Energy-momentum-conserving Landau form of the guiding-center Fokker-Planck collision operator

The guiding-center Fokker-Planck collision operator [1] describes particle collisions in the five-dimensional guiding-center phase space [2], where the fast gyroangle is asymptotically eliminated at lowest order in the slow collisional time scale. The test-particles and field-particles are treated independently in terms of full guiding-center distributions without the need of linearization. For the field-particle guiding-center representation, guiding-center Rosenbluth potentials are introduced. The phase-space divergence form of the guiding-center Fokker-Planck collision operator immediately guarantees its particle-conserving property, while its Landau form guarantees its energy-momentum-conserving properties, even when the guiding-center transformation is truncated at finite order. A linearized guiding-center Fokker-Planck collision operator suitable for gyrokinetic particle simulations is derived and compared with recent linearized gyrokinetic collision operators [3,4].\\[4pt] [1] A.J. Brizard, PoP {\bf 11}, 4429 (2004).\\[0pt] [2] E. Hirvijoki, A.J. Brizard, A. Snicker, and T. Kurki-Suonio, PoP {\bf 20}, 092505 (2013).\\[0pt] [3] B. Li and D.R. Ernst, PRL {\bf 106}, 195002 (2011).\\[0pt] [4] J. Madsen, PRE {\bf 87}, 011101 (2013).