Validity of the Force-Field Equation to Describe Cosmic Ray Modulation

It is shown that the widely used Force-Field (FF) approximation to the cosmic ray transport equation (TPE) does not work well in the outer heliopshere, in particular for anomalous cosmic rays (ACRs). The even simpler ConvectionDiffusion (CD) approximation produces better results in the outer heliosphere. Using a simple 1D solution to the TPE for comparison, we show that the widely used FF and CD approximations are po or in commonly occurring situations. The FF fares badly in the outer heliosphere and for ACRs in general, while the CD is only appropriate in the outer heliosphere. A full 1D solution is provided in the hop e that it may be more commonly used instead of these approximations.