Synchrotron function

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Synchrotron function

In mathematics the synchrotron functions are defined as follows (for x 0):[1]

  • First synchrotron function
  • Second synchrotron function
Thumb
First and second Synchrotron functions.

where Kj is the modified Bessel function of the second kind.

Use in astrophysics

In astrophysics, x is usually a ratio of frequencies, that is, the frequency over a critical frequency (critical frequency is the frequency at which most synchrotron radiation is radiated). This is needed when calculating the spectra for different types of synchrotron emission. It takes a spectrum of electrons (or any charged particle) generated by a separate process (such as a power law distribution of electrons and positrons from a constant injection spectrum) and converts this to the spectrum of photons generated by the input electrons/positrons.

References

Further reading

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