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**Unformatted text preview: **6. Synchrotron radiation 6.1 The energy loss rate Charges that move in a homogeneous magnetic field take a helical trajectory along the magnetic field line, for their motion component perpendicular the field is turned into gyration by the Lorentz force vectorv × vector B . So the charged particles are constantly accelerated and react with emission of radiation. For an isotropic distribution of relativistic charged particles in a homogeneous magnetic field this radiation process is called synchrotron radiation. A related radiation process is curvature radiation, which involve charged particles that stream along a curved magnetic field. Curvature radiation is important in pulsars, rapidly rotating neutron stars, that possess a dipole magnetic field that is inclined to the rotation axis. Near the poles the rotation induces a strong electric field along the direction of the local magnetic field, so electrons are accelerated to very high Lorentz factor along the magnetic field lines. Strong curvature radiation must then be expected which would appear to the outside observer as gamma-ray continuum emission. As for the other radiation processes involving accelerated charges the efficacy of the synchrotron process is strongly dependent on the mass of the radiating particle, so electrons radiate more efficiently than ions by many orders of magnitude. The electron energy loss rate for synchrotron radiation can be calculated by transforming Larmors formula from the electron restframe into the laboratory frame, in which the electron is moving relativistically. − ˙ E = P = 4 3 σ T c U B β 2 γ 2 (6 . 1 . 1) where U B = B 2 2 μ is the energy density of the magnetic field and σ T is the Thomson cross section. As in the case of inverse Compton scattering the energy loss rate scales quadratically with particle energy. The total energy loss rate of relativistic electrons is given by the sum of those for Coulomb scattering and ionization, relativistic bremsstrahlung, and synchrotron radiation and inverse Compton scattering. Neglecting the weak energy dependence that is carried by the Coulomb logarithm as well as the modifications of the inverse-Compton energy loss rate in the Klein-Nishina limit, the total electron energy loss rate of relativistic electrons has the functional form − ˙ E ( γ ) = A + B γ + C γ 2 A, B, C = constants (6 . 1 . 2) where the constants A and B include the density of ambient gas, whereas the constant C depends on the energy densities of the magnetic field and the ambient photon field. We will see later that the binomial form of the energy loss rate can induce spectral structures that carry information on the three constants and hence on the ambient gas density etc....

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