Modification of the Loss Cone for Energetic Particles


Porazik, P., Johnson, J. R., Kaganovich, I., & Sanchez, E. (2014). Modification of the loss cone for energetic particles. Geophysical Research Letters, 41(22), 8107-8113.


As part of this special issue on control systems for the energy sector, guest editors Sean Peisert and Jonathan Margulies put together a roundtable discussion so readers can learn about the security challenges facing the industrial control system/SCADA world from those who are on the front lines. The discussion touches on some of the hard problems of securing mission-critical systems in the real world, including the challenges of securing 20-year-old legacy infrastructures, defining vendors’ roles and responsibilities in security, and where research and new technologies are needed to fill today’s security gaps.


The optimal pitch angle which maximizes the penetration distance, along the magnetic field, of relativistic charged particles injected from the midplane of an axisymmetric field is investigated analytically and numerically. Higher-order terms of the magnetic moment invariant are necessary to correctly determine the mirror point of trapped energetic particles, and therefore the loss cone. The modified loss cone resulting from the inclusion of higher-order terms is no longer entirely defined by the pitch angle but also by the phase angle of the particle at the point of injection. The optimal orientation of the injection has a nonzero component perpendicular to the magnetic field line, and is in the plane tangential to the flux surface. Numerical integration of particle orbits were carried out for a relativistic electron in a dipole field, showing agreement with analytic expressions. The results are relevant to experiments, which are concerned with injection of relativistic beams into the atmosphere from aboard a spacecraft in the magnetosphere.

Key Points

  • Loss cones of energetic and low-energy particles may be significantly different
  • The difference results from next order terms of the magnetic moment
  • The qualitative and quantitative changes affect energetic particle precipitation

Read more from SRI