**Alain Brizard**, professor of physics, co-authored the following peer-reviewed publications: N. Tronko and A.J. Brizard, 2015, “Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories,” *Physics of Plasmas 22, 112507:1-10; *J.W. Burby, A.J. Brizard, and H. Qin, 2015, “Energetically-consistent collisional gyrokinetics,” *Physics of Plasmas 22, 100707:1-5; *and J.W. Burby, A.J. Brizard, P.J. Morrison, and H. Qin, 2015, “Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations,” *Physics Letters A 379, 2073-2077*.* *Alain also made these conference and seminar presentations:* “*Reduced collisional gyrokinetic dynamics in strongly magnetized plasmas,” NumKin 2015, Max-Planck-Institut für Plasma Physik, Garching (Germany), October 26-30, 2015; and three seminars given at the Swiss Plasma Center, Ecole Polytechnique Fédérale de Lausanne, Lausanne (Swiss Confederation):* *Variational Formulations of Hybrid Kinetic-MHD Models, November 13, 2015*; *Reduced Collision Operators for Gyrokinetic Applications, November 11, 2015*; *and, A guided Tour of Gyrokinetic Theory, November 9, 2015.

*(posted January 2016)*

**Alain Brizard**, professor of physics, has published two textbooks: (1) *An Introduction to Lagrangian Mechanics (2nd Edition),* World Scientific (2015); and (2) *Ray Tracing and Beyond*, with E.R. Tracy (William and Mary), A.S. Richardson (Naval Research Laboratory), and A.N. Kaufman (UC Berkeley), Cambridge University Press (2014). Alain has also been awarded a $145,000 grant from the U.S. Department of Energy for the next three years to support his summer research activities.

*(poster April 2015)*

Alain Brizard, professor of physics, had two articles accepted for publication in the peer-reviewed journal *Physics of Plasmas*: "Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation" in a collaboration with physicists from Aalto University (Finland); and "Beyond linear gyrocenter polarization in gyrokinetic theory." A third publication, "Exact conservation laws for the truncated gyrokinetic Vlasov-Poisson equations," in a collaboration with N. Tronko (York Plasma Institute, UK), also was published in the *Proceedings of the 40th European Physical Society Conference on Plasma Physics* (held in Helsinki, Finland, in June 2013). Alain's second textbook, *Ray Tracing and Beyond: Phase-space Methods in Plasma Wave Theory*, written in collaboration with A.N. Kaufman (Berkeley), E.R. Tracy (William and Mary), and A.S. Richardson (Naval Research Lab), was submitted to Cambridge University Press (with a tentative release date of January 2014). Lastly, Alain gave a seminar, "Guiding-center effects in gyrokinetic momentum conservation laws for axisymmetric tokamak plasmas," at the Princeton Plasma Physics Lab on August 22.

**Alain Brizard,** professor of physics, had two papers accepted for publication this summer: "Action-angle coordinates for the pendulum," to be published in Communications in Nonlinear Science and Numerical Simulation, and comment on "Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field" (with Loic de Guillebon), to be published in *Physics of Plasmas*. Alain also presented the seminar "Beyond linear polarization in gyrokinetic theory" at the Princeton Plasma Physics Laboratory (Princeton University) on July 31, 2012, and the Center for Theoretical Physics Luminy (Marseille, France) on July 18, 2012. Lastly, he submitted the following manuscripts for publication in *Physics of Plasmas:* "Gyrokinetic momentum conservation in truncated gyrokinetic Vlasov-Maxwell theory" (with Natalia Tronko, CFSA, Warwick University, UK), "Equivalent representations of higher-order Hamiltonian guiding-center theory" (with Natalia Tronko, CFSA, Warwick University, UK), and "Hamiltonian formulation of reduced Vlasov-Maxwell equations" (with Cristel Chandre and Emanuele Tassi, CPT Luminy, France).