T3P is a 3D parallel finite-element time-domain solver to calculate transient field response of a electromagnetic structure to imposed fields, and dipole or beam excitations.
In our approach, Ampere's and Faraday's laws are combined and integrated over time to yield inhomogeneous vector wave equation for the time integral of the electric field E:
\begin
\left( \epsilon \frac
+ \sigma_
\frac
+ \nabla \times \mu^{-1}\nabla\times \right) \int^t \emph
d \tau = -\emph
\end
with permittivity
$\epsilon = \epsilon_0 \epsilon_r $
and permeability
$\mu = \mu_0 \mu_r$
. In the current implementation, a constant value of the effective conductivity
$\sigma_
\tan \delta \cdot 2 \pi f \cdot \epsilon $
is assumed by fixing a frequency
$f$
, and the losses are specified by the loss tangent
$\tan \delta $
. As is common for Wakefield computations of rigid beams, the electric current source density J is given by a one-dimensional Gaussian particle distribution, moving at the speed of light along the beam line.