**Beam dynamics** in accelerator physics is a theoretically rich area, which deals with **instabilities** and **chaotic behavior** of the beam, effects on the beam from the adjacent conducting walls, pipe nonuniformities, and accelerating structure (**wakefields**); it studies **single particle motion** and **collective** effects.

One collective effect dominating the dynamics of intense beams at low energy is **space charge effect**. The electron beam is born at essentially rest energy in **photoinjector** experiencing **violent Coulomb repulsion**, which may dominate over external fields of the design beam elements (magnets and accelerating structures). This leads to a highly **nonlinear beam dynamics**, a whole class of phenomena similar to those typical of **nonequilibrium plasmas**.

One example of such nonlinearity (known as **virtual cathode instability**) is shown on the left (GIF animation). As laser intensity is increased for otherwise identical laser pulse shape (40 ps square time profile) incident on a photocathode placed in a constant accelerating gradient (3 MV/m), the space charge becomes so strong near the cathode that the accelerating electric field there is quenched and the beam **breaks apart** into two or more components. The temporal profile of electron bunches after emission is shown on the right. It is seen that the electron beam does not follow the laser at higher bunch charges (plotted on the left) developing instead deep modulations as if the cathode were being turned on and off (thus, the name).

Quantitative analysis of nonlinear behavior oftentimes requires **intensive computations**. Our group utilizes a 200-CPU computer cluster (affably known as *Feynman*), which is fully dedicated to our beam dynamics simulations. We use many advanced computational methods to explore nonlinear beam dynamics including some unorthodox ones such as **parallel multi-objective genetic algorithms**, the use of which was pioneered in our group. Presently, we are working on deploying such advanced algorithms for real-time control of complex and large-scale accelerator systems such as Cornell Electron Storage Ring (CESR).