## Abstract

Synchrotron radiation is emitted by relativistic electrons whose trajectories are bent by magnetic fields placed in the electron beam path. At a facility such as the Synchrotron Ultraviolet Radiation Facility (SURF) on the NIST Gaithersburg campus, the simple circular orbit permits calculation of the intensity and polarization of ultraviolet and x-ray radiation based on knowledge of the electron orbit radius, kinetic energy, and beam current. Historically, this intrinsic standard source has played (and continues to play) a role in calibration of ultraviolet and x-ray remote-sensing instruments. This is highly analogous to blackbodies that are used as intrinsic standard sources in the infrared spectral region. The conventional approach to calculating the polarization and intensity of synchrotron radiation used the Schwinger formula. This typically involves several approximations, including the need to consider short wavelengths only and to be far from the light source. We have developed a new method to calculate the electric and magnetic fields for synchrotron radiation fields at longer wavelengths and short distances, and without any explicit approximation or truncation of mathematical expressions for the fields. This is based on a lesser known addition theorem for Bessel functions due to Graf and others. We will present the method and quantify its accuracy for an ideal case as well as when one considers sensitivity of results to non-idealities in actual synchrotron performance. This furnishes information useful in the uncertainty analysis related to calibrations of ultraviolet and x-ray instruments.

Improved Formulas for Synchrotron Radiation

Synchrotron radiation is emitted by relativistic electrons whose trajectories are bent by magnetic fields placed in the electron beam path. At a facility such as the Synchrotron Ultraviolet Radiation Facility (SURF) on the NIST Gaithersburg campus, the simple circular orbit permits calculation of the intensity and polarization of ultraviolet and x-ray radiation based on knowledge of the electron orbit radius, kinetic energy, and beam current. Historically, this intrinsic standard source has played (and continues to play) a role in calibration of ultraviolet and x-ray remote-sensing instruments. This is highly analogous to blackbodies that are used as intrinsic standard sources in the infrared spectral region. The conventional approach to calculating the polarization and intensity of synchrotron radiation used the Schwinger formula. This typically involves several approximations, including the need to consider short wavelengths only and to be far from the light source. We have developed a new method to calculate the electric and magnetic fields for synchrotron radiation fields at longer wavelengths and short distances, and without any explicit approximation or truncation of mathematical expressions for the fields. This is based on a lesser known addition theorem for Bessel functions due to Graf and others. We will present the method and quantify its accuracy for an ideal case as well as when one considers sensitivity of results to non-idealities in actual synchrotron performance. This furnishes information useful in the uncertainty analysis related to calibrations of ultraviolet and x-ray instruments.