Abstract
Since the development of satellite space technology about 50 years ago the solar heliosphere is explored almost routinely by several spacecrafts carrying detectors for measuring the properties of the interplanetary medium including energetic charged particles (cosmic rays), solar wind particle densities, and electromagnetic fields. In 2012, the Voyager 1 spacecraft has even left what could be described as the heliospheric modulation region, as indicated by the sudden disappearance of low energy heliospheric cosmic ray particles. With the available in-situ measurements of interplanetary turbulent electromagnetic fields and of the momentum spectra of different cosmic ray species in different interplanetary environments, the heliosphere is the best cosmic laboratory to test our understanding of the transport and acceleration of cosmic rays in space plasmas. I review both the historical development and the current state of various cosmic ray transport equations. Similarities and differences to transport theories for terrestrial fusion plasmas are highlighted. Any progress in cosmic ray transport requires a detailed understanding of the electromagnetic turbulence that is responsible for the scattering and acceleration of these particles.
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