BeamBeam3d Code

The BeamBeam3d code was developed by Ji Qiang. Some references describing this code are:

• "Strong-Strong Beam-Beam Simulation Using a Green Function Approach," J. Qiang, M. Furman, and R. Ryne, Phys. Rev. ST Accel. Beams, vol 5, 104402 (October 2002).
• "A Parallel Particle-In-Cell Model for Beam-Beam Interactions in High Energy Ring Colliders," J. Qiang, M. Furman, and R. Ryne, J. Comp. Phys. vol. 198, 278 (2002).

The program generates beam bunches consisting of 10000-1000000 macroparticles according to a specified input distribution in phase space. Each macroparticle has a charge equivalent so that the total charge carried by all the particles in a bunch corresponds to a realistic accelerator bunch. All the particles are tracked with linear and 2nd order optics through a accelerator lattice. A resistive wall impedance kick may be applied as particles propagate through the accelerator.

At interaction points, the opposing beam bunches meet for beam-beam interactions. To calculate these interactions, the code uses a Poisson field solver to calculate the electromagnetic field generated on one beam bunch to produce a kick which is applied to each particle of an opposing beam bunch.

For a full 6D simulation, each bunch is divided longitudinally into slices. At a bunch crossing location, colliding bunches are sequentially stepped through each other. The full Poisson field computation is performed for particles in overlapping slices and an electromagnetic kick is applied to each particle. As the bunches pass through each other, the kicks from previous steps alter the positions of the particles as they drift to their new overlapped slice position. In this way, the head of the bunch can interact with the tail mediated via the beam-beam interaction with an opposing bunch giving rise to synchrobetatron collective modes.

A real machine such as the Fermilab Tevatron is subject to many other effects besides the the beam-beam interaction. A realistic simulation of the Tevatron requires adding many of these effects. Of particular interest are the conditions under which the Tevatron beam develops instabilities. Instabilities often develop because of unwanted coupling between transverse and longitudinal phase space. The RF cavities that provide longitudinal stability are also an energy source that can drive unstable behavior through impedance and chromatic effects.

To simulate the Tevatron, we have added these processes to the BeamBeam3d code:

• Measured coupled motion beam optics parameters
• Measured helical beam trajectory as induced by electrostatic separators
• Head-on as well as parasitic collision locations
• Multiple bunch tracking
• Resistive wall impedance model
• Machine chromaticity

Other effects such as radiation damping can also be applied.