# Modeling Laser Wakeﬁeld Accelerators in a Lorentz Boosted Frame

**Why it Matters**: Laser driven plasma waves can produce accelerating gradients orders of magnitude greater than standard accelerating structures. High quality electron beams of energy up to 1 GeV have been produced in just a few centimeters and 10-GeV stages being planned as modules of a conceptual future high energy collider.

**Key Challenges**: Detailed simulations are required to realize the promise of much shorter particle accelerators using this technique. Such simulations challenge or exceed current capabilities, in particular for high energy stages at GeV energies and beyond.

**Accomplishments**: Using novel numerical techniques based on special relativity, a new “boosted frame” can model laser-plasma wakeﬁeld accelerators in an optimal frame of reference, producing up to six orders of magnitude speed-up in calculations from ﬁrst principles of stages in the 1 TeV range, which is three orders of magnitude higher than the higher speedup reported previously for a 1-10 GeV range stage. For a 10 GeV stage, the speedup is over four orders of magnitude, which is one order of magnitude larger than the maximum speedup previously reported. The new results offered a veriﬁcation of the scaling of plasma accelerators to the 1 TeV range and provide highly efﬁcient tools for the detailed designs of experiments on new lasers such as BELLA.

**Principal Investigator**: Cameron Geddes, LBNL

**More Information**: See J.-L. Vay, C. G. R. Geddes, E. Cormier-Michel, and D. P. Grote, “Effects of hyperbolic rotation in Minkowski space on the modeling of plasma accelerators in a Lorentz boosted frame,” Phys. Plasmas 18, 030701 (2011), DOI:10.1063/1.3559483