# bunch(of particles) dynamics simulation

It would be interesting to have a little chat on the project rather than getting into details straight forward. Let me know when available and if interested! I'll try to make an intro to the subject here: Scientists and engineers are trying to build a machine( a linear beam line) that will provide us with very energetic x-rays. The advantage of these high-energetic x-rays is that they can probe matter [biological or technological(=chips etc.)] at the level of 0.1-1 Angstrom. To achieve these x-rays we first start with low energy/low speed electrons that we accelerate in bunches( a bunch of electrons is comprised of e.g. 10^9 electrons) by passing them through some radiofrequency RF accelerating cavities. In these cavities there is electric field(more precisely gradient) in the range of 20-100 MV/m that the particles of the bunch experience when the bunch enters the RF cavity. The thing is that the particles at the head of the bunch at the moment they enter the RF cavity they experience a different environment from the particles of the tail of the bunch (that follow the head particles). And not to say many words we describe this phenomenon as follows: The particles at the head of the bunch when enter the cavity they excite some kicks at the tail of the bunch leading to a banana shape of the bunch. That kind of effects we call Wakefield effects. Because this is a dynamical situation the banana shape oscillates cosine likely (or sinus likely) like the applied Voltage needed to make the electric field inside the RF cavity. After the RF cavity (from now on we will call it just RF) the bunch enters the Bunch Compressor (BC) which compress the bunch longitudinally. I forgot to tell you that the whole dynamics of the bunch is described by using the longitudinal and the transversal phasespace. Imagine that you cut the bunch transversely, then you'll get an ellipse. If you cut the bunch longitudinally (profil) you will again have an ellipse (phasespace diagrams).To clarify it consider (at 1st approximation) that longitudinal and transversal phasespaces are decoupled. Furthermore, the bunch can be described by its particles distribution(e.g Gaussian at the ideal case) energy versus micrometers. This means that the particles inside the bunch have different energy. What we want is to have a bunch with nearly all the particles ta the same energy - that is why we pass them through the bunch compressor BC. If you don't understand a lot it is not a problem. At 1st step we see the RF and BC as systems represented by two 2x2 matrices. These rae the transformation matrices that transfor the [ z , E]initial vector to the [z,E] final vector. These [z,E] are part of an 1X6 vector that describes the motion of a charged particle in 3d space,that is [ x, x', y, y', z, E] where [x, x',y, y'] describe the evolution in the transversal plane. Me and you we now focus at the longitudinal one whih evolutionis described by [z,E]. At this point I reccomend you read pages 1-3 from File(A_short_intro_to_bunch_compressors) attached. To get an idea for the whole vector representation take a look at the file(3d space...).What I want to do is an analytic formulation of the effect of its system to the bunch so that I can derive some key parameters like the Voltage of the RF and the phase of the RF. We start with fixed numbers that we know from other simulations and we want to achieve a certain goal (see file"Description"). Holla at me if interested. We can Skype and discuss everything when you want to. Cheers, Sosta! PS: don't take for granted the project budget and duration I chose, it's just bureaucracy

Skills: Matlab and Mathematica