Proof that stable monotonic equilibrium distributions in a continuous-focusing channel are necessarily axisymmetric

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1. R. C. Davidson, Physics of Nonneutral Plasmas (Addison-Wesley, Reading, MA, 1990), rereleased, World Scientific, Singapore, 2001, and references therein.
2. R. C. Davidson and H. Qin, Physics of Intense Charged Particle Beams in High Energy Accelerators (World Scientific, New York, 2001), and references therein.
3. M. Reiser, Theory and Design of Charged Particle Beams (John Wiley & Sons, Inc., New York, 1994), and references therein.
4. J. J. Barnard and S. M. Lund, U.S. Particle Accelerator School courses: Beam Physics with Intense Space-Charge, Waltham, MA, 2006, Lawrence Livermore National Laboratory, UCRL-TM-231628; and Lawrence Berkeley National Laboratory, LBNL-62783; Intense Beam Physics: Space-Charge, Halo, and Related Topics, Williamsburg, VA, 2004, Lawrence Livermore National Laboratory, UCRL-TM-203655; and Lawrence Berkeley National Laboratory, LBNL-54926; Space-Charge Effects in Beam Transport, Boulder, CO, 2001, Lawrence Berkeley National Laboratory, LBNL-49286.
5. R. A. Smith, T. M. O’Neil, S. M. Lund, J. J. Ramos, and R. C. Davidson, Phys. Fluids B 4, 1373 (1992) [SPIN].
6. T. K. Fowler, J. Math. Phys. 4, 559 (1963) [SPIN].
7. C. S. Gardner, Phys. Fluids 6, 839 (1963) [SPIN].
8. R. C. Davidson, Phys. Rev. Lett. 81, 991 (1998).
9. S. M. Lund, T. Kikuchi, and R. C. Davidson (unpublished).