A new Particle-in-Cell (PIC) method, that conserves energy exactly, is
presented. The particle equations of motion and the Maxwell's equations are
differenced implicitly in time by the midpoint rule and solved concurrently by
a Jacobian-free Newton Krylov (JFNK) solver. Several tests show that the finite
grid instability is eliminated in energy conserving PIC simulations, and the
method correctly describes the two-stream and Weibel instabilities, conserving
exactly the total energy. The computational time of the energy conserving PIC
method increases linearly with the number of particles, and it is rather
insensitive to the number of grid points and time step. The kinetic enslavement
technique can be effectively used to reduce the problem matrix size and the
number of JFNK solver iterations