicki and Lightman pg 181). To derive this relationship yourself, see problem 6.5 in Rybicki and Lightman.
 
These work to cancel themselves out to form \emph{mostly} linearly polarized emission. For an ensemble of particles following a power-law distribution in energy to the $-p$ degree, the intensity of radiation that is linearly polarized can be shown to be about 70 percent of the total intensity: $\Pi = (p+1)/(p+7/3)$. Knowing that in practice $p$ ranges from 2 to 3, we get back that the degree of polarization is roughly 70 percent (Rybicki and Lightman pg 181). To derive this relationship yourself, see problem 6.5 in Rybicki and Lightman.
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\section{Synchrotron Applications}
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\begin{figure}
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\centering
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\includegraphics[width=3in]{lhc.jpg}
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\caption{The Large Hadron Collider at CERN, a synchrotron particle accelerator. (Credit: Maximilen Brice/CERN)
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}
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Synchrotron is not only a kind of radiation, it is also a very common type of modern particle accelerator. In fact, the largest particle accelerator in the world, the Large Hadron Collider at CERN, is a synchrotron particle accelerator. These accelerators are ring-shaped structures that speed up particles in a loop via a magnetic field. The particle velocity is increased by strengthening the magnetic field of the accelerator over time. Particles in this type of accelerator can reach relativistic limits, copying the most common source of synchrotron radition, an electron orbiting a B-field, but on a much larger scale.
  
 
\section{Lorentz and Doppler Shift Derivations}
 
\section{Lorentz and Doppler Shift Derivations}

Revision as of 09:31, 12 December 2018